Beamforming for non-collaborative, space division multiple access systems

Abstract

A wireless communication system non-collaborative, multiple input, multiple output (MIMO) space division multiple access (SDMA) system determines subscriber station combining and weighting vectors that yield a high average signal-to-interference plus noise ratio (SINR). Each subscriber station independently transmits information to a base station that allows the base station to determine a weight vector w.sub.i for each subscriber station using the determined combining vector of the subscriber station. The i.sup.th combining vector corresponds to a right singular vector corresponding to a maximum singular value of a channel matrix between a base station and the i.sup.th subscriber station. Each subscriber station transmits signals using a weight vector v.sub.i, which corresponds to a left singular vector corresponding to a maximum singular value of a channel matrix between the i.sup.th subscriber station and the base station. The base station uses the weight vector w.sub.i to determine the signal transmitted by the i.sup.th subscriber station.

Claims

1. A method for operating a user equipment (UE) device that includes a plurality of UE antennas, the method comprising: receiving downlink pilot signals from a base station; determining, based on the pilot signals, a combining vector for receiving signals from the base station through the plurality of UE antennas, wherein individual components of the combining vector respectively correspond to the plurality of UE antennas; transmitting a known pilot sequence to the base station using the determined combining vector; receiving, through the plurality of UE antennas, a communication signal from the base station after transmitting the known pilot sequence; and determining using the combining vector, the data carried in the received communication signal.

2. The method of claim 1, further comprising: receiving channel output symbols from respective UE antennas of the plurality of UE antennas in response to a transmission of channel input symbols by the base station; and recovering an estimate of a data signal by weighting the channel output symbols from the respective UE antennas of the plurality of UE antennas with respectively corresponding components of the combining vector.

3. The method of claim 1, wherein the combining vector is determined based on an estimate of the channel using the pilot signals from the base station.

4. The method of claim 1, wherein the base station is configured to weight a data signal using a weighting vector in order to determine channel input symbols received by the UE device.

5. The method of claim 4, wherein the weighting vector is based on the known pilot sequence sent to the base station using the determined combining vector.

6. The method of claim 5, wherein the weighting vector is further based on uplink transmissions from one or more additional UE devices.

7. The method of claim 1, wherein the combining vector is a selected right singular vector of a channel estimate, wherein selected right singular vector corresponds to a maximal singular value of the channel estimate.

8. A user equipment (UE) device comprising: a plurality of UE antennas; and a transceiver coupled to the UE antennas and configured to: receive downlink pilot signals from a base station; determine, based on the pilot signals, a combining vector for receiving signals from the base station through the plurality of UE antennas, wherein individual components of the combining vector respectively correspond to the plurality of UE antennas; transmit a known pilot sequence to the base station using the determined combining vector; receive, through the plurality of LTE antennas, a communication signal from the base station after transmitting the known pilot sequence; and determine, using the combining vector, the data carried in the received communication signal.

9. The UE device of claim 8, wherein the ransceiver is further configured to: receive channel output symbols from respective UE antennas of the plurality of UE antennas in response to a transmission of channel input symbols by the base station; and recover an estimate of a data signal by weighting the channel output symbols from the respective UE antennas of the plurality of UE antennas with respectively corresponding components of the combining vector.

10. The UE device of claim 8, wherein the transceiver is further configured to determine the combining vector based on an estimate of the channel using the pilot signals from the base station.

11. The UE device of claim 8, wherein the base station is configured to weight a data signal using a weighting vector in order to determine channel input symbols received by the UE device.

12. The UE device of claim 11, wherein the weighting vector is based on the known pilot sequence sent to the base station using the determined combining vector.

13. The UE device of claim 12, wherein the weighting vector is further based on uplink transmissions from one or more additional UE devices.

14. The UE device of claim 8, wherein the combining vector is a selected right singular vector of a channel estimate, wherein selected right singular vector corresponds to a maximal singular value of the channel estimate.

