GB2466928A

GB2466928A - Precoding selection for a user in a THP MIMO system

Info

Publication number: GB2466928A
Application number: GB0900331A
Authority: GB
Inventors: Fengming Cao; Ngoc-Dung Dao
Original assignee: Toshiba Research Europe Ltd
Current assignee: Toshiba Europe Ltd
Priority date: 2009-01-09
Filing date: 2009-01-09
Publication date: 2010-07-14
Anticipated expiration: 2029-01-09
Also published as: GB0900331D0; GB2466928B

Abstract

In a Multiple In Multiple Out (MIMO) system of receivers each having nr antennas employing nonlinear Tomlinson-Harashima precoding (THP) in K independent data streams forming an nrxK channel matrixH, interference between data streams is first reduced by pre-subtracting known interference elements (B-I) from a channel symbol vector in a feedback loop containing a modulus operation (MOD) and transformed into vectorXby a feed-forward matrixFH. Channel matrixHis decomposed with LQ decomposition to generate a feedback matrixBand a diagonal matrixG-1which eliminates interference, and a receiver combination matrixRcalculated. To maximise capacity, the transmitter must select a precoding scheme based on channel knowledge, for which exhaustive searching becomes intractable for large user numbers.Rfor a given user number is therefore determined by maximising the square of the norm of a diagonal element of a triangular matrix generated by the Gram-Schmidt process during LQ decomposition of matrixRHfor each MIMO channel (Step 13 in fig. 3). This allows performance to be flexibly adjusted according to the number of active users.

Description

METHOD AND APPARATUS FOR USE IN A MIMO SYSTEM

FIELD OF THE INVENTION

The present invention relates to determining a method for use in a MIMO system and to an associated apparatus. In particular the present invention relates to a method of predicting receiver combining vectors in a MIMO system employing Tomlinson-Harashima (TH) precoding and comprising a plurality of receivers each having plural receive antennae.

BACKGROUND OF THE INVENTION

In known multiple-input multiple output (MIMO) systems employing precoding, channel knowledge can be used at the transmitter in order to enhance the quality of the communication links. Complex baseband notation may be used to express K independent spatial streams of data to be transmitted from a MIMO system comprising K transmit and R receive antennae as: y=Hx+n (1) where H is the R x K channel matrix, x the Kx 1 transmit vector of complex symbols, y the fl x 1 receive vector, and n a R X 1 zero-mean white Gaussian distributed noise vector with variance TOMLINSON-HARASHIMA PREcODING (TH P) Nonlinear precoding/multiuser MIMO has been newly developed in recent years and is considered a promising technique to improve the capacity of a transmission system. Several non-linear precoding schemes are know. A popular known scheme is Tomlinson-Harashima precoding (THP). This scheme owes its popularity to its simplicity and good performance.

In multiuser THP interference between data streams is reduced or eliminated by pre-subtracting known interference elements in a feedback loop.

A modulo operation is further used to reduce the power of the transmitted signal, as is set out, for example, in Windpassinger C, Fischer R.F.H., Vencel T, Huber, J.B.;," Precoding in Multiantenna and Multiuser Communications", IEEE Wireless Communications, IEEE Transactions on Volume 3, Issue 4, July 2004 Page(s):1305 -1316, Spencer, Q.H.; Swindlehurst, A.L.; Haardt, M.;., "Zero-Forcing Methods for Downlink Spatial Multiplexing in Multiuser MIMO Channels", IEEE Trans. On Signal Processing, Feb. 2004 Volume 52, Issue 2, Feb. 2004 Page(s):461 -471 and in Dafei Wang; Jorswieck, E.A.; Sezgin, A.; Costa, E.; "Joint Tomlinson-Harashima Precoding with Diversity Techniques for Multiuser MIMO Systems"; IEEE VTC 2005 Volume 2, 30 May-i June 2005 Page(s):1017 -1021, all of which are incorporated herein in their entirety by this reference.

