GB2478603A - Linear Multiuser Precoding with Multiple-Receive Antenna Receivers - Google Patents

Abstract

A method for creating a schedule for jointly designing receive combining vectors for the receivers in a MIMO system is described. In a transmitter side of a multiuser minimum square error linear precoding MIMO system comprising a transmitter with plural transmit antennae and a plurality of receivers each with plural receive antennae, the method comprises obtaining channel information for the transmit channels between receiver antennae and transmitter antennae and establishing an order for determining the receiver combining vectors of the receivers by selecting as a next receiver in the order, a receiver that minimally increases the mean square data transmission error, based on the channel information of any receivers previously selected in the order and any unselected receivers. The method further comprises determining receive combining vectors in the established order so as to minimise the mean square error of previously selected receivers. Data signals received at the receivers are combined using the receive combining vector of the receiver.

Description

Linear Multiuser Precoding with Multiple-Receive Antenna Receivers

FIELD OF THE INVENTION

The present invention relates to multiple-in multiple-out (MIMO) linear multiuser precoding for receivers having multiple receive antennae. The present invention moreover relates to creating a schedule for jointly designing receive combining vectors for the receivers in the MIMO system.

BACKGROUND OF THE INVENTION

Figure 1 shows a wireless communication system comprising a base station with M transmit antennae in communicative contact with K users/receivers. Each of the K receivers has Nk (k =1,2,..., K) receiver antennae. The base station sends K data streams simultaneously to K receivers such that each receiver receives one data stream. At the transmitter side, the signal vector s is precoded by a precoder P to produce a transmitted vector x. A linear receive combiner for combining the signals received through multiple receive antennae is provided in each receiver to improve reception quality. Following receiver combination the combined signal is input into a data detector.

The system shown in Figure 1 can be mathematically described in the following form. Let Hk (of size Nk x M) and Ck (of size lx Nk) be the channel matrix and receiver combining vector of receiver k. The effective channel of receiver k as seen by the base station is: bkckHk (1) To keep the noise power unchanged, the norm of the combining vectors are all 1, i.e. IICkI = 1 The effective channel matrix is: h1 11= (2) bx If base station employs a linear minimum mean square error (MMSE) precoding, as disclosed by M. Joham, W. Utschick, and J.A. Nossek, "Linear transmit processing in MIMO communications systems," IEEE Transactions on Signal Processing, vol.53, no.8, pp. 2700-2712, Aug. 2005 and C. B. Peel, B. M. Hochwatd, and A. L. Swindlehurst, "A vector-perturbation technique for near-capacity multiantenna multiuser communication-part I: channel inversion and regularization," IEEE Transactions on Communications, vol.53, no.1, pp. 195-202, Jan. 2005 (the entireties of which are incorporated herein by reference), then the precoding matrix P can be expressed as: (H K P=flIH H+_IMI H (3) ":r) where Etr is the total transmit power, M is an MxM identity matrix and the superscript H denotes a matrix transpose conjugate operation. /3 is a power normalisation factor given by: Eir I I jj.\ (4) tr(F2H H) where:

-H---K

F=H H+-IM (5) Let Y,k be the received signal at antenna i of receiver k. The combined receive signal of receiver k follows: Zk Ck [Y1,k Y2,k YNkk] (6) The linear zero-forcing (ZF) precoder proposed in the above mentioned Joham et at and the Peel et al papers can be obtained by removing the term in equations (3) and (5).

It is desirable to design linear receiver combining vectors Ck for a given set of receivers such that the total distortion, measured by the sum of mean square error (MSE) of all receivers, is minimized. Solutions to this problem are known. A. M. Khachan, A. J. Tenenbaum, and R. S. Adve disclose in "Linear Processing for the Downlirk in Multiuser MIMO Systems with Multiple Data Streams," IEEE International Conference on Communications, 2006. ICC 06, vol.9, no., pp.4113-4118, June 2006 (the entirety of which is incorporated by this reference) a method of jointly design the precoding matrix and receiver combining vectors based on the duality of uplink-downlink channels. Khachan et al show that the receiver combing vectors designed for the downlink (point-to-multipoint communications) can be solved by design receivers' beamformirig in the uplink (multipoint-to-point communications). Khachan et al first compute the virtual uplink transmit beamforming of all receivers. Then receiver combining vectors and transmitter's precoding matrix is derived. The virtual uplink beamforming can be iteratively computed using the alternating optimization algorithm disclosed in S. Serbetli and A. Yener, "Transceiver optimization for multiuser MIMO systems," IEEE Transactions on Signal Processing, vol.52, no.1, pp. 214-226, Jan.

2004. The method proposed by Serbetli requires some optimization tools. Additionally, the iteration process may not give optimal or near optimal solution for a fixed number of iterations.

In some known methods, for example the method disclosed in A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications, Cambridge, U.K.: Cambridge University Press, 2003, the entirety of which is incorporated herein by this reference, the combining vectors are selected by taking the left singular vector corresponding to the dominant singular value of receivers' channel matrices. This method may suffer from significant performance loss since the combining vectors of receivers are not jointly designed.

Another method of exploiting the diversity of multiple receive antennas is antenna selection, as, for example, disclosed by S. Sigdel and W. A. Krzymien in "Simplified Fair Scheduling and Antenna Selection Algorithms for Multi-user MIMO Orthogonal Space-Division Multiplexing Downlink," IEEE Transactions on Vehicular Technology, vol.58, no.3, pp.1329-1344, March 2009, the entirety of which is incorporated herein by this reference. One antenna of receivers is selected using the receiver orthogonality criterion of T. Yoo, A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming," IEEE Journal on Selected Areas in Communications, vol.24, no.3, PP. 528-541, March 2006 (the entirety of which is incorporated by this reference), so that the resulted channel vectors of receivers are more likely orthogonal. This method causes significant performance loss since the received signals of unused receive antennas are wasted.

EP 1 505 741 discloses a MIMO system in which in each receiver an eigenvalue decomposition of the channel matrix of the receiver is performed to determine the characteristics of the transmit channel. Once these characteristics have been determined they are transmitted upstream to the transmitter/base station by each receiver. The transmitter/base station sequentially selects the receivers by selecting, as the next receiver, the receiver for which the transmit channel characteristics is least correlated to the channel characteristics of the remaining unselected channels.

US 2008/0260051 discloses a method for simultaneous data transmission on a plurality of spatial channels. A first channel is selected and a weighted rate metric for this channel is determined. Further channels are only selected if the weighted rate metric for the further channel, when taken in combination with the previously selected channels, is larger than the previously detected rate metric.

EP 1 775 855 discloses another known multi-user multi-antenna system. In this system a conventional scheduler may be used and, based on the receivers selected by this scheduler, transmit filters are calculated and transmitted to the receivers. The receivers use these transmit filters, together with their channel matrix, as receiver filters.

Co-pending UK patent application number 0905588.0 discloses a receiver selection method for multi-user precoding for multiple receivers having one receive antenna each.

SUMMARY OF THE INVENTION

Multiuser precoding is an efficient approach to reach the capacity of multiuser spatial multiplexing of downlink channels. When receivers have multiple receive antennas, the signals of multiple receive antennas can be combined to improve the reception quality. Furthermore, if base station knows the channel matrices of alt receivers, the receiver combining vectors of all receivers can be jointly designed to optimize the system-wide performance.