15. A non-transitory memory medium for operating a user equipment (UE) device that includes a plurality of UE antennas, wherein the memory medium stores program instructions, wherein the program instructions, when executed by a processor, cause the UE device to implement: receiving downlink pilot signals from a base station; determining, based on the pilot signals, a combining vector for receiving signals from the base station through the plurality of UE antennas, wherein individual components of the combining vector respectively correspond to the plurality of UE antennas; transmitting a known pilot sequence to the base station using the determined combining vector; receiving, through the plurality of UE antennas, a communication signal from the base station after transmitting the known pilot sequence; and determining, using the combining vector, the data carried in the received communication signal.

16. The memory medium of claim 15, wherein the program instructions, when executed by the processor, further cause the UE device to implement: receiving channel output symbols from respective UE antennas of the plurality of UE antennas in response to a transmission of channel input symbols by the base station; and recovering an estimate of a data signal by weighting the channel output symbols from the respective UE antennas of the plurality of UE antennas with respectively corresponding components of the combining vector.

17. The memory medium of claim 15, wherein the combining vector is determined based on an estimate of the channel using the pilot signals from the base station.

18. The memory medium of claim 15, wherein the base station is configured to weight a data signal using a weighting vector in order to determine channel input symbols received by the UE device.

19. The memory medium of claim 18, wherein the weighting vector is based on the known pilot sequence sent to the base station using the determined combining vector, and wherein the weighting vector is further based on uplink transmissions from one or more additional UE devices.

20. The memory medium of claim 15, wherein the combining vector is a selected right singular vector of a channel estimate, wherein selected right singular vector corresponds to a maximal singular value of the channel estimate.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention may be better understood, and its numerous objects, features and advantages made apparent to those skilled in the art by referencing the accompanying drawings. The use of the same reference number throughout the several figures designates a like or similar element.

(2) FIG. 1 (labeled prior art) depicts a wireless communication system that employs SDMA.

(3) FIG. 2 (labeled prior art) depicts a base station and subscriber stations in an SDMA, MIMO wireless communication system.

(4) FIG. 3 depicts a wireless communication system with a base station and subscriber stations.

(5) FIG. 4 depicts an embodiment of the wireless communication system in FIG. 3.

(6) FIG. 5 depicts a non-collaborative, SDMA-MIMO downlink communication process.

(7) FIG. 6 depicts a non-collaborative, SDMA-MIMO uplink communication process.

(8) FIG. 7 depicts a simulated comparison of the wireless system in FIG. 4 and conventional systems.

(9) FIG. 8 depicts a simulated comparison of the wireless system in FIG. 4 and conventional systems in the presence of statistical interference.

DETAILED DESCRIPTION

(10) A wireless communication system non-collaborative, multiple input, multiple output (MIMO) space division multiple access (SDMA) system determines subscriber station combining and weighting vectors that yield a high average signal-to-interference plus noise ratio (SINR). Each subscriber station independently transmits information to a base station that allows the base station to determine a weight vector w.sub.i for each subscriber station using the determined combining vector of the subscriber station. In at least one embodiment, the i.sup.th combining vector from the i.sup.th subscriber station is derived from or is generated to be substantially equivalent to a right singular vector corresponding to a maximum singular value of a channel matrix between a base station and the i.sup.th subscriber station. Each subscriber station transmits signals using a weight vector v.sub.i, and the weight vector v.sub.i is derived from or is generated to be substantially equivalent to a left singular vector corresponding to a maximum singular value of a channel matrix between the i.sup.th subscriber station and the base station. The base station uses the weight vector w.sub.i to determine the signal transmitted by the i.sup.th subscriber station. In at least one embodiment, a resulting signal-to-interference plus noise (SINR) improvement results.

(11) A channel matrix H.sub.i specifies the transmission channel gain between a transmitter and an i.sup.th receiver. In a non-collaborative, SDMA-MIMO system determining a combining vector v.sub.i in a receiver that corresponds to a right singular vector corresponding to a substantially maximal singular value of channel matrix Hi, and using the combining vector v.sub.i to determine the weight vector used to transmit signals to the receiver can improve the average SINR of the signals.

(12) FIG. 3 depicts a wireless communication system 300 with a base station 302 and m subscriber stations 304.1 through 304.m. The wireless communication system 300 is a non-collaborative, MIMO-SDMA system. Thus, each base station 302 includes an array of multiple antennas for communicating with the subscriber stations 304.1 through 304.m, and each subscriber station includes respective antenna arrays for communicating with the base station 302. The number of antennas in the antenna arrays is station dependent. Preferably, the base station 302 includes at least as many antennas as the number of subscriber stations.