A block diagram of a multiuser THP system is shown in Figure 1. a denotes a vector of input data symbols that are to be transmitted through K information links. The block 5 performs the above mentioned mod ulo function included in THP, creating channel symbol vector. is fed back to a summation point 10 through feedback matrix W1 where it is combined with the input data symbol vector a to pre-subtract known interference elements, as mentioned above. The channel symbol vector X is transformed into the vector X by the feed-forward matrix Fh'. As mentioned above, [denotes the channel matrix. During transmission each channel is subject to noise contribution, indicated in Figure 1 by the addition of noise components n1 to K' which are assumed to be zero-mean white Gaussian distributed noise components. Once received the data signals are scaled at multipliers 35 by a scaling factor g1 tOg. A further modulo operation creates a copy of the input data elements a1 to OK in the receiver.

Channel matrix H can be decomposed with LQ decomposition as: H=SF (2) where F is a unitary matrix and F" is the above mentioned feed-forward matrix. S is a lower triangular matrix. The feedback matrix B can be obtained as: B=GS (3) with G =diag(g1,g2,...,g) -_diag(1/s11,...,1/s) (4) The feedback matrix B consequently has a triangular structure. As a result of this structure the channel symbols ik,k=l,...,K are successively generated from the data symbols {a,+jIa1,aE{�1,�3,...;�('-1)}) as follows, where M means the modulation order: k-I (5) Xk = ak, k = 1,...,K.

Generating the channel symbols Xk in this manner would increase transmit power significantly. The THP modulo operation avoids this problem by reducing the transmit symbols into the boundary region of P. Mathematically, integer multiples of 2VA7 are added to the real and imaginary part of Xk by the modulo operation. The channel symbols k following the modulo operation are defined as: k-i (6) Xk ak + Pk - , k = 1,..., K. where Pk {2-(p/-I-JQ)j p1, PQ E Z}. Thus, instead of feeding the data symbols into the linear pre-equalization, the effective data symbols Vk ak + Pk are passed intoB, which is implemented by the feedback structure 15 shown in Figure 1. The signal received at the receiver can thus be expressed as: y = Hx+n =GBFFHWIv+n = G'v+n =G1(a+p)+n (7) As G' is diagonal there is no interference among the users. Following receipt of the signal at the receiver and after the scaling operation of G at multipliers 35 shown in Figure 1 the received signal is fed into the modulo operation element 40 at the receiver and the original sequence ak is recovered since the modulo operation is a unique operation.

The received signal to noise ratio of the kth data stream is known to be: SNRk I 2 (8) wherein Skk is the kth diagonal element of s.

As shown above, THP creates parallel and independent unit-gain AWGN channel with a noise variance / I 12. The capacity of such a system is known to be: K (9) CZfthP =1og2(1+o Skk 12/u2) USER SELECTION/ORDERING FOR THP In order to maximise the transmission capacity of the system and to utilize the user scheduling gain, the transmitter need to select a given user subset for precoding from all possible users when the active user number is larger than the number of available transmitter antennae. Optimally an exhaustive search based on the capacity C'" for a zero forcing Tomlinson-Harashima precoding (zfthp) system is performed according to: * =argmaxC" (10) where (1 is the user subset with cardinality with I) I=K. Due to the complexity of such an exhaustive search for larger user numbers, however, conducting an exhaustive search becomes unfeasible and the use of sub-optimal selection/ordering methods may be required.

JOINT TRANSCEIVER THP

When the users are equipped with multiple receiver antennas additional diversity gains can be exploited. Figure 2 shows a block diagram of THP system comprising receivers with multiple antennae. As can be seen from this figure, the signals received by the various antennae of each receiver, are operated upon by the receiver combination vector r,.

For a system comprising K> 1 antennae at the transmitter and K receivers, with the kth receiver being equipped with Nk> 1 antennae, the receiver channel can be expressed in the form of a Nk x K matrix "K' The combination vector for the kth receiver rk is then a 1 x Nk vector. For a system of this type the received signal comprising the receiver combination vector can be expressed as: Ry=RHx+Rn=G1RIIF'1B'v+Rn (11) wherein R is a block-diagonal matrix comprising the receiver combination vectors r1 to rk.