According to an aspect of the present invention there is provided a method performed in a transmitter side of a multiuser minimum square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae and a plurality of receivers. Each receiver of the plurality of receivers comprises a plurality of receive antennae. The method is a method of scheduling receivers from among the plurality of receivers and comprises obtaining, for some or all of the receivers, receiver channel information that quantifies the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter and establishing an order for determining the receiver combining vectors of the some or all of the receivers. The order is established by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error. The establishing of the order is based on the channel information of any receivers previously selected in the order and of unselected receivers. The number of receivers attempting to participate in data transmission with the transmitter can be lower or equal to the number of data streams that the transmitter is able to support. In this case the method determines the order in which the receiver combining vectors of the receivers are to be determined. If, however, the number of receivers attempting to participate in data transmission with the transmitter is higher than the number of data streams the transmitter is able to support, then the method only selects up to a number of receivers for data communication that corresponds to the maximum number of data streams that the transmitter can support. In both cases the order in which the receiver combining vectors are to be determined to minimise the means square data transmission error is established. In the latter case those receivers that would contribute most to the mean square error may also be automatically excluded from data communication with the transmitter.

A receiver combining vector for a receiver may be calculated after the receiver has been selected as the next receiver in the order and before the next receiver in the order is selected. In this case the determined receiver combining vector can be used in subsequent steps when other receivers are selected as part of the order and/or when the receiver combining vectors for such other receivers are determined.

Alternatively a number of receivers are placed in the order before receiver combining vectors that are to be used in the number of receivers are determined. The order in which all of the receiver combining vectors of selected receivers/of all receivers that can be supported by the transmitter are determined may, for example, be determined before any of the receiver combining vectors that are to be used in the receivers for data transmission are determined.

The above two alternatives are equally viable and may have individual advantages and disadvantages. It may, for example be necessary for the receiver combining vector of a receiver to be known before the next receiver in the order can be determined. In the first alternative, this is not a problem as the receiver combining vectors are determined before a next receiver is allocated its place in the order. If, however, a number or all of the receivers are placed in the order, then approximate receiver combining vectors may need to be used to complete the ordering process before the actual receiver combining vectors that are to be used in the receivers can be determined. It is, for example possible to, prior to determining said order, to determine for each receiver a preliminary receiver combining vector that fulfils C, = mrckHkll wherein Ck corresponds to a plurality of possible receiver combining vectors. The receiver that fulfils this requirement can be identified using singular value decomposition, hereinafter referred to as SVD, of the term in the norm. The preliminary receiver combining vector may be the left singular vector corresponding to the maximum singular value determined in the SVD. Alternatively, the preliminary receiver combining vectors can be determined using eigenvalue decomposition, hereinafter referred to as EVD, in a manner discussed in more detail below.

Having obtained such a preliminary receiver combing vectors, the receivers can, despite the fact that they comprise more than one antenna, be treated as if they were a single antenna receivers. This renders the ordering of the receivers less computationally expensive and was found to introduce only negligible additional contributions to the means square error, if any, The actual receiver combining vectors that are to be used in the receivers, can be determined once the order in which this task is to be completed has been established. A next, -th receiver in the order can be selected such that, when the -th receiver is operated using its associated preliminary receiver combining vector the n-th receiver minimally contributes to the means square data transmission error.

The next, 1-th receiver in the order can be a receiver fulfilling: arg max (i + g (c,Hk)H) Ilg 112 wherein k is an index of unselected receivers in a set, Hk is the channel matrix of receiver k and comprises the said channel information, superscript H denotes a matrix transpose conjugate operation, IgII is the norm of the matrix g, and g is useable for determining the n-th receiver, wherein: --1! g_c k whereinA' is a matrix useable for determining the n-th receiver and including matrices A1 and g, that had been used for the selection of the preceding, (n-1)-th receiver, wherein: A = A1 -g (i + g (ckPHk)H) Returning to a way of selecting receivers for the order in which, once a receiver has been identified as the next receiver in the order, the receiver combining vector is determined before the next, -th receiver is found for the order, and to the way in which a next, 1-th receiver in the order is found, the remaining unselected receivers can be considered as constituting a set L of unselected receivers with indices k The next, 1-th receiver from may be required to have a receiver combining vector Ck that fulfils: CkHkA2H c argmax ki,Hckll=1 Ck (INk + HkA'H' )Ck wherein 11k is the channel matrix of receiver k comprising the said channel information and superscript H denotes a matrix transpose conjugate operation, I is a Nk x Nk identity matrix, wherein Nk is the number of receiver antennae of each receiver, whe rein: A' = A1 -g (1 + g1 (ck "k,, )H)1 g1 wherein A is the matrix K' for the selection of a current, n -th receiver in the order, A, is the matrix A'that has been used for the selection of the preceding, (n-1)-th, receiver in the order, Ck is the receiver combining vector of the (n_i) -th receiver and Hk is the channel matrix of the (n -1) -th receiver, with A' = aIM, wherein M is the number of transmitter antennae of the transmitter, a=K/E,, wherein K is the number of data streams between the transmitter and the receivers and E,,. is the total transmitter power; and g_, = ckHkA It will be appreciated that, for the selection of the first receiver in the order K' -I K' K' a M, as above stated and that this matrix becomes the matrix "-for the selection of the second receiver to the order and that the matrices A C Hk and g_, are updated to refer to those matrices used as current matrices in the immediately preceding selection step.

The next receiver in the order may be identified by performing an EVD of the matrix °k (IN + HkA'H)' HkA2H' for some or all receivers k from among the set A of unselected receivers. The next receiver selected for the order is the receiver for which the maximum eigenvalue of the matrix °k is the largest. The receiver combining vector that is to be used with this receiver is the eigenvector of the matrix °k of the selected receiver that is associated with the largest eigenvalue of the matrix Ok.

The next receiver in the order may alternatively be identified by performing a singular value decomposition of the matrix °k = (IN + HkA'H')' HkK2H', for some or all receivers k from among the set A of unselected receivers. The next, n -th receiver in the order is then the receiver for which the maximal singular value of the matrix °k is the largest. The receiver combining vector that is to be used with this receiver is the singular vector corresponding to the largest singular value of the matrix °k of the selected receiver.

Irrespective of whether EVD or SVD are used, the present methods all allow the determining of a schedule for calculating receiver combining vectors that eliminate the need for iterative optimization of transmitter precoder and receiver combiners, and associated determination steps, as is the case in, for example, the above mentioned Khachan et al paper. In the Khachan et al paper the receiver combing vectors are moreover determined in a random order. This may not always lead to the best results.

The present methods address this problem by scheduling the receiver combining vectors to be determined in a way that minimises mean square data transmission error.

The above methods have other advantages. When compared to, for example, the dominant eigenmode selection technique disclosed in A. Paulraj, R. Nabar, and D. Gore, "Introduction to Space-Time Wireless Communications", Cambridge, U.K., Cambridge University Press, 2003, it can be seen that the present methods allow joint optimisation of the receiver combining vectors, while the dominant eigenmode selection technique the combining vectors are not jointly designed and are merely chosen as the left singular vector corresponding to the largest singular value.

S. Sigdel and W. A. Krzymien, "Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink," IEEE Transactions on Vehicular Technology, vol.58, no.3, pp.1329-1344, March 2009 use only one receive antenna from each receiver. The present methods in contrast use several receiver antennae per receiver and consequently exhibit better performance.

In both of the above (EVD and SVD) ways of receiver selection the steps of selecting the next receiver in the order also yields the final receiver combining vector for the selected receiver. However, to select a single receiver, the number of EVDs/SVDs that need to be performed corresponds to the number of remaining unselected receivers. The inverse of the matrix (IA' + HkA'H) that forms part of the matrix °k may be calculated by calculating N, -INHk(A+HkHk)Hk. The inverse of the matrix (A + H'Hk) required in the latter term may in turn be calculated by matrix update.

