Interference suppression in CDMA systems

[0001] This application claims benefit of provisional appln 60/171,604 Dec. 23, 1999 and provisional appln 60/243,727 Oct. 30, 2000.

[0002] The invention relates to Code-Division Multiple Access (CDMA) communications systems, which may be terrestrial or satellite systems, and in particular to interference suppression in CDMA communications systems.

[0003] Code-Division Multiple Access communications systems are well known. For a general discussion of such systems, the reader is directed to a paper entitled “Multiuser Detection for CDMA Systems” by Duel-Hallen, Holtzman and Zvonar, IEEE Personal Communications, pp. 46-58, April 1995.

[0004] In CDMA systems, the signals from different users all use the same bandwidth, so each user's signal constitutes noise or interference for the other users. On the uplink (transmissions from the mobiles) the interference is mainly that from other transmitting mobiles. Power control attempts to maintain the received powers at values that balance the interference observed by the various mobiles, but, in many cases, cannot deal satisfactorily with excessive interference. Where mobiles with different transmission rates are supported within the same cells, the high-rate mobiles manifest strong interference to the low-rate mobiles. On the downlink (transmission towards the mobiles) transmissions from base-stations of other cells as well as strong interference from the same base-station to other mobiles may result in strong interference to the intended signal. Downlink power control may be imprecise or absent altogether. In all these so called near-far problem cases, the transmission quality can be improved, or the transmitted power reduced, by reducing the interference. In turn, for the same transmission quality, the number of calls supported within the cell may be increased, resulting in improved spectrum utilization.

[0005] Power control is presently used to minimize the near-far problem, but with limited success. It requires a large number of power control updates, typically 800 times per second, to reduce the power mismatch between the lower-rate and higher-rate users. It is desirable to reduce the number of communications involved in such power control systems, since they constitute overhead and reduce overall transmission efficiencies. Nevertheless, it is expected that future CDMA applications will require even tighter power control with twice the number of updates, yet the near-far problem will not be completely eliminated. It is preferable to improve the interference suppression without increasing the number of transmissions by the power control system.

[0006] Multiuser detectors achieve interference suppression to provide potential benefits to CDMA systems such as improvement in capacity and reduced precision requirements for power control. However, none of these detectors is cost-effective to build with significant enough performance advantage over present day systems. For example, the complexity of the optimal maximum likelihood sequence detector (MLSD) is exponential in the number of interfering signals to be cancelled, which makes its implementation excessively complex. Alternative suboptimal detectors fall into two groups: linear and subtractive. The linear detectors include decorrelators, as disclosed by K. S. Schneider, “Optimum detection of code division multiplexed signals”, IEEE Trans. on Aerospace and Electronic Systems, vol. 15, pp. 181-185, January 1979 and R. Kohno, M. Hatori, and H. Imai, “Cancellation techniques of co-channel interference in asynchronous spread spectrum multiple access systems”, Electronics and Communications in Japan, vol. 66-A, no. 5, pp. 20-29, 1983. A disadvantage of such decorrelators is that they cause noise enhancement.

[0007] Z. Xie, R. T. Short, and C. K. Rushforth, “A family of suboptimum detectors for coherent multiuser communications”, IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 683-690, May 1990, disclosed the minimum mean square error linear (MMSE) detector, but such detectors are sensitive to channel and power estimation errors. In both cases, the processing burden still appears to present implementation difficulties.

[0008] Subtractive interference cancellation detectors take the form of successive interference cancellers (SIC), as disclosed by R. Kohno et al., “Combination of an adaptive array antenna and a canceller of interference for direct-sequence spread-spectrum multiple-access system”, IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 675-682, May 1990, and parallel interference cancellers (PIC) as disclosed by M. K. Varanasi and B. Aazhang, “Multistage detection in asynchronous code-division multiple-access communications”, IEEE Trans. on Communications, vol. 38, no. 4, pp. 509-519, April 1990, and R. Kohno et al., “Combination of an adaptive array antenna and a canceller of interference for direct-sequence spread-spectrum multiple-access system”, IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 675-682, May 1990. Both SIC detectors and PIC detectors require multi-stage processing and the interference cancellation achieved is limited by the amount of delay or complexity tolerated. These detectors are also very sensitive to channel, power and data estimation errors.

[0009] One particular subtractive technique was disclosed by Shimon Moshavi in a paper entitled “Multi-User Detection for DS-CDMA Communications”, IEEE Communications Magazine, pp. 124-136, October 1996. FIG. 5 of Moshavi's paper shows a subtractive interference cancellation (SIC) scheme in which the signal for a particular user is extracted in the usual way using a matched filter and then spread again using the same spreading code for that particular user, i.e., the spreading code used to encode the signal at the remote transmitter. The spread-gain signal then is subtracted from the signal received from the antenna and the resulting signal is applied to the next user's despreader. This process is repeated for each successive despreader. Moshavi discloses a parallel version that uses similar principles.

[0010] A disadvantage of this approach is its sensitivity to the data and power estimates, i.e., their accuracy and the sign of the data. A wrong decision will result in the interference component being added rather than subtracted, which will have totally the wrong effect.

[0011] For more information about these techniques, the reader is directed to a paper by P. Patel and J. Holtzman entitled “Analysis of a Simple Successive Interference Cancellation Scheme in a DS/CDMA System”, IEEE Journal on Selected Areas in Communications, Vol. 12, No. 5, pp. 796-807, June 1994.

[0012] In a paper entitled “A New Receiver Structure for Asynchronous CDMA: STAR—The Spatio-Temporal Array-Receiver”, IEEE Transaction on Selected Areas in Communications, Vol. 16, No. 8, October 1998, S. Affes and P. Mermelstein (two of the present inventors), disclosed a technique for improving reception despite near/far effects and multi-user interference. In contrast to known systems in which the spread-again signal is supplied to the input of the despreader of the channel to be corrected, Affes' and Mermelstein's proposed system treated all of the users signals together and processed them as a combined noise signal. If the components of the received signal from the different users were uncorrelated and all had equal power, or substantially equal power, this process would be optimal. In practice, however, there will be significant differences between the power levels at which the different users signals are received at the base station antenna. The same applies to the downlink. For example, a data user may generate much more power than a voice user simply because of the more dense information content of the data signal. Also, imperfect power control will result in power differences, i.e., channel variations may result in received powers different from their intended values, despite the best effort of the power-control process to equalize them.

[0013] The present invention addresses the need for improved interference suppression without the number of transmissions by the power control system being increased, and, to this end, provides a receiver for a CDMA communications system which employs interference subspace rejection to obtain a substantially null response to interference components from selected user stations. Preferably, the receiver also provides a substantially unity response for a propagation channel via which a corresponding user's “desired” signal was received.

[0014] According to one aspect of the invention, there is provided a receiver suitable for a base station of a CDMA communications system comprising at least one base station (11) having a transmitter and a said receiver and a multiplicity (U) of user stations (10¹, . . . , 10^U) including a plurality (U′) of user stations served by said at least one base station, each user station having a transmitter and a receiver for communicating with said at least one base station via a corresponding one of a plurality of channels (14¹, . . . , 14^U), the base station receiver for receiving a signal (X(t)) comprising components corresponding to spread signals transmitted by the transmitters of the plurality of user stations, each of said spread signals comprising a series of symbols spread using a spreading code unique to the corresponding user station, said base station receiver comprising:

• • [0015] a plurality (U′) of receiver modules (20¹, . . . , 20^NI, 20^d) each for deriving from successive frames of the received signal (X(t)) estimates of said series of symbols of a corresponding one of the user stations,
  • [0016] preprocessing means (18) for deriving from the received signal (X(t)) a series of observation matrices (Y_n) each for use by each of the receiver modules (20) in a said frame to derive an estimate of a symbol of a respective one of said series of symbols, and
  • [0017] means (19,44;44/1,44/2) for deriving from each observation matrix a plurality of observation vectors (Y_n; Y_n−1; Z_n¹ . . . Z_n^NI; Z_n^d) and applying each of the observation vectors to a respective one of the plurality of receiver modules (20¹, . . . , 20^NI, 20^d); each receiver module comprising;
    • [0018] channel identification means (28) for deriving from one of the observation vectors a channel vector estimate (Ĥ_n¹, . . . , Ĥ_n^NI; Ŷ_0,n^d; Ŷ_0,n−1ⁱ) based upon parameter estimates of the channel between the base station receiver and the corresponding user station transmitter;
    • [0019] beamformer means (27¹, . . . , 27^NI, 27^d; 47^d) having coefficient tuning means (50) for producing a set of weighting coefficients in dependence upon the channel vector estimate, and combining means (51,52) for using the weighting coefficients to weight respective ones of the elements of a respective one of the observation vectors and combining the weighted elements to provide a signal component estimate (ŝ_n¹, . . . , ŝ_n^U); and
    • [0020] symbol estimating means (29¹, . . . , 29^U, 30¹, . . . , 30^U) for deriving from the signal component estimate an estimate ({circumflex over (b)}_n¹, . . . , {circumflex over (b)}_n^U) of a symbol (b_n¹, . . . , b_n^U) transmitted by a corresponding one of the user stations (10¹, . . . , 10^U),
  • [0021] wherein said receiver further comprises means (42,43) responsive to symbol estimates $\left({\hat{b}}_n^1,\dots ,{\hat{b}}_n^{\mathrm{NI}};g^1,g^2,g^3;g^{l_{+1n}}\right)$
  • [0022]  and to channel estimates (_n¹ . . . _n^NI; _n−1ⁱ) comprising at least said channel vector estimates (Ĥ_n¹, . . . , Ĥ_n^NI) for channels (14¹, . . . , 14^NI) of a first group (I) of said plurality of user stations (10¹, . . . , 10^NI) to provide at least one constraint matrix (Ĉ_n) representing interference subspace of components of the received signal corresponding to said predetermined group, and in each of one or more receiver modules (20A^d) of a second group (D) of said plurality of receiver modules, the coefficient tuning means (50A^d) produces said set of weighting coefficients in dependence upon both the constraint matrix (Ĉ_n) and the channel vector estimates (Ĥ_n^d) so as to tune said one or more receiver modules (20A^d) each towards a substantially null response to that portion of the received signal (X(t)) corresponding to said interference subspace.

[0023] Embodiments of the invention may employ one of several alternative modes of implementing interference subspace rejection (ISR), i.e. characterizing the interference and building the constraint matrix. In a first embodiment, using a first mode conveniently designated ISR-TR, each receiver module in the first group generates its re-spread signal taking into account the amplitude and sign of the symbol and the channel characteristics. The re-spread signals from all of the receiver modules of the first group are summed to produce a total realization which is supplied to all of the receiver modules in the second group.

[0024] Where each receiver module of the second set uses decision feedback, it further comprises delay means for delaying each frame/block of the observation vector before its application to the beamformer.

[0025] Whereas, in ISR-TR embodiments, just one null constraint is dedicated to the sum, in a second embodiment, which uses a second mode conveniently designated ISR-R, estimated realisations of all the interferers are used, and a null constraint is dedicated to each interference vector. In this second embodiment, in each receiver module of the first set, the symbols spread by the spreader comprise estimated realisations of the symbols of the output signal. Also, the constraint waveforms are not summed before forming the constraint matrix. Thus, the receiver module estimates separately the contribution to the interference from each unwanted (interfering) user and cancels it by a dedicated null-constraint in the multi-source spatio-temporal beamformer. In most cases, estimation of the interference requires estimates of the past, present and future data symbols transmitted from the interferers, in which case the receiver requires a maximum delay of one symbol and one processing cycle for the lower-rate or low-power users and, at most a single null constraint per interferer.

[0026] In a third embodiment of the invention which uses a third mode conveniently designated ISR-D, i.e. the observation vector/matrix is decomposed over sub-channels/fingers of propagation path and the beamformer nulls interference in each of the sub-channels, one at a time. In most cases, the maximum number of constraints per interferer is equal to the number of sub-channels, i.e. the number of antenna elements M multiplied by the number of paths P.

[0027] In a fourth embodiment using a fourth mode conveniently designated ISR-H because it implements null-responses in beamforming using hypothetical realisations of the interference, without any delay, each receiver module of the first group further comprises means for supplying to the spreader possible values of the instant symbols of the output signal and the spreader supplies a corresponding plurality of re-spread signals to each of the receiver modules of the second group. In each receiver module of the second group, the despreader despreads the plurality of re-spread signals and supplies corresponding despread vectors to the beamformer. This embodiment suppresses any sensitivity to data estimation errors and, in most cases, requires a maximum of 3 null constraints per interferer.

[0028] In a fifth embodiment using a fifth mode conveniently designated ISR-RH because it uses the past and present interference symbol estimates, in each receiver module of the first group, the spreader spreads the symbols of the output signal itself and, in each receiver module of the second group, the beamformer then implements null-responses over reduced possibilities/hypotheses of the interference realization. Conveniently, application of the output of the first despreader to the beamformer will take into account the time required for estimation of the interferer's symbol. In most cases, the beamformer will provide a maximum of 2 null constraints per interferer.

[0029] In any of the foregoing embodiments of the invention, the channel identification unit may generate the set of channel vector estimates in dependence upon the extracted despread data vectors and the user signal component estimate.

[0030] For each of the above-identified modes, the receiver modules may employ either of two procedures. On the one hand, the receiver module may apply the post-correlation observation vector to the channel identification unit but supply the observation matrix itself directly to the beamformer, i.e. without despreading it. The constraint matrix then would be supplied to the beamformer without despreading.

[0031] Alternatively, each receiver module could supply the post-correlation observation vector to both the channel identification unit and the beamformer. In this case, the receiver module would also despread the constraint matrix before applying it to the beamformer.

[0032] Where the reception antenna comprises a plurality of antenna elements, the beamformer unit may comprise a spatio-temporal processor, such as a filter which has coefficients tuned by the estimated interference signals.

[0033] The receiver modules may comprise a first set that are capable of contributing a constraint waveform to the constraint matrix and a second set that have a beamformer capable of using the constraint matrix to tune the specified null response and unity response. In preferred embodiments, at least some of the plurality of receiver modules are members of both the first set and the second set, i.e. they each have means for contributing a constraint waveform and a beamformer capable of using the constraint matrix.

[0034] In practice, the receiver modules assigned to the stronger user signals will usually contribute a constraint waveform and the beamformer units of the receiver modules assigned to other user signals will be capable of using it.