r, 0 0 0 (12) Or 0 0 R= 2 00 0 O 0 0 rK According to the principle of Zero-forcing THP, the feed-forward matrix F and the feedback matrix S can be obtained by LQ decomposition according to: RH=SF (13) The capacity of the system can be maximised or the BER achieved by the system can be minimised by making an appropriate selection for R. There are known ways for determining R Dafei Wang; Jorswieck, E.A.; Sezgin, A.; Costa, E.; "Joint Tomlinson-Harashima Precoding with Diversity Techniques for Multiuser MIMO Systems"; IEEE \TC 2005 Volume 2, 30 May- 1 June 2005 Page(s):1017 -1021. incorporated by reference in its entirety above and Stankovic, V.; Haardt, M.; "Successive optimization Tomlinson-Harashima precoding (SO THP) for multi-user MIMO systems"; IEEE ISACPP 2005 Volume 3, 18-23 March 2005 Page(s):iii/1 117 -ui/i 120, which is incorporated in its entirety herein in its entirety by this reference, use block diagonalisation to generate the precoding vector and combining vector. Wang et. al. moreover use diversity techniques, such as space-time block coding (STBC), to enhance system performance. Methods of this kind are disadvantageous in that the computation of the precoding and combining vectors is highly complex and therefore highly demanding in terms of the required resources for their execution in practice.

Mm Huang, Limin Xiao, Yunzhou Li, Shidong Zhou, Jing Wang; "Per-Layer Optimization in Multiuser MIMO Systems with Tomlinson-Harashima Precoding"; IEICE Transactions 90-B(6); pp 1535-1 539; 2007, the entirety of which is herein incorporated by this reference, use OR decomposition with Householder transformation to compute the precoding and combining vectors.

Even though this solution it is less complex than a solution using block diagonalisation, its execution nevertheless requires considerable computational resources.

SUMMARY OF THE INVENTION

According to an aspect of the present invention there is provided a method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding. The method comprises determining receiver combining vectors based on the interrelationship between the Gram-Schmidt process and LQ decomposition, This manner of determining the receiver combining vectors is considerably less computationally demanding than the above discussed known methods of determining receiver combining vectors.

According to another aspect of the present invention there is provided a method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding. The method comprises determining a receiver combining vector as being the vector maximising the square of the norm of a diagonal element of a triangular matrix generated by the Gram-Schmidt process when performing LQ-decomposition of a matrix that comprises for each channel of the MIMO system the products of the receiver combining matrix and a channel matrix.

The vector maximising the square of the norm of the diagonal element may be the left singular vector associated with the maximum singular value of the diagonal element. Due to the nature of the Gram-Schmidt process each diagonal element is only dependent on the elements/receivers preceding it in the process but not on the elements/receivers that will be dealt with in later steps of the Gram-Schmidt process. Determining a receiver combining vector for a particular receiver thus only requires taking interfering elements of those data streams/channels into account for which in an earlier step of the Gram-Schmidt process a receiver combining vector had been determined. The method according to this aspect of the present invention thus enables sequential computation of the receiver combining vectors, with a receiver combining vector being determined in each step of the Gram-Schmidt process.

Each of the receiver combining vectors may further jointly be determined together with an associated precoding matrix. In this case the receiver combining vectors and associated precoding matrices may become available in a sequential fashion.

According to another aspect of the present invention there is provided a method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding and supporting K data streams associated with K receivers. Each receiver of the system comprises a plurality of antennae.

The method comprises performing singular value decomposition of a channel matrix H1 associated with the first receiver to determine a first receiver combining vector r1. The first receiver combining vector r1 is the left singular vector associated with the maximum singular value of the channel matrix H1.

Subsequently receiver combining vectors r2 to FK for the second to Kth receivers can be sequentially determined by performing singular value decomposition of matrices P2 to 1k defined by: for 2 �= k �= K. The receiver combining vectors r2 to rK are the left singular vectors of the respective matrices P2 to k that are associated with the maximum singular value of the respective matrix P2 to k* Hk is the channel matrix associated with the k-th receiver, I is the identity matrix, 1 = for i liriHi II = I (that is for the first receiver in the system that is being considered in the process) and f I*iPi for 1 < i �= k-i (that is for receivers that are being Ir I1 considered subsequent to the first receiver). The matrices P correspond to the matrix Pk above but applying to steps 1 < i k-i of the Gram-Schmidt process preceding the current, k-th step.