The process of calculating the EVD of the matrix °k may alternatively be put to a different use. It is discussed above that the order of the receivers can be determined first before the final receiver combining vectors that are to be used by the receivers are determined. This manner of determining the receiver order, however, relies on the determination of preliminary receiver combining vectors, which (as discussed above) permit treating of the receivers as if they had only a single receive antennae. In the above discussion an SVD based method of determining these preliminary receiver combining vectors is discussed. An alternative manner in which the preliminary receiver combining vectors can be determined may comprise calculating the largest eigenvalue of the matrix °k for each receiver and the associated eigenvector and using the so determined eigenvector as the preliminary receiver combining vector. In this case, A' a'IM for all receivers, as the above discussed matrix updates for the matrix A' cannot be completed in the absence of knowledge of the order in which the receiver combining vectors should be determined to minimise the mean square error.

The receiver combining vectors determined in this instance are, however, preliminary and that the correct receiver combining vectors that are to be used in the receivers will in any case be determined later, as discussed above.

The method may further comprise providing a codebook of possible receiver combining vectors and selecting from among a plurality of possible combinations of receivers with receiver combining vectors from the codebook the combination that increases the mean square data transmission error the least. The receiver combining vectors may thus be limited to a number of receiver combining vectors that are known at the transmitter before receiver channel data is taken into account. The codebook of the transmitter may also be known/stored at the receiver, so that, once a receiver combining vector has been selected as the most suitable for the receiver, it is not necessary for the receiver combining vector to be transmitted to the receiver, Instead, the selected receiver combining vector could simply be identified to the receiver. If the codebook is a matrix, this could, for example, be done by identifying the row or column of the matrix that comprises the selected receiver combining vector by its index. Doing so limits the amount of transmission overhead associated with identifying the receiver combining vector to the receiver.

The codebook can be a codebook matrix C. For each receiver with index k within a set of unselected receivers, the codebook Ccan be multiplied with a channel matrix 1k of the receiver. The channel matrix 1k comprises the channel information and a matrix Hk = CHk is thus formed. The method may further comprise determining the index k of the n -th receiver in the order and the row index j within the matrix 11k that fulfil: ilk (J, :)A2 ilk (j, :) arg max --kEE,j1,...R 1 + Hk (j, :)A' ilk (j, :) wherein R is the number of receiver combining vectors in the codebook matrix C and wherein H denotes a matrix transpose conjugate operation, wherein the matrix A for the selection of the "-th receiver is: A1 = A1 -g1(i+g1i'1)' g1 wherein g1 = hL A1 and hL H (j,,:), wherein H is the matrix H of the (n-1)-th receiver immediately preceding the n-th receiver in the order and j_1the selected row index within this matrix HL.

The codebook may comprise fixed possible receiver combining vectors that remain the same for each of the receivers for which the codebook is used. It is, however, not necessary that the same codebook is used for all of the receivers.

Instead different codebooks, each individually comprising its own fixed possible receiver combining vectors, can be used for different receivers. Each receiver may, for example, be assigned an individual codebook, wherein the assigned codebooks for the receiver differ.

The codebook may also comprise a possible receiver combining vector that can be adapted to the particular receiver for which the codebook is to be used. This adaptive possible receiver combining vector may be the left singular vector corresponding to the dominant singular value determined by a singular value decomposition of a channel matrix comprising the said receiver's channel information.

The adaptive possible receiver combining vector may only form part of the codebook and be present alongside the above mentioned fixed possible receiver combining vectors. It will be appreciated that, if the codebook comprises an adaptive possible receiver combining vector, different codebooks will be used for different receivers.

If it is determined in the transmitter that the adaptive/adapted possible receiver combining vector is the most optimal receiver combining vector, then the receivers are required to perform a singular value decomposition to determine the receiver combining vector.

The above codebook based selection method optimises the selection of combining vectors from a codebook based on the mean square error criterion using either greedy or pre-deterministic search for the best combining vector.

The method of the present invention is of course not limited to simply determining the order in which the receive combining vectors of selected/ordered receivers are to be determined by may also include the determining of the receiver combining vectors for the receivers in the order. The receiver combining vectors may be determined so that the mean square error achieved by the previously selected receivers is only minimally increased by the next receiver in the order, for which the receiver combining vector is being determined. Determining the receiver combining vectors may be based on the channel information and on previously determined receiver combining vectors. The method may further comprise transmitting the receiver combining vectors to the receivers in which they are to be used, transmitting data from the transmitter to the receivers and combining data signals received by the plurality of receive antennae of a receivers using the receive combining vector in the receivers.

Transmitters may comprise means, for example software or hardware means, for computing an SVD of a matrix. These means may be used in their normal use for a purpose different from calculating any of the above mentioned SVD. Such SVD means can, however, routinely be idle and may be used during idle periods to calculate any or all of the above SVDs required for receiver ordering and/or determination of the receiver combining vectors.

According to another aspect of the present invention there is provided a method performed in a transmitter side of a multiuser minimum square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae and a plurality of receivers. Each receiver of the plurality of receivers comprises a plurality of receive antennae. The method is a method of scheduling receivers from among the plurality of receivers and comprises obtaining, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter and establishing an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information of any receivers previously selected in the order and of unselected receivers. The method further comprises determining receive combining vectors for the receivers in the order so as to minimise the mean square error of previously selected receivers. The determining is based on the channel information and takes into account receivers for which receive combining vectors have already been determined.

The above described methods can also comprise transmitting data from the transmitter to the receivers and combining data signals received by the plurality of receive antennae of a receiver using the receive combining vector of the receiver.

According to another aspect of the present invention there is provided an apparatus for scheduling receivers from among a plurality of receivers in a multiuser minimum square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae. Each receiver of the plurality of receivers comprises a plurality of receive antennae. The apparatus comprises a channel estimator arranged to obtain, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter and a scheduler that is arranged to establish an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information.

According to another aspect of the present invention there is provided a multiuser minimum square error linear precoding MIMO system comprising an apparatus for scheduling receivers from among a plurality of receivers in the MIMO system, the MIMO system further comprising a transmitter with a plurality of transmit antennae, wherein each receiver of the plurality of receivers comprises a plurality of receive antennae. The apparatus comprises a channel estimator arranged to obtain, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter and a scheduler that is arranged to establish an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information. The apparatus moreover includes a processor arranged to determine receiver combining vectors for said receivers in the said order in a manner that minimises the mean square error of previously selected receivers. The processor is arranged to base making the determination on the channel information and taking into account receivers for which receiver combirung vectors have already been determined. The MIMO system further comprises a transmitter for transmitting data from the transmitter to the receivers. Wherein the receivers individually comprise combiners that are arranged to combine data signals received by the plurality of receive antennae of a receiver using the receiver combining vector determined by the processor.

The transmitter side of the MIMO system may be a base station, a mobile base station.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described by way of example only and with reference to the accompanying drawings, in which: Figure 1 shows a system model of multiuser linear precoding with multi-antenna receivers; Figure 2 shows a flow chart of a first algorithm according to a preferred embodiment of the present invention; Figure 3 shows a receiver selection algorithm with reduced computational complexity according to an embodiment of the present invention; Figure 4 shows a combination of the two algorithms shown in Figures 2 and 3; Figure 5 shows an alternative, codebook based algorithm according to an embodiment of the present invention; Figure 6 illustrates simulations results of a performance comparison between conventional algorithms and new algorithms introduced herein for a system employs linear MMSE precoding, 4 transmit antennas, 4 receivers, each receiver has 2 receive antennas, wherein 4QAM is used; and Figure 7 shows a comparison of the performances of conventional and new algorithms for a system employing linear MMSE precoding, 4 transmit antennas, 4 receivers, each receiver has 4 receive antennas and 4QAM.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the following a step-by-step general solution to the problem of designing linear receiver combining vectors Ck for a given set of receivers, such that the total distortion, measured by the sum of mean square error (MSE) of all receivers, is minimized, is discussed in the section entitled "General Solution". Following the general discussion two algorithms for reducing the complexity of, and consequently the computational expense associated with, the general algorithm are discussed in the sections entitled "Low-Complexity Matrix Inversion" and "Fast User Ordering".

