Decoding techniques for multi-antenna systems

[0001] This application claims priority of European Application No. 00303784.3, which was filed on May 5, 2000.

[0002] The invention relates to a wireless radiofrequency data communication system comprising:

[0003] a base-station comprising a multiple of N first groups and a signal processing-unit comprising memory means and processing means, wherein each first group comprises a receiver-unit provided with a receiver and at least one antenna which is connected to the receiver-unit, wherein the signal processing-unit is connected with each of the first groups for processing receive-signals generated by each of the first groups, and

[0004] a multiple of M second groups for transmitting radiofrequency signals to the first groups, wherein each second group comprises a transmitter-unit provided with a transmitter and at least one antenna which is connected to the transmitter-unit,

[0005] wherein the memory means of the signal processing-unit are provided with information about the transfer-functions of radiofrequency signals from each of the antennas of the second groups to each of the antennas of the first groups, and wherein the transmitters and receivers operate on essentially the same radiofrequency or radiofrequency-band.

[0006] Wireless radiofrequency data communication systems of this type are known and find their applications in a variety of fields. An example of such an application can be found in the domain of digital communication for electronic-mail. In this application each personal computer can be provided with at least one second set so that the personal computer can be incorporated in an network. The base-station may in that case be connected with a server of the network. Further examples are given, for instance, in the domain of mobile telephony. In the case of mobile telephony the base-station is a telephony exchange. In the majority of the applications more than one second set wants to communicate with the base-station. This means that the second group transmits signals to this base-station and also receives signals from this base-station. Since it would not be acceptable if all second groups would have to wait for each other's communication to be finished, there is a need for simultaneous communication. Simultaneous communication allows more second groups to communicate at the same time with the base-station. A straightforward and common way of realising simultaneous communication is to assign different radiofrequencies to the respective second groups. In this way all data signals can be separated easily by the first groups in the base-station by frequency selective filters. Furthermore, the base-station can communicate with each second group at the specific radiofrequency which has been assigned to the second group. A transmitted radiofrequency signal contains the actual information to be transmitted to the receiver. This actual information has been modulated on the radiofrequency carrier-signal. Several techniques have been developed for modulating information on the carrier-signal like frequency-modulation, phase-modulation amplitude-modulation et cetera.

[0007] A radiofrequency signal which is transmitted by a second group travels from the antenna of the second group along so-called travel-paths to the antennas of the first groups. During the travelling, depending of the specific travel-path, the radiofrequency signal is attenuated and also a phase-distortion is incurred on the radiofrequency signal. The phase-distortion of the radiofrequency signal can be corrected by the signal processing-unit in the base-station on the basis of the information about the transfer-functions. This can be of special interest if information is modulated on the radio-frequency signal according to a phase-modulation technique.

[0008] It is an object of the invention to provide in a detection system which increases the communication capacity of the wireless communication system per frequency or frequency-band used by the system. In particular it is an object of the invention to increase the data communication capacity from the second groups to the first groups by creating multiple separate simultaneous data communication channels. More in particular it is an object of the invention to provide in a detection system comprising M simultaneous separated communication signals for which the multiple of first groups N may be less, equal or greater than the multiple M of second groups.

[0009] The present invention therefore provides in a wireless radiofrequency data communication system which is characterised in that the signal processing-unit is arranged to process, in use, the receive-signals on the basis of the Maximum Likelihood Detection method, such that for each second group of the second groups an individual communication channel is formed with the base-station wherein these communication channels are generated simultaneously and separately from each other.

[0010] In this manner multiple communication channels are realised on the same frequency, or within the same frequency-band, based on the principle that the signals can be separated thanks to the different characteristics of the transfer-functions. Due to the Maximum Likelihood detection technique this holds for the cases wherein the number N of first groups is greater, equal or less than the number M of second groups. Hence the data communication capacity per frequency or frequency-band is indeed increased. The geometry of the configuration of the communication system determines the transfer functions which belong to the different travel-paths between the antennas of the first groups and the second groups in the base-station. These transfer functions are expressed by complex numbers. Each complex number expresses the transfer function between one antenna of one of the first groups and one antenna of the second group. The amplitude of the complex number is the attenuation of the signal's strength and the phase of the complex number is the phase modulation incurred during transmission along the travel-path. Since the used frequencies are relatively high, the transfer functions depend largely on the configuration.

[0011] An embodiment according to the invention is characterised in that each transmitter comprises means for modulating an information signal on a radiofrequency signal according to the Quadrature Amplitude Modulation (QAM) method, wherein so-called QAM-symbols are transmitted, and that each receiver comprises means for demodulating information signals from a received radiofrequency signal. The Quadrature Amplitude Modulation is an amplitude- and/or phase-modulation technique in which information in binary format is modulated on a radiofrequency signal.

