Apparatus and method of enhancing transmit diversity

[0002] Related subject matter is disclosed in the following application and assigned to the same assignee hereof: U.S. patent application Ser. No. 09/294,661 entitled, “Method And Apparatus For Downlink Diversity In CDMA Using Walsh Codes,” inventors R. Michael Buehrer, Robert Atmaram Soni, and Jiann-an Tsai, filed on Apr. 19, 1999.

[0003] Third generation wireless communication systems include downlink (i.e., communication link from a base station to a mobile-station) performance improvement techniques. One technique for improving downlink performance is to use, at the base station, a transmit diversity scheme (also referred to herein as diversity gain).

[0004] Transmit diversity can be used to improve fading distribution in the received signal, and is typically achieved using an antenna array configuration having M antenna elements spaced far apart and transmitting identical signals. By spacing the antenna elements far apart, fading is distributed since each of the signals will travel a different path from its transmitting antenna element to the mobile-station and experience a different distortion or fading process. Thus, the mobile-station receives identical signals affected by different fading processes or distortions. Since each signal should experience a different distortion or fading process, it becomes less probable that all the signals will undergo deep fades. Thus, fading distribution is improved.

[0005] When the received signals are properly combined by the mobile-station, the result is a signal with an improved bit error rate due to improved fading distribution although average signal-to-noise ratio remains approximately the same as if transmit diversity was not employed. In order to combine the received signals, the mobile-station needs to be capable of separating the individual received signals from each other. Separating the individual received signals is difficult if the signals were transmitted using a same frequency. Different frequencies may be used to transmit the individual signals such that separation of the received signals is easier. However, such method consumes additional bandwidth, which is undesirable. A same frequency may be used to transmit the signals in code division multiple access (CDMA) systems employing delay diversity techniques, which would allow signals to be separated through long spreading codes. Although additional bandwidth is not consumed, this technique causes mutual interference due to multipaths being intentionally created by the delay diversity techniques.

[0006] One technique for avoiding the mutual interference problem is orthogonal transmit diversity, which applies only to coded systems. Orthogonal transmit diversity involves transmitting alternate data bits modulated with different Walsh codes from different antenna elements. Diversity is gained in the decoding process when a convolutional code is employed with a Viterbi decoder, but not on the data bits itself since the antenna elements are transmitting only alternate data bits (and not all the data bits or the entire signal). In systems with weak convolutional or other error correction codes (for example, due to puncturing), the performance gained by orthogonal transmit diversity techniques may degrade.

[0007] The weakness of orthogonal transmit diversity may be overcome using a technique referred to herein as space time spreading (STS). STS involves transmitting all data bits (but not necessarily the same representations of the data bits) on two antenna elements using different Walsh codes, thus diversity is achieved on the data bits. No coding is required to achieved diversity (although coding may still be used), thus diversity will not degrade if coding is weak.

[0008] FIG. 1 depicts a wireless communication system 10 employing STS. Wireless communication system 10 comprises at least one base station 12 having two antenna elements 14-1 and 14-2, wherein antenna elements 14-1 and 14-2 are spaced far apart for achieving transmit diversity. Base station 12 receives a signal S for transmitting to mobile-station 16. Signal S is alternately divided into signals s_eand s_o, wherein signal s_ecomprises even data bits and signal s_ocomprises odd data bits. Signals s_eand s_oare processed to produce signals S^14-1and S^14-2. Specifically, s_eis multiplied with Walsh code w₁to produce signal s_ew₁; a conjugate of signal s_ois multiplied with Walsh code w₂to produce signal s_o*w₂; signal s_ois multiplied with Walsh code w₁to produce s_ow₁; and a conjugate of signal s_eis multiplied with Walsh code w₂to produce s_e*w₂. Signal s_ew₁is added to signal s_o*w₂to produce signal S^14-1(i.e., S^14-1=s_ew₁+s_o*w₂) and signal s_e*w₂is subtracted from signal s_ow₁to produce signal S^14-2(i.e., S^14-2=s_ow₁−s_e*w₂) Signals S^14-1and S^14-2are transmitted over antenna elements 14-1 and 14-2, respectively.