(13) In at least one embodiment of wireless communication system 300, all of the m subscriber stations 304 include an independent combining vector v determination module 306 that independently determines respective combining vectors from an associated channel matrix H. In other embodiments, a subset of the m subscriber stations includes the independent combining vector v determination module 306. The i.sup.th subscriber station 304.i in wireless communication system 300 determines a combining vector v.sub.i from the channel matrix H.sub.i independently, without reference to any channel or weighting information from any other subscriber station, base station, or any other external data source. The subscriber station 304.i transmits information to the base station 302 that allows the base station to generate a weighting vector w.sub.i for use in transmitting signal si to the subscriber station 304.i. The information transmitted to the base station 302 can be any information that allows the base station 302 to obtain or derive the combining vector v.sub.i and to generate the weighting vector w.sub.i. For example, when the same channel matrix is used to transmit and receive, such as in a time division duplex (TDD) system, the subscriber station 304.i can transmit the combining vector v.sub.i. The base station receives H.sub.iv.sub.i, and, knowing H.sub.i, can derive the combining vector v.sub.i and determine weighting vector w.sub.i.

(14) In another embodiment, the channel matrices used for transmitting and receiving are different (e.g. H.sub.iT and H.sub.iR, from the i.sup.th subscriber station's perspective), such as in a frequency division duplex (FDD) system. For the subscriber station 304.i to receive and the base station 302 to transmit, the subscriber station 304.i can, for example, feed back the combining vector v.sub.i and channel matrix Ha either separately or as a product to the base station 302. In at least one embodiment, the base station 302 can estimate the channel matrix H.sub.iT when the subscriber station 304.i transmits the product H.sub.iT•v.sub.i and/or the subscriber station 304.i transmits a known pilot sequence using vector v.sub.i. The base station 302 receives v.sub.i and channel matrix H.sub.iR, either separately or as a product, and, thus, can determine the combining vector w.sub.i. In another embodiment, codes can be used to identify predetermined combining vectors. In at least one embodiment, the independent determination of the combining vector v.sub.i and subsequent determination of the base station weight vector w.sub.i using the combining vector v.sub.i result in an optimal average SINR over a period of time.

(15) FIG. 4 depicts an embodiment of wireless communication system 300 in more detail. The wireless communication system 400 includes a base station 402 with an antenna array 406 of N antennas. The wireless communication system 400 also includes m different subscriber stations 404.1 through 404.m, each with an antenna array 408.1 through 408.m. The number of antennas in each subscriber station antenna array can vary between subscriber stations. The MIMO channel from the base station 402 to the ith subscriber station 404.i is denoted by H.sub.i, i∈{1, 2, . . . , m}. The channel matrix H.sub.i is an N×k matrix of complex entries representing the complex coefficients of the transmission channel between each transmit-receive antenna pair, where N represents the number of base station 402 antennas, and k represents the number of antennas of the i.sup.th subscriber station.

(16) A non-collaborative, SDMA-MIMO communication process between base station 402 and subscriber stations 404.1 through 404.m can be conceptually separated into an uplink process and a downlink process. In a downlink process, the base station 402 is the transmitter, N equals the number of antennas used for transmitting on the base station 402, and k.sub.i represents the number of antennas of the i.sup.th subscriber station 404.1 used to receive the transmitted signal. In an uplink process, the subscriber station 404.i is the transmitter, and the base station 402 is the receiver.

(17) In a downlink process, the vector v.sub.i determination module 410.i determines a combining vector v.sub.i for combining the signals received by each of the k antennas of subscriber station 404.i. The coefficients of vector y.sub.i represent each of the signals received by each of the k.sub.i antennas of subscriber station 404.i. In an uplink process, the vector v.sub.i determination module 410.i also determines a beamforming weighting vector v.sub.i for transmitting a signal from subscriber station 404.i to base station 402. In at least one embodiment, base station 402 and each of subscriber stations 404.1-404.m include a processor, software executed by the processor, and other hardware that allow the processes used for communication and any other functions performed by base station 402 and each of subscriber stations 404.1-404.m.