[0012] In a favourable embodiment of the invention the wireless communication system is characterised in that the signal processing-unit is arranged to calculate, in use, a detection signal x_DET according to

[0013] where arg_{over set} min( . . . ) is a function which, according to (I), yields that vector x_DET out of a set x_SET of P vectors x^p_SET (p1, . . . , P) for which the length rH x^p_SET of the complex N-dimensional vector rH x^p_SET is minimal, wherein r is a complex N-dimensional vector r₁, . . . , r_i, . . . , r_N^T with r_i being the signal received by the i^th first group of the N first groups, H is a complex N*M matrix containing transfer-functions h_im (i1, . . . , N; m1, . . . , M), wherein h_im is the transfer-function for transmission from the m^th second group of the M second groups to the i^th first group of the N first groups, and where x^p_SET is the p^th complex M-dimensional vector x^p_{SET, 1}, . . . , x^p_{SET, m}, . . . , x^p_{SET, M}^T of the set X_SET, wherein the vectors x^p_SET in the set X_SET contain possible combinations of values which can be assigned by the second groups to an information signal x, where x is a M-dimensional vector x₁, . . . , x_m, . . . , X_M^T with x_m being the information signal transmitted by the m^th second group of the M second groups to the first groups and where x_m is one individual communication signal. Equation (1) is based on the model

[0014] where n is a complex N-dimensional noise vector n₁, . . . , n_i, . . . n_N^T containing noise terms picked up during reception. The model (II) gives the relation between the transmitted signal xx₁, . . . , x_m, . . . , x_M^T and the received signal rr₁, . . . , r_i, . . . , r_N^T in the base-station. The detection method according to the invention tries to match a fixed number of possible combinations of values for x in the equation (I). These possible value combinations are the vectors x^p_SET, (p1, . . . , P), which all together constitute the set X_SET. The detection signal x_DET is that vector x^p_SET in the set X_SET which minimizes the length of the vector rH x^p_SET.

[0015] In a further embodiment the wireless radiofrequency data communication system is characterised in that the processing unit is arranged to apply, in use, the following approximation (III) in the calculation of (I) $\begin{array}{cc}r-{\mathrm{Hx}}_{\mathrm{SET}}^p=\underset{i=1,,N}{}\left(\mathrm{Real}\left({\left[r-{\mathrm{Hx}}_{\mathrm{SET}}^p\right]}_i\right)+\mathrm{Im}\left({\left[r-{\mathrm{Hx}}_{\mathrm{SET}}^p\right]}_i\right)\right),& \left(\mathrm{III}\right)\end{array}$

[0016] wherein _{i1, . . . , N}( . . . ) is a summation over the index i from 1 to N over the argument (Real(rH x^p_SETi)Im(rH x^p_SETi)), where (.) yields the absolute value of its input argument and where Real( . . . ) is a function which, in equation (III), yields the real part of its complex argument rH x^p_SETi, with rH x^p_SETi being the i^th component of the complex N-dimensional vector rH x^p_SET, and where Im( . . . ) is a function which, in equation (III), yields the imaginary part of its complex argument rH x^p_SET1. The expression (III) offers a valuable approximation and simplification for the evaluation of equation (I).

[0017] An embodiment of the invention which is of special interest is a wireless radiofrequency data communication system characterised in that the set X_SET comprises all possible combinations of values which can be assigned to the signal x by the second groups.

[0018] In a preferred embodiment of the invention the wireless radiofrequency data communication system is characterised in that the signal processing-unit is arranged to find, in use, the detection signal x_DET according to a Reduced Search Technique wherein a search-tree is passed through according to the following steps 1 to 7:

[0019] Step 1: calculate the lengths of the complex vectors v corresponding to all combinations of possible values which can be assigned to x₁, . . . , x_L, wherein v is given by $\begin{array}{cc}v=\left(r-\underset{i=1,,L}{}{h}_i*x_{\mathrm{SET},i}^p\right),& \left(\mathrm{IV}\right)\end{array}$

[0020] where _{i1, . . . , L}( . . . ) is a summation over the index i from 1 to L over the complex argument h_i*x^p_{SET, i} and where h_i is the i^th column h_{1, i}, . . . , h_{N, 1}^T of the matrix H;

[0021] Step 2: select the K combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, L} corresponding to the K smallest lengths of v as well as the K vectors v itself and set mL1;

[0022] Step 3: calculate the lengths of the C*K new vectors v given by

[0023] where v_old is one of the K vectors v resulting from the preceding step and where h_m is the m^th column of H;

[0024] Step 4: select those K combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, m} that correspond to the K smallest lengths of v as well as the K vectors v itself and set mm_old1, where m_old is m from the preceding step;