[0009] Mobile-station 16 receives signal R comprising γ₁(S^14-2)+γ₂(S^14-2), wherein γ₁and γ₂are distortion factor coefficients associated with the transmission of signals S^14-1and S^14-2from antenna elements 14-1 and 14-2 to mobile-station 16, respectively. Distortion factor coefficients γ₁and γ₂can be estimated using pilot signals, as is well-known in the art. Mobile-station 16 decodes signal R with Walsh codes w₁and w₂to respectively produce outputs:

[0010] W₁=γ₁s_e+γ₂s_o  equation 1

[0011] W₂=γ₁s_o*−γ₂s_e*  equation 1a

[0012] Using the following equations, estimates of signals s_eand s_o, i.e., ŝ_eand ŝ_o, may be obtained:

[0013] ŝ_e=γ₁^*W₁−γ₂W₂^*=s_e(|γ₁|²+|γ₂|²)+noise  equation 2

[0014] ŝ_o=γ₂^*W₁+γ₁W₂^*=s_o(|γ₁|²+|γ₂|²)+noise′  equation 2a

[0015] STS, however, does not scale naturally to more than two antenna elements to enhance diversity gain without having to reduce data rate. Accordingly, there exists a need to enhance diversity gain without reducing data rate.

[0016] The present invention is a method and apparatus for enhancing diversity gain without reducing data rate by increasing the number of antenna elements for purposes of improving signal-to-noise ratio at a receiver. In one embodiment, the present invention is employed using an antenna array having a first antenna group with at least two antenna elements and a second antenna group with at least one antenna element. The first and second antenna groups are spaced approximately ten carrier wavelengths or more apart from each other, and the antenna elements belonging to the first antenna group are spaced approximately a half carrier wavelength or less apart from each other.

[0017] A signal is processed for transmission over the antenna array by first generating a plurality of data streams from the signal. A first plurality of representative data streams is derived from the plurality of data streams, and a second plurality of representative data streams is derived from the plurality of data streams. Each of the first plurality of representative data streams is phase-shifted and encoded using different orthogonal codes, and each of the second plurality of representative data streams is encoded using different orthogonal codes, wherein a different orthogonal code is used to encode representative data streams of the first and second plurality of representative data streams generated from a same data stream of the plurality of data streams, and the first and second plurality of representative data streams are representatives of the plurality of data streams that allow for the plurality of data streams to be recovered at a receiver after encoding and transmission. The encoded and phase shifted first plurality of representative data streams being transmitted over the first antenna group, and the encoded second plurality of representative data streams being transmitted over the second antenna group.

[0018] In one embodiment of the present invention, a pilot signal is transmitted along with the encoded and phase shifted first plurality of representative data streams over each antenna element belonging to the first antenna group, and a pilot signal is transmitted along with the encoded plurality of representative data streams being transmitted over each antenna element belonging to the first antenna group. The pilot signal being transmitted over each antenna element in the first and second antenna groups may be identical or different (in terms of orthogonal codes being applied to each pilot signal or sequence of bits comprising each pilot signal).

[0019] The features, aspects, and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings where

[0020] FIG. 1 depicts a wireless communication system employing space time spreading techniques in accordance with the prior art;

[0021] FIG. 2 depicts a wireless communication system employing code division multiple access techniques in accordance with the present invention;

[0022] FIG. 3 depicts a transmission process in accordance with the present invention; and

[0023] FIGS. 4 and 5 depict schematic diagrams of transmitters for signal processing at a base station equipped with a two group, two antenna element per group, antenna array configuration in accordance with one embodiment

[0024] FIG. 2 depicts a wireless communication system 20 employing code division multiple access (CDMA) techniques in accordance with the present invention. Wireless communication system 20 comprises at least one base station 22 having an antenna array 23 and a transmitter 24. Antenna array 23 comprises antenna groups 24-n, where n=1, . . . , N and N≧2. Each group 24-n having antenna elements 26-mεn, where m is an antenna element index for the associated group 24-n, mεn=1, . . . Mεn, and ΣMεn≧N+1 (i.e., Mεn≧1 but Mεn≧2 for at least one group 24-n). Note that Mεn may be a different value for different antenna groups 24-n. Base station 22 employs an antenna array configuration and a signal processing technique based on the antenna array configuration to achieve N-fold diversity gain while increasing signal-to-noise ratio by an average M-fold, as will be described herein.

[0025] Antenna array 23 is configured in the following manner to provide for N-fold diversity gain and average M-fold signal-to-noise ratio improvement. First, groups 24-n are spaced a sufficient distance apart such that signals transmitted from different groups experience independent or uncorrelated fading, thereby allowing fore N-fold diversity gain. Second, antenna elements 26-mεn belonging to a same group 24-n are closely spaced such that signals transmitted from these antenna elements 26-mεn experience correlated fading, thereby allowing for average M-fold signal-to-noise improvement when antenna elements 26-mεn are co-phased.