[0035] The receiver module may comprise an MRC beamformer and an ISR beamformer and be adapted to operate in multi-stage, i.e., for each symbol period of frame, it will carry out a plurality of iterations. In the first iteration, the constraints set generator will receive the “past” and “future” estimates from the MRC beamformer and the “past” symbol estimate, i.e., from the previous frame, and process them to produce a new symbol estimate for the first iteration. In subsequent iterations of the current symbol period or frame, the constraints-set generator will use the “future” estimate from the MRC beamformer, the previous estimate from the ISR beamformer and the symbol estimate generated in the previous iteration. The cycle will repeat until the total number of iterations have been performed, whereupon the output from the receiver module is the desired estimated symbol for the current frame which then is used in the similar iterations of the next frame.

[0036] The ISR receiver module comprising both an MRC beamformer and an ISR beamformer may comprise means {101Q^d} for extracting from the ISR beamformer (47Q^d) an interference-reduced observation vector and reshaping the latter to produce an interference-reduced observation matrix for despreading by the despreader. The channel identification unit then uses the despread interference-reduced observation vector to form interference-reduced channel vector estimates and supplies them to the residual MRC beamformer for use in adapting the coefficients thereof.

[0037] The ISR beamformer may process blocks or frames of the observation vector that are extended by concatenating a current set of data with one or more previous frames or blocks of data.

[0038] The different receiver modules may use different sizes of frame.

[0039] In order to receive signals from a user transmitting multicode signals, the ISR receiver module may comprise a plurality of ISR beamformers and despreaders, each for operating upon a corresponding one of the multiple codes. The channel identification unit then will produce a channel vector estimate common to all of the multicodes, spread that channel vector estimate with each of the different multicodes and supply the resulting plurality of spread channel vector estimates to respective ones of the plurality of ISR beamformers.

[0040] The channel identification unit of the multicode ISR receiver module may receive its post-correlation observation vector from a despreader (19^d,δ) which uses a compound code comprising each of the multicodes weighted by the corresponding symbol estimate from a respective one of a corresponding plurality of decision-rule units. The despreader will use the compound code to despread the observation matrix and supply the corresponding compound post-correlation observation vector to the channel identification unit. The channel identification unit will use that vector to produce the channel vector estimate and spread it using the different ones of the multicodes to produce the spread channel vector estimates.

[0041] The ISR receiver module may comprise a despreader 19S^d,1, . . . , 19S^d,F using a plurality of codes which comprise segments of a main code specified for that user. Each segment corresponds to a symbol, and to a symbol duration in a large block of data, the number of segments being determined by the data rate, i.e., number of symbols within a block, of that user. Each receiver module may have a different number of segments assigned thereto according to the data rate of the corresponding user.

[0042] Embodiments of the invention may be adapted for use in a user/mobile station capable of receiving user-bound signals transmitted by a plurality of base stations each to a corresponding plurality of users, the receiver then comprising a selection of receiver modules each corresponding to a different base station and configured to extract a preselected number of said user-bound signals. Where the particular user/mobile station is included in the preselected number, the receiver module may comprise a similar structure to the above-mentioned multicode receiver, the plurality of despreaders being adapted to despread the observation matrix using respective ones of a set of codes determined as follows: (1) a pre-selected number NB of base stations from which the mobile receives signals and which have been selected for cancellation—represented by index ν′ which ranges from 1 to NB; (2) a preselected number (1 to NI) of interferers per base station preselected for cancellation; (3) the data rates of the selected interferers.

[0043] Thus, according to a second aspect of the invention, there is provided a user station receiver for a CDMA communications system comprising a plurality (NB) of base stations (11) and a multiplicity (U) of user stations (10¹, . . . , 10^U), at least a plurality (U′) of the user stations being in a cell associated with one of said base stations and served thereby, said one base station having a plurality of transmitter modules for spreading user signals for transmission to the plurality (U′) of user stations, respectively, and a receiver for receiving spread user signals transmitted by the plurality (U′) of user stations, the user stations each having a receiver for receiving the corresponding spread user signal transmitted by the base station, said plurality (U′) of user stations each having a unique spreading code assigned thereto for use by the user station and the corresponding one of the base station transmitter modules to spread the user signals of that user for transmission,

[0044] the spread user signals transmitted from the base station transmitter modules to a particular one of the plurality (U′) of user stations propagating via a plurality of channels (14¹, . . . , 14^U′), respectively,

[0045] the receiver of a particular one of said plurality (U′) of user stations receiving a signal (X(t)) comprising components corresponding to spread user signals for said particular user station and spread user signals transmitted by other transmitter modules of said plurality (NB) of base stations for other users, each of said spread user signals comprising a series of symbols spread using the spreading code associated with the corresponding one of the user stations,

said user station receiver comprising:

• • [0046] a plurality (NB) of receiver modules (20^ν′) each for deriving from successive frames of the received signal (X(t)) estimates of sets of said series of symbols from a corresponding one of the base stations,
  • [0047] preprocessing means (18) for deriving from the received signal (X(t)) a series of observation matrices (Y_n) each for use by each of the receiver modules (20^ν′) in a said frame to derive estimates of sets of said symbols, and
  • [0048] means (19,44) for deriving from each observation matrix a plurality of sets of observation vectors (Y_n^ν′,1,1, . . . , Y_n^ν′,NI,FNI; Z_n^ν′,1,1, . . . , Z_n^ν′,NI,FNI) and applying each of the sets of observation vectors to a respective one of the plurality of receiver modules (20^ν′);
    • [0049] each receiver modules comprising;
    • [0050] channel identification means (28T^ν′) for deriving from the respective one of the sets of observation vectors a set of spread channel vector estimates (Ŷ_0,n^ν′,1,1, . . . , Ŷ_0,n^ν′,NI,FNI) based upon parameter estimates of the channel between the corresponding one of the base stations and said user station;
    • [0051] beamformer means (47T^ν′1,1, . . . , 47T^ν′,NI,FNI) having coefficient tuning means for producing sets of weighting coefficients in dependence upon the sets of channel vector estimates, respectively, and combining means for using each of the sets of weighting coefficients to weight respective ones of the elements of a respective one of the observation vectors and combining the weighted elements to provide a corresponding set of signal component estimates (ŝ_n^ν′,1,1, . . . , ŝ_n^ν′,NI,FNI) and
    • [0052] symbol estimating means (29T^ν′,1,1, . . . , 29T^ν′,NI,FNI) for deriving from the set of signal component estimates a set of estimates ({circumflex over (b)}_n^ν′,1,1, . . . , {circumflex over (b)}_n^ν′,NI,FNI) of symbols spread by the corresponding one of the transmitter modules and transmitted by the base station;
  • [0053] said user station receiver further comprising means (42,43) responsive to said symbol estimates ({circumflex over (b)}_n^ν′,1,1, . . . , {circumflex over (b)}_n^ν′,NI,FNI; g_n¹, g_n², g_n³) and channel estimates (_n^ν′) from each of said plurality (NB) of receiver modules, said channel estimates comprising at least channel vector estimates (Ĥ_n^ν′) for channels (14^ν′) between the user station receiver and said base stations, for providing at least one constraint matrix (Ĉ_n) representing interference subspace of components of the received signal corresponding to said spread signals, and in each of said receiver modules (20^ν′), the coefficient tuning means produces said sets of weighting coefficients in dependence upon both the constraint matrix (Ĉ_n) and the channel vector estimates so as to tune said receiver module (20^ν′) towards a substantially null response to that portion of the received signal (X(t)) corresponding to said interference subspace.

[0054] Where the signal destined for the particular user/mobile station is not one of the preselected number of signals from the corresponding base station, the receiver may further comprise an ISR receiver module which has means for updating the ISR beamformer coefficients using the channel vector estimates from at least some of the receiver modules that have generated such channel vector estimates for the preselected signals for the same base station.

[0055] Where the rates of the different users are not known to the instant mobile station, the codes may comprise a fixed number of segments N_m which is predetermined as a maximum data rate to be received. Any slower rates will effectively be oversampled for processing at the higher rate.

[0056] The complexity of the multicode embodiments may be reduced by reducing the number of codes that are used by the despreaders. In particular, the bank of despreaders may use a set of codes that represent summation of the codes of the different NI interferers, to form a compound code which reduces the total number of codes being used in the despreaders.

[0057] According to another aspect of the invention, there is provided a STAR receiver comprising an MRC beamformer which operates upon an observation vector which has not been despread.

[0058] Of course, that does not preclude having all channels feed their interference components to all other channels.

[0059] Receivers embodying the present invention can operate in a multiple-input, multiple-output (MIMO) system, i.e. with multiple transmit antennas and multiple receive antennas.

[0060] The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description, in conjunction with the accompanying drawings, of preferred embodiments of the invention.

[0110] In the following description, identical or similar items in the different Figures have the same reference numerals, in some cases with a suffix.

[0111] The description refers to several published articles. For convenience, the articles are cited in full in a numbered list at the end of the description and cited by that number in the description itself. The contents of these articles are incorporated herein by reference and the reader is directed to them for reference.

[0112] FIGS. 1 and 2 illustrate the uplink of a typical asynchronous cellular CDMA system wherein a plurality of mobile stations 10¹ . . . 10^U communicate with a base-station 11 equipped with a receiving antenna comprising an array of several antenna elements 12¹ . . . 12^M. For clarity of depiction, and to facilitate the following detailed description, FIGS. 1 and 2 illustrate only five of a large number (U) of mobile stations and corresponding propagation channels of the typical CDMA system, one for each of a corresponding plurality of users. It will be appreciated that the mobile stations 10¹ . . . 10^U will each comprise other circuitry for processing the user input signals, but, for clarity of depiction, only the spreaders are shown in FIG. 2. The other circuitry will be known to those skilled in the art and need not be described here. Referring to FIG. 2, the mobile stations 10¹ . . . 10^U comprise spreaders 13¹ . . . 13^U, respectively, which spread a plurality of digital signals b_n¹ . . . b_n^U of a corresponding plurality of users, respectively, all to the same bandwidth, using spreading codes c¹(t) . . . c^U(t), respectively. The mobile stations 10¹ . . . 10^U transmit the resulting user signals to the base station 11 via channels 14¹ . . . 14^U, respectively, using a suitable modulation scheme, such as differential binary phase shift keying (DBPSK). Each of the mobile stations 10¹ . . . 10^U receives commands from the base station 11 which monitors the total received power, i.e. the product of transmitted power and that users code and attenuation for the associated channel and uses the information to apply power control to the corresponding signals to compensate for the attenuation of the channel. This is represented in FIG. 2 by multipliers 15¹ . . . 15^U which multiply the spread signals by adjustment factors ψ¹(t) . . . ψ^U(t), respectively. The array of M omni-directional antenna elements 12¹ . . . 12^M at the base station 11 each receive all of the spread signals in common. The channels 14¹ . . . 14^U have different response characteristics H¹(t) . . . H^U(t), respectively, as illustrated in more detail in FIG. 1, for only one of the channels, designated channel 14^u. Hence, channel 14^u represents communication via as many as P paths between the single antenna of the associated mobile station 10^U and each of the base station antenna elements 12¹ . . . 12^M. The other channels are similarly multipath.

[0113] As before, it is presumed that the base station knows the spreading codes of all of the mobile stations with which it communicates. The mobile stations will have similar configurations so only one will be described. Thus, the mobile station 10^u first differentially encodes its user's binary phase shift keyed (BPSK) bit sequence at the rate 1/T, where T is the bit duration, using circuitry (not shown) that is well-known to persons skilled in this art. As illustrated in FIG. 3, its spreader 13^u then spreads the resulting differential binary phase shift keyed (DBPSK) sequence b_n^u (or b^u(t) in the continuous time domain as represented in FIG. 3) by a periodic personal code sequence c_l^u (or c^u(t) in the continuous time domain) at a rate 1/T_c, where T_c is the chip pulse duration. The processing gain is given by L=T/T_c. For convenience, it is assumed that short codes are used, with the period of c^u(t) equal to the bit duration T, though the system could employ long codes, as will be discussed later, with other applications and assumptions. Over one period T, the spreading code can be written as: $\begin{array}{cc}{c}^u\left(t\right)=\sum _{l=0}^{L-1}{c}_l^u\varphi \left(t-l{T}_c\right),& \left(1\right)\end{array}$
where c_l^u=±1 for l=0, . . . , L−1, is a random sequence of length L and φ(t) is the chip pulse as illustrated in FIG. 3. Also, with a multipath fading environment with P resolvable paths, the delay spread Δτ is small compared to the bit duration (i.e. Δτ T).

[0114] As illustrated in FIGS. 4(a) and 4(b), following signal weighting by the power control factor ψ_pc^u(t)², the spread signal is transmitted to the base station 11 via channel 14^u. FIG. 4(a) shows the “real” situation where the channel characteristics comprise a normalized value H^u(T) and a normalization factor ψ_ch^u(T) which relates to the “amplitude” or attenuation of the channel, i.e. its square would be proportional to the power divided by the transmitted power. In FIG. 4(a), power control is represented by a multiplier 17^u, and the subscript “pc”. FIG. 4(b) shows that, for convenience, the channel characteristics can be represented (theoretically) by the normalized value H^u(t) and the normalization factor ψ_ch^u(t) included in a single power factor ψ^u(t) which is equal to ψ_pc^u(t)ψ_ch^u(t). ψ_pc^u(t) is the factor by which the transmitted signal is amplified or attenuated to compensate for channel power gain in ψ_ch^u(t) and to maintain the received power (ψ^u(t))² at the required level.

[0115] In such a CDMA system, the signal of each of the mobile stations 10¹ . . . 10^U constitutes interference for the signals of the other mobile stations. For various reasons, some of the mobile stations will generate more interference than others. The components of one of these “strongly interfering” user stations and its associated channel are identified in FIGS. 1 and 2 by the index “i”. The components of one of the other “low-power” user stations and its associated channel also are illustrated, and identified by the index “d”. The significance of this grouping of “interfering” and “low-power” user stations will be explained later.

[0116] At the base station 11, the spread data vector signals X¹(t) . . . X^U(t) from the base station antenna elements 12¹ . . . 12^M, respectively, are received simultaneously, as indicated by the adder 16 (FIG. 2), and the resulting observation vector X(t) is supplied to the receiver (see FIG. 5). The sum of the spread data vectors (signals) X¹(t) . . . X^U(t) will be subject to thermal noise. This is illustrated by the addition of a noise signal component N_th(t) by adder 16. The noise signal N_th(t) comprises a vector, elements of which correspond to the noise received by the different antenna elements.