(18) The uplink channel and the downlink channel may be the same or different depending upon the choice of communication scheme. For example, the uplink and downlink channels are the same for time division duplex (TDD) communication schemes and different for frequency division duplex (FDD) schemes.

(19) FIG. 5 depicts a non-collaborative, SDMA-MIMO downlink communication process 500 that represents one embodiment of a downlink communication process between base station 402 and subscriber stations 404.1 through 404.m. Referring to FIGS. 4 and 5, in operation 502, the base station 402 transmits a pilot signal to each of subscriber stations 404.1-404.m. After reception of the pilot signal by the subscriber stations 404.1-404.m, using a pilot-based channel estimation technique, subscriber stations 404.1-404.m can respectively estimate channel matrices Ĥ.sub.l through Ĥ.sub.m, where the “^” symbol indicates an estimated value. Pilot-based channel estimation techniques are well-known in the art.

(20) In operation 506, for all i, vector v.sub.i determination module 410.i of the i.sup.th subscriber station 404.i uses the estimated channel matrix Ĥ.sub.i to determine a combining vector v.sub.i, i∈{1, 2, . . . , m}. At least in the absence of interference generated by sources other than base station 402 and subscriber stations 404.1-404.m (“external noise interference”), the combining vector v.sub.i corresponds to the right singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i . The right singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i can be determined from the maximum singular value decomposition of channel matrix Ĥ.sub.i . In at least one embodiment, the combining vector v.sub.i equals the right singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i as indicated in Equation [4]:
v.sub.i=v.sub.SVD(rt)=SV.sub.max(Ĥ.sub.i)right   [4].

(21) The singular value decomposition of matrix Ĥ.sub.i is determined using Equation [5]:
Ĥ.sub.i=UDV.sup.H   [5].
where the N×k matrix D is a diagonal matrix that contains singular values on the diagonal and zeros off the diagonal, the matrix U is an N×N unitary matrix, and the matrix V is k.sub.i×k.sub.i unitary matrix whose columns are the right singular vectors for the corresponding singular value in matrix D.

(22) Thus, in accordance with Equations [4] and [5], the combining vector v.sub.i is the vector from the column in V corresponding to the maximum diagonal value in matrix D.

(23) In at least one embodiment, the i.sup.th combining vector from the i.sup.th subscriber station is derived from or is generated to be substantially equivalent to a right singular vector corresponding to a maximum singular value of a channel matrix between a base station and the i.sup.th subscriber station. The combining vector v.sub.i corresponding to the right singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i can be determined using other processes. For example, the combining vector v.sub.i corresponding to the right singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i could be determined from the right singular vector corresponding to a non-maximal singular value of the estimated channel matrix Ĥ.sub.i and using one or more factors to modify the result to at least substantially obtain v.sub.SVD(rt).

(24) In at least one embodiment, the i.sup.th combining vector is designed in an environment where the channels H.sub.i, i∈{1, 2, . . . , m}, between the base station 402 and each subscriber station 404 are statistically independent of one another. This statistical independence represents the general case since any time the base station 402 would not select subscriber stations to share an SDMA burst profile if there is insufficient channel separation between the subscriber stations.

(25) When external, statistical interference is present, the choice of the combining vector that will yield an improved SINR is determined using a comparison of the SINR from at least two combining vectors. In at least one embodiment, external statistical interference refers to interference whose characteristics can be estimated statistically. In the presence of external, statistical interference, the i.sup.th receiving subscriber station uses available information about the interference to determine the combining vector v.sub.i. The vector v.sub.i determination module 410.i determines which combining vector provides the best SINR. In at least one embodiment, two types of interference are considered. The first type is instantaneous interference with an instantaneous interference measure b.sub.I. The instantaneous interference measure b.sub.I is a k×1 vector with the j.sup.th entry in the bi representing instantaneous, external noise on the j.sup.th antenna j∈{1, 2, . . . , k}. The second type of interference is statistical interference with an average, external interference represented by a zero mean with covariance matrix R.sub.I.