[0025] Step 5: if m<M then go to Step 3, else go to step 6;

[0026] Step 6: calculate the lengths of the C*K new vectors v given by

[0027] Step 7: the detection signal x_DET is determined as that combination of values x_DETx^p_{SET, 1}, . . . x^p_{SET, M} which corresponds to the vector v with the smallest length,

[0028] wherein K and L are predetermined fixed integer values which control the size P of the set X_SET and wherein the constellation size C of the system is the number of values x^p_{SET, m} which can be assigned by one of the second groups to one component x_m(m1, . . . , M) of x and where V_old is one of the K vectors v resulting from Step 3, the calculated detection signal x_DET is the combination of values x^p_SET corresponding to the smallest vector v. In this manner the requisite number of calculations for obtaining the detection signal x_DET is known on beforehand, since the number P of vectors in the set X_SET is pre-determined by selecting values for K and L.

[0029] An alternative embodiment according to the invention is characterised in that the signal processing-unit is arranged to find, in use, the detection signal x_DET according to a Reduced Search Technique wherein a search-tree is passed through according to the following steps 1 to 7:

[0030] Step 1: calculate the values of the lengths of the C vectors v according to the C possible values x^p_{SET, 1}

[0031] wherein h₁ is the first column of H;

[0032] Step 2: select those combinations of values for x^p_{SET, 1} for which the lengths of v are smaller than T, as well as the corresponding vectors v and set m2;

[0033] Step 3: calculate the lengths of the new vectors v given by

[0034] wherein v_old is one of the vectors v resulting from the preceding step and where h_m is the m^th column of H, and adjust the treshold T;

[0035] Step 4: select those combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, m} for which v is smaller than T, discard the other combinations and set mm_old1, where m_old is m from the preceding step;

[0036] Step 5: if m<M then go to Step 3, else go to step 6,

[0037] Step 6: calculate the lengths of the new vectors v given by

[0038] Step 7: the detection signal x_DET is determined as that combination of values x_DETx^p_{SET, 1}, . . . , x^p_{SET, M} which corresponds to the vector v with the smallest length,

[0039] wherein T is a predetermined fixed threshold value which controls the size P of the set x_SET and wherein the constellation size C of the system is the number of values x^p_{SET, m} which can be assigned by one of the second groups to one component x_m(m1, . . . , M) of x, and wherein v_old is one of the vectors v resulting from step 3, the calculated detection signal x_DET is the combination of values x^p_SET corresponding to the smallest vector v. In this embodiment the number of requisite calculations for obtaining the detection signal x_DET is not known on beforehand since the number of vectors v which are selected in the respective steps 2 and 4 may vary from step tot step, depending on the adjusted value for the threshold T and the noise n in the signal r.

[0040] A further embodiment of the wireless radiofequency data communication system according to the invention is characterised in that the signal processing-unit is arranged to find, in use, the detection signal x_DET according to a Reduced Search Technique which also comprises the following steps:

[0041] Step A1: calculate an inner product z of the vector r with the u^th column h_u of the matrix H, where u is an integer 1uM, according to:

[0042] where h*_u is the complex conjugated and transposed of h_u;

[0043] Step A2: calculate C^M1 terms Interf corresponding to all possible value combinations which can be assigned to x₁, . . . , x_u1, x_u1, . . . , x_M, wherein the terms Interf are defined according to: $\begin{array}{cc}\mathrm{Interf}=\underset{\left(i=1,,Miu\right)}{}{x}_i*\left(h_u^{*}*h_i\right),& \left(\mathrm{XI}\right)\end{array}$

[0044] wherein _{(i1, . . . , Miu)} is a summation over the index i from 1 to M with the exception of the integer u;

[0045] Step A3: estimate, on the basis of the equations (X), (XI) and z according to:

[0046] where z is an approximation of z, the value for x_u corresponding to each of the value combinations x₁, . . . , x_u1, x_u1, . . . , x_M, and constitute a test set X_SET comprising C^M1 vectors x^p_SET, wherein each vector x^p_SET represents a value combination x₁, . . . , x_u1, x_u, x_u1, . . . , x_M;

[0047] Step A4: determine the detection signal X_DET according to equation (A), wherein the test set is defined with the C^M1 vectors x^p_SET from the preceding step.

[0048] In an embodiment of the wireless radiofrequency data communication system according to the invention the multiple N of first groups exceeds the multiple M of second groups.

[0049] In another embodiment of the wireless radiofrequency data communication system according to the invention the multiple N of first groups is less than the multiple M of second groups.

[0050] In still another embodiment of the wireless radiofrequency data communication system according to the invention the multiple N of first groups is equal to the multiple M of second groups.