[0117] FIG. 5 illustrates a spatio-temporal array receiver (STAR) for receiving the signal X(t) at the base station 11. Such a receiver was described generally by two of the present inventors in reference [13]. The receiver comprises means, namely a preprocessing unit 18 and a plurality of despreaders 19¹ . . . 19^U, for deriving observation vectors from the observation matrix, and a plurality of spatio-temporal receiver (STAR) modules 20¹ . . . 20^U, each having its input connected to the output of a respective one of the despreaders 19¹ . . . 19^U. As shown in FIG. 6, the preprocessing unit 18 comprises a matched filter 22, a sampler 23 and a buffer 24. Matched filter 22 convolves the antenna array signal vector X(t), which is an M×1 vector, with a matched pulse φ(T_c−t) to produce the matched filtered signal vector Y(t) which then is sampled by sampler 23 at the chip rate 1/T_c, element by element. The sampler 23 supplies the resulting M×1 vectors Y_n,l, at the chip rate, to buffer 24 which buffers them to produce an observation matrix Y_n of dimension M×(2L−1). It should be noted that, although the present inventors' Canadian patent application No. 2,293,097 and U.S. Provisional application No. 60/171,604 had a duplicate of this preprocessing unit 18 in each of the despreaders 19¹ . . . 19^U, it is preferable to avoid such duplication and use a single preprocessor 18 to preprocess the received antenna array signal vector X(t).

[0118] The despreaders 19¹ . . . 19^U each have the same structure, so only one will be described in detail with reference to FIG. 7 which illustrates despreader 19^u. Thus, despreader 19^u comprises a filter 25^u and a vector reshaper 26^u. The observation matrix Y_n is filtered by filter 21^u using the pseudo-random number sequence c_L−1^u corresponding to that used in the spreader 13^u of the transmitter, i.e. c_l^u, to produce the postcorrelation observation matrix Z_n^u for user u. Vector reshaper 26^u concatenates the columns of the M×L matrix Z_n^u to form a post-correlation observation vector Z_n^u of dimension ML×1. It should be noted that the vector reshaper 26^u need not be a distinct physical element but is depicted as such to represent a mathematical function. In practice, the function will likely be determined merely by allocation of resources, such as memory.

[0119] Referring again to FIG. 5, the post-correlation observation vectors Z_n¹ . . . Z_n^U from despreaders 19¹ . . . 19^U are processed by the STAR modules 20¹ . . . 20^U, respectively, to produce symbol estimates {circumflex over (b)}_n¹ . . . {circumflex over (b)}_n^U corresponding to the transmitted symbols b_n¹ . . . b_n^U (see FIG. 2) and power estimates ${\left({\hat{\psi }}_n^I\right)}^2\dots {\left({\hat{\psi }}_n^U\right)}^2$
which are supplied to subsequent stages (not shown) of the receiver for processing in known manner.

[0120] The STAR modules 20¹ . . . 20^U each comprise the same elements, so the construction and operation of only one of them, STAR module 20^u, will now be described.

[0121] The STAR module 20^u comprises a beamformer 27^u, a channel identification unit 28^u, a decision rule unit 29^u and a power estimation unit 30^u. The channel identification unit 28^u is connected to the input and output, respectively, of the beamformer 27^u to receive the post-correlation observation vector Z_n^u and the signal component estimate ŝ_n^u, respectively. The channel identification unit 28^u replicates, for each frame M×L the characteristics H^u(t), in space and time, of the associated user's transmission channel 14^u. More specifically, it uses the post-correlation observation vector Z_n^u and signal component estimate ŝ_n^u to derive a set of parameter estimates Ĥ_n^u, which it uses to update the weighting coefficients W_n^u of the beamformer 27^u in succeeding symbol periods. The symbol period corresponds to the data frame of M×L elements.

[0122] The beamformer 27^u comprises a spatio-temporal maximum ratio combining (MRC) filter which filters the space-time vector Z_n^u to produce the despread signal component estimate ŝ_n^u, which it supplies to both the decision rule unit 29^u and the power estimation unit 30^u. The decision-rule unit 29^u outputs a binary symbol {circumflex over (b)}_n^u according to the sign of the signal component estimate ŝ_n^u. The binary output signal constitutes the output of the decision rule unit 30^u and is an estimate of the corresponding user signal b_n^u spread by spreader 13^u of the corresponding user station 10^u (FIGS. 1 and 2).

[0123] The signal component estimate ŝ_n^u is processed in subsequent parts of the receiver. For example, it may be differentially decoded and, possibly, deinterleaved and then data decoded—if the corresponding inverse operations were done before transmission.

[0124] The power estimation unit 30^u uses the raw signal component estimate ŝ_n^u to derive an estimate ${\left({\hat{\psi }}_n^u\right)}^2$
of the power in that user's signal component ŝ_n^u of the antenna array signal vector X(t) and supplies the power estimate ${\left({\hat{\psi }}_n^u\right)}^2$
to the subsequent stages (not shown) of the receiver for derivation of power level adjustment signals in known manner.

[0125] The receiver shown in FIG. 5 will perform satisfactorily if there are no strong interferers, i.e., if it can be assumed that all users transmit with the same modulation and at the same rate, and that the base-station knows all the spreading codes of the terminals with which it is communicating. On that basis, operation of the receiver will be described with reference to the user channel identified by index u.

[0126] At time t, the antenna array signal vector X(t) received by the elements 12¹ . . . 12^M of the antenna array of the one particular cell shown in FIGS. 1 and 2 can be written as follows: $\begin{array}{cc}X\left(t\right)=\sum _{u=1}^U{X}^u\left(t\right)+N^{\mathrm{th}}\left(t\right)& \left(2\right)\end{array}$
where U is the total number of mobile stations whose signals are received at the base-station 11 from inside or outside the cell, X^u(t) is the received signal vector from the mobile station 10^u, i.e., of index u, and N^th(t) is the thermal noise received at the M antenna elements. The contribution X^u(t) of the u-th mobile station 10^u to the antenna-array signal vector X(t) is given by: $\begin{array}{cc}\begin{array}{c}{X}^u\left(t\right)={\psi }^u\left(t\right)H^u\left(t\right)\otimes c^u\left(t\right)b^u\left(t\right)\\ ={\psi }^u\left(t\right)\sum _{p=1}^P{G}_p^u\left(t\right){\varepsilon }_p^u\left(t\right)c^u\left(t-{\tau }_p^u\left(t\right)\right)b^u\left(t-{\tau }_p^u\left(t\right)\right)\end{array}& \text{(2a)}\end{array}$
where H^u(t) is the channel response vector of the channel 14^u between the u-th mobile station 10^u and the array of antenna elements and {circle around (×)} denotes time-convolution. In the right-hand term of the above equation, the propagation time-delays τ_p^u(t) ∈[0,T] along the P paths, p=1, . . . , P, (see FIG. 1), are chip-asynchronous, G_p^u(t) are the propagation vectors and ε_p^u(t)² are the power fractions along each path $\left(i.e.,\sum _{p=1}^p{{\varepsilon }_p^u\left(t\right)}^2=1\right)$
of the total power ψ^u(t)² received from the u-th mobile station 10^u. The received power is affected by path-loss, Rayleigh fading and shadowing. It is assumed that G_p^u(t), ε_p^u(t)² and ψ^u(t)² vary slowly and are constant over the bit duration T.

[0127] In the preprocessing unit 18 (see FIG. 6), the antenna array signal vector X(t) is filtered with the matched pulse to provide the matched-filtering signal vector Y_n(t) for frame n as follows: $\begin{array}{cc}{Y}_n\left(t\right)=\frac{1}{T_c}{\int }_{D_{\varphi }}X\left(\mathrm{aT}/2+\mathrm{nT}+t+t^{\prime }\right)\varphi \left(t^{\prime }\right)d{t}^{\prime }& \left(3\right)\end{array}$
where D_φ denotes the temporal support of φ(t) and a ∈{0,1} stands for a possible time-shift by T/2 to avoid, if necessary, the frame edges lying in the middle of the delay spread (see reference [13]). For the sake of simplicity, it is assumed in the following that a=0. Note that for a rectangular pulse D_φ is [0,T_c]. In practice, it is the temporal support of a truncated square-root raised- cosine.

[0128] It should be noted that the above description is baseband, without loss of generality. Both the carrier frequency modulation and demodulation steps can be embedded in the chip pulse-shaping and matched-filtering operations of Equations (1) and (3), respectively.

[0129] Thus, after sampling at the chip rate 1/T_c and framing over 2L−1 chip samples at the bit rate to form a frame, the preprocessing unit 18 derives the M×(2L−1) matched-filtering observation matrix:
Y_n=[Y_n,0, Y_n,1, . . . , Y_n,2L−2],  (4)
where Y_n,l=Y_n(lT_c).

[0130] In the despreader 19^u (see FIG. 7), the post-correlation vector for frame number n for user number u is obtained as: $\begin{array}{cc}{Z}_{n,l}^u=\frac{1}{L}\sum _{k=0}^{L-1}{Y}_{n,l+k}{c}_k^u.& \left(5\right)\end{array}$
Framing this vector over L chip samples at the bit rate forms the post-correlation observation matrix:
Z_n^u=[Z_n,0,^u, Z_n,1^u, . . . , Z_n,L−1^u].  (6)
The post-correlation data model (PCM) (see reference [13]) details the structure of this matrix as follows:
Z_n^u=H_n^us_n^u+N_PCM,n^u,  (7)
where Z_n^u is the spatio-temporal observation matrix, H_n^u is the spatio-temporal propagation matrix, s_n^u=b_n^uψ_n^u is the signal component and N_PCM,n^u is the spatio-temporal noise matrix. Equation 7 provides an instantaneous mixture model at the bit rate where the signal subspace is one-dimensional in the M×L matrix space. For convenience, the vector reshaper 26^u of despreader 19^u transforms the matrices Z_n^u, H_n^u and N_PCM,n^u into (M×L)-dimensional vectors Z_n^u, H_n^u and Z_PCM,n^u respectively, by concatenating their columns into one spatio-temporal column vector to yield the following narrowband form of the PCM model (see reference [13]):
Z_n^u=H_n^us_n^u+N_PCM,n^u  (8)
To avoid the ambiguity due to a multiplicative factor between H_n^u and s_n^u, the norm of H_n^u is fixed to $\sqrt{M}.$

[0131] The PCM model significantly reduces inter-symbol interference. It represents an instantaneous mixture model of a narrowband source in a one-dimensional signal subspace and enables exploitation of low complexity narrowband processing methods after despreading. Processing after despreading exploits the processing gain to reduce the interference and to ease its cancellation in subsequent steps by facilitating estimation of channel parameters.

[0132] As discussed in reference [13], the spatio-temporal array-receiver (STAR) can be used to detect each user separately at the base-station 11. In addition to exploiting the processing gain to reduce interference, the STAR allows accurate synchronization and tracking of the multipath delays and components and shows inherent robustness to interference. The STAR also allows coherent combining of the data. This receiver is found to provide fast and accurate time-varying multipath acquisition and tracking. Moreover, it significantly improves call capacity by spatio-temporal maximum ratio combining (MRC) in a coherent detection scheme implemented without a pilot signal. For the sake of clarity, the steps of STAR that are relevant to the implementation of the present invention will be reviewed briefly below, with reference to receiver module 20^u of FIG. 5.

[0133] As shown in FIG. 5, the despreader 19^u supplies the post-correlation observation vector Z_n^u, to both the channel identification unit 28^u and the MRC beamformer 27^u of STAR module 20^u. Using spatio-temporal matched filtering (W_n^u=Ĥ_n^u/M) (i.e. spatio-temporal maximum ratio combining, W_n^u″Ĥ_n^u=1), the STAR module 20^u provides estimates of signal component s_n^u, its DBPSK bit sequence b_n^u and its total received power ${\left({\psi }_n^u\right)}^2$
as follows: $\begin{array}{cc}{\hat{s}}_n^u=\mathrm{Real}\left\{{\underset{\_}{W}}_n^{u^H}{\underset{\_}{Z}}_n^u\right\}=\mathrm{Real}\left\{\frac{{\widehat{\underset{\_}{H}}}_n^{u^H}{\underset{\_}{Z}}_n^u}{M}\right\},& \left(9\right)\\ {\hat{b}}_n^u=\mathrm{Sign}\left\{{\hat{s}}_n^u\right\},& \left(10\right)\\ {\left({\hat{\psi }}_n^u\right)}^2=\left(1-\alpha \right){\left({\hat{\psi }}_{n-1}^u\right)}^2+\alpha {{\hat{s}}_n^u}^2,& \left(11\right)\end{array}$
where α is a smoothing factor. It should be noted that with ad hoc modifications, differential modulation and quasi-coherent differential decoding still apply with DMPSK. Orthogonal modulation can even be detected coherently by STAR without a pilot (references [17] and [18]). Using the post-correlation observation vector Z_n^u and the new signal component estimate ŝ_n^u from the beamformer 27^u, the channel identification unit 28^u provides an estimate {circumflex over (H)}_n^u of the channel 14^u for user station 10^u. The channel identification unit 28^u updates the channel vector estimate {circumflex over (H)}_n^u by means of a decision feedback identification (DFI) scheme whereby the signal component estimate ŝ_n^u is fed back as a reference signal in the following eigen-subspace tracking procedure:
{tilde over (H)}_n+1^u=Ĥ_n^u+μ(Z_n^u−Ĥ_n^uŝ_n^u)ŝ_n^u,  (12)
where μ is an adaptation step-size. Alternatively, the product {circumflex over (ψ)}_n^u{circumflex over (b)}_n^u could be fed back instead of the signal component estimate ŝ_n^u. It should be noted that, if the modulation is complex, the second occurrence of signal component estimate Ŝ_n^u should be replaced by its conjugate (Ŝ_n^u). This DFI scheme allows a 3 dB coherent detection gain in noise reduction by recovering the channel phase offsets within a sign ambiguity without a pilot. Note that a reduced-power pilot can be used to avoid differential coding and decoding (reference [21]). The procedure that further enhances the channel vector estimate Ĥ_n+1^u to obtain Ĥ_n+1^u from the knowledge of its spatio-temporal structure (i.e. manifold) allows a fast and accurate estimation of the multipath time-delays {circumflex over (τ)}_1,n^u, . . . , {circumflex over (τ)}_P,n^u in both the acquisition and the tracking modes (both versions of this procedure can be found in reference [13]). This improved estimation accuracy achieves robustness to channel estimation errors, and reduces sensitivity to timing errors, when STAR is used in multiuser operation.

[0134] For further information about STAR, the reader is directed to the articles by Affes and Mermelstein identified as references [13] and [17] to [21].