[0026] In an illustrative example, antenna array 23 comprises of two groups 24-1 and 24-2, wherein group 24-1 has antenna elements 26-1ε1 and 26-2ε1 and group 24-2 has antenna elements 26-1ε2 and 26-2ε2. Groups 24-1 and 24-2 are spaced approximately ten carrier wavelengths (10λ) or more apart, antenna elements 26-1ε1 and 26-1ε1 are spaced approximately a half carrier wavelength (λ/2) apart, and antenna elements 26-1ε2 and 26-2ε2 are spaced approximately a half carrier wavelength (λ/2) apart. Although the exact inter-antenna element spacing is not crucial, it is not desirable to have inter-antenna element spacing greater than a half carrier wavelength since grating lobes may be introduced. To facilitate understanding of the present invention, the illustrative example will also be used herein to describe the signal processing technique with respect to a single signal S intended for mobile-station 28 (ignoring signals intended for other mobile-stations).

[0027] The signal processing technique is based on the antenna array configuration and is embodied in transmitter 24, which can be any combination of software and/or hardware, such as ASICs, DSPs, repeaters, mixers, modulators, filters and summers, for processing signal S in accordance with the present invention. The signal processing technique involves encoding representative data streams generated from signal S with Walsh (or some other orthogonal) codes such that signal S may be recovered at mobile-station 28 (or another receiver) and phase shifting the representative data streams to improve signal-to-noise ratio at mobile-station 28. The first part of the signal processing technique processes signal S for transmission over antenna array 23 such that it may be recovered at mobile-station 28. First, D data streams s_dare generated from signal S, where d=1, . . . , D and D is N rounded up to the nearest power of two. In the illustrative example, signal S may be alternately divided into two data streams s₁and s₂, i.e., D=2. Note that data streams s_dmay be generated from signal S in some manner other than alternately dividing signal S. For example, each data stream s_dmay include all of the bits comprising signal S, some or all data streams s_dmay include bits that are in other data streams, bits in each data stream s_dmay be repeated and/or inversed, etc.

[0028] Next, a representative of each data stream s_dis encoded using Walsh codes w_rfor transmission over each antenna element 26-mεn, where r=1, . . . , R and R≧D. The manner in which the representatives of each data stream s_dare encoded are based on the following three concepts. First, for data streams s_dbeing transmitted over antenna elements 26-mεn belonging to a same group 24-n, representatives of different data streams s_dare multiplied with different Walsh codes w_r. Second, for data streams s_dbeing transmitted over antenna elements 26-mεn belonging to different groups 24-n, representatives of same data streams s_dare multiplied with different Walsh codes w_r. Third, the representatives of data streams s_d(also referred to herein as “representative data streams f_g(s_d)”) being encoded for transmission over each antenna element 26-mεn are chosen from the set $\begin{array}{cc}{f}_g\left(s_d\right)=\{\begin{array}{cc}{s}_d& \mathrm{for}g=1\\ -s_d& \mathrm{for}g=2\\ 0& \mathrm{for}g=3\\ s_d^{*}& \mathrm{for}g=4\\ -s_d^{*}& \mathrm{for}g=5\end{array}& \mathrm{equation}3\end{array}$

[0029] (where the asterisk * indicates that the term is a transposed conjugate) such that $\begin{array}{cc}\sum _{r=1}^R{f}_g\left(s_d^n\right){w_r\left[f_g\left(s_{d^{\prime }}^{n^{\prime }}\right)w_r\right]}^{*}=0& \mathrm{equation}4\end{array}$

[0030] where the superscripts indicate the antenna group 24-n over which data stream s_dwill be transmitted, n′=1, . . . ,N, n′≠n, d′=1, . . . ,D and d′≠d. Note that the third encoding concept involves choosing representative data streams f_g(s_d) such that data streams s_dcan mathematically be recovered, i.e., terms cancel out, after encoding at mobile-station 28.

[0031] The above described three encoding concepts can alternately be explained using transmission matrix T, for example, for the illustrative two group antenna array configuration and signal S: $\begin{array}{cc}T=\left[\begin{array}{cc}{s}_d^n& s_{d^{\prime }}^{n^{\prime }}\\ S_{d^{\prime }}^{n^{*}}& -s_d^{{n^{\prime }}^{*}}\end{array}\right]& \mathrm{equation}5\end{array}$

[0032] Transmission matrix T having the following properties: each column corresponds to an antenna group 24-n and includes representative data streams f_g(s_d) for each data stream s_dto be transmitted over the corresponding antenna group 24-n (e.g., s_dⁿand s_d′^n*are transmitted over antenna elements belonging to group 24-n, and s_d′^n′ and −s_d^n′*are transmitted over antenna elements belonging to group 24-n′); no row or column should include more than one representative of a same data stream s_d; and any column multiplied with transposed conjugates of another column results in a value of zero (e.g., s_dⁿs_d′^n′*+s_d′^n*(−s_d^n′)=0), i.e., data streams s_dcan mathematically be recovered after encoding at mobile-station 28. Each row of representative data streams f(s_d) in transmission matrix T is multiplied with a different Walsh code w_r. By multiplying each row of transmission matrix T with a different Walsh code w_r, the aforementioned three encoding concepts are satisfied.