[0051] In the accompanying drawings, in which certain modes of carrying out the present invention are shown for illustrative purposes:

[0052] FIG. 1 is a diagram schematically showing a wireless data communication system according to the invention;

[0053] FIG. 2 is a diagram illustrating the use of Quadrature Amplitude Modulation (QAM) symbols by the wireless data communication system of FIG. 1.

[0054] FIG. 3 is a diagram illustrating the use of Quadrature Amplitude Modulation (QAM) symbols by a wireless data communication system which contains three first groups and two second groups.

[0055] FIG. 4 is a diagram illustrating the use of Quadrature Amplitude Modulation (QAM) symbols by a wireless data communication system which contains one first group and two second groups.

[0056] FIG. 5 is a diagram showing a search tree for illustrating the principle of Reduced Search Techniques in an embodiment of a wireless data communication system according to the invention.

[0057] An embodiment of a wireless radiofrequency data communication system according to the invention is shown in FIG. 1. This wireless radiofrequency data communication system comprises a base-station 2 which comprises a signal processing-unit 4 and multiple first groups 6.i (i1, 2, . . . , N). Each first group 6.i comprises a receiver-unit 10.i provided with a receiver, and at least one antenna 12.i which is connected to the receiver-unit 10.i. In this example each first group 6.i comprises one antenna 12.i connected to the receiver-unit 10.i. The signal processing-unit 4 is at one side connected to each of the first groups 6.i, i1 ,2, . . . , N, and at another side connected to each of the coding/decoding-units 14.m, m1, 2, . . . , M. Furthermore, the system comprises multiple second groups 16.m (m1, 2, . . . , M), wherein each second group 16.m comprises at least a transmitter-unit 18.m and at least one antenna 20.m which is connected to said transmit-unit 18.m. Each of the second groups 16.m is connected with a coding/decoding-unit 22.m, m1, 2, . . . , M.

[0058] In the configuration of FIG. 1 the second groups can belong to mobile communication stations. An example of this is the situation wherein notebooks are provided with at least one second group. In this situation the notebooks can communicate via the second groups to the base-station. The base-station can be an internet and/or an intranet server. In general the number M of second groups will vary during the operation of the base-station.

[0059] The second groups 16.m (m1, 2, . . . , M) can simultaneously transmit radiofrequency signals on essentially the same radiofrequency or radiofrequency-band to the first groups 6.i. The radiofrequency signal which is transmitted from the second group 16.m travels from this second group along travel-paths T_im(i1, 2, . . . , N) to the respective first groups 6.i (i1, 2, . . . , M). The travel-path T_im is the travel-path from the second group 16.m to the first group 6.i. For each travel-path T_{i, m} a transfer-function can be defined which is expressed with a complex number h_im. The amplitude of the him is the attenuation of the signal's strength and the phase of h_im is the phase modulation incurred during transmission along the travel-path. The processing-unit 4 comprises memory means provided with information about the transfer-functions of radiofrequency signals along said travel-paths.

[0060] Furthermore the processing-unit 4 comprises processing means for processing receive-signals generated by each of the first groups.

[0061] In FIG. 1 a radiofrequency transmission signal x^RF_m is generated by the second group 16.m and transmitted to the first groups 6.i (i1, . . . , N). The generation of this radiofrequency transmission signal is as follows. The input to the coding/decoding-unit 22.m is a so-called Quadrature Amplitude Modulated symbol (short: QAM-symbol). This QAM-symbol is expressed as a complex number (an example of such a complex number is: 12j, where the real part of the QAM-symbol is 1 and the complex part is 2). Said QAM-symbol is modulated by the coding/decoding-unit 22.m on a low-frequency signal, which yields x_m. This data-signal x_m is the input of the transmit-unit 18.m, which transmit-unit modulates x_m on a radiofrequency signal yielding the radiofrequency signal x^RF_m. The radiofrequency signal x^RF_m is transmitted by the antenna 20.m to the first groups.

[0062] Each first group 6.i, i1, . . . , N receives a radiofrequency signal r^RF_i in the antenna 12.i, this signal r^RF_i is a result of the interference of all transmitted signals x^RF_m, m1, . . . , M. The signal r^RF_i is demodulated by the receiver-unit 10.i to a low-frequency receive-signal r_i which contains the modulated information of data-signal x_m. The N receive-signals r_i, i1, . . . , N are fed to the input of the signal processing-unit 4. The signal processing unit 4 calculates M output signals x_{i, DET}, i1, . . . , M. Each output signal x_{i, DET} is an estimation for the data-signal x_i. The detection signal x_{i, DET} is imputed to the coding/decoding-unit 14.i, i1, . . . , N, which unit generates the QAM-symbol c_{i, DET}. This QAM-symbol is an estimation for the QAM-symbol c_i.