The method may further comprise, when determining a said receiver combining vector r2 to rK, performing singular value decomposition of the channel matrix Hk associated with the receiver for which the receiver combining vector is to be determined to determine the left singular vector associated with the maximum singular value of the channel matrix 11k The correlation of the said left singular vector of the matrix k with the left singular vector of the channel matrix is then determined. If this correlation exceeds a predetermined value the receiver combining vector for the receiver under consideration is set to the left singular vector of the channel matrix Hk. If the correlation exceeds the predetermined value, the two left singular vectors are taken to be sufficiently similar for the left singular vector of the channel matrix Hk to represent the channel combining vector determined as the left singular vector of the matrix k As the receivers can determine the left singular vector associated with the maximum singular value of the channel matrix Hk themselves it is not necessarily required for the receiver combining vector to be transmitted from the apparatus determining the receiver combining vectors to the receivers if the above determined correlation is deemed sufficiently large. In this case the receivers can thus simply determine the appropriate receiver combing vectors themselves based on the channel matrix, which is under normal circumstances known to the receiver. By avoiding the need to transmit the receiver combining vector to the receiver the amount of transmission overhead is reduced. If the correlation does not exceed the predetermined value the receiver combining vector may be set to the singular vector of k corresponding to the maximum singular value.

A change in the number of receivers in a MIMO system may influence the transmission quality, e.g. by affecting the amount of channel interference.

Thus, if a change in the number of receivers participating in the MIMO system is detected it may be desirable for the receiver combining vectors to be determined again. This opportunity may also be used to select a new set of uses that are permitted to participate in the system, for example in a case where a receiver no longer participates in the system and bandwidths for communicating with a previously non-participating user has become available.

The predetermined correlation value determining the threshold for selection between the receiver combination vector determined solely based on the channel matrix of the receiver and the receiver combination vector determined in the manner described above using the Gram-Schmidt process may also be set to a new value, for example based on the altered number of users participating in the system.

This has been recognised as being advantageous in its own right and according to another aspect of the present invention there is provided a method of estimating a receiver combining vector for use in a MIMO system based on a channel matrix associated with a receiver in the system. The method comprises estimating a receiver combining vector taking into account likely interference between signals transmitted to the receiver and signals transmitted to other receivers. The receiver combining vector is also determined based solely on the receiver's channel matrix and a correlation between the thus estimated and thus determined receiver combining vectors is computed. If this correlation exceeds a predetermined threshold value the receiver combining vector that has been determined based solely on the receiver's channel matrix is selected as the receiver combining vector for the receiver the vector is associated with.

An indication that the selected receiver combing vector is the receiver combining vector determined based solely on the receiver's channel matrix may also be transmitted to the receiver.

According to another aspect of the present invention there is provided a method of selecting a receiver from among a number of available receivers for participation in a MIMO system employing Tomlinson-Harashima precoding, wherein the system is arranged to support K data streams and wherein each of the available receivers comprises a plurality of antennae and is associated with a channel matrix. The method comprises selecting one or more receivers for participation in said system and determining a receiver combining vector for each selected receiver. A k-th receiver is then selected for participation in the system by performing singular value decompositions of a number of matrices k associated with a corresponding number of unselected receivers to determine a corresponding number of left singular values associated with the maximum singular values of the respective matrix The receiver having the left singular value with the highest norm is selected as the k-th receiver. The matrices k are defined as: k wherein Hk is the channel matrix of a receiver under consideration, I is the identity matrix and: = r1111 for i=1 lriJI II = rP1 for 1 <i �= k-I wherein H1 is the channel matrix associated with the first previously selected receiver and r1 is the receiver combining vector of the first previously selected receiver, r1 is the receiver combining vector of the i-th previously selected receiver and P1 correspond to the matrices k associated with the respective previously selected receivers. This selection method permits selection of the one of the remaining receivers that maximises the capacity of the MIMO system when is acts in parallel with the already selected receivers.

As a receiver only experiences interference with previously selected receivers there is no need to select the first receiver in the above described manner. Instead the first receiver may be selected in a computationally less demanding fashion, for example by performing singular value decompositions of the channel matrices of some or all available receivers, determining the left singular vector associated with the maximum singular value of each channel matrix and selecting the receiver having the maximum singular vector with the highest norm as the first receiver. The second to K-th receivers may then further be sequentially selected. k 2 in the first sequential selection step. k is then incremented for each sequential selection step.