[0033] It should be understood that for a different number of groups 24-n and/or different number of mobile-stations (or signals S for transmission), the aforementioned transmission matrix properties would remain the same but the size of transmission matrix T would change. In one embodiment, for N groups of antenna elements and Z mobile-stations, the transmission matrix would have N columns and D×Z number of rows. For example, if there were one mobile-station and three antenna groups 24-n (i.e., N=3), each signal S for each mobile-station would be split into four data streams (i.e., D=4). The corresponding transmission matrix would have three columns and four rows (i.e., D×Z=4), wherein each data stream s_dfor each mobile-station would be in each column but not in every row.

[0034] Applying the variables of the illustrative example, transmission matrix T would be as follows: $\begin{array}{cc}T=\left[\begin{array}{cc}{s}_1^1& s_2^2\\ s_2^{1^{*}}& -s_1^{2^{*}}\end{array}\right]& \mathrm{equation}\text{5a}\end{array}$

[0035] The representative data streams f(s_d) in rows one and two are multiplied with Walsh codes w₁and w₂, respectively, to produce signals s₁¹w₁, s₂^1*w₂, s₂²w₁and −s₁^2*w₂, wherein signals s₁¹w₁and s₂^1*w₂are transmitted over antenna group 24-1 and signals s₂²w₁and −s₁^2*w₂are transmitted over antenna group 24-2. Alternately, representative data streams s₂²and/or −s₁^2*in column two may be multiplied with Walsh codes other than Walsh codes w₁and w₂, respectively, so long as the Walsh codes are different from the Walsh codes being used to encode respective representative data streams s₂^1*and/or s₁¹in column one.

[0036] The second part of the signal processing technique involves phase shifting the data streams s_d(or their representatives) to improve signal-to-noise ratio at mobile-station 28. This part uses complex weights v_mεnto co-phase antenna elements 26-mεn such that signals transmitted from a same group 24-n arrive at mobile-station 28 in-phase. Each antenna element 26-mεn has an associated complex weight v_mεncomprising of an in-phase component c_mεn¹and a quadrature-phase component c_mεn^Q, as is well-known in the art. Complex weights v_mεnare set equal to e^−jθin order to maximize signal-to-noise ratio (SNR) at mobile-station 28, wherein θ_mεnrepresents a phase difference between signals sent from antenna elements 26-mεn as seen at mobile-station 28. Disclosed herein for illustration purposes are two techniques for determining complex weights v_mεn. This should not be construed to limit the present invention in any manner.

[0037] In a first technique, complex weights v_mεnare based on estimates of θ_mεnfrom uplink information. This technique requires an uplink phased antenna array for measuring θ_mεn^up, which is θ_mεnfor the uplink. After measuring θ_mεn^up, the following equation can be used to estimate θ_o, which represents an angle of arrival for an uplink signal, i.e., a geometric angle formed between a line drawn from base station 22 to mobile-station 28 and antenna array 23: $\begin{array}{cc}{\theta }_{m\in n}^{\mathrm{up}}=\frac{2\pi }{{\lambda }^{\mathrm{up}}}{d}_{m\in n}\cos {\theta }_o& \mathrm{equation}6\end{array}$

[0038] where d_mεnis the distance between antenna elements 26-mεn and an arbitrary reference, and λ^uprepresents a carrier wavelength for the uplink signal. Upon estimating θ_o, complex weights v_mεnare set as follows: $\begin{array}{cc}{v}_{m\in n}=e^{-j\frac{2\pi }{{\lambda }^{\mathrm{down}}}{d}_{m\in n}\cos {\theta }_o}& \mathrm{equation}7\end{array}$

[0039] where λ^downrepresents a carrier wavelength for a downlink signal. Note that this technique for determining complex weights v_mεnassumes that the distances between antenna elements 26-mεn within a same group 24-n are known, the antenna elements 26-mεn within a same group 24-n are phase matched, and symmetry exists between uplink angle-of-arrivals and downlink angle-of-arrivals. Such assumptions are reasonable or may be easily obtained through calibration, as is known in the art.