[0063] The operation of the signal processing unit 4 will now be elucidated on the basis of a mathematical framework. The relation between the data-signals x_m, m1, . . . , M and the receive-signals r₁, i1, . . . , N is given with the following vector equation:

[0064] where r is a N-dimensional complex vector r₁, . . . , r_i, . . . , r_N^T, where H is a complex N*M-matrix containing the transfer-functions h_im, (i1, . . . , N; m1, . . . , M) and wherein x is a M-dimensional complex vector x₁, . . . , x_m, x_M^T. The noise vector n is a N-dimansional complex vector n₁, . . . , n_i, . . . , n_N^T, with n_i being the noise term picked up during reception of the signal r^RF_i. The signal processing unit 4 calculates detection signals x_DETx_{1, DET}, . . . , x_{M, DET}^T which are estimations for the data-signals x. These calculations are performed according to the Maximum Likelihood method. It has to be noted here that the detection signals are sometimes called Maximum Likelihood signals. One important aspect of the Maximum Likelihood approach is that use is made of the knowledge that the QAM-symbol c_m, m1, . . . , M can only take on a limited number of values. This number is called the constellation size C of the second group. So, the data-signal x_m for a particular m can only take on C different values. This implicates that the total number of possible different value combinations of the data-vector x is C^M. All these C^M different value combinations together constitute the test set X_SET, wherein the p^th element of the set is a value combination which is a complex M-dimensional vector x^p_SET. This implicates that the signal processing unit can calculate a detection signal by trying to match all elements of the set and choosing the best fit according to (XIII). In order to save processing time it is also possible only to match the elements of a subset of the set. For the latter approach several reduced search techniques are developed according to the invention. The detection signals which are found by matching elements of the set are called Maximum Likelihood signals.

[0065] The signal processing-unit 4 can find the Maximum Likelihood detection signal in particular according to the following algorithm. This algorithm will be described in mathematical terms. The detection signals x_DET are calculated by the signal-processing-unit 4 according to $\begin{array}{cc}{x}_{\mathrm{DET}}={\arg }_{\mathrm{over}\mathrm{set}}\min \left(r-{\mathrm{Hx}}_{\mathrm{SET}}^p\right),& \left(\mathrm{XIV}\right)\end{array}$

[0066] where arg_{over set} min( . . . ) is a function which, according to (XIV), yields that vector x_DET out of a set x_SET of P vectors x^p_SET(p1, . . . , P) for which the length rH x^p_SET of the complex N-dimensional vector rH x^p_SET is minimal and where x^p_SET is the p^th complex M-dimensional vector x^p_{SET, 1}, . . . , x^p_{SET, m}, x^p_{SET, M} of the set x_SET, wherein the vectors x^p_SET in the set X_SET contain possible combinations of values which can be assigned by the second groups to an information signal x, where x_m is one individual communication signal. Since the data-signals x_m m1, . . . , M are transmitted simultaneously each detection signal x_{m, DET} results in the generation of one of M simultaneous data communication signals.

[0067] The principle of the Maximum Likelihood Detection method will now be illustrated with the schematic FIG. 2. This figure shows QAM-sybols c_m m1, . . . , M which are the possible inputs to the coding/decoding units 22.m. The QAM-symbol c₁ is marked with a * 26.1 and equals (1j). Each diagram 24.m contains a QAM-symbol c_m which can take on 4 different values. These possible values are marked with 0 28.m. The actual possible values for the QAM-symbols are (1j), (1j), (1j) and (1-j). Thus here the constellation size C of the second groups is C4. As is explained before the QAM-symbols are the information which is modulated on the corresponding data signal x_m. However, from a mathematical point of view the QAM-symbols are identical to the signals x_m. So, the value of the low-frequency signal x₁ in the example of FIG. 2 is (1j) and the value of x_M is (1j). The transmission and the subsequent reception of the QAM-symbols to the first groups 6.i takes place via radiofrequency carrier signals. The mathematical formulation of this transmission is a transformation of the vector x with the matrix H and an addition of noise n, see equation (XIII). This is illustrated with the transformation block 30 which contains M input-signals x_m m1, . . . , M and N output-signals r_i i1, . . . , N. The values of the output signals r_i i1, . . . , N are represented with * marks 34.i in the diagrams 32.i. Each diagram 32.i contains one received component r_i of r. As a consequence of the time-varying nature of H and as a consequence of noise the values of r_i will generally vary, even if the QAM-symbols c_m would have continuously constant values. Now the signal processing unit 4 calculates the transformation of all possible number of value combinations in the test set (or a subset of the test set) of the QAM-symbols, in order to try these elements in (XIV), according to:

[0068] The complete test set comprises PC^M combinations (but for a subset of the test set P<C^M). Equation (XV) yields possible receive-signals in the situation of absence of noise. These signals are indicated with 0 marks 36.i in the diagrams 32.i. Finally, the Maximum Likelihood solution is that value combination x^p_SET in the test set, which corresponds to the 0 marks of its components, for which the value

[0069] is minimal. In the case in which the vectors r and r^p_SP only comprise one component the Maximum Likelihood solution is found with the 0 in diagram 32.1 which is closest to the *.