[0135] If, as was assumed in reference [13], the spatio-temporal noise vector N_PCM,n^u is partially uncorrelated, power control on the uplink is generally able to equalize the received signal powers. However, the assumption that noise is uncorrelated becomes untenable on the downlink due to path-loss and shadowing and when the power of particular users (e.g., “priority links”, acquisition, higher-order modulations or higher data-rates in mixed-rate traffic) is increased intentionally. Within a particular cell, there may be users having many different strengths, perhaps because of different data rates. FIG. 8 illustrates, as an example, a cell in which there are four different sets of users arranged hierarchically according to data rate. The first set I comprises users which have relatively high data rates, the second set M1 and third set M2 both comprise users which have intermediate data rates, and the fourth set D comprises users which have relatively low data rates. In practice, the receivers of the high data rate users of set I will not need to cancel any outset interference from the users in sets M1, M2 and D, but their transmissions will contribute to interference for the receiver modules in those sets. Intermediate data rate users in sets M1 and M2 will need to cancel “outset” interference from the high data rate users of the set I but not from the users in set D. They will themselves be contributors of “outset” interference to the users in set D. The receivers of users in set D must cancel “outset” interference from sets I, M1 and M2.

[0136] It is also possible for a receiver of a user within a particular set to cancel “inset” interference from one or more users within the same set; and itself be a contributor to such “inset” interference. Embodiments of the invention applicable to these “outset” and “inset” situations will be described hereinafter. In the description, where a particular user's signal is treated as interference and cancelled, it will be deemed to be a “contributor” and, where a particular user's receiver module receives information to enable it to cancel another user's interference, it will be deemed to be a “recipient”. To simplify the description of the preferred embodiments described herein, it will be assumed that all users employ the same modulation at the same rate. For the purpose of developing the theory of operation, initially it will be assumed that, among the mobile stations in the cell, there will be a first set I of “strong” contributor users, one of which is identified in FIGS. 1 and 2 by index “i”, whose received signal powers are relatively high and hence likely to cause more interference, and a second set D of “low-power” recipient users, one of which is identified in FIGS. 1 and 2 by index “d”, whose received signal powers are relatively low and whose reception may be degraded by interference from the signals from the strong users. In order to receive the low-power users adequately, it usually is desirable to substantially eliminate the interference produced by the high-power users. For simplicity, most of the preferred embodiments of the invention will be described on the basis that the high-power users can be received adequately without interference suppression. It should be appreciated, however, that the “strong” user stations could interfere with each other, in which case one could also apply to any interfering mobile the coloured noise model below and the near-far resistant solution proposed for the low-power user, as will be described later.

[0137] Assuming the presence of NI interfering users assigned the indices i=1 to NI, then the spatio-temporal observation vector of any interfering user (u=i∈{1, . . . , NI}) is given from Equation 8 by:
Z_nⁱ=H_nⁱs_nⁱ+N_PCM,nⁱ,  (13)
where N_PCM,nⁱ can still be assumed to be an uncorrelated white noise vector if the processing gain of this user is not very low. On the other hand, from the point of view of any low-power user (u=d∉{1, . . . , NI}), the spatio-temporal observation vector is: $\begin{array}{cc}\begin{array}{c}{\underset{\_}{Z}}_n^d={\underset{\_}{H}}_n^d{s}_n^d+{\underset{\_}{I}}_{\mathrm{PCM},n}^d+{\underset{\_}{N}}_{\mathrm{PCM},n}^d\\ ={\underset{\_}{H}}_n^d{s}_n^d+\sum _{i=1}^{\mathrm{NI}}{\underset{\_}{I}}_{\mathrm{PCM},n}^{d,i}+{\underset{\_}{N}}_{\mathrm{PCM},n}^d,\end{array}& \left(14\right)\end{array}$
where, in addition to the uncorrelated white noise vector N_PCM,n^d, there is included a total interference vector I_PCM,n^d which sums a random coloured spatio-temporal interference vector from each interfering mobile denoted by I_PCM,n^d,i for i=1, . . . , NI. At frame number n, the realization of the vector I_PCM,n^d,i results from matched-pulse filtering, chip-rate sampling, despreading with c_l^d, bit-rate framing, and matrix/vector reshaping of the received signal vector Xⁱ(t) from the i-th interfering mobile using Equations (3) to (6).

[0138] The receiver shown in FIG. 5 would receive the signals from all of the user stations independently of each other. It should be noted that there is no cross-connection between the receiver modules 20¹, . . . , 20^U, specifically between their STAR modules 20¹ . . . 20^u . . . 20^U, for suppression of interference from the signals of mobile stations which constitute strong interferers. While the matched beamformer of Equation (9) is optimal in uncorrelated white noise, it is suboptimal when receiving the low-power users due to spatial-temporal correlation of the interference terms. To allow the accommodation of additional users in the presence of much stronger interfering mobiles in the target cell, in embodiments of the present invention the receiver of FIG. 5 is upgraded to obtain much stronger near-far resistance, specifically by adapting the beamformer of Equation (9) to reject the interference contributions from the interfering strong users.

[0139] In the general case, the total interference I_PCM,n^d experienced by a user d in set D is an unknown random vector which lies at any moment in an interference subspace spanned by a matrix, say C_PCM,n^d (i.e., I_PCM,n^d∈Vec{C_PCM,n^d}) with dimension depending on the number of interference parameters (i.e., power, data, multipath components and delays) assumed unknown or estimated a priori. As will become apparent from the following descriptions of preferred embodiments, in practice, the matrix C_PCM,n^d, which will be referred to as the constraint matrix, can be derived and estimated in different ways. To achieve near-far resistance, the beamformer must conform to the following theoretical constraints: $\begin{array}{cc}\{\begin{array}{c}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{H}}_n^d=1,\\ {\underset{\_}{W}}_n^{d^H}{C}_{\mathrm{PCM},n}^d=0,\end{array}\Rightarrow \{\begin{array}{c}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{H}}_n^d=1,\\ {\underset{\_}{W}}_n^{d^H}{I}_{\mathrm{PCM},n}^d=0.\end{array}& \left(15\right)\end{array}$

[0140] The first constraint provides a substantially distortionless response to the low-power user while the second instantaneously rejects the interference subspace and thereby substantially cancels the total interference. This modification of the beamforming step of STAR will be referred to as interference subspace rejection (ISR).

[0141] With an estimate of the constraint matrix Ĉ_PCM,n^d available (as described later), the ISR combiner (i.e., the constrained spatio-temporal beamformer) W_n^d after despreading is obtained by: $\begin{array}{cc}{Q}_{\mathrm{PCM},n}^d={\left({\hat{C}}_{\mathrm{PCM},n}^{d^H}{\hat{C}}_{\mathrm{PCM},n}^d\right)}^{-1},& \left(16\right)\\ {\Pi }_{\mathrm{PCM},n}=I_{M*L}-{\hat{C}}_{\mathrm{PCM},n}^d{Q}_{\mathrm{PCM},n}^d{\hat{C}}_{\mathrm{PCM},n}^{d^H},& \left(17\right)\\ {\underset{\_}{W}}_n^d=\frac{{\Pi }_{\mathrm{PCM},n}^d{\underset{\_}{\hat{H}}}_n^d}{{\underset{\_}{\hat{H}}}_n^{d^H}{\Pi }_{\mathrm{PCM},n}^d{\underset{\_}{\hat{H}}}_n^d},& \left(18\right)\end{array}$
where I_M*L denotes a M*L×M*L identity matrix. First, the projector Π_PCM,n orthogonal to the constraint matrix Ĉ_PCM,n is formed. It should be noted from Equations (16) and (17) that the inverse matrix Q_PCM,n^d is not the direct inverse of constraint matrix C_PCM,n^d but part of the pseudo-inverse of C_PCM,n^d. For convenience, however, it will be referred to as the inverse matrix hereafter. Second, the estimate of the low-power response vector {circumflex over (Y)}_n^d is projected and normalized.

[0142] Whereas, using the above constraints, the ISR beamformer may process the low-power user's data vector after it has been despread, it is possible, and preferable, to process the data vector without first despreading it. In either case, however, the data vector will still be despread for use by the channel identification unit. Although it is computationally more advantageous to do so without despreading, embodiments of both alternatives will be described. First, however, the spread data model of Equation (2) will be reformulated and developed and then used to derive various modes that implement ISR combining of the data, without despreading, suitable for different complementary situations.

Data Model Without Despreading

[0143] The observation matrix Y_n of Equation (4) which provides the post-correlation matrix Z_n of Equation (7) by despreading and framing at the bit rate, can be expressed as: $\begin{array}{cc}{Y}_n=\sum _{u=1}^U{Y}_n^u+N_n^{\mathrm{pth}},& \left(19\right)\end{array}$
where each user u contributes its user-observation matrix Y_n^u, obtained by Equations (3) and (4) with X(t) replaced by X^u(t) in Equation (3), and where the preprocessed thermal noise contributes:
N_n^pth=[N^pth(nT),N^pth(nT+T_c), . . . , N^pth(nT+(2L−2)T_c)].  (20)

[0144] Using the fact that any bit-triplet [b_n−1^u, b_n^u, b_n+1^u] contributing to channel convolution (see Equation (2a) in Y_n^u can be composed as:
[b_n−1^u, b_n^u, b_n+1^u]=b_n−1^u[1, 0, 0]+b_n^u[0, 1, 0]+b_n+1^u[0,0,1],  (21)
the sequence b^u(t) can be locally approximated over the n-th block by means of the canonic generating sequences g¹(t), g²(t) and g³(t) in FIG. 25 as:
b^u(t)=b_n^ug^l0,n(t)+b_n−1^ug^l−1,n(t)+b_n+1^ug^l+1,n(t),  (22)
where the indices l_0,n, l_−1,n, l_+1,n∈{1, 2, 3} are permuted at each block so that the corresponding canonic generating sequences locally coincide with [0, 1, 0], [1, 0, 0] and [0, 0, 1], respectively. Assuming slow time-variations of ψ(t) and H(t) compared to the symbol duration:
Y_n^u=s_n^uY_0,n^u+s_n−1^uY_−1,n^u+s_n+1^uY_+1,n^u,  (23)
where the canonic user-observation matrices Y_k,n^u are obtained by Equations (3) and (4) with X(t) in Equation (3) replaced, respectively for k=−1, 0, +1, by:
X_k^u(t)=H^u(t){circle around (×)}g^lcm(t)c^u(t).  (24)
Good approximations of Y_−1,nu and Y_+1,nu can be actually obtained at each iteration by L simple backward/forward shifts of the columns of Y_0,n^u with zero column inputs.

[0145] It should be noted that the canonic generating sequences allow more accurate reconstruction (e.g., overlap-add) of time-varying channels. Also, the resulting decomposition in Equation (23) holds for long PN codes.

[0146] It should be noted that this decomposition also holds for any complex-valued symbol-triplet [b_n−1^u, b_n^u, b_n+1^u]. With ad hoc modifications, therefore, the ISR approach according to this invention applies to any complex modulation (e.g., MPSK, MQAM, even analog). This new signal decomposition is used to derive the different implementations of ISR which will be described later.

[0147] With respect to the low-power user assigned the index d and the NI strong interfering mobiles assigned the indices i=1, . . . , NI, the observation vector obtained by reshaping the observation matrix, before despreading, can now be rewritten as:
Y_n=Y_0,n^ds_n^d+I_ISI,n^d+I_n+N_n,  (25)
where the first canonic observation vector Y_0,n^d appears as the “channel” vector of the low-power user d. The total interference vector before despreading: $\begin{array}{cc}\begin{array}{c}{\underset{\_}{I}}_n=\sum _{i=1}^{\mathrm{N1}}{\underset{\_}{Y}}_n^i=\sum _{i=1}^{\mathrm{N1}}\left\{s_n^i{\underset{\_}{Y}}_{0,n}^i+s_{n-1}^i{\underset{\_}{Y}}_{-1,n}^i+s_{n+1}^i{\underset{\_}{Y}}_{+1,n}^i\right\}\\ =\sum _{i=1}^{\mathrm{NI}}\left\{s_n^i{\underset{\_}{Y}}_{0,n}^i+{\underset{\_}{I}}_{\mathrm{ISI},n}^i\right\},\end{array}& \left(26\right)\end{array}$
is the sum of the interfering signal vectors Y_nⁱ and:
I_ISI,n^u=s_n−1^uY_−1,n^u+s_n+1^uY_+1,n^u,  (27)
is the intersymbol interference (ISI) vector of user u. In large processing gain situations, the self ISI vector I_ISI,n^d can be combined with the uncorrelated spatio-temporal noise vector N_n, leading to the following data vector model before despreading:
Y_n=Y_0,n^ds_n^d+I_n+N_n,  (28)

[0148] Despreading the observation vector in the above equation with the spreading sequence of the low-power user d provides the data vector model after despreading in Equation (14). It is possible to derive a finer decomposition of the data model to allow implementation of one or more of the ISR modes over diversities.