Alternatives for simplifying the discussed algorithms are then presented in the section entitled "Alternative Implementations" and the use of code books of receiver combining vectors is explored in the section entitled "Codebook-Based Receiver Combining Vectors"

GENERAL SOLUTION

The design criterion used in this solution is to minimize the mean square error (MSE) of the precoder. The MSE can be expressed in the following form: (E --H =tr--HH +IKJ (7) wherein K is a KxK identity matrix.

An alternative form of the MSE can be derived in the following manner. Let a be defined as a = K / E1,. and H UDVH be a singular value decomposition, wherein U and V are unitary matrices and D is a diagonal matrix. It follows that: cv=tr(a'flui" +I,J1 = tr(a1UDIYJUJI +1k) :tr[U(czDD" +1k) u"] (8) a1d2+1 wherein d. is the i -th element of the diagonal matrix D. (The cyclic property of the trace operation, tr(ABC)=ir(CAB), is used to obtain the fourth line of equation (8) above.) To compute MSE a matrix inversion operation needs to be performed repeatedly. However, the computational complexity associated with such an operation is prohibitively high. This problem can be avoided by considering another quantity ç defined as: I -H--\I ,=tra'H H-ElM) tr(a1VDHDVN +IM) tr[V(a1Dh1D+IM) VH] (9) ct1d + 1 =M-K+yi.

Minimizing the MSE cii of the linear MMSE precoder is consequently equivalent to minimizing the quantity q. The objective of designing linear receiver combining vectors Ck for a given set of receivers such that the total distortion, measured as the sum of mean square error (MSE) of all receivers, is minimized can be mathematical stated as: \-1 {c1,c2,...,cK}=arg. inin trH H+czIM) (10) subjectto llckH=1 Vk=1,2,...,K.

It is not believed that the global solution of equation (10) is tractable. In the following a low-complexity near-optimal approach to compute the combining vectors of receivers based on equation (10) is, however, provided. The algorithm disclosed as part of approach proceeds in a step-wise fashion and identifies from among all of the thus far unselected receivers participating in the selection process, in each step, the unselected receiver that minimally increases the MSE of the precoder. In other words, in each step of the selection process one thus far unselected receiver is selected so that the distortion experienced by the already selected receivers and by the newly selected receiver increases by the minimally possible amount.

The algorithm makes use of the matrix inversion lemma, which states that for a nxn positive definite matrix A and a nxl vector a: (A+aa') K' .-A'a(1+a'K'a) a'1A (11) Let ={k1,k2...,k_1} be the set of indices of n-i already selected receivers, whose combining vectors have been computed. Let Hc be the channel matrix containing the effective channels of these receivers: h1 c1H1 -h2 cH 22 (12) hn-i C_1II_1 Let A be A ll Hc + aIM. Let be a set of thus far unselected receivers, whose combining vectors are to be computed. Let a" -hk _ckHk (13) where k e i. Since A is positive definitive, K' is also positive definitive. Equation (11) can be re-written to read: (iiiIQ + hhk + aIM) A -K'h' (i+ hkA hk)1 bkA (14) Using g hkA, equation (14) can be simplified to read: (iII-+fik+aIM)' =K' -1 (15) =A'_(1+gkh) IIgkI The left hand side of equation (15) corresponds to the matrix term of equation (10) that is to be inverted, taking into account all of the previously selected receivers of the set and an additional receiver k. The right hand side of equation (15) can be as a substitute for the matrix term of equation (10) that is required to be inverted, so that those receivers that minimally increase MSE can be found using equation (10) without requiring the matrix inversion on the left hand side of equation (15). Equation (15) also makes it clear that equation (10) can be applied in an iterative fashion.

Using the matrix inversion lemma of equation (11) together with equation (13), equation (10) can be re-written to show that the combining vector of the next receiver k satisfies: 1) . Ac'HHkckA' 1k,c Jarg mn tr A -_____________ kEEC41 I +CkIIkAHkCk (16) CkHkAHk Ck =arg max kE&ck=1 Ck (INk + HkA'H)Ck wherein is a Nk x Nk identity matrix.

Equation (16) forms the basis for two consecutive operations. In a first operation the combining vectors Ck of all remaining receivers of the set are computed. Then the receiver that minimally contributes to the increment of MSE will be selected.

The solution of equation (16) is known in the theory of matrix analysis. For a receiver i e, the best combining vector is the eigenvector corresponding to the largest elgenvalue of the generalized eigenvalue decomposition (EVD). Let Xk=HkA2H (17) 4 +HkAH' (18) using an eigenvalue decomposition of Y1Xk as Y'Xk EkDkE', where Dk is a diagonal matrix comprising the eigenvalues, Dk =diag(d1,d2,...,dk), wherein Nk is the number of unselected receivers, and wherein Ek is a square matrix comprising the eigenvectors. If dkf is the largest eigenvalue of matrix Y'X, the best combining vector of receiver i is: Ck =Ek(:,j)! (19) Additionally, when the combining vector is the one in equation (19), the corresponding eigenvalue can be calculated according to: CkHkAHkCk - (1 II A -111H \ H -k,j (20) Ck1N +Ltk!1 Lik)Ck Equation (20) is used to quickly compute the right hand side of equation (16), which is the selection criterion for the next user.

The general solution of the optimal combining vector for a receiver k is given in equation (19).

Once all maximum eigenvalue of each of the unselected receivers of set L have been determined, they can be compared to each other. The largest elgenvalue out of the maximum eigenvalues that have been determined for the uses identifies the receiver out of the unselected receivers of the set Lt that will introduce the least distortion, as measured by the sum of mean square error (MSE). The receiver with the maximal value of dkJ will be selected to compute the combining vector using equation (19).

When selecting the first receiver, no channel matrices of previously selected receivers can be taken into account, so that A = aIx.

The above described process can be expressed in pseudo code in the manner

shown in Table 1.

The EVD in line 5 of the above N-I algorithm can be computed by the Power method (as described, for example, in C. Golub and C. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins University Press, 1996, the entirety of which is incorporated herein by this reference). The above N-I algorithm is nevertheless complex. The complexity of the N-I algorithm is largely determined by requiring multiple matrix inversion (IN +HkA'H')' in step 4 and multiple eigenvalue decompositions in step 5.

Algorithm N-I can be expressed in a simplified manner in the way shown in Figure 2. In step 100 channel data is obtained and initialisation steps, such as those of steps I and 2 of Table I are performed. In step 110 the receiver that minimally contributes to the data transmission means square error of the precoder is determined.

This is achieved by using eigenvalue decomposition as discussed above. One eigenvalue decomposition operation for each of the unselected receivers in the set A is required every time step 110 is performed. The receiver with the highest maximum eigenvalue from among all of the unselected receivers is identified in step 110 and chosen as the next receiver in the order.

-1 input Hk(k=1,2,...,K), a, A={1,2,...,K}, c»==� 2 Initialization: compute A' = aIf 3 forn=1:K 4 compute °k =(IN. ÷HkAIH)'HkA2H1,VkEA compute EVD: °k E*DkE',Vk e A where Dk = diag(d1, dk2, ..., dkNk) 6 {k,j}=arg max (dkf) VkE,j=1,...,N 7 c =E (:,)", I. =ckH, g=h,A1 B update A1 +-K' -gH (i+ gH) g End 11 output: combining vectors Ck (1,2,. . ., K) Table 1: Algorithm N-I, General Computation of Receiver combining vectors with Greedy receiver Ordering In step 120 the receiver combining vector for which the thus selected receiver contributes minimally to the data transmission mean square error of the thus far selected receivers and itself is then determined. if, in step 130 it is determined that the number of selected receivers correspond to the maximum number of desired receivers, or to a maximum number of receivers that can be supported by the MIMO system, then the algorithm proceeds to step 140, where the receiver combining vectors for all selected receivers are made available. These receiver combining vectors can, for example, be transmitted to the individual receivers, so that the receivers can start using the appropriate receiver combining vector in data communication between the transmitter and the receivers. If it is determined in step 130 that further receivers should be selected, then the algorithm returns to step 120 to select the next receiver in the order.