[0070] FIG. 3 gives a more detailed example of a wireless data communication system according to the invention where the number of first groups N3, the number of second groups M2 and the constellation size C2. In total there are 4 possible value combinations which can be assigned to the data-signals x. In this example the data-signal is x(0j), (0j)^T. Since the number of first groups is greater than the number of second groups a robust communication system, fairly insensitive to noise, is realised. The possible values for the components of the data-signals x are schematically indicated with 0 marks 26.1 in the diagrams 24.1 and 24.2 in FIG. 3. The test set comprises all these possible value combinations (P4), so the test set X_SET is given with:

[0071] where:

[0072] wherein the notation X_SET . . . ; . . . means that X_SET is the set of all vectors which are enumerated between the brackets . . In this case the matrix H containing the transfer-functions is a complex 3*2-matrix. The transformation of the elements of the test set X_SET (see (XVII)) according to (XV) results in 4 vectors r^p_SP, each of which has 3 components. The values of the respective components of the vectors r^p_SP are depicted in the respective diagrams 32.1, 32.2 and 32.2 of FIG. 3 and marked with 0 marks 36.i, i1, 2, 3. The transformation of the data-signal x according to (XIII) yields the receive signal r. The respective components of this signal are indicated with * marks 34.i in the respective diagrams 32.1, 32.2 and 32.2 of FIG. 3. Note that despite the relation x'x¹_SET the signal r is unequal to r¹_SP as a consequence of the noise n. The Maximum Likelihood solution is found according to (XIV). Note that 2 simultaneous data communication channels are generated, which channels are the components of the vector x (the first channel is x₁ and the second channel is x₂).

[0073] FIG. 4 gives an example of a wireless data communication system in which there are more second groups (M2) than first groups (N1). However, with the detection algorithm according to the invention the signal processing-unit sometimes can recover the transmitted M-dimensional data-signal x. In this case the data-signal x(0j), (0j)^T. The constellation size C2. So, there are 4 possible value combinations which can be assigned to the data-signals x. The possible values for the components of these data-signals are indicated with 0 marks 26.1 in the diagrams 24.1 and 24.2 of FIG. 4. The test set comprises all these possible value combinations (P4), so the test set X_SET is given with (XVII). In this example the matrix H containing the transfer-functions is a complex 1*2-matrix:

[0074] where the column h₁ is identical to the scalar h₁₁ and the column h₂ is identical to the scalar h₁₂. The transformation of the elements of the test set X_SET(see (XVII)) according to (XV) results in 4 scalars r^p_SP. The values of these 4 scalars r^p_SP are depicted in the diagrams 32.1 of FIG. 4 and marked with 0 marks 36.1. The transformation of the data-signal x according to (XIII) yields the receive signal r. In this example this signal is also a scalar which is indicated with a * mark 34.1 in the diagrams 32.1 of FIG. 4. Note that despite the relation xx_SET the signal r is unequal to r¹_SP as a consequence of the noise n. The Maximum Likelihood solution is found according to (XIV) and is given with the 0 mark which is closest to the * mark 34.1.

[0075] The calculations of the signal processing unit based on the equation (XIV) can be approximated with the following expression in order to save processing time: $\begin{array}{cc}r-{\mathrm{Hx}}_{\mathrm{SET}}^p=\underset{i=1,,N}{}\left(\mathrm{Real}\left({\left[r-{\mathrm{Hx}}_{\mathrm{SET}}^p\right]}_i\right)+\mathrm{Im}\left({\left[r-{\mathrm{Hx}}_{\mathrm{SET}}^p\right]}_i\right)\right),& \left(\mathrm{XIX}\right)\end{array}$