Finer Decomposition of the Data Model Over Diversities

[0149] Thus, Equation (2a) can be further decomposed over the N_f=MP diversity branches or fingers in such a way that the observation signal contribution X^u,f(t) received by the m-th antenna along the p-th path for f=(p−1)M+m=1, . . . , N_f can be separated as follows: $\begin{array}{cc}{X}^u\left(t\right)=\sum _{f=1}^{N_f}{X}^{u,f}\left(t\right).& \left(29\right)\end{array}$
The observation signal contribution from the f-th finger is defined as: $\begin{array}{cc}\begin{array}{c}{X}^{u,f}\left(t\right)={\psi }^u\left(t\right)H^{u,f}\left(t\right)\otimes c^u\left(t\right)b^u\left(t\right)\\ ={\psi }^u\left(t\right)G_p^{u,f}\left(t\right){\varepsilon }_p^u\left(t\right)b^u\left(t-{\tau }_p^u\left(t\right)\right)c^u\left(t-{\tau }_p^u\left(l\right)\right),\end{array}& \left(30\right)\end{array}$
where the propagation vector from the f-th finger is: $\begin{array}{cc}{G}_p^{u,f}\left(t\right)={\gamma }_f^u\left(t\right){\underset{\_}{R}}_m.& \left(31\right)\end{array}$
In the above equation, the scalar γ_f^u(t) is the channel coefficient over the f-th finger and R_m=[0, . . . , 0, 1, 0, . . . , 0]^T is a M×1 vector with null components except for the m-th one. With the above definitions, one can easily check the following decompositions of the channel and the propagation vectors: $\begin{array}{cc}{H}^u\left(t\right)=\sum _{f=1}^{N_f}{H}^{u,f}\left(t\right),& \left(32\right)\\ G_p^u\left(t\right)=\sum _{m=1}^M{G}_p^{u,\left(p-1\right)M+m}\left(t\right).& \left(33\right)\end{array}$
Accordingly, after preprocessing, the matched-filtering observation matrix can be decomposed as follows: $\begin{array}{cc}{Y}_n=\sum _{u=1}^U{Y}_n^u+N_n^{\mathrm{pth}}=\sum _{u=1}^U\sum _{f=1}^{N_f}{\psi }_n^u{\zeta }_{f,n}^u{Y}_n^{u,f}+N_n^{\mathrm{pth}},& \left(34\right)\end{array}$
where each user u contributes its user-observation matrices Y_n^u,f from fingers f=1, . . . , N_f, obtained by Equations (3) and (4) with X(t) replaced by X^u,f(t) in Equation (3). Note that the complex channel coefficient ζ_f^u(nT)=γ_f^u(nT)ε_p^u(nT) is separated from the matrix¹ Y_n^u,f which contains a purely-delayed replica of the spread-data without attenuation or phase offset from finger f. This matrix, which is obtained by Equations (3) and (4) with X(t) in Equation (3) replaced by:
X^u,f(t)=R_mδ(t−τ_p(t)){circle around (×)}b^u(t)c^u(t),  (35)
can be further decomposed over the canonic generating sequences as follows:
Y_n^u,f=b_n^uY_0,n^u,f+b_n−1^uY_−1,n^u,f+b_n+1^uY_+1,n^u,f,  (36)
where the canonic user-observation matrices Y_k,n^u,f from finger f are obtained by Equations (3) and (4) with X(t) in Equation (3) replaced, respectively for k=−1, 0, +1, by:
X_k^u,f(t)=R_mδ(t−τ_p(t)){circle around (×)}g^l1,n(t)c^u(t),  (37)
where δ(t) denotes the Dirac impulse. Therefore one obtains: $\begin{array}{cc}{Y}_n=\sum _{n=1}^U\sum _{f=1}^{N_f}\sum _{k=-1}^{+1}{s}_{n+k}^u{\zeta }_{f,n}^u{Y}_{k,n}^{u,f}+N_n^{\mathrm{pth}}.& \left(38\right)\end{array}$
A coarser decomposition over fingers of the total interference vector before despreading defined in Equation (26) gives: $\begin{array}{cc}{\underset{\_}{I}}_n=\sum _{i=1}^{\mathrm{NI}}{\underset{\_}{Y}}_n^i=\sum _{i=1}^{\mathrm{NI}}\sum _{f=1}^{N_f}{\psi }_n^i{\zeta }_{f,n}^i{\underset{\_}{Y}}_n^{i,f}.& \left(39\right)\end{array}$
After despreading with the spreading sequence of the low-power user d, it gives: $\begin{array}{cc}{\underset{\_}{I}}_{\mathrm{PCM},n}^d=\sum _{i=1}^{\mathrm{NI}}{\underset{\_}{I}}_{\mathrm{PCM},n}^{d,i}==\sum _{i=1}^{\mathrm{NI}}\sum _{f=1}^{N_f}{\psi }_n^i{\zeta }_{f,n}^i{\underset{\_}{I}}_{\mathrm{PCM},n}^{d,i,f}.& \left(40\right)\end{array}$
Embodiments of the invention which use the above decompositions of interference, denoted as ISR-D implementations before and after despreading, will be described later with reference to FIGS. 16 and 23.

[0150] ¹This matrix is real-valued in the case of a binary modulation.

ISR Combining Before Despreading

[0151] As described hereinbefore, the combining step of STAR is implemented without despreading by replacing Equation (9) for the low-power user with: $\begin{array}{cc}{\hat{s}}_n^d=\mathrm{Real}\left\{{\underset{\_}{W}}_n^{d^H}{\underset{\_}{Y}}_n\right\},& \left(41\right)\end{array}$
where the spatio-temporal beamformer W_n^d now implements ISR without despreading to reject I_n by complying with the following constraints (see Equation (15)): $\begin{array}{cc}\{\begin{array}{c}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{Y}}_{0,n}^d=1,\\ {\underset{\_}{W}}_n^{d^H}{C}_n=0,\end{array}\Rightarrow \{\begin{array}{c}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{Y}}_{0,n}^d=1,\\ {\underset{\_}{W}}_n^{d^H}{\underset{\_}{I}}_n=0,\end{array}& \left(42\right)\end{array}$
and C_n is the constraint matrix without despreading that spans the interference subspace of the total interference vector I_n (i.e., I_n∈Vec{C_n}).

[0152] The constraint matrix without despreading, C_n, is common to all low-power users. Thus, it characterizes the interference subspace regardless of the low-power user. In contrast, each constraint matrix after despreading C_PCM,n^d in Equation (15) is obtained by despreading C_n with the spreading sequence of the corresponding low-power user. Therefore ISR combining before despreading, although equivalent to beamforming after despreading, is computationally much more advantageous.

[0153] In contrast to the “after despreading” case described earlier, when the data vector is not despread before processing by the ISR combiner (i.e., the constrained spatio-temporal beamformer) W_n^d the estimate of the constraint matrix Ĉ_n is obtained by: $\begin{array}{cc}{Q}_n={\left({\hat{C}}_n^H{\hat{C}}_n\right)}^{-1},& \left(43\right)\\ {\Pi }_n=I_{M*\left(2L-1\right)}-{\hat{C}}_n{Q}_n{\hat{C}}_n^H,& \left(44\right)\\ {\underset{\_}{W}}_n^d=\frac{{\Pi }_n{\widehat{\underset{\_}{Y}}}_{0,n}^d}{{\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}{\Pi }_n{\widehat{\underset{\_}{Y}}}_{0,n}^d},& \left(45\right)\end{array}$
where I_M*(2L−1) denotes a M*(2L−1)×M*(2L−1) identity matrix. As before, it can be seen from Equations (43) and (44) that the inverse matrix Q_n is not the direct inverse of constraint matrix Ĉ_n but part of the pseudo-inverse of Ĉ_n. It should also be noted that the above operations are actually implemented in a much simpler way that exploits redundant or straightforward computations in the data projection and the normalization. As before, the projector Π_n orthogonal to the constraint matrix Ĉ_n is formed once for all low-power users. This would have not been possible with ISR after despreading. Second, the estimate of the low-power response vector {circumflex over (Y)}_0,n^d is projected and normalized. The estimate {circumflex over (Y)}_0,n^d is reconstructed by reshaping the following matrix:
Ŷ_0,n^d=Ĥ_n^d{circle around (×)}g_n^l0,nc_l^d,  (46)
the fast convolution with the channel matrix estimate being implemented row-wise with the spread sequence. The symbol {circle around (×)} denotes overlap—add over the past, current and future blocks of the spread sequence to be convolved with a finite-size channel-matrix; hence g_n^l0,n is introduced in Equation 46 to isolate the net contribution from the current sequence block. The channel vector estimate {circumflex over (H)}_n^d, i.e. Ĥ_n^d, is provided by STAR as explained earlier and includes the total contribution of the shaping pulse φ(t) matched with itself [13]. If the channel time-variations are slow, the channel coefficients can be assumed constant over several symbol durations [20], thereby reducing the number of computationally expensive despreading operations required (see FIG. 9).

[0154] It should be noted that, although these ISR modes have formulations that are analogous whether ISR is implemented with or without first despreading the data vector, ISR combining of the data without it first being despread reduces complexity significantly.

[0155] Receivers which implement these different ISR modes will now be described, using the same reference numerals for components which are identical or closely similar to those of the receiver of FIG. 5, with a suffix indicating a difference. A generic ISR receiver which does so without despreading of the data will be described first, followed by one which does so after despreading of the data. Thereafter, specific implementations of different ISR modes will be described.

[0156] Thus, FIG. 9 illustrates a receiver according to a first embodiment of the invention which comprises a first set I of “strong user” receiver modules 20¹ . . . 20^NI which are similar to those in the receiver of FIG. 5, and, separated by a broken line 34, a second set D of “low-power” user receiver modules which differ from the receiver modules of set I but are identical to each other so, for convenience, only one, STAR module 20A^d having a modified beamformer 47A^d, is shown. The outputs of the decision rule units 29¹, . . . , 29^NI and of the channel identification units 28¹, . . . , 28^NI from the set I modules are shown coupled to a constraints-set generator 42A which processes the corresponding symbol estimates and channel vector estimates to produce a set of N_c constraints _n={_n¹, . . . , _n^Nc}. The constraints-set generator 42A may, however, use hypothetical symbol values instead, or a combination of symbol estimates and hypothetical values, as will be described later. Each individual constraint lies in the same observation space as the observation matrix Y_n from preprocessor 18. The constraints-set generator 42A supplies the set of constraints _n to a constraint matrix generator 43A which uses them to form a constraint matrix Ĉ_n and an inverse matrix Q_n which supplies it to the beamformer 47^d and each of the corresponding beamformers in the other receiver modules of set D. The actual content of the set of constraints _n and the constraint matrix Ĉ_n will depend upon the particular ISR mode being implemented, as will be described later.

[0157] The observation vector deriving means in the receiver of FIG. 9 also comprises a vector reshaper 44 which reshapes the observation matrix Y_n from the preprocessing unit 18 to form an observation vector Y_n, having dimension M(2L−1) and supplies it to the beamformer 47A^d and to each of the other beamformers in the other receiver modules in set D.

[0158] The STAR module 40A^d comprises a channel identification unit 28A^d, a decision rule unit 27A^d and a power estimation unit 30A^d which are similar to those of the STAR modules 20¹ . . . 20^U described hereinbefore. The STAR module 20A^d is associated with a despreader 19^d which also is part of the observation vector deriving means. The despreader 19^d despreads the observation matrix Y_n using the spreading code for user d and supplies the resulting post-correlation observation vector Z_n to the channel identification unit 28A^d only. The decision rule unit 27A^d and power estimation unit 30A^d produce output symbol estimates {circumflex over (b)}_n^d and power estimates ${\left({\hat{\psi }}_n^d\right)}^2,$
respectively. The ISR beamformer 47A^d of STAR module 20A^d produces corresponding signal component estimates ŝ_n^d but differs from the MRC beamformers 27^l . . . 27^NI because it operates upon the observation vector Y_n, which has not been despread. In a manner similar to that described with respect to FIG. 5, the channel identification unit 28A^d receives the post-correlation observation vector Z_n^d and the signal component estimate ŝ_n^d and uses them to derive the spread channel vector estimates Ŷ_0,n^d, which it uses to update the weighting coefficients W_n^d of the beamformer 47A^d in succeeding symbol periods. The symbol period corresponds to the spread data frame of M(2L−1) elements. The coefficients of the ISR beamformer 47A^d also are updated in response to the constraint matrix Ĉ_n and its inverse Q_n, as will be described later. As shown in FIG. 9, the same matrices Ĉ_n and Q_n are supplied to all of the receiver modules in set D, specifically to their beamformers.

[0159] As shown in FIG. 10, the constraint matrix generator means 43A comprises a bank of vector reshapers 48A¹, . . . , 48A^Nc and a matrix inverter 49A. Each of the vector reshapers 48A¹, . . . , 48A^Nc reshapes the corresponding one of the set of constraints-set matrices _n¹, . . . , _n^Nc to form one column of the constraint matrix Ĉ_n, which is processed by matrix inverter 49A to form inverse matrix Q_n. For simplicity of description, it is implicitly assumed that each of the columns of Ĉ_n is normalized to unity when collecting it from the set of constraints _n.

[0160] As also illustrated in FIG. 10, beamformer 47A^d can be considered to comprise a coefficient tuning unit 50A^d and a set of M(2L−1) multipliers 51₁^d . . . 51_M(2L−1)^d. The coefficient tuning unit 50A^d uses the constraint matrix Ĉ_n, the inverse matrix Q_n and the channel vector estimates {circumflex over (Y)}_0,n^d to adjust weighting coefficients W_1,n^d* . . . W_M(2L−1),n^d* according to Equation (45) supra. The multipliers 51₁^d . . . 51_M(2L−1)^d use the coefficients to weight the individual elements Y_1,n . . . Y_M(2L−1),n, respectively, of the observation vector Y_n. The weighted elements are summed by an adder 52^d to form the raw filtered symbol estimate ŝ_n^d for output from the beamformer 47A^d.

[0161] An alternative configuration of receiver in which the low-power STAR modules of set D implement ISR beamforming after despreading of the observation matrix Y_n from preprocessor 18 will now be described with reference to FIGS. 11 and 12, which correspond to FIGS. 9 and 10. The receiver shown in FIG. 11 is similar to that shown in FIG. 9 in that it comprises a preprocessing unit 18 which supplies the observation matrix Y_n to the set I receiver modules 20¹, . . . , 20^NI, a constraints-set generator 42B and a constraint matrix generator means 43B. It does not, however, include the vector reshaper 44 of FIG. 9 and each of the low-power user STAR modules in set D has a modified beamformer. Thus, modified beamformer 47B^d operates upon the post-correlation observation vector Z_n^d from the output of the despreader 19^d which is supplied to both the channel identification unit 28B^d and the beamformer 47B^d. The channel identification unit 28B^d generates channel vector estimates Ĥ_n^d and supplies them to the beamformer 47B^d which updates its coefficients in dependence upon both them and a user-specific constraint matrix Ĉ_PCM,n^d and user-specific inverse matrix Q_PCM,n^d. It should be noted that the constraint matrix generator means 43B supplies user-specific constraint and inverse matrices to the other receiver modules in set D.

[0162] Referring now to FIG. 12, the common constraint matrix generator means 43B comprises a bank of user-specific constraint matrix generators, one for each of the receiver modules of set D, and each using a respective one of the spreading codes of the users of set D. Since the only difference between the user-specific constraint matrix generators is that they use different spreading codes, only user-specific constraint matrix 43B^d is shown in FIG. 12, with the associated beamformer 47A^d. Thus, user-specific constraint matrix generator 43B^d comprises a bank of despreaders 55B^d,1, . . . , 55B^d,Nc and a matrix inverter 46B^d. The despreaders 55B^d,1, . . . , 55B^d,Nc despread respective ones of the N_c matrices in the set of constraints _n to form one column of the individual constraint matrix Ĉ_PCM,n^d implicitly normalized to unity. The matrix inverter 46B^d processes individual constraint matrix Ĉ_PCM,n^d to form inverse matrix Q_PCM,n^d. The user-specific constraint matrix generator 43B^d supplies the constraint matrix Ĉ_PCM,n^d and inverse matrix Q_PCM,n^d to the coefficient tuning unit 50B^d of beamformer 47B^d. As shown in FIG. 12, the beamformer 47B^d has ML multipliers 51₁^d . . . 51_ML^d which multiply weighting coefficients W_1,n^d* . . . W_ML,n^d* by elements Z_1,n^d . . . Z_ML,n^d of the post-correlation observation vector Z_n^d. As before, adder 52^d sums the weighted elements to form the signal component estimate ŝ_n^d. The beamformer coefficients are timed according to Equation (18).