[0040] The second technique for determining complex weights v_mεnrelies on receiving information regarding phases at which signals transmitted from antenna array 23 arrive at mobile-station 28. Such information is also referred to herein as “feedback information” and is transmitted from mobile-station 28 to base station 22 over an uplink channel. Since complex weights v_mεndepend on the angle of arrival θ_oat base station 22, complex weights v_mεnneed only be updated at the rate which θ_ochanges, which is relatively slow compared to the rate at which channels fade. Thus, less update information regarding changes in θ_ois required, and less capacity (in the uplink channel) is required.

[0041] Disclosed for illustration purposes are several methods of feedback. It should be noted that other methods of feedback are possible, and the present invention should therefore not be limited to the ones described herein. In a first method, a dedicated pilot signal (to be used by all mobile-stations) is transmitted on each antenna element, wherein each pilot signal is unique for the antenna element from which it is being transmitted, e.g., Walsh code used on each antenna element for the pilot signal is different. Upon receiving the pilot signals, mobile-station 28 records the phases and feeds back such recordations for each received pilot signal to base station 22. Note that mobile-station 28 could feedback phases for every received pilot signal, or a phase of a pilot signal for a reference antenna element within a group along with phases of other pilot signals for antenna elements within the group relative to the reference antenna element.

[0042] In a second method, a dedicated pilot signal is also transmitted from each antenna element within antenna array 23, and only the phase of one pilot signal from a reference antenna element is fed back by mobile-station 28 to base station 22. If inter-antenna element spacing is constant within a group, the phases of each antenna element should differ by a constant phase Δθ, which is represented by the following equation: $\begin{array}{cc}\Delta \theta =\frac{2\pi d}{{\lambda }^{\mathrm{down}}}\cos {\theta }_o& \text{equation 8}\end{array}$

[0043] While this method is simpler and requires less feedback, it is more sensitive to non-ideal inter-antenna element spacing.

[0044] A third method involves feeding back changes in phases based on previous phase measurements. This method requires some tuning between an update rate, an update step size and memory in measurement at mobile-station 28. If the memory is too long, error will build up and an incorrect reference will be used at the mobile-station for feedback decisions. A starting point is required which can be obtained by setting an initial absolute phase or by having an adaptive step size.

[0045] Upon processing and phase shifting each data stream s_din accordance with the above described signal processing technique, signals S^mεncomprising of the resulting data streams at associated power levels along with pilot signals are transmitted over antenna elements 26-mεn. The remainder of the application will be describe herein with respect to the illustrative example and transmission matrix T. For simplicity sake, the references q and k will be used hereinafter to refer to antenna elements 26-mε1 and 26-mε2 belonging to groups 24-1 and 24-2, respectively. For example, signals S^qand S^krefer to signals S^mεnto be transmitted over antenna elements 26-mε1 and 26-mε2 (or antenna elements q and k), respectively. Based on the signal processing technique of the present invention, signals S^qare defined by the following equation:

[0046] S^q={square root over (Pv_q(s₁w₁−s₂^*w₂)+{square root over (Pw_q-pilot  equation 9

[0047] where P_qand P_q-pilotrepresent respective transmit powers for signal S^qand a pilot signal over antenna element q; w_q-pilotis a Walsh code used for the pilot signal on antenna element q; w₁and w₂are extended Walsh codes associated with the mobile-station to which signal S is intended; and w_q-pilot, w₁and w₂are orthogonal to each other. In a preferred embodiment, w₂is a complement of w₁, i.e., w₂={overscore (w)}₁, such that only one Walsh code is used per mobile-station (in a two group, two antenna element per group, antenna array configuration).

[0048] Similarly, signals S^kare defined by the following equation:

[0049] S^k={square root over (Pv_k(s₂w₁+s₁^*w₂)+{square root over (Pw_k-pilot  equation 10

[0050] where P_kand P_k-pilotrepresent respective transmit powers for signal S^kand a pilot signal over antenna element k; w_k-pilotis a Walsh code used for the pilot signal on antenna element k; and w_k-pilot, w₁and w₂are orthogonal to each other. Note that no individual weighing via complex weights v_qand v_kare applied to the pilot signal because all mobile-stations will be using the same pilot signal to estimate distortion factor coefficients γ₁and γ₂for antenna groups 24-1 and 24-2, as will be described herein. Further note that the pilot signal Walsh codes w_q-pilotand w_k-pilotmay be identical or different for some or all antenna elements q and k.