[0076] wherein _{i1, . . . , N} ( . . . ) is a summation over the index i from 1 to N over the argument (Real(rH x^p_SETi)Im(rH x^p_SETi)), where (.) yields the absolute value of its input argument and where Real( . . . ) is a function which, in equation (XIX), yields the real part of its complex argument rH x^p_SETi, with rH x^p_SETi being the i^th component of the complex N-dimensional vector rH x^p_SET, and where Im( . . . ) is a function which, in equation (XIX), yields the imaginary part of its complex argument rH x^p_SET1. The signal processing-unit 4 finds the Maximum Likelihood detection signal according to (XIV). With this equation the detection signal is found by trying to fit elements of the test set X_SET. Since the test set comprises C^M elements this can easily lead to a huge amount of processing time. To reduce the processing time the invention provides in an algorithm which can limit the search to a subset of X_SET. A first algorithm which provides in an intelligent way of choosing a pre-determined subset of X_SET is given below and is called a Reduced Search Technique. In this Reduced Search technique a search-tree is passed through according to the following steps 1 to 7:

[0077] Step 1: calculate the lengths of the complex vectors v corresponding to all combinations of possible values which can be assigned to x₁, . . . , x_L. The vector v is given with $\begin{array}{cc}v=\left(r-\underset{i=1,,L}{}{h}_i*x_{\mathrm{SET},i}^p\right),& \left(\mathrm{XX}\right)\end{array}$

[0078] where _{i1, . . . , L} ( . . . ) is a summation over the index i from 1 to L over the complex argument h_i*x^p_{SET, i} and where h_i is the i^th column h^{1, i}, . . . , h_{N, i}^T of the matrix H;

[0079] Step 2: Select the K combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, L} corresponding to the K smallest lengths of v as well as the K vectors v itself and set mL1;

[0080] Step 3: Calculate the lengths of the C*K new vectors v given by

[0081] where v_old is one of the K vectors v resulting from the preceding step and where h_m is the m^th column of H;

[0082] Step 4: Select those K combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, m} that correspond to the K smallest lengths of v as well as the K vectors v itself and set mm_old1, where m_old is m from the preceding step;

[0083] Step 5: If m<M then go to Step 3, else go to step 6;

[0084] Step 6: Calculate the lengths of the C*K new vectors v given by

[0085] Step 7: the detection signal x_DET is determined as that combination of values x_DETx^p_{SET, 1}, . . . , x^p_{SET, M} which corresponds to the vector v with the smallest length,

[0086] wherein K and L are predetermined fixed integer parameters which control the size P of the set X_SET and where v_old is one of the K vectors v resulting from Step 3, the calculated detection signal x_DET is that element of the set X_SET for which the vector v is smallest. The principle of this reduced search technique is schematically illustrated in diagram 38 of FIG. 5 (according to the example of FIG. 4). In this example the pre-determined parameter L1 and K4. Furthermore, the constellation size C2, the number of second groups M2, the number of first groups N1, the matrix H is given with (XVIII) and the test set is defined with (XVII). The received vector r is a scalar r. The first stage 40 of the algorithm is to evaluate (XX). This results in principle in four lengths v1, v2, v3 and v4 corresponding to four vectors v (note that in this example v and h₁ and h₂ are all scalars): $\begin{array}{cc}\begin{array}{c}v1=r-h_1*x_{\mathrm{SET},1}^1=r-h_1*j\\ v2=r-h_1*x_{\mathrm{SET},1}^2=r-h_1*\left(-j\right)\\ v3=r-h_1*x_{\mathrm{SET},1}^3=r-h_1*j=v1\\ v4=r-h_1*x_{\mathrm{SET},1}^4=r-h_1*\left(-j\right)=v2.\end{array}& \left(\mathrm{XXIII}\right)\end{array}$

[0087] These values v1 and v2 are shown in FIG. 5 in Step 1 of the algorithm 42. According to Step 2 both values v1 and v2 are selected. Hereafter, in Step 3 and Step 4 the lengths of 4 new vectors v are calculated. These 4 new lengths are: $\begin{array}{cc}\begin{array}{c}v1=r-h_1*j-h_2*j\\ v2=r-h_1*\left(-j\right)-h_2*j\\ v3=r-h_1*j-h_2*\left(-j\right)\\ v4=r-h_1*\left(-j\right)-h_2*\left(-j\right).\end{array}& \left(\mathrm{XXIV}\right)\end{array}$

[0088] These four lengths 44 are depicted in FIG. 5. From Step 5 of the algorithm a jump is made to Step 6. Finally, in Step 6 the calculation of the Maximum Likelihood detection signal is finished. In this case the detection signal equals the test vector x⁴_SET: x_DETx⁴_SET. In the algorithm stated above the processing load of the signal processing-unit 4 is known on beforehand and can be controlled with the parameters K and L. It is important to note that the detection signal comprises two components whereas the receive-signal r only comprises one component. So, in principle two separate simultaneous communication channels are formed. This example shows an important aspect of the nature of the detection algorithm according to the invention, namely that the number of receivers may be less than the number of transmitters, and thus the number of receivers may also be less than the number of simultaneous communication channels.