(26) In at least one embodiment, vector v.sub.i determination module 410.i chooses v.sub.i=v.sub.SVD as defined by Equation [4] during at least a first period of time and chooses v.sub.i=v.sub.null(I or S) during at least a second period of time depending upon whether v.sub.SVD or v.sub.nullI provide a better SINR, wherein the subscripts “I” and “S” respectively signify vectors determined for instantaneous and statistical interference. For instantaneous interference, for C>0v.sub.i=v.sub.nullI, and otherwise v.sub.i=v.sub.SVD, where C for instantaneous interference is defined in at least one embodiment by Equation [6]:

(27) $\begin{array}{cc}C={.Math.H_1{v}_{\mathrm{nullI}}.Math.}^2-\frac{{\sigma }_n^2}{{\sigma }_n^2+\frac{1}{k}{.Math.b_I.Math.}^2}{.Math.H_1{v}_{\mathrm{SVD}}.Math.}^2,& \left[6\right]\end{array}$
where:
T.sup.H=Null(b.sub.I);
v.sub.nullI=T.Math.SV.sub.max (T.sup.HH.sub.1.sup.HH.sub.1T);
v.sub.SVDSV.sub.max(H.sub.i); and
σ.sub.n.sup.2 represents noise variance measured during a time of no transmission.
T.sup.H equals the complex conjugate of the null space of vector b.sub.I. Vector b.sub.I is an N dimensional vector representing instantaneous interference. The null space of matrix T is, thus, the set of N-1 vectors which satisfy T.sup.Hb.sub.I=0.

(28) The left entry on the right hand side of Equation [6] represents the signal-to-noise ratio (SNR) obtained using v.sub.nullI, and the right entry represents the SNR obtained using vector v.sub.SVD.

(29) For statistical interference, for C>0 v.sub.i=v.sub.nullS, and otherwise v.sub.i=v.sub.SVD, where C for statistical interference is defined in at least one embodiment by Equation [7]:

(30) $\begin{array}{cc}C={.Math.H_1{v}_{\mathrm{nullS}}.Math.}^2-\frac{{\sigma }_n^2}{{\sigma }_n^2+\frac{1}{k}{.Math.\mathrm{tr}\left(R_I\right).Math.}^2}{.Math.H_1{v}_{\mathrm{SVD}}.Math.}^2;& \left[7\right]\end{array}$
where:
.sub.T=T=R.sub.I.sup.1/2=UΣ.sup.1/2;
v.sub.nullI=T.Math.SV.sub.max(T.sup.HH.sub.1.sup.HH.sub.1T);
v.sub.SVD=SV.sub.max(H.sub.i); R.sub.I=R.sub.I=UΣU.sup.H, which is the eigen value decomposition of covariance matrix R.sup.I, and covariance matrix R.sub.I represents statistical interference, zero mean,
R.sub.I.sup.1/2=UΣ.sup.1/2, tr(RI) is the trace matrix of matrix RI, and σ.sub.n.sup.2 represents noise variance measured during a time of no transmission.

(31) The left entry on the right hand side of Equation [7] represents the signal-to-noise ratio (SNR) of vector v.sub.nullS, and the right entry represents the SNR of vector v.sub.SVD.

(32) In operation 508, once the combining vector v.sub.i is determined, the subscriber station 404.i transmits information to the base station 402 that allows the base station 402 to generate a weight vector w.sub.i that is complimentary to the combining vector v.sub.i and, thus, at least in the absence of external interference, provides a SINR improvement over conventional systems. As described above, in at least one embodiment, when the same channel matrix H is used to transmit and receive, such as in a TDD system, the subscriber station 404.i transmits the combining vector v.sub.i o the base station 404 via channel H.sub.i. The base station receives H.sub.iv.sub.i, and, knowing H.sub.i, can derive the combining vector v.sub.i and determine a complimentary weighting vector w.sub.i as subsequently described. In another embodiment, when the channel matrices used for transmitting and receiving are different (e.g. H.sub.iT and H.sub.iR, from the i.sup.th subscriber station's perspective), such as in an FDD system, in at least one embodiment, the subscriber station 304.i can transmit the combining vector v.sub.i and channel matrix H.sub.iR. The base station 302 receives H.sub.iTH.sub.i/Rv.sub.i, and, thus, can determine the combining vector w.sub.i from H.sub.iTH.sub.i/Rv.sub.i. In another embodiment of FDD, the base station 302 can determine an estimate of the channel matrix H.sub.iR and H.sub.iT in for example, a well-known manner, and the subscriber station 304.i transmits only the combining vector v.sub.i. The base station 302 can then determine the combining vector from H.sub.iTv.sub.i. In another embodiment, codes correlated to a set of predetermined combining vectors or codes representing the combining vector v.sub.i can be used to determine combining vector v.sub.i. In a non-collaborative system, the vector v.sub.i determination module 410.i determines the i.sup.th combining vector v.sub.i independently of the weight vector w.sub.i of base station 402 and independently of the combining vectors of any other subscriber station.