[0163] Either of these alternative approaches, i.e. with and without despreading of the data vector supplied to the beamformer, may be used with each of several different ways of implementing the ISR beamforming, i.e. ISR modes. It should be noted that all cases use a constraint matrix which tunes the ISR beamformer to unity response to the desired channel and null response to the interference sub-space. In each case, however, the actual composition of the constraint matrix will differ.

[0164] Specific embodiments of the invention implementing the different ISR modes without despreading of the data will now be described with reference to FIG. 13 to 20, following which embodiments implementing the same ISR modes after despreading will be described with reference to FIGS. 21 to 26.

Interference Subspace Rejection Over Total Realisation (ISR-TR)

[0165] The receiver unit shown in FIG. 13 is similar to that shown in FIG. 9 in that it comprises a set I of receiver modules 20^1, . . . , 20^NI for processing signals of NI strongly interfering mobile stations and a set D of receiver modules for signals of other, “low-power”, users. The receiver modules of set D are identical so only receiver module 21C^d, for channel d, is shown in FIG. 13. As in the receiver of FIG. 9, the observation matrix Y_n from preprocessor 18 is supplied directly to each of the despreaders 19¹ . . . 19^NI of the set I receiver modules. Before application to each of the receiver modules of set D, however, it is delayed by one symbol period by a delay element 45 and reshaped by vector reshaper 44. The resulting observation vector Y_n−1 is supplied to the beamformer 47C^d and to each of the other beamformers in the set D receiver modules (not shown). STAR receiver module 20C^d is associated with despreader 19d and, in addition to beamformer 47C^d, comprises channel identification unit 28C^d, decision rule unit 29C^d and power estimation unit 30C^d which are similar to those shown in FIG. 9. The set of channel estimates _n¹, . . . , _n^NI, which are supplied to the constraints-set generator 42C comprise the channel vector estimates Ĥ_n¹, . . . , Ĥ_n^NI and the power estimates {circumflex over (ψ)}_n¹, . . . , {circumflex over (ψ)}_n^NI, respectively.

[0166] The constraints-set generator 42C comprises a bank of respreaders 57C¹ . . . 57C^NI each having its output connected to the input of a respective one of a corresponding bank of channel replication units 59C¹ . . . 59C^NI by a corresponding one of a bank of multipliers 58C¹ . . . 58C^NI. The respreaders 57C¹ . . . 57C^NI are similar so only one, respreader 57C^u, is illustrated in FIG. 14. Respreader 57C^u is similar to the corresponding spreader 13^u (FIG. 3) in that it spreads the symbol {circumflex over (b)}_n^u from the corresponding decision rule unit 29C^u using a periodic personal code sequence c_l^u at a rate 1/T_c, where T_c is the chip pulse duration. It differs, however, in that it does not include a shaping-pulse filter. The effects of filtering both at transmission with the shaping-pulse (see FIGS. 2 and 3) and at reception with the matched shaping-pulse (see FIGS. 5 and 6) are included baseband in the channel vector estimate Ĥ_n^u or Ĥ_n^u, as disclosed in reference [13].

[0167] Referring again to FIG. 13 and, as an example, receiver module 20C¹, replication of the propagation characteristics of channel 14¹ is accomplished by digital filtering in the discrete time domain, i.e. by convolution at the chip rate of the channel vector estimate Ĥ_n¹ with the respread data {circumflex over (b)}_n¹c_l¹. This filtering operation immediately provides decomposed estimates of the signal contribution of user station 10¹ to the observation matrix Y_n. Thus, respreader 57C¹ respreads the symbol {circumflex over (b)}_n¹ from decision rule unit 29C¹, multiplier 58C¹ scales it by the total amplitude estimate {circumflex over (ψ)}_n¹ and channel replication filter 59C¹ filters the resulting respread symbol using the channel vector estimate Ĥ_n¹ from channel identification unit 28C¹. The symbol estimates from the other STAR modules in set I are processed in a similar manner.

[0168] It should be noted that the respreaders 57C¹ . . . 57C^NI, multipliers 58C¹ . . . 58C^NI and channel replication filters 59C¹ . . . 59C^NI correspond to the elements 13¹, 15¹ and 14¹ in the interfering user channel of FIG. 2. The coefficients of the channel replication filter units 59C¹ . . . 59C^NI are updated in successive symbol periods by the channel identification units 28C¹ . . . 28C^NI using the same coefficients Ĥ_n¹ . . . Ĥ_n^NI, corresponding to the transmission channels 14¹ . . . 14^NI, respectively, used to update their respective MRC beamformers 27C¹ . . . 27C^NI. It will be appreciated that the re-spread signals Ŷ_n−1¹ . . . Ŷ_n−1^NI from the channel replication filter units 59C¹ . . . 59C^NI, respectively, include information derived from both the sign and the amplitude of each symbol, and channel characteristics information, and so are the equivalents of the set I strong interferer's spread signals as received by the base station antenna elements 12¹ . . . 12^M.

[0169] The constraint-set generator 42C also comprises an adder 60 coupled to the outputs of the channel replication units 59C¹ . . . 59C^NI. The adder 60 sums the estimates Ŷ_n−1¹ . . . Ŷ_n−1^NI of the individual contributions from the different interferers to form the estimate Î_n−1 of the total interference from the NI interferers in the received observation matrix Y_n. The sum can be called total realization (TR) of the interference. In this embodiment, the constraint matrix generator simply comprises a single vector reshaper 43C which reshapes the total realization matrix Î_n−1 to form the vector {circumflex over (I)}_n−1 which, in this embodiment, constitutes the constraint matrix C_n. It should be noted that, because the constraint matrix really is a vector, the inverse matrix Q_n reduces to a scalar and, assuming implicit normalization, is equal to 1. Hence, no matrix inverter is needed.

[0170] The reshaped vector Î_n−1 is supplied to the ISR beamformer 47C^d of receiver module 20C^d and to the beamformers of the other receiver modules in set D. The beamformer 47C^d uses the reshaped vector Î_n−1 and the channel vector estimates Ŷ_0,n−1^d to update its coefficients, according to Equation (45), for weighting of the elements of observation vector Y_n−1.

[0171] The beamformer 47C^d adjusts its coefficients so that, over a period of time, it will nullify the corresponding interference components in the observation vector Y_n−1 from the vector reshaper 44 and, at the same time, tune for a unity response to the spread channel vector estimate so as to extract the raw signal component estimate ŝ_n−1^d substantially without distortion.

[0172] ISR-TR constitutes the simplest way to characterize the interference subspace, yet the most difficult to achieve accurately; namely by a complete estimation of the instantaneous realization of the total interference vector Î_n in a deterministic-like approach. The constraint matrix is therefore defined by a single null-constraint (i.e., N_c=1) as: $\begin{array}{cc}{\hat{C}}_n=\left[\frac{{\widehat{\underset{\_}{I}}}_n}{{\widehat{\underset{\_}{I}}}_n}\right]=\left[\frac{\sum _{i=1}^{\mathrm{NI}}{\widehat{\underset{\_}{Y}}}_n^i}{\sum _{i=1}^{\mathrm{NI}}{\widehat{\underset{\_}{Y}}}_n^i}\right]& \left(47\right)\end{array}$
where each estimate Ŷ_nⁱ is reconstructed by reshaping the following matrix:
Ŷ_nⁱ={circumflex over (ψ)}_nⁱĤ_nⁱ{circle around (×)}{circumflex over (b)}_nⁱc_lⁱ.  (48)

[0173] For each interfering user assigned the index i=1, . . . , NI, this mode uses estimates of its received power ({circumflex over (ψ)}_nⁱ)² and its channel Ĥ_nⁱ, both assumed constant over the adjacent symbols and made available by STAR. This mode also requires a bit-triplet estimate [{circumflex over (b)}_n−1ⁱ, {circumflex over (b)}_nⁱ, {circumflex over (b)}_n+1ⁱ] of each interfering user (see Equation (23)). To obtain estimates of the signs of the interferer bits for both the current and next iterations (i.e., {circumflex over (b)}_nⁱ and {circumflex over (b)}_n+1ⁱ) the ISR-TR mode requires that the processing of all the low-power users be further delayed by one bit duration and one processing cycle (pc), respectively. The one-bit delay is provided by the delay 45 in FIG. 13.

[0174] In the ISR-TR mode and in the alternative ISR modes to be described hereafter, the interference (due to the strongest users) is first estimated, then eliminated. It should be noted that, although this scheme bears some similarity to prior interference cancellation methods which estimate then subtract the interference, the subtraction makes these prior techniques sensitive to estimation errors. ISR on the other hand rejects interference by beamforming which is robust to estimation errors over the power of the interferers. As one example, ISR-TR would still implement a perfect null-constraint if the power estimates were all biased by an identical multiplicative factor while interference cancellers would subtract the wrong amount of interference. The next mode renders ISR even more robust to power estimation errors.

[0175] The receiver illustrated in FIG. 13 may be modified to reduce the information used to generate the interfering signal estimates Ŷ_n−1¹ . . . Ŷ_n−1^NI, specifically by omitting the amplitude of the user signal estimates, and adapting the ISR beamformer 47C^d to provide more (NI) null constraints. Such a modified receiver will now be described with reference to FIG. 15.

Interference Subspace Rejection Over Realisations (ISR-R)

[0176] In the receiver of FIG. 15, the receiver modules in set I are identical to those of FIG. 13. Receiver module 20D^d has the same set of components as that shown in FIG. 13 but its beamformer 47D^d differs because the constraint matrix differs. The constraints-set generator 42D differs from that shown in FIG. 13 in that it omits the multipliers 58C¹ . . . 58C^NI and the adder 60. The outputs from the power estimation units 30¹ . . . 30^NI are not used to scale the re-spread signals from the respreaders 57C¹ . . . 57C^NI, respectively. Hence, in the receiver of FIG. 15, the signals {circumflex over (b)}_n¹ . . . {circumflex over (b)}_n^NI from the STAR modules 20¹ . . . 20^NI, respectively, are re-spread and then filtered by channel replication filter units 59C¹ . . . 59C^NI, respectively, to produce user specific observation matrices Ŷ_n−1¹ . . . Ŷ_n−1^NI, respectively, as the constraints-set _n. In contrast to the receiver of FIG. 13, however, these respread matrices are not summed but rather are processed individually by the constraint matrix generator 43D, which comprises a bank of vector reshapers 48D¹ . . . 48D^NI and a matrix inverter 49D (not shown but similar to those in FIG. 10). The resulting constraint matrix Ĉ_n, comprising the column vectors {circumflex over (Y)}_n−1¹, . . . , {circumflex over (Y)}_n−1^NI is supplied, together with the corresponding inverse matrix Q_n, to each of the receiver modules in set D. Again, only receiver module 20D^d is shown, and corresponds to that in the embodiment of FIG. 13. Each of the vectors Ŷ_n−1¹ . . . Ŷ_n−1^NI, represents an estimate of the interference caused by the corresponding one of the strong interference signals from set I and has the same dimension as the reshaped observation vector Y_n−1.

[0177] In this ISR-R mode, the interference subspace is characterized by normalized estimates of the interference vectors Ŷ_n¹. Consequently, it spans their individual realizations with all possible values of the total received powers (ψ_nⁱ)². The constraint matrix is defined by NI null-constraints (i.e., N_c=NI) as: $\begin{array}{cc}{\hat{C}}_n=\left[\frac{{\underset{\_}{\hat{Y}}}_n^1}{{\widehat{\underset{\_}{Y}}}_n^1},\dots ,\frac{{\underset{\_}{\hat{Y}}}_n^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_n^{\mathrm{NI}}}\right],& \left(49\right)\end{array}$
where each estimate Ŷ_nⁱ is reconstructed by reshaping the following matrix:
Ŷ_nⁱ=Ĥ_nⁱ{circle around (×)}{circumflex over (b)}_nⁱc_i^l.  (50)

[0178] It should be noted that, in the reconstruction of Ŷ_nⁱ, the total amplitude of the i-th interferer {circumflex over (ψ)}_nⁱ (see FIG. 15) has been omitted intentionally; hence the higher robustness expected to near-far situations as well as the enlarged margin for power control relaxation.

Interference Subspace Rejection Over Diversity (ISR-D)

[0179] The ISR-D receiver shown in FIG. 16 is predicated upon the fact that the signal from a particular user will be received by each antenna element via a plurality of sub-paths. Applying the concepts and terminology of so-called RAKE receivers, each sub-path is termed a “finger”. In the embodiments of FIGS. 9, 11, 13 and 15, the channel identification units estimate the parameters for each finger as an intermediate step to estimating the parameters of the whole channel. In the ISR-D receiver shown in FIG. 16, the channel identification units 28E¹ . . . 28E^NI supply the whole channel vector estimates Ĥ_n¹ . . . Ĥ_n^NI respectively, to the beamformers 27¹ . . . 27^NI, respectively, as before. In addition, they supply the sets of channel estimates _n¹ . . . _n^NI comprising a sub-channel vector estimate for each individual sub-channel or finger, to the constraints-set generator 42E. The set of channel estimates _nⁱ comprises the subchannel vector estimates Ĥ_n^i,1, . . . , Ĥ_n^i,Nf. The constraints-set generator 42E is similar to that shown in FIG. 15 in that it comprises a bank of respreaders 57¹ . . . 57^NI but differs in that the channel replication units 59D¹ . . . 59D^NI are replaced by sub-channel replication units 59E¹ . . . 59E^NI, respectively. The sub-channel replication units 59E¹ . . . 59E^NI convolve the respread symbols with the sub-channel vector estimates Ĥ_n^1,1 . . . Ĥ_n^1,Nf; . . . ; Ĥ_n^NI,1, . . . , Ĥ_n^NI,Nf respectively, to produce normalized estimates Ŷ_n−1^1,1 . . . Ŷ_n−1^1,Nf; . . . ; Ŷ_n−1^NI,1, . . . , Ŷ_n−1^NI,Nf of the sub-channel-specific observation matrices decomposed over fingers. Hence, the matrices span the space of their realizations with all possible values of the total received powers (ψ_nⁱ)² and complex channel coefficients ζ_f,nⁱ. The estimates are supplied to a constraint matrix generator 43E which generally is as shown in FIG. 10 and produces the constraint matrix accordingly.