[0051] The transmitted signals S^qand S^karrive at mobile-station 28 as signal R. See FIG. 3, which depicts the transmission process. Signal R is represented by the following equation: $\begin{array}{cc}R=\underset{q=1}{\sum ^{M\in 1}}{S}^q{\gamma }_1{e}^{{\mathrm{j\theta }}_q}+\underset{k=1}{\sum ^{M\in 2}}{S}^k{\gamma }_2{e}^{{\mathrm{j\theta }}_k}+\mathrm{noise}& \text{equation 11}\end{array}$

[0052] where γ₁and γ₂represent distortion factor coefficients (or time-varying multiplicative distortion due to Rayleigh fading) seen from respective groups 24-1 and 24-2, ${\theta }_q=\frac{2\pi }{\lambda }{d}_q\cos {\theta }_o,{\theta }_k=\frac{2\pi }{\lambda }{d}_k\cos {\theta }_o,$

[0053] and noise is temporally and spatially white complex Gaussian noise. Distortion factor coefficients γ₁and γ₂can be estimated using pilot signals, as is well-known in the art. Specifically, γ₁and γ₂are estimated using the following equations:

[0054] Γ_q=∫w_q-pilotr·dt=γ_qe^jθ  equation 12

[0055] Γ_k=∫w_k-pilotr·dt=γ_ke^jθ  equation 12a

[0056] where Γ_qand Γ_kare integrations of the pilot signal transmitted over antenna elements q and k, and γ_qand γ_kare the distortion factor coefficients corresponding to antenna elements q and k. In one embodiment, γ₁and γ₂in equation 11 are distortion factor coefficients corresponding to a pilot signal estimated from a single reference antenna element in group 24-1 and 24-2, or average distortion factor coefficients corresponding to two or more antenna elements in each group 24-1 and 24-2. Alternately, γ₁and γ₂can correspond to the appropriate γ_qand γ_kin equation 11.

[0057] Assuming that the channel distortion is static over an integration period, by correlating received signal R with Walsh codes w₁and w₂(after removing a long pseudo-random noise code), correlation outputs W₁and W₂are respectively obtained: $\begin{array}{cc}{W}_1=\underset{q=1}{\sum ^{M\in 1}}\sqrt{P_q}{v}_q{e}^{{\mathrm{j\theta }}_q}{\gamma }_1{s}_1+\underset{k=1}{\sum ^{M\in 2}}\sqrt{P_k}{v}_k{e}^{{\mathrm{j\theta }}_k}{\gamma }_2{s}_2+{\mathrm{noise}}_1^{\prime }& \text{equation 13}\\ W_2=\underset{k=1}{\sum ^{M\in 2}}\sqrt{P_k}{v}_k{e}^{{\mathrm{j\theta }}_k}{\gamma }_2{s}_1^{*}-\underset{q=1}{\sum ^{M\in 1}}\sqrt{P_q}{v}_q{e}^{{\mathrm{j\theta }}_q}{\gamma }_1{s}_2^{*}+{\mathrm{noise}}_2^{\prime }& \text{equation 13a}\end{array}$

[0058] where noise₁′ and noise₂′ represent noise after being correlated with Walsh codes w₁and w₂, respectively.

[0059] Using the distortion factor coefficients γ₁and γ₂, decision statistics can be created for estimating s₁and s₂, i.e., ŝ₁and ŝ₂. Such decision statistics are as follows:

[0060] ŝ₁=f{{circumflex over (γ)}₁^*W₁+{circumflex over (γ)}₂W₂^*}  equation 14

[0061] ŝ₂=f{{circumflex over (γ)}₂^*W₁−{circumflex over (γ)}₁W₂^*}  equation 14a

[0062] where f{•} is an appropriate decision function, and W₁* and W₂* represent transposed conjugates of W₁and W₂.

[0063] Expanding equation 14 and assuming perfect channel knowledge, estimate ŝ₁is represented as follows: $\begin{array}{cc}{\hat{s}}_1=f\left\{s_1\left(\underset{q=1}{\sum ^{M\in 1}}\sqrt{P_q}{v}_q{e}^{{\mathrm{j\theta }}_q}{\left|{\gamma }_1\right|}^2+\underset{k=1}{\sum ^{M\in 2}}\sqrt{P_k}{v}_k{e}^{{\mathrm{j\theta }}_k}{\left|{\gamma }_2\right|}^2\right)+\dots \left(\underset{q=1}{\sum ^{M\in 1}}\sqrt{P_q}{v}_q{e}^{{\mathrm{j\theta }}_q}-\underset{k=1}{\sum ^{M\in 2}}\sqrt{P_k}{v}_k{e}^{{\mathrm{j\theta }}_k}\right){\gamma }_1^{*}{\gamma }_2{s}_2+{\gamma }_1^{*}{\mathrm{noise}}_1^{\prime }+{\gamma }_2{\mathrm{noise}}_2^{\prime *}\right\}& \text{equation 15}\end{array}$

[0064] The same is done for equation 14a to obtain estimate ŝ₂. Based on the estimates ŝ₁and ŝ₂, signal S (or S^qand/or S^k) may be re-constructed at mobile-station 28.