(33) In operation 510, the base station 402 determines the transmit beamforming weight vector w.sub.i that is complimentary to combining vector v.sub.i. The base station 402 determines the weight vector w.sub.i with the goal of eliminating cross-channel interference. In a normalized context, the cross-channel interference can be eliminated by designing the complimentary weight vector w.sub.i using combining vector v.sub.i in accordance with Equation [8]:

(34) $\begin{array}{cc}{w}_i^H{H}_j{v}_j=\{\begin{array}{cc}1& \mathrm{If}i=j\\ 0& \mathrm{If}i\ne j\end{array}.& \left[8\right]\end{array}$
In at least one embodiment, the weight vector w.sub.i is complimentary to combining vector v.sub.i when Equation [8] is satisfied.

(35) The method used in operation 510 to determine the weight vector w.sub.i, and, thus, spatially separate the subscriber stations 404.1-404.m is a matter of design choice. In at least one embodiment, the linearly constrained minimum variance (LCMV) algorithm is employed at the base station 404 to determine complimentary weight vector w.sub.i.

(36) Following is a general description of application of the LCMV applied in at least one embodiment of operation 510 to determine the weight vector w.sub.i using the combining vector v.sub.i from subscriber station 404.i. The base station 402 has N antennas and transmits to m subscriber stations 404 where, preferably, m≤N. The complex vector channels seen by the base station 402 to each of the m subscriber stations 404 are represented by h.sub.1, h.sub.2, . . . , h.sub.m, where h.sub.i=Ĥ.sub.iv.sub.i, and X =[h.sub.1, h.sub.2, . . . , h.sub.m].

(37) A general goal of an SDMA-MIMO communication system is to design a set of m, N-dimensional beamforming vectors w.sub.i, i∈{1, 2, . . . , m} corresponding to each subscriber station 404 so that the transmission to one subscriber station has minimal interference with transmission to other subscriber stations while achieving a specified gain to the intended recipient subscriber station. For the sake of simplicity, assume that the specified gain of a signal intended for a subscriber station is unity and that the gains to other subscriber stations are zero to ensure no intra-system interference. Then the design constraint for the weight vectors can be specified in accordance with Equation [9]:
X.sup.HW=D   [9]
where D=Im, Im is an m×m identity matrix, and
W=[w.sub.1, w.sub.2, . . . , w.sub.m]  [10],
where w.sub.i, i∈{1, 2, . . . , m}, represents the weight vector used for beamforming transmission to the i.sup.th subscriber station 404.i. Equation [9] can be posed as an LCMV problem in the following manner:

(38) $\begin{array}{cc}{w}_i=\arg \underset{w}{\min }\left(w^{H}w\right)& \left[11\right]\end{array}$
such that:
X.sup.Hw=e.sub.i   [12]
where e.sub.i is the all-zero column vector except for the i.sup.th entry which is equal to one.

(39) The LCMV solution solves a least squares problem which is the minimum transmit power solution for the signal transmitted to subscriber station 404.i while meeting the given gain and interference constraints. Another way to view the LCMV solution is to look at the signal-to-noise ratio (SNR) obtained with unit (normalized) transmit power. If the signal power is 6.sub.s.sup.2 and the noise power is σ.sub.n.sup.2, the SNR obtained for subscriber station 404.i for weight vector w.sub.i is given by:

(40) $\begin{array}{cc}{\mathrm{SNR}}_i=\frac{1}{w_i^H{w}_i}\frac{{\sigma }_s^2}{{\sigma }_n^2}.& \left[13\right]\end{array}$

(41) The LCMV solution maximizes the SNRT that can be obtained by subscriber station 404.i with a fixed transmit power (normalized to one (1) in this case) under the given constraints. In at least one embodiment, differential gains/SNR to different subscriber stations can be ensured by setting different values for the elements of the diagonal matrix D in Equation [9].