In the following a methods reducing the complex of the above algorithm is discussed.

Two Low-CoMpLExITy ALGORITHMS Low-C0MPLExIrY MATRIX INVERSION The complexity of the N-I algorithm can be reduced if the number of matrix inversions required for computing the matrix °k is reduced. In the following an alternative way of computing matrix inversion is disclosed. Applying the matrix inversion lemma of equation (11) to the matrix inverted that is required by line 4 of the N-I algorithm provides: (INk + HkA'H' = INk(A+ H'Hk)1 H' (21) The inversion of matrix A+H'Hk in equation (21) can be calculated by matrix update. Applying the matrix inversion lemma of equation (11) again to the matrix that is to be inverted on the right hand side of equation (21) but this time using the vector a'' Hk(j,:) for j=1,...,N1 the matrix (A+H(:,j)Hk(:,j))' can be updated step-by-step for j 1,..., N.

FAST RECEIVER ORDERING

The above discussed algorithm N-I requires that, in each loop, the receiver having the largest value of maximal eigenvalue is identified. As a consequence a large number of EVD decompositions are required. In the -th loop, for example, there are K-n+1 EVD decompositions needed. In the following a way of determining the order in which the receiver combining vectors should be computed according to the criteria of mininiising distortion is discussed. This way of computed selecting receivers is less greedy/computationally expensive than the above discussed "greedy" algorithm N-I.

Once a predetermined receiver order has been established, only one EVD is needed in each loop for computing the receiver combining vector of the selected receiver. The algorithm described in the following brings about a negligible performance loss compared to the greedy receiver ordering algorithm N-I.

In the "greedy" N-I algorithm for receiver selection and the calculation of receiver combining vectors a loop n = 2: K is performed. In each of the iterations of this loop K-n EVD decompositions need to be calculated. Additionally K EVD decompositions need to be calculated to identify the first selected receiver, prior to the start of the loop. Following the EVD decompositions in each pass of the loop the receiver combining vectors of all receivers are calculated according to equation (19).

However, only one of these receiver combining vectors is selected. The other vectors are discarded. In the following the nature of all of the combining vectors computed in the first loop is considered.

Equation (16) provides, for each receiver, the objective function for determining a receiver combining vector: --H -. "H TT A2T.H k A-2L CkiikJ-t k Ck Uki Ilk Ck = max = max (22) Ck1 k (INk + HkA'H) hkCkHk,CkIJ1 1 + hkA'bk Using A' = a'IM, as in the first loop of Algorithm N-I, equation (22) becomes: a_2 hkH 2 Ck = 2 = max llhdll (23) hk=ckHk.IiH=1 1 + a' hk hk=ckHk,tck=1 The solution of equation (23) is the left singular vector corresponding to the largest singular value of Hk. Using a singular value decomposition (SVD) of receiver channel matrix as Hk = UkSkVkH value provides the desired receiver combining vector according to: Ck = Uk (1, :) (24) In the first loop, the EVD-based and SVD-based solutions are consequently identical. As the SVD-based solution selects the receiver that has the largest effective channel power, it is now also clear that the EVD based solution also selects the receiver with the largest effective channel power in the first loop.

Once the SVD of all channel matrices has been completed the so determined receiver combining vectors Ck of all receivers can preliminarily and for the purpose of receiver selection be used alongside the receivers channel matrix to compute the receivers' effective channels hk using equation (1). In effect, through the use of the preliminary receiver combining vector Ck all receivers are treated as if they have only one receive antenna with (effective) channel vector Ilk. Algorithm N-I is then used to sort the receivers. Thus the receivers that minimally contributes to the MSE of the previously precoded receivers is identified in a step-by-step fashion.

Since only the effective channels vectors of receivers are the input to Algorithm N-I, there is no need to make matrix inversions and EVD decompositions in loops other than loop 1. Algorithm N-I is therefore modified as follows to provide the new algorithm N-I-A shown in Table 2.

1 Hk(k=1,2,...,K), a, t={1,2,...,K}, e=� Compute, for each receiverkof the sets, the receiver combining vector Ck, either using the EVD-based method of equation (19) or the SVD-based method of equation (24). Let 2 dk of each receiver either be the largest eigenvalue obtained by EVD-based method applied to the channel matrix of each receiver or the largest singular value obtained by SVD-based method applied to the channel matrix of each receiver.

3 compute hk = CkHk Vk E 4 compute A' = aI/ k1=argmaxd 7 forn=2:K 8 update A1 -A -g' (i + gh' )1 g 9 compute g =hkA', VkEL n kE 12 End 13 Output: set of ordered indices of receivers ® Table 2: Algorithm N-I-A, Fast Receiver Ordering Algorithm Steps 2 -4 of the above ordering algorithm are discussed above with respect of either the general solution provided by the greedy algorithm N-I or with respect to the above comparison of EVID and SVD based methods of computing receiver combining vectors the first time the loop in the greedy algorithm N-I is executed. In step 5, the first step of ordering the receivers, the receiver associated with the largest eigenvalue/singular value is identified and added, in step 6, to the set of selected receivers ® and removed from the set of unselected receivers i.\. An update matrix g for updating the matrix A in conformity with equation (15) above is further defined in step 6.

Each of the other K -1 receivers is selected during one execution of the loop initiated in line 7 of the Table 2 algorithm. The selection of each receiver starts with an update of the matrix K1 to take the vector g of the first selected receiver k1 defined in step 6 or the matrix k, of the receiver selected in a previous pass n-i of the loop, as defined in step 9 into account. In step 9 a new vector g is computed.

In step 10 equation (15) is solved. The first term on the right hand side of equation (15) can hereby be ignored, as it is the same for all receivers k that are still part of the set A of unselected receivers. The term K' of equation (15) can hereby be ignored as the same for all unselected users. The result of step 10 is the index of the receiver that minimises the MSE of the precoder when taking previously selected receivers into account. A newly selected receiver g is added, in step 11, to the set of selected receivers ® and removed from the set of unselected receivers A. In step 11 of the algorithm shown in Table 2 the newly selected receiver is included in the set ® of selected receivers and excluded from the set A of unelected receivers. The set 0 of selected receivers forms the output of the algorithm shown in Table 2.

The algorithm N-I-A can be illustrated in a more general form in the form shown in Figure 3. In step 200 of the Figure 3 algorithm the initialisation steps also used in step 100 of Figure 2 are performed. In step 210 the effective channel power for each of the possible receivers is determined. This can be done using EVD or SVD, as discussed above. Preliminary receiver combining vectors are also determined for each of the possible receivers, wherein the preliminary receiver combining vectors are the vectors that would, if used in the receivers, maximise the effective channel power of the receiver. It will, however, be appreciated that the preliminary receiver combining vectors are not intended for use in the receivers and merely provide an aide for determining a suitable order in which the actual receiver combining vectors are to be determined.

In step 220 the receiver that, when operated using its preliminary receiver combining vector, has the highest effective channel power is selected as the first receiver in the order. In step 230 subsequent receivers are selected such that the next selected receiver is the receiver that, when operated using its preliminary receiver combining vector, increases the means square data transmission error for the previously selected receivers and itself the least. Step 230 is repeated until it is determined in step 240 that the number of receivers provided in order corresponds to a desired number of receivers or to a maxim number of receivers that can be supported by the MIMO system, such as a number of receivers that correspond to the maximum number of data streams K. Once the correct number of receivers has been placed in order, the order of these receivers is output.

Pseudo code of the N-I algorithm shown in Table I can be modified to account for the altered receiver selection algorithm provided by the above discussed algorithm, as illustrated in Table 2. A thus altered receiver algorism, referred to in the following as algorithm N-li, is illustrated in Table 3.