The above threshold based receiver combining method may also be applied to the process of receiver selection. In this case the method may further comprise determining a receiver combining vector for a selected receiver by performing a singular value decomposition of the matrix k of the selected receiver to determine the left singular vector associated with the maximum singular value of the matrix Pk. A singular value decomposition of the matrix Hk of the selected receiver may then be performed to determine the left singular vector associated with the maximum singular value of the matrix Hk. Similar to the above described manner a correlation between the two left singular vectors may then be determined. If the correlation exceeds a predetermined value the receiver combining vector may be defined as being the left singular value of the matrix Hk that is associated with the maximum singular value of the matrix Hk.

If the correlation does not exceed the predetermined value the receiver combining vector may be defined as being the left singular value of the matrix k that is associated with the maximum singular value of the matrix k Applying this technique at the receiver selection stage provides a number of advantages.

Firstly all receiver combining vectors are available following completion of the receiver selection process. . Moreover, receiver selection is based on the actual receiver combining vectors that will be used in the system. This has the advantage that during later receiver selection steps those receivers will be selected that maximise system capacity, even in a real life scenario in which non-optimal receiver combining vectors have been selected.

It will be appreciated from the above that the invention provides a solution to design transceiver precoding, wherein the strategy to generate the receiver combining vector is flexible and could be adjusted to different user number scenarios to balance the performance and forward overhead. In practice, the number of active users communicating with a transmitter may vary depending on different application scenarios. Aspects of the present invention account for this while providing performance comparable to that of known techniques but with significant reduced feed forward overhead.

It will be appreciated that the present invention also extends to apparatus arranged to operate to put one or more of the above described aspects into effect. Such apparatus may, for example, be a base station or an access point.

It will moreover be appreciated that the present invention also extends to recording media comprising instructions that, if executed in a base station or an access point, cause the base station or access point to perform an above described method.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment 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 block diagram of a multiuser THP system; Figure 2 shows a block diagram of THP system comprising receivers with multiple antennae; Figure 3 shows a sequence diagram of a second example of the present invention; Figure 4 shows the dependence of BER performance of an embodiment of the present invention on user number and various choices for the predetermined value and Figure 5 shows the dependence of BER performance of an embodiment of the present invention on various choices for the predetermined value.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In known THP methods, such as the methods discussed above, receiver combination vectors are designed without consideration of excessive transmission overheads or indeed without the number of receivers in mind. In the following a method of determining receiver combination vectors allowing minimisation of both BER and transmission overheads is described. The method is flexible in that it can adapt to different receiver numbers.

RH can be expressed as: ijH1 = . =H=SF (14) rKIIK hK The Gram-Schmidt process can then be used to generate LQ decomposition of H = SF as follows: u1:iIii[ fa U2It (15) UK K <lK,1k >k K K k=1 k=1 k=1 IIUKD where (c,e)e = cee means the projection of row vector c on vector e. u, to "K are the rows of matrix s and f, to K are the elements of the matrix F Each element k is thus obtained by projection onto the orthogonal complement of span(f),i=1,2,..,k-1 for any 1�=i!=j�= K,'(f,,f1) 0 Based on the above, the LQ decomposition of H can be written as follows: iii 1111111 ° ° =SF= <> h'.11 ° ° * (16) <hK,fl> <hK,f2> Ik'II K From equations (9), (14), (15) and (16), the capacity of a THP system with receiver combination can be written as follows: C" =Jog2(1+a Js 2 /2) log2(1+ a lu1 112 /)+ 1og2(1+ : IlUkil k-I 2 (17) /a)+1og2(1 +7 IHk(I-f7ff) /u) From equation (17) it is clear that the capacity C can be maximized k-I 2 by maximizing the term rkHk(L-f7fJ) during kth step in the Gram-Schmidt process shown in equation(1 5). The receiver combination rk is the left singular vector of Hk(I->f7fJ) that corresponds to the maximal singular value which k-I 2 maximises rkHk(I-f7fJ) . For simplification of description, we will in the j=I following refer to the singular vector corresponding to the maximal singular value as the maximal singular vector.