[0089] In another embodiment of the wireless data communication system the signal processing-unit 4 also finds the Maximum Likelihood detection signal according to (XIV). However, in this embodiment the processing load of the signal processing-unit 4 is not known on beforehand. The subset of the test set is X_SET is controlled with a real value threshold parameter T. The algorithm of this Reduced Search Technique is given below and comprises seven steps:

[0090] Step 1: Calculate the values of the lengths of the C vectors v according to the C possible values x^p_{SET, 1}

[0091] Step 2: Select those combinations of values for x^p_{SET, 1} for which the lengths of v are smaller than T, as well as the corresponding vectors v and set m2;

[0092] Step 3: Calculate the lengths of the new vectors v given by

[0093] wherein v_old is one of the vectors v resulting from the preceding step and adjust the treshold T;

[0094] Step 4: Select those combinations of values for x^p_{SET, 1}, . . . , x^p_{SET, m} for which v is smaller than T, discard the other combinations and set mm_old1, where m_old is m from the preceding step;

[0095] Step 5: If m<M then go to Step 3, else go to step 6,

[0096] Step 6: Calculate the lengths of the new vectors v given by

[0097] Step 7: the detection signal x_DET is determined as that combination of values x_DETx^p_{SET, 1}, x^p_{SET, M} which corresponds to the vector v with the smallest length,

[0098] wherein v_old is one of the vectors v resulting from step 3. The principle of this algorithm can also be illustrated with FIG. 5. The relevant parameters in the example of FIG. 5 are M2, N1, C2. After the first Step the 4 vectors v result, the lengths of these vector are given with (XXIII). Also a pre-determined threshold value T₁ 46 which is applied in Step 2 is presented in the FIG. 5. As a result of the threshold T₁ 46 the branch rh₁*j (corresponding to v1 and v3 in (XXIII)) is discarded in the subsequent Steps. This means that only the lengths of the vectors v2 and v4 are calculated in Step 3 of the algorithm. Hereafter the threshold T₁ 46 is adjusted to the new threshold value T₂ 48 for the next Step 4. Next, the Steps 4 and 5 are performed, which includes the selection of the smallest vectors v, after which the algorithm jumps to Step 6. Step 6 selects the Maximum Likelihood detection signal between the two left test signals x²_SET and x⁴_SET. The Maximum Likelihood solution appears to be x_DETx⁴_SET.

[0099] The embodiments of the wireless data communication system comprising the Reduced Search Techniques as described hereinbefore can also be applied with a modification for providing a further reduction in processing time. According to this modification a factor C less test vectors in the test set have to be checked out in equation (I). In said modification the signal processing-unit is arranged to find, in use, the detection signal x_DET according to a Reduced Search Technique which also comprises the following steps:

[0100] Step A1: calculate an inner product z of the vector r with the u^th column h_u of the matrix H, where u is an integer 1<uM, according to:

[0101] where h*_u is the complex conjugated and transposed of h_u;

[0102] Step A2: calculate C^{M 1} terms lnterf corresponding to all possible value combinations which can be assigned to x₁, . . . , xx_u1, x_u1, . . . , x_M, wherein the terms Interf are defined according to: $\begin{array}{cc}\mathrm{Interf}=\underset{\left(i=1,,Miu\right)}{}{x}_i*\left(h_u^{*}*h_i\right),& \left(\mathrm{XXIX}\right)\end{array}$

[0103] wherein _{(i1, . . . ,Miu)} is a summation over the index i from 1 to M with the exception of the integer u;

[0104] Step A3: estimate, on the basis of the equations (XXVIII), (XXIX) and z according to:

[0105] where z is an approximation of z, the value for x_u corresponding to each of the value combinations x₁, . . . , x_u1, x_u1, . . . , x_M, and constitute a test set X_SET comprising C^M1 vectors x^p_SET, wherein each vector x^p_SET represents a value combination x₁, . . . , X_u1, x_u, x_u1, . . . , x_M;

[0106] Step A4: determine the detection signal X_DET according to equation (A), wherein the test set is defined with the C^M1 vectors x^p_SET from the preceding step. The approximation (XXX) is based on the assumption that the noise n can be neglected.

[0107] In accordance with the provisions of the patent statutes, the present invention has been described in what is considered to represent its preferred embodiments. However, it should be noted that the invention can be practised otherwise than as specifically illustrated and described without departing from its spirit or scope. For example, the wireless data communication system according to the invention can be used not only for simplex communication (from the second groups to the first groups) but also for duplex data communication (from the second groups to the first groups and vice versa). In the latter case the communication from the first groups to the second groups may or may not be arranged in such a way as to obtain a multiple of simultaneous data communication channels.