[0065] Recall that no individual weighing (on a per mobile-station or user basis) of complex weights v_qand v_kwere applied to pilot signals transmitted over antenna elements q and k because all mobile-stations were using the same pilot signal to estimate distortion factor coefficients γ₁and γ₂. But the processing of received signal R assumes that the pilot signals have been properly weighted—that is, the mobile-stations estimate distortion factor coefficients γ₁and γ₂using complex weights v_q=e^−jθand v_k=e^−jθ. Since the pilot signals have not been properly weighted, complex weights v_qand v_kare not actually equal to e^−jθand e^−jθ, i.e., assumption is incorrect, there will be some error in processing the signal at mobile-station 28 causing degradation in performance.

[0066] One manner of correcting this problem is to assign unique pilot signals to each mobile-station, i.e., per user pilot signals. If per user pilot signals were assigned, then complex weights v_qand v_kcan be applied to the pilot signals. Thus, the transmitted signal for mobile-station or user z over antenna elements q and k would be:

[0067] S_z^q={square root over (Pv_q(s₁w₁−s₂^*w₂)+{square root over (Pv_qw_{q-pilot for user z}  equation 16

[0068] S_z^k={square root over (Pv_k(s₂w₁+s₁^*w₂)+{square root over (Pv_kw_{k-pilot for user z}  equation 16a

[0069] where w_{q-pilot for user z}and w_{k-pilot for user z}represent the assigned pilot signal Walsh codes for user z being transmitted over antenna elements q and k.

[0070] At mobile-station 28, distortion factor coefficients γ_q−zand γ_k−zfor user z can be estimated using the following equations:

[0071] Γ_q−z≐∫w_{q-pilot for user z}r·dt=γ_q−ze^jθ  equation 17

[0072] Γ_k−z=∫w_{k-pilot for user z}r·dt=γ_k−ze^jθ  equation 17a

[0073] Signals s₁and s₂can be estimated from the following equations: $\begin{array}{cc}{\hat{s}}_1={\left(\underset{q=1}{\sum ^{M\in 1}}{\Gamma }_{q-z}\right)}^{*}{W}_1+\left(\underset{k=1}{\sum ^{M\in 2}}{\Gamma }_{k-z}\right)W_2^{*}& \text{equation 18}\\ {\hat{s}}_2={\left(\underset{k=1}{\sum ^{M\in 2}}{\Gamma }_{k-z}\right)}^{*}{W}_1-\left(\underset{q=1}{\sum ^{M\in 1}}{\Gamma }_{q-z}\right)W_2^{*}& \text{equation 18a}\end{array}$

[0074] FIGS. 4 and 5 depict schematic diagrams of transmitters 40 and 50 for signal processing at base station 22 having a two group, two antenna element per group, antenna array configuration in accordance with one embodiment. Transmitter 40 comprises a first transmitter portion 42 and a second transmitter portion 44 for signal processing at group 24-1 for antenna elements 24-1-1 and 24-1-2, and transmitter 50 comprises a first transmitter portion 52 and a second transmitter portion 54 for signal processing at group 24-2 for antenna elements 24-2-1 and 24-2-2, respectively.

[0075] As shown in FIG. 4, first transmitter portion 42 comprises a plurality of symbol repeaters 402, 404, 406 and 408, mixers 410, 412, 414, 416, 422, 424, 426, 428, 438 and 440, summers 418, 420, 430, 432 and 442 and baseband filters 434 and 436. Symbol repeaters 402, 404, 406 and 408 receive a plurality of input signals Y_I1, Y_Q1, Y_I2and Y_Q2, wherein signals Y_I1, Y_Q1, Y_I2and Y_Q2correspond to in-phase signal s_e, quadrature-phase signal s_e, in-phase signal s_oand quadrature-phase signal s_o, respectively. Signals Y_I1, Y_Q1, Y₁₂and Y_Q2are repeated by symbol repeaters 402, 404, 406 and 408 as indicated by the plus “+” and minus “−” signs between parenthesis in FIG. 4. For example, for each bit or symbol of signal Y_I1, symbol repeater 402 outputs the same bit or symbol twice, i.e., ++, whereas for each bit or symbol of signal Y_I2, symbol repeater 406 outputs the same bit followed by an inverse of the same bit, i.e., +−. The outputs of symbol repeaters 402 and 404 are mixed with Walsh code w₁at mixers 410 and 412 whereas the outputs of symbol repeaters 406 and 408 are mixed with Walsh code w₂at mixers 414 and 416. The outputs of mixers 410 and 414 are summed by summer 418, and the outputs of mixers 412 and 416 are summed by summer 420.