[0180] The constraint matrix Ĉ_n is simply defined by N_fNI null-constraints (i.e., N_c=N_f×NI=M×P×NI) as: $\begin{array}{cc}{\hat{C}}_n=\left[\frac{{\underset{\_}{\hat{Y}}}_n^{1,1}}{{\widehat{\underset{\_}{Y}}}_n^{1,1}},\dots ,\frac{{\underset{\_}{\hat{Y}}}_n^{1,N_f}}{{\widehat{\underset{\_}{Y}}}_n^{1,N_f}},\dots ,\frac{{\underset{\_}{\hat{Y}}}_n^{\mathrm{NI},1}}{{\widehat{\underset{\_}{Y}}}_n^{\mathrm{NI},1}},\dots ,\frac{{\underset{\_}{\hat{Y}}}_n^{\mathrm{NI},N_f}}{{\widehat{\underset{\_}{Y}}}_n^{\mathrm{NI},N_f}}\right],& \left(51\right)\end{array}$
Each estimate Ŷ_n^i,f is reconstructed by reshaping the following matrix:
Ŷ_n^i,f=Ĥ_n^i,f{circle around (×)}{circumflex over (b)}_nⁱc_lⁱ.  (52)

[0181] It should be noted that, in the reconstruction of Ŷ_n^i,f, the total amplitude of the i-th interferer {circumflex over (ψ)}_nⁱ as well as the channel coefficients ζ_f,nⁱ (see FIG. 1) are intentionally omitted; hence the relative robustness of ISR-D to power mismatch, like ISR-R. Unlike other modes, it additionally gains robustness to channel identification errors and remains sensitive only to the estimated channel parameters remaining, namely the multipath time-delays, and to symbol estimation errors.

[0182] It should be noted that, in the receivers of FIGS. 13, 15 and 16, estimation errors of the interference bit signs may introduce differences between the estimated constraints and the theoretical ones. Hence, although ISR-D, ISR-R and ISR-TR modes are satisfactory in most situations, it is possible that the realisation could be erroneous, which would affect the validity of the interference cancellation. Additionally, estimation of the signs of the interference bits for reconstruction in the ISR-D mode, as in the ISR-R and ISR-TR modes, requires that the processing of all of the low-power users be further delayed by one bit duration, i.e., by delay 45, and one processing cycle (pc). To avoid these drawbacks, alternative ISR approaches to implementation of the constraints of Equation (42) are envisaged and will now be described, beginning with ISR-H which avoids processing delays and is completely robust to data estimation errors.

Interference Subspace Rejection Over Hypotheses (ISR-H)

[0183] It is possible to use a set of signals which represent all possible or hypothetical values for the data of the interfering signal. Each of the interfering signals constitutes a vector in a particular domain. It is possible to predict all possible occurrences for the vectors and process all of them in the ISR beamformer and, therefore, virtually guarantee that the real or actual vector will have been nullified. As mentioned, the strong interferers are relatively few, so it is possible, in a practical system, to determine all of the likely positions of the interference vector and compensate or nullify all of them. Such an alternative embodiment, termed Interference Subspace Rejection over Hypotheses (ISR-H) because it uses all possibilities for the realisations, is illustrated in FIG. 17.

[0184] The components of the interferer receiver modules of set I, namely the despreaders 19¹ . . . 19^NI and STAR modules 20¹ . . . 20^NI, are basically the same as those in the receiver of FIG. 15 and so have the same reference numbers. In the embodiment of FIG. 17, however, the constraints-set generator 42F differs because the symbol estimates {circumflex over (b)}_n¹ . . . {circumflex over (b)}_n^NI from the outputs of the decision rule units 29¹ . . . 29^NI are not supplied to the respreaders 57F¹ . . . 57F^NI, respectively, but are merely outputted to other circuitry in the receiver (not shown).

[0185] Instead, bit sequence generators 63F¹ . . . 63F^NI each generate the three possibilities g_n¹, g_n², g_n³, which cover all possible estimated values of the previous, current and next bits of the estimated data sequences {circumflex over (b)}_n¹ . . . {circumflex over (b)}_n^NI, including the realisation itself (as explained later), and supply them to the respreaders 57F¹ . . . 57F^NI, respectively, which each spread each set of three values again by the corresponding one of the spreading codes. The resulting re-spread estimates are filtered by the channel replication filters 59F¹ . . . 59F^NI, respectively, to produce, as the constraint set, the matrix estimates Ŷ_0,n¹, Ŷ_−1,n, Ŷ_+1,n¹; . . . ; Ŷ_0,n^NI, Ŷ_−1,n^NI, Ŷ_+1,n^NI. The bit sequence generators could, of course, be replaced by storage units.

[0186] The constraint matrix generator 43F is generally as shown in FIG. 10 and processes the set of estimate matrices to form the column vectors {circumflex over (Y)}_0,n¹, {circumflex over (Y)}_−1,n, {circumflex over (Y)}_+1,n¹; . . . ; {circumflex over (Y)}_0,n^NI, {circumflex over (Y)}_−1,n^NI, {circumflex over (Y)}_+1,n^NI of constraint matrix Ĉ_n, which it supplies with corresponding inverse matrix Q_n, in common to the beamformer 47F^d and the beamformers of the other set D receiver modules.

[0187] Receiver module 20F^d comprises similar components to those of the receiver module 20E^d shown in FIG. 16. It should be noted, however, that, because the “next” bit is being hypothesized, it need not be known, so the delay 45 is omitted.

[0188] As mentioned above, the two bits adjacent to the processed bit of the i-th interferer contribute in each bit frame to the corresponding interference vector (symbol) to be rejected. As shown in FIG. 18, enumeration of all possible sequences of the processed and adjacent bits gives 2³=8 triplets, each of three bits. Only one of these triplets could occur at any one time at each bit iteration as one possible realization that generates the user-specific observation matrix Ŷ_nⁱ. These eight triplets can be identified within a sign ambiguity with one of the four triplets identified as (a) . . . (d) in the left-hand part of FIG. 18, since the four triplets (e) . . . (h) are their opposites.

[0189] It should be appreciated that the bit sequence generators 63¹ . . . 63^NI (FIG. 17) each supply only three values, g_n¹, g_n², g_n³ because the dimension of the generated signal subspace is 3. It should be noted that frames of duration 3T, taken from these sequences at any bit rate instant, reproduce the eight possible realisations of the bit triplets of FIG. 18. Therefore, at any bit iteration, the bit sequence b_nⁱ of the interfering mobile station can be locally identified as the summation of the generating sequences g_n^k, k=1, . . . , 3 weighted by the bit signs b_n−1ⁱ, b_nⁱ and b_n+1ⁱ. Replacing the estimate {circumflex over (b)}_nⁱ in Equation (50) by g_n^k, k=1, . . . , 3, , yields canonic observation matrices that span all possible realisations of the received signal vector from the i-th interfering mobile within a sign ambiguity.

[0190] In the ISR-H embodiment of FIG. 17, the interference subspace is characterized by normalized estimates of the canonic interference vectors {circumflex over (Y)}_k,nⁱ. Accordingly, it spans their individual realizations with all possible values of the total received powers (ψ_n¹)² and bit triplets [b_n−1¹, b_nⁱ, b_n+1ⁱ]. The constraint matrix is defined by 3NI null-constraints (i.e., N_c=3NI) as: $\begin{array}{cc}{\hat{C}}_n=\left[\frac{{\underset{\_}{\hat{Y}}}_{0,n}^1}{{\widehat{\underset{\_}{Y}}}_{0,n}^1},\frac{{\underset{\_}{\hat{Y}}}_{-1,n}^1}{{\widehat{\underset{\_}{Y}}}_{-1,n}^1},\frac{{\underset{\_}{\hat{Y}}}_{+1,n}^1}{{\widehat{\underset{\_}{Y}}}_{+1,n}^1},\dots ,\frac{{\underset{\_}{\hat{Y}}}_{0,n}^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_{0,n}^{\mathrm{NI}}},\frac{{\underset{\_}{\hat{Y}}}_{-1,n}^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_{-1,n}^{\mathrm{NI}}},\frac{{\underset{\_}{\hat{Y}}}_{+1,n}^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_{+1,n}^1}\right],& \left(53\right)\end{array}$
where each estimate {circumflex over (Y)}_k,nⁱ is reconstructed, respectively, for k=−1, 0, +1 by reshaping the following matrix:
Ŷ_k,nⁱ=Ĥ_nⁱ{circle around (×)}g_n^lcmc_lⁱ.  (54)

[0191] It should also be noted that, in the reconstruction above, only the channel vector estimates (assumed stationary over the adjacent symbols) are needed for complete interference rejection regardless of any 2D modulation employed (see FIG. 19); hence the extreme robustness expected to power control and bit/symbol errors of interferers. The ISR-H combiner coefficients are symbol-independent and can be computed less frequently when the channel time-variations are slow.

[0192] Merging of the D mode with the H mode along the decomposition of Equation (38) yields ISR-HD (hypothesized diversities) with a very close form to the decorrelator. This ISR-HD mode requires a relatively huge number of constraints (i.e., 3N_fNI). Consequently, the ISR-HD mode is not considered to be practical at this time.

[0193] In fact, it would be desirable to reduce the number of constraints required by the ISR-H receiver described above. This can be done using an intermediate mode which is illustrated in FIG. 20 and in which the receiver modules of both sets I and D are similar to those of FIG. 15; most of their components are identical and have the same reference numbers. In essence, the constraint-set generator 42G of the receiver in FIG. 20 combines the constraint-set generators of FIGS. 15 and 17 in that it uses estimated symbols and hypothetical values. Thus, it comprises a bank of respreaders 57G¹ . . . 57G^NI, a corresponding bank of channel replication units 59G¹ . . . 59G^NI and a bank of symbol generators 63G¹ . . . 63G^NI. In this case, however, each of the symbol generators 63G¹ . . . 63G^NI supplies only one symbol to the corresponding one of the respreaders 57G¹ . . . 57G^NI, which receive actual symbol estimates {circumflex over (b)}_n¹ . . . {circumflex over (b)}_n^NI, respectively, from the decision rule units 29¹, . . . , 29^NI, respectively. It should be appreciated that, although the symbol generators 63G¹, . . . , 63G^NI each supply only one symbol for every actual symbol or realization from the corresponding one of the decision rule units 29¹, . . . , 29^NI, that is sufficient to generate two hypothetical values of “future” symbols b_n+1¹, . . . , b_n+1^NI for every one of the symbol estimates {circumflex over (b)}_n+1¹ . . . {circumflex over (b)}_n+1^NI since only two hypothetical values of the symbols, namely 1 and −1, are required. The respreaders 57G¹, . . . , 57G^NI supply the spread triplets to the channel replication units 59G¹ . . . 59G^NI which filter them, using the channel vector estimates Ĥ_n¹ . . . Ĥ_n^NI, respectively, to produce pairs of matrices Ŷ_r,n¹, Ŷ_−1,n¹; . . . Ŷ_r,n^NI, Ŷ_+1,n^NI and supply them to the constraint matrix generator 43G which is configured generally as shown in FIG. 9. The constraint matrix generator 43G reshapes the matrices Ŷ_r,n¹, Ŷ_+1,n¹; . . . Ŷ_r,n^NI, Ŷ_+1,n^NI to form vectors {circumflex over (Y)}_r,n¹, Ŷ_+1,n¹; . . . Ŷ_r,n^NI, Ŷ_+1,n^NI which then are used as the column vectors of the constraint matrix Ĉ_n. The constraint matrix generator 43G supplies the constraint matrix Ĉ_n and the corresponding inverse matrix Q_n in common to the beamformer 47G^d and the beamformers of other receiver modules in set D.

[0194] Hence, the beamformer 47G^d uses the past symbol estimate {circumflex over (b)}_n−1ⁱ of the interference data as well as the present one {circumflex over (b)}_nⁱ (delayed by one processing cycle, i.e. the time taken to derive the interference estimates), and the unknown sign of b_n+1ⁱ reduces the number of possible bit triplets and the corresponding realisations for each interference vector to 2.

[0195] The receiver of FIG. 20, using what is conveniently referred to as ISR-RH mode for reduced hypotheses over the next interference bits, rejects reduced possibilities of the interference vector realisations. Compared to the receiver of FIG. 17 which uses the ISR-H mode, it is more sensitive to data estimation errors over {circumflex over (b)}_n−1ⁱ and {circumflex over (b)}_nⁱ and requires only 2 constraints per interferer instead of 3.

[0196] Using the previous and current bit estimates of interferers, uncertainty over the interference subspace can be reduced and it can be characterized by the following matrix of 2NI null-constraints (i.e., N_c=2NI):
where: $\begin{array}{cc}{\hat{C}}_n=\left[\frac{{\underset{\_}{\hat{Y}}}_{r,n}^1}{{\widehat{\underset{\_}{Y}}}_{r,n}^1},\frac{{\underset{\_}{\hat{Y}}}_{+1,n}^1}{{\widehat{\underset{\_}{Y}}}_{+1,n}^1},\dots ,\frac{{\underset{\_}{\hat{Y}}}_{r,n}^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_{r,n}^{\mathrm{NI}}},\frac{{\underset{\_}{\hat{Y}}}_{-1,n}^{\mathrm{NI}}}{{\widehat{\underset{\_}{Y}}}_{-1,n}^{\mathrm{NI}}}\right],& \left(55\right)\\ {\underset{\_}{\hat{Y}}}_{r,n}^1={\hat{b}}_n^i{\underset{\_}{\hat{Y}}}_{0,n}^i+{\hat{b}}_{n-1}^l{\underset{\_}{\hat{Y}}}_{-1,n}^i,& \left(56\right)\end{array}$
and where each estimate Ŷ_k,nⁱ is reconstructed by reshaping the matrices in Equation (38), respectively for k=−1, 0, +1. It should be noted that this mode requires a delay of one processing cycle for the estimation of the current interference bits.

[0197] The ISR-RH mode has the advantage of reducing the number of null-constraints as compared to the ISR-H mode. A larger number of null-constraints indeed increases complexity, particularly when performing the matrix inversion in Equation (43), and may also result in severe noise enhancement, especially when the processing gain L is low. As the number of strong interferes NI increases in a heavily loaded system, the number of null-constraints (2NI and 3NI) approaches the observation dimension M×(2L−1) and the constraint-matrix may become degenerate. To reduce complexity, guarantee stability in the matrix inversion of Equation (43), and minimize noise enhancement, the constraint matrix Ĉ_n in Equations. (43) and (44) is replaced by the orthonormal interference subspace of rank K that spans its column vectors as follows: $\begin{array}{cc}{\hat{V}}_n=\mathrm{Vec}\left\{{\hat{C}}_n\right\}=\left\{{\underset{\_}{\hat{V}}}_{n,1},\dots ,{\underset{\_}{\hat{V}}}_{n,k},\dots ,{\underset{\_}{\hat{V}}}_{n,K}\right\},& \left(57\right)\end{array}$
to yield the projector Π_n=I_M*(2L−1)−{circumflex over (V)}_n{circumflex over (V)}_n^H used in Equation (31), which replaces matrix inversion operation by matrix orthonormalization. The Gram-Schmidt orthonormalization procedure is used, which implements a cumulative increasing-rank cascade of “corank” −1 projections, like in linear SIC [28], except that projections there are formed differently for direct cancellation. Ultimately, after orthonormalization, ISR exploits a “corank” −N_c projection to implement N_c null-constraints in the combining step. This projection could be implemented as a cascade of N_c corank-1 projections. It should be noted that orthonormalization becomes unnecessary if we check that Ĉ_n is close to orthonormal (i.e., Ĉ_n∝{circumflex over (V)}_n).