(42) In at least one embodiment of operation 512, the base station 402 transmits m different signals to the m subscriber stations 404.1-404.m on the same time-frequency channel. The modulated data to be transmitted to subscriber station 404.i is denoted by si. Each of the m signals si through sm are transmitted through all the N base station 402 antennas 408 using unique complex antenna weights w.sub.1 through w.sub.m. In at least one embodiment, the actual signal transmitted on each base station 402 antenna is a superposition of vectors x.sub.1 through x.sub.m, where x.sub.i=s.sub.iw.sub.i and i∈{1, 2, . . . , m}.

(43) Subscriber station 404.1 has ki antennas in antenna array 406.1. In operation 514, the subscriber station 404.1 receives signal vector yi. In at least one embodiment, for subscribers station 404.1, signal vector y.sub.1 is defined by Equation [14]:

(44) $\begin{array}{cc}{y}_1=s_1{\hat{H}}_1^H{w}_1+\underset{i=2}{\overset{m}{.Math.}}{s}_i{\hat{H}}_1^H{w}_i+n,& \left[14\right]\end{array}$

(45) where “sl” the data to be transmitted to subscriber station 404.1, “Ĥ.sub.1.sup.H” represents the complex conjugate of the estimated channel matrix Ĥ.sub.1, w.sub.i is the ith beamforming, N dimensional weighting vector, and the vector n represents external noise interference for i∈{1, 2, . . . , m}. The superscript “H” is used herein to represent a complex conjugate operator. The jth element of the received signal vector yi represents the signal received on the jth antenna of subscriber station 404.i, j∈{1, 2, . . . , k}. Equation [14] can be used for all yi by letting the first term on the right hand side of RHS of Equation [14] be the desired receive signal while the summation terms represent co-channel interference.

(46) The subscriber station 404.i then weights and sums the receive signal vector y.sub.i using the combining vector v.sub.i used by base station 402 to generate w.sub.i to determine the desired output data signal z.sub.i, which is an estimate of the transmitted data signal s.sub.i, in accordance with Equation [15]:
Z.sub.i=Ŝ.sub.i=v.sub.i.sup.Hy.sub.i   [15].

(47) FIG. 6 depicts a non-collaborative, SDMA-MIMO uplink communication process 600 that represents one embodiment of an uplink communication process between base station 402 and subscriber stations 404.1 through 404.m. In operation 602, the base station determines an estimate of the uplink channel matrix Ĥ.sub.1 if the uplink channel matrix Ĥ.sub.1 is not already known to the base station 402. In some communication processes, such as the TDD process, the estimated uplink channel matrix Ĥ.sub.1 corresponds directly to the estimated downlink channel matrix Ĥ.sub.i . If the base station 402 does not know the uplink channel process, in one embodiment, operation 602 determines uplink channel matrix Ĥ.sub.1 in the same manner as operation 502 except that the roles of the subscriber stations 404.1-404.m and the base station 402 are reversed.

(48) In operation 604, during transmission by subscriber station 404.i, vector v.sub.i determination module 410.i determines a weight vector v.sub.i. The weight vector v.sub.i corresponds to the left singular vector corresponding to the maximal singular value of the k.sub.i×N estimated uplink channel matrix Ĥ.sub.i as indicated by Equation [16]:
v.sub.i=v.sub.SVD(left)=SV.sub.max({circumflex over (H)}.sub.i).sub.left   [16].

(49) The singular value decomposition of matrix H.sub.i is determined using Equation [17]:
Ĥ.sub.i=UDV.sup.H   [17].
where the N×k.sub.i matrix D is a diagonal matrix that contains singular values on the diagonal and zeros off the diagonal, the matrix U is an N×N unitary matrix whose columns are the left singular vectors for the corresponding singular value in matrix D, and the matrix V is a k.sub.i×k.sub.i unitary matrix.