I input Hk(k=1,2,...,K), a, L\={1,2,...,K}, =� 2 initialization: A1 = aIM compute Ck either by EVD-based method in equation (19) or SVD-based method in equation (24) 4 hk=CkHkVkE/X sort receivers by using algorithm in Table 2 to provide l,k2,...,kK) 6 1i -ckHk, g=hkK' 7 forn=2:K 8 update K' +_A'_g"(1+gh'1)g 9 Compute o (N, +HK'H') HA2H' io Compute EVD: 0 EDE', P diag(d,,d2,...,d) j = arg max (d1) 12 c:=E(:,j), h, =cHk, g=hA1 13 End 14 output: combining vectors Ck (k = 1,2,..., K) Table 3: Algorithm N-li, Low-Complexity Computation of Receiver combining vectors with Fast Receiver Ordering A comparison of algorithms N-I and N-Il reveals that steps I and 2 of both algorithms are identical and thus do not require explicit discussion. Algorithm N-Il, however, differs in steps 3 to 5 from algorithm N-I, as in steps 3 to 5 of algorithm N-Il the order of the receivers is determined in the manner disclosed in Table 2fAlgorithms N-I-A. The loop initiated in step 7 of Table 3 and running to step 13 of Table 3 uses the same manner as algorithm N-I of Table I for determining the receiver combining vectors, albeit dispensing with receiver selection step 6 of algorithm N-I, as the order in which the receiver combining vectors are to be determined has already been determined in steps 3 to 5 of the algorithm N-Il. It will be appreciated that the loop extending from step 7 to step 13 of the algorithm N-Il bases the determination of the actual receiver combining vector (as opposed to the preliminary receiver combining vector used for determining the receiver order) only on final receiver combining vectors that have been determined in previous passes of the loop, and on the receiver combining vector of receiver k1determined in the EVD or SVD decomposition that forms part of step 3 of algorithm N-Il/step 2 of algorithm N-I-A.

The inversion of matrix IN +HA'H' in step 9 of algorithm N-Il can be computed by the matrix update method described above in the section on low-complexity matrix inversion.

Figure 4 shows a conceptual illustration of the algorithms N-Il. Steps 300 and 340 correspond to steps 100 and 140 in Figure 2. While in Figure 2 both of steps 110 and 120 are placed inside a loop, only the step in which the actual receiver combining vector is determined, step 320 in Figure 4 (corresponding to step 120 in Figure 2) is placed in the loop. Placing the selection step 310 of Figure 3 outside of the loop is possible because the selection process of Figure 2, which is used in Figure 3 does not require the actual receiver combination vectors (which in both the Figure 2 and 4 processes are determined inside the loop by steps 120 and 320 respectively) to determined the order in which the actual receiver combining vectors are to be determined, as discussed above. A consequence of this is that the number of EVDs or SVD performed in the ordering step (steps 110 and 310 respectively) does, in Figure 4, not have to be placed in the loop. Consequently the number of EVDs or SVDs necessary for determining the receiver combining vectors can be reduced.

Comparing the number of EVO decompositions of two algorithms N-I and N-Il, the number of EVD decompositions needed in algorithm N-I for selecting a single receiver corresponds to the number of receivers that remain unselected at the time of receivers selection. Algorithm N-I thus needs: K+(K-1)+(K-2)+...+1=K(K+1)/2 (25) EVD decompositions. Algorithm N-Il on the other hand needs K EVD decompositions to select the first receivers and determine the receiver order in the N-I-A part of the algorithm illustrated in Table 2 and a further K-i EVD decompositions to determine the actual receiver combining vectors that minimise the MSE of the precoder for the selected receiver order. Algorithm N-Il thus requires: K+K-1=2K-1 (26) EVD decompositions. Thus, for a large number of receivers the saving in computational resources achieved by algorithm N-Il are very significant.

ALTERNATIVE IMPLEMENTATIONS

Both algorithms N-I and N-Il make/may make use the EVD decomposition of matrix 0. Extensive simulations have, however, shown that 0 is can be almost a normal matrix. Therefore, the maximal eigenvalue and maximal singular value of 0 though different, are quite similar. The EVD decomposition step used in algorithms N-I and potentially used in algorithm N-Il can thus be replaced by a SVD operation without introducing large errors.

Moreover, hardware implementing the N-I or N-Il algorithms may comprise SVD modules that are, at times, idle. Such modules may be re-used for determining maximal singular values of the matrix 0 as part of the algorithms N-I and N-Il, if the EVD in these algorithms is replaced by a SVD. Algorithms N-I and N-Il modified in this manner result in Algorithms N-Ill and N-IV. The person skilled in the art will readily appreciate that pseudocodes of these algorithms N-UI and N-IV are copies of the pseudocodes of algorithms N-I and N-Il respectively but with SVD operations instead of EVD operations.

CODEBOOK-BASED RECEIVER COMBINING VECTORS

From the above it is evident that receiver combining vectors of receivers should be jointly designed to minimise distortion of the transmitted signals. The algorithms proposed above, however, require either EVD or SVD decompositions. In the following a way of further reducing the number of EVD/SVD decompositions is discussed.

The problem of interest is to find a combining vector Ck for receiver k that minimizes the objective function in equation (16). As discussed above, the optimal solution requires eigenvalue decomposition, while a near optimal solution can be achieved using single value decomposition.

To reduce the number of EVD and/or SVD operations further a codebook of combining vectors, in which each codebook vector has unit norm, may be used. The concept of codebook has previously been used in digital communications. For example in multiuser precoding, the codebook contains precoding vectors for receivers, as disclosed in M. Sharif and B. Hassibi, "On the capacity of MIMO broadcast channels with partial side information," IEEE Transactions on Information Theory, vol.51, no.2, pp. 506-522, Feb. 2005, the content of which is incorporated herein by this reference.

Codebooks containing receiver combining vectors are disclosed in C..-B. Chae, D. Mazzarese, and R. W. Heath, "Coordinated Beamforming for Multiuser MIMO Systems with Limited Feedforward," Fortieth Asilomar Conference on Signals, Systems and Computers, 2006. ACSSC 06, vol., no., pp.1511-1515, Oct. 29 2006-Nov. 1 2006 (the content of which is incorporated herein by this reference) and in C.-B. Chae, D. Mazzarese, T. lnoue, and R. W. Heath, "Coordinated Beamforming for the Multiuser MIMO Broadcast Channel With Limited Feedforward," IEEE Transactions on Signal Processing, vol.56, no.12, pp. 6044-6056, Dec. 2008 (the content of which is incorporated herein by this reference). In the following the application of the known concept of using a codebook of predetermined values is applied to the design of receiver combining vectors. The novelty of this approach is the combination of the codebook concept with the design criterion for selecting receiver combining vectors of equation (16) together with either of the above described greedy receiver ordering method of algorithm N-I or fast receiver ordering method of algorithm N-Il.

The algorithms proposed above can be modified to incorporate codebock-based receiver combining vectors. Table 4, for example, shows a modified Algorithm N-I using codebook-based combining vectors.

One suitable codebook structure for receivers may comprise two parts, one part comprising adaptive codewords and one part comprising fixed codewords. The use of adaptive codewords is envisaged to provide a way of adapting to the real channel matrices, while the use of fixed codewords gives more freedom for systems to optimize the precoding matrix. For example, the following codebook Ckfor receiver k consists of 3Nk 4-icombining vectors.

Ck (I: Nk,:) I (identity matrix of proper size), Ck(Nk: 2Nk,:) F (discrete Fourier transfrom matrix), Ck (2Nk: 3Nk,:) = R (unitary random matrix), (27) Ck(3Nk +1,:) = Uk(:,1)" (where Hk = UkSkVP).