[0076] The output of summer 418 is mixed with in-phase and quadrature-phase pseudo-random number codes PN_Iand PN_Qby mixers 422 and 424, and the output of summer 420 is mixed with the in-phase and quadrature-phase pseudo-random number codes PN_Iand PN_Qby mixers 428 and 426, respectively. The outputs of mixers 422 and 426 are summed by summer 430, and the outputs of mixers 424 and 428 are summed by summer 432. The outputs of summers 430 and 432 are filtered by baseband filters 434 and 436 and then modulated via mixers 438 and 440 onto carrier signals defined by the functions cos(2πf_ct) and sin(2πf_ct), respectively. The outputs of mixers 438 and 440 are added together using summer 442 before being transmitted as signal S₁in signal S1 over antenna element 24-1-1.

[0077] Second transmitter portion 44 of transmitter 40 comprises a plurality of symbol repeaters 444, 446, 448 and 450, mixers 452, 554, 456, 458, 464, 466, 468, 470, 476, 478, 480, 482, 492 and 494, summers 460, 462, 472, 474, 484, 486 and 496 and baseband filters 488 and 490. Symbol repeaters 444, 446, 448 and 450, mixers 452, 545, 456 and 458, summers 460 and 462 operate in a manner substantially identical to their counterparts in first transmitter portion 42, i.e., symbol repeaters 402, 404, 406 and 408, mixers 410, 412, 414 and 416 and summers 418 and 420.

[0078] The outputs of mixers 460 and 462 are then co-phased or phase-shifted such that the signal to be transmitted over associated antenna element 24-1-2 arrives in-phase at destination mobile-station 28 with the signal to be transmitted over antenna element 24-1-1. Specifically, the output of mixer 460 is mixed with the in-phase and quadrature-phase components c_Iand c_Qof complex weight v associated with antenna element 24-1-2 using mixers 464 and 468, whereas the output of mixer 462 is mixed with the in-phase and quadrature-phase components c_Iand c_Qof complex weight v associated with antenna element 24-1-2 using mixers 466 and 470. The outputs of mixers 464 and 470 are summed by summer 472, and the outputs of mixers 466 and 468 are summed by summer 474. The output of summer 472 is provided as inputs to mixers 476 and 478, and the output of summer 474 is provided as inputs to mixers 480 and 482. Mixers 476, 478, 480, 482, 492 and 494, summers 484, 486 and 496 and baseband filters 488 and 490 operate in a manner substantially identical to their counterparts in first transmitter portion 42, i.e., mixers 422, 424, 426, 428, 438 and 440, summers 430, 432 and 442, and baseband filters 434 and 436.

[0079] Note that first transmitter portion 42 does not include components for co-phasing the signal to be transmitted over its associated antenna element 24-1-1 because such signal is being used as the reference signal against which the signal to be transmitted over antenna element 24-1-2 is to be co-phased. It should be understood that first transmitter portion 42 may also include components for co-phasing its associated signal. If group 24-1 had additional antenna elements, the transmitter may include additional transmitter portions identical to second transmitter portion 44 except for the complex weight being applied.

[0080] The first and second transmitter portions 52 and 54 of transmitter 50 operate in a manner substantially identical to the first and second transmitter portions 42 and 44 of transmitter 40. The notable exceptions are as follows. Symbol repeaters 502, 504, 506, 508, 544, 546, 548 and 550 are configured to signals Y_I1, Y_Q1, Y_I2and Y_Q2such that their outputs are not identical to the outputs of their respective counterparts in transmitter 40. For example, symbol repeater 502 is a “+−” repeater, whereas its counterpart symbol repeater 402 is a “++” repeater. Another difference is that the outputs of symbol repeaters belonging to transmitter 50 are mixed with Walsh codes different from the Walsh codes used to mix the outputs of their respective counterparts in transmitter 40. For example, the output of symbol repeater 504 is mixed with Walsh code w₂, whereas the output of its counterpart symbol repeater 404 is mixed with Walsh code w₁.

[0081] Although the present invention has been described in considerable detail with reference to certain embodiments, other versions are possible. Therefore, the spirit and scope of the present invention should not be limited to the description of the embodiments contained herein.