[0198] In practice, {circumflex over (V)}_n can hardly reflect the real rank of Ĉ_n. It corresponds to the subspace of reduced rank {circumflex over (K)}≦N_c with the highest interference energy to cancel. To further minimize noise enhancement, one can also increase the observation dimension M×(2L−1), as will be described later as “X option”, and so on.

[0199] Another alternative that reduces noise enhancement constrains the beamformer to implement a close-to-null response towards each null-constraint instead of an exact null-response. This “relaxation” of the null-response leaves more degrees of freedom for ambient noise reduction (i.e., less amplification). It usually amounts to upper-bounding the amplitude of the beamformer response towards each null-constraint to be less than a maximum threshold. This technique is well-known and classified in the literature as a “robust beamforming” method. We can combine it with ISR to reduce noise enhancement.

[0200] Constraint relaxation in robust beamforming is usually solved as an optimization problem under constraints using the Lagrange multipliers technique. Without going into the mathematical details of such derivations, we directly provide intuition-based solutions that extend ISR beamforming in a seamless manner. We extend Equations (43) to (45) as follows: $\begin{array}{cc}{\stackrel{\_}{C}}_n={\hat{C}}_n{\Lambda }_n,& \left(\mathrm{I1}\right)\\ {\stackrel{\_}{Q}}_n={\left({\stackrel{\_}{C}}_n^H{\stackrel{\_}{C}}_n+\lambda I_{N_c}\right)}^{-1},& \left(\mathrm{I2}\right)\\ {\Pi }_n=I_{M*\left(2L-1\right)}-{\stackrel{\_}{C}}_n{\stackrel{\_}{Q}}_n{\stackrel{\_}{C}}_n^H,& \left(\mathrm{I3}\right)\\ {\underset{\_}{W}}_n^d=\frac{{\Pi }_n{\underset{\_}{Y}}_{0,n}^d}{{\underset{\_}{Y}}_{0,n}^{d^H}{\Pi }_n{\underset{\_}{Y}}_{0,n}^d},& \left(\mathrm{I4}\right)\end{array}$
where Λ_n is a N_c×N_c diagonal matrix of positive weights and λ an additional weighting factor.

[0201] The above extended ISR solution reduces to that of Equations (43) to (45) by setting Λ_n=I_Nc and λ=0. It also covers the particular case of MMSE (minimum mean square error) combining also known in the beamforming literature as MVDR (minimum variance distortionless response) beamforming. Along the model equation (28), the MMSE or MVDR beamforming solution is given by: $\begin{array}{cc}{\underset{\_}{W}}_n^d=\frac{R_{\underset{\_}{I}+\underset{\_}{N}}^{-1}{Y}_{0,n}^d}{{\underset{\_}{Y}}_{0,n}^{d^N}{R}_{\underset{\_}{I}+\underset{\_}{N}}^{-1}{\underset{\_}{Y}}_{0,n}^d},& \left(\mathrm{I5}\right)\end{array}$
where R_1+Nis the correlation matrix of the interference-plus-noise vector I_n+N_n. Assuming that the additive noise vector is spatially and temporally uncorrelated with variance σ_N², R_1+N is given by:
R_1+N=C_nΦ_nC_n^H+σ_N²I_M*(2L−1),  (I6)
where C_n is the constraint matrix defined along one of the ISR modes described previously, but without normalization column-wise. Depending on the signal parameters assumed unknown a priori (cf., discussion above Equation (15)), the conditional statistical mean in R_1+N gives rise to a particular interference decomposition in C_n along the corresponding ISR mode. The N_c×N_c diagonal matrix Φ_n holds the power of the unknown signal parameters along which interference is decomposed.

[0202] In the TR mode, interference characterization is quasi-deterministic with:
Φ_n=[1].
In the R mode, we have: ${\Phi }_n=\mathrm{diag}\left[{\left({\stackrel{\_}{\psi }}_n^1\right)}^2,\dots ,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2\right],$
while in the D mode, we have: ${\Phi }_n=\mathrm{diag}\left[\left({\stackrel{\_}{\psi }}_n^1\right){{\stackrel{\_}{\zeta }}_{1,n}^1}^2,\dots ,{\left({\stackrel{\_}{\psi }}_n^1\right)}^2{{\stackrel{\_}{\zeta }}_{N_f,n}^1}^2,\dots ,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2{{\stackrel{\_}{\zeta }}_{1,n}^{\mathrm{NI}}}^2,\dots ,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2{{\stackrel{\_}{\zeta }}_{N_f,n}^{\mathrm{NI}}}^2\right],$
where ({overscore (ψ)}_nⁱ)² and |{overscore (ζ)}_NΓnⁱ|² both denote local averages in time of (ψ_nⁱ)² and |ζ_NΓnⁱ|², respectively. The H mode gives: ${\Phi }_n=\mathrm{diag}\left[{\left({\stackrel{\_}{\psi }}_n^1\right)}^2,{\left({\stackrel{\_}{\psi }}_n^1\right)}^2,{\left({\stackrel{\_}{\psi }}_n^1\right)}^2,\dots ,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2,{\left({\stackrel{\_}{\psi }}_n^{\mathrm{NI}}\right)}^2\right].$

[0203] Using the inversion lemma, the inverse of R_1+N can be written as: $\begin{array}{cc}{R}_{\underset{\_}{I}+\underset{\_}{N}}^{-1}=\frac{1}{{\sigma }_n^2}\left[I_{M*\left(2L-1\right)}-C_n{\Phi }_n^{1/2}\left({\Phi }_n^{1/2}{C}_n^H{C}_n{\Phi }_n^{1/2}+{\sigma }_n^2{I}_{N_{\sigma }}\right){\Phi }_n^{1/2}{C}_n^H\right],& \left(\mathrm{I7}\right)\end{array}$
The MMSE or MVDR beamforming can therefore be identified with the extended ISR solution using:
λ={circumflex over (σ)}_N²,  (I8)

[0204]
and: ${\Lambda }_n=\{\begin{array}{c}\left[1\right]\mathrm{in}\mathrm{the}\mathrm{TR}\mathrm{mode},\\ \left[{\hat{\psi }}_n^1,\dots ,{\hat{\psi }}_n^{\mathrm{NI}}\right]\mathrm{in}\mathrm{the}R\mathrm{mode},\\ \left[{\hat{\psi }}_n^1{\hat{\zeta }}_{1,n}^1,\dots ,{\hat{\psi }}_n^1{\zeta }_{N_{f}n}^1,\dots ,{\hat{\psi }}_n^{\mathrm{NI}}{\zeta }_{1,n}^{\mathrm{NI}},\dots ,{\hat{\psi }}_n^{\mathrm{NI}}{\hat{\zeta }}_{N_{f}n}^{\mathrm{NI}}\right]\mathrm{in}\mathrm{the}D\mathrm{mode},\\ \left[{\hat{\psi }}_n^1,{\hat{\psi }}_n^1,{\hat{\psi }}_n^1,\dots ,{\hat{\psi }}_n^{\mathrm{NI}},{\hat{\psi }}_n^{\mathrm{NI}},{\hat{\psi }}_n^{\mathrm{NI}}\right]\mathrm{in}\mathrm{the}H\mathrm{mode}.\end{array}$

The instantaneous estimates in the equation above can be further averaged or smoothed in time. The columns of the constraint matrix estimate Ĉ_n are reconstructed without normalization.

[0205] Although the MMSE version of ISR serves as a method to reduce noise enhancement, it is still sensitive to hard-decision errors for modes using decision feed-back. Using weights in a different way is a method to reduce sensitivity to hard-decision errors. We notice that the ISR combined signal estimate can be formulated as: $\begin{array}{cc}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{Y}}_n={\left({\underset{\_}{Y}}_{0,n}^{d^H}{\Pi }_n{\widehat{\underset{\_}{Y}}}_{0,n}^d\right)}^{-1}{\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}\left({\underset{\_}{Y}}_n-{\hat{C}}_n{Q}_n{\hat{C}}_n^H{\underset{\_}{Y}}_n\right),& \left(\mathrm{I9}\right)\\ ={\left({\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}{\Pi }_n{\widehat{\underset{\_}{Y}}}_{0,n}^d\right)}^{-1}{\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}\left({\underset{\_}{Y}}_n-{\hat{C}}_n{\underset{\_}{\upsilon }}_n\right),& \left(\mathrm{I10}\right)\\ ={\left({\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}{\Pi }_n{\widehat{\underset{\_}{Y}}}_{0,n}^d\right)}^{-1}{\widehat{\underset{\_}{Y}}}_{0,n}^{d^H}\left({\underset{\_}{Y}}_n-{\widehat{\underset{\_}{I}}}_n^1-\dots -{\widehat{\underset{\_}{I}}}_n^{N_c}\right).& \left(\mathrm{I11}\right)\end{array}$
The last reformulation stresses that Ĉ_nυ_n can be understood as a sum of estimated interference vectors corresponding to the ISR mode applied. For instance each of these estimates corresponds to an interfering user in ISR-R. It can be shown that if tentative decisions, used to form the i-th constraint, are wrong, the corresponding constraint will sometimes be amplified rather than rejected². This amplification is mitigated by considering the alternative projector:
 Π_Λ,n=I−C_nQ_nΛ_nC_n^H,  (I12)
where Λ_n is a diagonal matrix of weights. Using this projection, Equation (I11) is modified as: $\begin{array}{cc}{\underset{\_}{W}}_n^{d^H}{\underset{\_}{Y}}_n={\left({\underset{\_}{\hat{Y}}}_{0,n}^{d^H}{\Pi }_{\Lambda ,n}{\underset{\_}{Y}}_{0,n}^d\right)}^{-1}{\underset{\_}{\hat{Y}}}_{0,n}^{d^H}\left({\underset{\_}{Y}}_n-{\left\{{\Lambda }_n\right\}}_{1,1}{\underset{\_}{\hat{I}}}_n^1-\dots -{\left\{{\Lambda }_n\right\}}_{N_c,N_c}{\widehat{\underset{\_}{I}}}_n^{N_c}\right).& \text{(I13)}\end{array}$
This modification means that the interferer is never completely rejected although tentative decisions are all correct; however, the penalty arising from wrong decisions is reduced as well. For ISR-R and ISR-D it can be shown that the optimal weight to be applied to columns representing interferer i is {Λ_n}_i,i(1−2SER(i)) where SER(i) is the Symbol Error Rate of the tentative decisions associated with interferer i.

[0206] ² This is true when the tentative decision, which is in error, is temporally overlapping the current bit.

[0207] It should be noted that each of the receivers of FIGS. 13, 15, 16, 17 and 20 could be modified to perform ISR “after despreading” of the observation matrix Y_n, in effect in much the same way that the generic “after despreading” receiver of FIG. 11 differs from the generic “without despreading” receiver of FIG. 9. Such modified receivers will now be described with reference to FIGS. 21 to 26.

[0208] Thus, in the ISR-TR receiver shown in FIG. 21, which corresponds to that shown in FIG. 13, the delay 45 delays the observation matrix Y_n from the preprocessing unit 18 by 1 bit period and supplies the resulting delayed observation matrix Y_n−1, in common, to each of the low-power user receiver modules in set D. Only one of these receiver modules, 20H^d, is shown in FIG. 21, since all are identical. The observation matrix Y_n−1 is despread by despreader 19^d and the resulting post-correlation observation vector Z_n−1^d is supplied to both the channel identification unit 28H^d and the beamformer 47H^d. The receiver modules of set I and the constraints-set generator 42C are identical to those in the receiver shown in FIG. 13, and supply the matrices Ŷ_n−1¹ . . . Ŷ_n−1^NI to an adder 60 which adds them to form the total interference matrix Î_n−1 which it supplies to each of the receiver modules in set D.

[0209] Receiver module 20H^d is similar to that shown in FIG. 13 but has a second despreader 43H^d which uses the spreading code for user d to despread the total interference matrix Î_n−1 to form the user-specific constraint matrix as a single column vector Î_PCM,n−1^d. This despreader 43H^d, in effect, constitutes a user-specific constraint matrix generator because the constraint matrix is a vector and an inverse matrix is not needed. Also, in this case, the channel identification unit 28H^d supplies the channel vector estimate Ĥ_n−1^d to the beamformer 47H^d.

[0210] It should be noted that the despread data vector Z_n−1^d is equal to H_n^ds_n^d+I_PCM,n^d, +N_n^d, where H_n^d is the channel response for user station 10^d, s_n^d is the signal transmitted by the mobile station 10^d of user d, and I_PCM,n^d is the interference component present in the signal Z_n^d as a result of interference from the signals from the other user stations 10ⁱ in set I, where I_PCM,n^d is as defined in Equation (14). The value N_PCM,n^d is additional noise which might comprise, for example, the summation of the interference from all of the other users on the system at that time, as well as thermal noise. “Other users” means other than those covered by the channels in set I.

[0211] As before, the coefficients of the beamformer 47H^d are tuned according to Equations (16) to (18) and the constraint matrix is defined by a single null-constraint (i.e., N_c=1) as: $\begin{array}{cc}{\hat{C}}_{\mathrm{PCM},n}^d=\left[\frac{{\widehat{\underset{\_}{I}}}_{\mathrm{PCM},n}^d}{{\widehat{\underset{\_}{I}}}_{\mathrm{PCM},n}^d}\right]=\left[\frac{\sum _{i=1}^{\mathrm{NI}}{\widehat{\underset{\_}{I}}}_{\mathrm{PCM},n}^{d,i}}{\sum _{i=1}^{\mathrm{NI}}{\widehat{\underset{\_}{I}}}_{\mathrm{PCM},n}^{d,i}}\right]& \left(58\right)\end{array}$
where the estimate Î_PCM,n^d is obtained by despreading the matrix Î_n (see Equations (47) and (48)) with the spreading sequence of the desired low-power user.