The last codeword, Ck(3Nk + 1,:), is the left singular vector corresponding to the dominant singular value, which is the adaptive codeword. The codebook also includes the antenna selection case (line 1 of equation (27)). Thus this codebook is a generalization of dominant eigenmode selection as disclosed in A. Paulraj, R. Nabar, and D. Gore, "Introduction to Space-Time Wireless Communications", Cambridge, U.K., Cambridge University Press, 2003, incorporated by reference above, and receive antenna selection as disclosed in S. Sigdel and W. A. Krzymien, "Simplified Fair Scheduling and Antenna Selection Algorithms for Multiuser MIMO Orthogonal Space-Division Multiplexing Downlink," IEEE Transactions on Vehicular Technology, vol.58, no.3, pp.1329-1344, March 2009, which has also been incorporated by reference above. The present algorithm is distinguished over these publications in that the present algorithms not only find a suitable criterion to select the receive combination mode for each receiver, but also jointly select the (best) receiver operation modes of all receivers that minimise the MSE of the precoder.

input Hk (k = 1,2,..., K), a, {i, 2,..., K}, 0 codebook C of size RxM 2 Initialization: compute Hk = CHk Vk E L 3 forn=1:K --Hk(j,:)A2Hk(j,:) 4 1k,j=arg max -- ) keA,j=l RI --Hk(j,:)A'IIk(j,:)'' = C(j,:), h, =Hk, (j,:), g = 6 update A _A_1_gJt(1+ghfl 1g 8 End 9 output: combining vectors Ck (k = 1,2,.. .,K) Table 4: Algorithm N-V, Codebook-based Design of Receiver combining vectors with Greedy Receiver Ordering Discussing now the algorithm N-V illustrated in Table 4 in more detail, in the first step the starting parameters are defined in the same manner as in the other above discussed algorithms. Additionally the codebook C is defined in step 1. The codebook may only comprise a number of possible receiver combining vectors that are fixed. The same codebook may in this case be used for all receivers. Alternatively, different codebooks, each comprising only fixed possible receiver combining vectors may be used for different receivers or receiver groups. As discussed above with reference to equation (27) the codebooks may further comprise an adaptive receiver combining vector. In this case the codebook Ck used differs from receiver to receiver, at least in the adaptive possible receiver combining vector, and defining the codebooks Ck in the first step of the Table 4 algorithm also comprises determining the left singular vector corresponding to the dominant singular value using an singular value decomposition of the channel matrix HK. The fixed possible receiver combining vector section of the codebooks Ck used for the different receivers can also differ.

Following the definition of the codebooks Ck the channel matrix HK I multiplied with the relevant codebook Ck for each receiver, to create for each receiver, a matrix HK comprising all possible effective channels that are permitted by the entries in the codebook Ck.

These effective channel matrices HK form the input for a loop extending over steps 3 to 8 of the algorithm N-V of Table 4. This loop is executed K times. In each pass of the loop the one of the combining vectors in the codebook Ck that, if used by receivers Ic,, increases the MSE of the precoder least. This selection is achieved by solving the form of equation (16) shown in step 4 of the N-V algorithm of Table. The search performed in step 4 provides the index of the combining vector in the codebook Ck that minimally increases, when used for receiverk,,, the MSE of the precoder. This vector is then extracted from the codebook Ck and assigned as the receiver combining vectorc1 in step 5 of the algorithms N-V. Equally, the effective channel matrix of a receiver Ic,, is extracted from the effective channel matrix 11K' to allow updating of the vector g in step 5 and subsequent updating of the matrix A' in step 6. This updating of the matrix A' of course ensures that, when the receiver combining vector of the next receiver is selected on the next pass of the loop, this selection takes due notice of the operation of those receivers that have had their receiver combining vectors already selected, so that MSE of the precoder is minimised. In step 7 the receiver for which a receiver combining vector has been extracted from the codebook is added to the set of receivers Q and removed from the set of receivers.

It will be appreciated from the above that algorithm N-V requires K SVD decompositions in total, one for each of the K users. If the SVD-based/adaptive codeword for i-th receiver is selected, the base station will send a specific instruction to the i-th receiver, instructing the i-th receiver to generate the SVD-based receiver combining vector. Thus, there is no need to send the whole combining vector to the receiver. Additionally, if the i-th receiver terminal does not have a SVD module, the codebook for this receiver may remove the last codeword; in this case, there are only fixed codewords for this receiver.

Figure 5 show a schematic of the algorithm N-V. The initialisation step 400 is the same as the initialisations steps 100, 20 and 300 used in Figures 2 to 4 but additionally includes the provision of a codebook, such as the codebook of equation (27). In step 410 a number of desired combinations of receivers and receiver combination vectors (from the codebook) are then generated. Multiplying the codebook with the channel matrix of a receiver provides all of the possible combinations of the receiver combining vectors in the codebook and the receiver. Such a multiplication can be performed for every receiver. In step 420 the one of the combinations that increases the mean square data transmission error of the thus far selected receivers is determined. It will be appreciated that, by making this selection of a combination, not only the receiver is selected but also the receiver combining vector that allows the receiver to operate in a manner in which minimises the receiver's contribution to means square error. Once a receiver combination vector has been found for a sufficient/desired number of receivers the receiver combination vectors can be output (for example to the receivers) in step 440.

SUMMARY OF EMBODIMENTS

The above discussed algorithms are summarised and compared in Table 5.

Algorithm Summary

N-I -Greedy receiver ordering -Combining vectors are eigenvectors corresponding to the largest eigenvalues -Requires K(K+1)/2 EVD decompositions N-I-A Fast receiver ordering method to avoid greedy receiver ordering N-Il -Low-complexity, fast, predetermined receiver ordering -Combining vectors are eigenvectors corresponding to the largest eigenvalues -Require 2K-i EVO decompositions N-Ill -Alternative implementation of Algorithm N-I -Greedy receiver ordering -Combining vectors are the left singular vector corresponding to the largest singular values -Require K(K + 1)/2 SVD decompositions.

N-IV -Alternative implementation of Algorithm N-Il -Fast, predetermined receiver ordering -Combining vectors are the eft singular vectors corresponding to the largest singular values -Require 2K-i SVD decompositions N-V -Reduces complexity of Algorithms N-I/II/Ill/IV -Combining vectors are searched for/selected from a codebook -Requires a number of SVD decompositions that corresponds to the number of users that determine that the optimal codeword is the codeword determined using SVD (thus the number of SVD composition required is at most K)

EXAMPLES

The performance of the above algorithms has been evaluated by means of simulations and compared to the performance of the most well-known methods: dominant eigenmode (an example of which is disclosed in A. Paulraj, R. Nabar, and 0.

Gore, Introduction to Space-Time Wireless Communications, Cambridge, U.K.: Cambridge University Press, 2003) and receive antenna selection of S. Sigdel and W. A. Krzymien, "Simplified Fair Scheduling and Antenna Selection Algorithms for Multi-user MIMO Orthogonal Space-Division Multiplexing Downlink," IEEE Transactions on Vehicular Technology, vol.58, no.3, pp.1329-1344, March 2009. The latter two methods are also referred to in the following as conventional algorithms C-I and C-Il, respectively.

The Rayleigh channel model has been employed in the simulations, where receiver's channels are uncorrelated. The base station has 4 transmit antennas. There are 4 receivers. 4QAM signal is used for alt receivers, receivers' channel matrices are completely known at the base station. The adaptive codebook given in equation (27) has been used for all receivers.

In Figures 6 and 7 plot the total average uncoded bit error rate (BER) of the system against the total transmit power and compare the performances of the proposed algorithms are shown for linear MMSE precoding when each receivers has 2 and 4 receive antennas respectively. It is shown that all of the above discussed methods outperform the conventional techniques C-I and C-Il. Especially, the algorithms with fast receiver ordering perform slightly better than the algorithms with greedy receiver ordering at high signal-to-noise (SNR) ratio. This result reveals that the greedy receiver search does not always lead to the optimal receiver order.