(50) Thus, in accordance with Equations [16] and [17], the weight vector v.sub.i is the vector from the column in U corresponding to the maximum diagonal value in matrix D.

(51) In at least one embodiment, the i.sup.th weighting vector from the i.sup.th subscriber station is derived from or is generated to be substantially equivalent to a left singular vector corresponding to a maximum singular value of a channel matrix between a base station and the i.sup.th subscriber station. In at least one embodiment, the weight vector v.sub.i corresponding to the left singular vector corresponding to the maximal singular value of the estimated channel matrix Ĥ.sub.i can be determined using other processes. For example, the weight vector v.sub.i corresponding to the left singular vector corresponding to the maximal singular value of the estimated channel matrix H.sub.i could be determined from the left singular vector corresponding to a non-maximal singular value of the estimated channel matrix H.sub.i and using one or more factors to modify the result to at least substantially obtain v.sub.SVD(left).

(52) In operation 606, subscriber station 404.i sends a signal s.sub.iv.sub.i to base station 402.

(53) In operation 518 for TDD, the base station estimates 5, using weight vector w.sub.i, which is the same as the weight vector w.sub.i used during the downlink process, Assuming that the received signal is the vector v.sub.i, signal vector v.sub.i is defined by Equation [18]:

(54) $\begin{array}{cc}\underset{\_}{y_1}=s_1\underset{\_}{{\hat{H}}_1^H{v}_1}+\underset{i=2}{\overset{m}{.Math.}}{s}_i\underset{\_}{{\hat{H}}_1^H{v}_n}+n;& \left[18\right]\end{array}$

(55) where “s.sub.1” the data to be transmitted to base station 402, “Ĥ.sub.i.sup.H” represents the complex conjugate of the estimated channel matrix Ĥ.sub.i, v.sub.i is the beamforming weight vector of subscriber station 404.1 i.sup.th beamforming, N dimensional weighting vector, and n represents external noise interference for i∈{1, 2, . . . , m}. The superscript “H” is used herein to represent a complex conjugate operator. The j.sup.th element of the received signal vector v.sub.i represents the signal received on the j.sup.th antenna of base station, j∈{1, 2, . . . , N}. The first term on the right hand side of RHS of Equation [14] is the desired receive signal while the summation terms represent co-channel interference.

(56) In operation 608, the base station 404 then weights and sums the receive signal vector v.sub.i using the weight vector w.sub.i form the desired output data signal, z.sub.i, that estimates the transmitted signal 5, in accordance with Equation [15]:
z.sub.i=ŝ.sub.i=w.sub.i.sup.Hy.sub.i  [19].

(57) FIG. 7 depicts a simulated comparison 700 between wireless communication in wireless communication system 400 using non-collaborative, SDMA-MIMO communication process 500 and conventional maximal ratio combining (MRC) processes. For the simulation, the number of base station transmit antennas N=5, and, for each subscriber station, the number of receive antennas k=2. The results are shown for a variable number of subscriber stations. The curve 702 depicts the SNR achieved using non-collaborative, SDMA-MIMO communication process 500. The curve 704 depicts the SNR achieved using MRC, and the curve 707 depicts the SNR achieved using MRC with maximum SINR. The curve 702 depicts a 3-4 dB gain when transmitting to multiple subscriber stations.

(58) FIG. 8 depicts a simulated comparison 800 between wireless communication in wireless communication system 400 when determining v.sub.i in the presence of external statistical interference and conventional maximal ratio combining (MRC) processes. For the simulation, the number of base station transmit antennas N=5, and, for each subscriber station, the number of receive antennas k=2. The results are shown for a variable number of subscriber stations. The curve 702 depicts the SNR achieved using non-collaborative, SDMA-MIMO process of determining v.sub.i in the presence of statistical interference. The curve 804 depicts the SNR achieved using MRC, and the curve 808 depicts the SNR achieved using MRC with maximum SINR. The curve 802 depicts a 3-4 dB gain.

(59) Although the present invention has been described in detail, it should be understood that various changes, substitutions and alterations can be made hereto without departing from the spirit and scope of the invention as defined by the appended claims.