Claims (19)

1. CLAIMS: 1. A method performed in a transmitter side of a multiuser minimum square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae and a plurality of receivers, each receiver of the plurality of receivers comprising a plurality of receive antennae, the method comprising: obtaining, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter; establishing in the transmitter an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver that minimally increases the mean square data transmission error, based on the channel information of any receivers previously selected in the order and of unselected receivers.
2. 2. A method according to Claim 1, further comprising calculating a receiver combining vector for a receiver after it has been selected as the next receiver in the order and before the next receiver in the order is selected.
3. 3. A method according to Claim 1, wherein a number of receivers are placed in the said order before receiver combining vectors that are to be use in the number of receivers are determined.
4. 4. A method according to Claim 3, further comprising, prior to determining said order, determining for each receiver a preliminary receiver combining vector c, that 2 fulfils c = max ckHk, wherein Ck corresponds to a plurality of possible receiver Ck H=' combining vectors and Hk comprising said receiver channel information associated with a respective receiver.
5. 5. A method according to Claim 4, wherein a next, n-th receiver, in the order is selected such that, when the n-th receiver is operated using its associated preliminary receiver combining vector ca,, it minimally contributes to the means square data transmission error.
6. 6. A method according to Claim 4 or 5, further comprising performing a singular value decomposition of a channel matrix of unselected receivers to determine a largest singular value of the channel matrix and an associated left singular vector for use as the preliminary receiver combining vector.
7. 7. A method according to Claim 5 or 6, wherein the next, n-th receiver in the order is a receiver fulfilling: arg max (i + g,, (c,Hk)H)' I 112 wherein k is an index of unselected receivers in a set A, Hk is the channel matrix of receiver k and comprises the said channel information, superscript H denotes a matrix transpose conjugate operation, lg,jI is the norm of the matrix g, and g is useable for determining the n-th receiver, wherein: gkfl =cHA', VkEA whereinA' is a matrix useable for determining the n-th receiver and including matrices A1 and g that had been used for the selection of the preceding, (n-1)-th receiver, wherein: A1 = A1 -g (i + (ckPHk)H)
8. 8. A method according to Claim I or 2, wherein a next, n-th receiver in the order has a receiver index k from among a setA of unselected receivers and a receiver combining vector Ck fulfilling: CkHkA2H c' argm.x Ck (lArk + ILA Hk)Ck wherein Hk is the channel matrix of receiver k comprising the said channel information and superscript H denotes a matrix transpose conjugate operation, N S a Nk x Nk identity matrix, wherein Nk is the number of receiver antennae of each receiver, wherein: = -g (i + g1 (ck Hk)H) wherein A' is the matrix A' for the selection of a current, n -th receiver in the order, A is the matrix K' that has been used for the selection of the preceding, (n-1)-th, receiver in the order, Ck is the receiver combining vector of the (n-1)-th receiver and H is the channel matrix of the (n-1)-th receiver, with Aj' = a'IM, wherein M is the number of transmitter antennae of the transmitter, a = K / E,,., wherein K is the number of data streams between the transmitter and the receivers and E,,. is the total transmitter power; and g_1 = c Hk A
9. 9. A method according to Claim 8, further comprising performing an eigenvalue decomposition of the matrix °k = (IN + HkA'H' )1 IIkA2H', for some or all receivers k from among the set A of unselected receivers, wherein the next receiver selected for the order is the receiver for which the maximum eigenvalue of the matrix °k is the largest.
10. 10. A method according to Claim 8, further comprising performing an singular value decomposition of the matrix °k (IN + HkA'H)' HkA2H, for some or all receivers k from among the set A of unselected receivers, wherein the next, n-th receiver in the order is the receiver for which the maximal singular value of the matrix O is the largest.
11. 11. A method according to Claim 9 or 10, wherein the inverse of the matrix (IN +HkAIH7) is calculated by calculating N, NHk(AIkhlk)Hk
12. 12. A method according to Claim 11, wherein the inverse of the matrix (A+H'Hk) is calculated by matrix update.
13. 13. A method according to Claim 1, further comprising providing a codebook of possible receiver combining vectors and selecting from among a plurality of possible combinations of receivers with receiver combining vectors from the codebook the combination that increases the mean square data transmission error the least.
14. 14. A method according to Claim 13, wherein the codebook is a codebook matrix C and wherein, for each receiver k of a set of unselected receivers, the codebook C is multiplied with a channel matrix Hk comprising said channel information to form a matrix "k CHk, the method further comprising determining the index k of the n -th receiver in the order and the row index j within the matrix Hk for which: ilk (f, :)A2 ilk (j, :)H arg max --keE,j=1....,R 1 + Hk (j, :)A' Hk (f,:)" wherein R is the number of receiver combining vectors in the codebook matrix C and wherein H denotes a matrix transpose conjugate operation, wherein the matrix A for the selection of the -th receiver is: A' = A1 -g1 (i + g_1h) g_ wherein g_1 = hL,A1 and hL H (j,i,:), wherein H is the matrix H of the (n -1) -th receiver immediately preceding the n -th receiver in the order and j,, the selected row index within this matrix H
15. 15. A method according to Claim 13 or 14, wherein a possible receiver combining vector in a codebook for a said receiver is the left singular vector corresponding to the dominant singular value determined by a singular value decomposition of a channel matrix comprising the said receiver's channel information.
16. 16. A method according to Claim 6, 10 or 15, wherein the transmitter comprises singular value decomposition means and wherein said singular value decomposition means are used to calculate the singular value decompositions according to Claim 6, 100115 when otherwise idle.
17. 17. A method performed in a transmitter side of a multiuser minimum square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae and a plurality of receivers, each receiver of the plurality of receivers comprising a plurality of receive antennae, the method a method of scheduling receivers from among the plurality of receivers, the method comprising: obtaining, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter; establishing an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information of any receivers previously selected in the order and of unselected receivers; determining receive combining vectors for said receivers in the said order so as to minimise the mean square error of previously selected receivers, said determining based on the channel information and taking into account receivers for which receive combining vectors have already been determined; and transmitting data from the transmitter to the receivers and combining data signals received by the plurality of receive antennae of a receiver using the receiver combining vector of the receiver.
18. 18. An apparatus for scheduling receivers from among a plurality of receivers in a multiuser minimum mean square error linear precoding MIMO system that comprises a transmitter with a plurality of transmit antennae, wherein each receiver of the plurality of receivers comprises a plurality of receive antennae, the apparatus comprising: a channel estimator arranged to obtain, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter; and a scheduler that is arranged to establish an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information.
19. 19. A multiuser minimum square error linear precoding MIMO system comprising an apparatus for scheduling receivers from among a plurality of receivers in the MIMO system, the MIMO system further comprising a transmitter with a plurality of transmit antennae, wherein each receiver of the plurality of receivers comprises a plurality of receive antennae, the apparatus comprising: a channel estimator arranged to obtain, for some or all of the receivers, receiver channel information quantifying the properties of transmit channels between receiver antennae of the receiver and transmit antennae of the transmitter; a scheduler that is arranged to establish an order for determining the receiver combining vectors of the some or all of the receivers by selecting as a next receiver in the order a so far unselected receiver from the some or all of the receivers that minimally increases the mean square data transmission error, based on the channel information; a processor arranged to determine receive combining vectors for said receivers in the said order in a manner that minimises the mean square error of previously selected receivers, the processor arranged to base making the determination on the channel information and taking into account receivers for which receive combining vectors have already been determined; and a transmitter for transmitting data from the transmitter to the receivers; the receivers individually comprising combiners arranged to combine data signals received by the plurality of receive antennae of a receiver using the receive combining vector determined by the processor.