It will be appreciated that, when r is the maximal singular vector of Hk(I -f1'f), the transmitter need to keep the receiver informed of the combining vector rk. The need to transmit the combining vector rk to the receiver, however, increases the forward transmission overhead from transmitter to receiver.

It was realised that, under certain circumstances the maximal singular vector r, offlk(I-f7fJ) can be very similar to the maximum singular vector of Hk. As Hk is already known at the receiver, the combining vector r can be directly and independently determined at the receiver without any need for this vector to be transmitted to the receiver by the transmitter.

In view of this, the transmitter may generate the receiver combination vector rk for the kth receiver, where rk is the maximal singular vector of either Hk(I-f7fJ)or 11k* In order to determine whether the receiver combination vector r should be the maximal singular vector of Hk(I -f1"f) (in case this maximum singular vector is deemed too dissimilar from the maximum singular vector of Hk) or of Hk (in case the two mentioned maximum singular vectors are deemed sufficiently similar for the maximum singular vector of llk(I-f7fJ) to be represented by the maximum singular vectors of Ilk)the transmitter computes both the maximum singular vectors of Hk(I->ffJ)and of Hk and correlates the two thus computed maximal singular vectors. Good correlation between the two thus computed vectors indicates that the maximum singular vector of "k is similar or even nearly identical to the maximum singular vector of IIk(I-f7fJ). Thus, if the two calculated maximum singular vectors closely correlate the maximum singular vector of Hk may be used as the combination vector instead of the maximum singular vector of Hk(I -f7f). If the maximum singular vector of Ilk is determined in this manner to be a suitable receiver combination vector z this receiver combination vector Fk can be determined in the receiver itself and does not need to be communicated from the transmitter to the receiver, thereby reducing the amount of required forward transmission overhead.

A threshold value 13 is defined for deciding whether or not the correlation between the above maximum singular vectors is sufficient to warrant the use of the maximum singular vector of Hk as the receiver combination vector rk. If the correlation between the above two maximum singular vectors exceeds this threshold 13, then the kth receiver combining vector rk will be the maximum singular vector of Hk to minimise forward overhead. Otherwise the ktI receiver combining vector r will be the maximum singular vector of Hk(1-f7fJ) to ensure adequate BER performance.

In the method a transmitter can flexibly adjust the threshold 13 to accommodate different application scenarios, for example a change in the number of users attempting to use a transmission system. It may, for example, be desirable to raise the threshold 13 in cases where only a few receivers attempt use the transmission system, so as to increase the probability that the receiver combining vector r is the maximal singular vector of Hk(I-f7fj).

Otherwise, the threshold can be reduced to increase the probability that rk is maximal singular vector of Hk.

It is also envisaged that, under certain circumstances the threshold 13 may be set to either 1 or 0. In these cases the receiver combining vector rk is always the maximal singular vector of Hk(I -f7f)(for 13 =1) and Hk (for 13 =0) respectively.

Example 1: Number of receivers = number of transmitter antennae The disclosed method will now be described further by way of a first example in which the number of users attempting to participate in the system corresponds to the number of available transmitter antennae. In this first example all of the users can receive data transmission and no user selection needs to be performed. However, it is of course still required for the receiver combining vectors rk of the k receivers to be determined/optimised.

The channel for K users can be expressed as: (18) In a first step of the method the threshold 13 is initialised. Single value decomposition of the first user's channel H1 is then performed according to: H1U1D1Vt' (19) In view of equations (15) and (16) it is clear that the first user can be treated in isolation, as the first user's channel JI does not experience any interference from other channels. The precoding vector f1 for use in precoding the first user's channel in the transmitter and the first user's receiver combining vector r1 can then be determined by: r1 U1(:, 1)H H1 and (20) f -_1_ Once the precoding vector f1 and the first user's receiver combining vector r1 are known, the precoding vectors f2to k and the combining vectors r2 to r, for other users can be sequentially determined for the kth user with 1<k�=K by defining: Pk=Hk(I->f7fj) (21) where Hk is the user's channel and I is the identity matrix. A decision is then made if the combining vector rk is to be the maximal singular vector of ilk(I-fjfJ) or of Rk based on the threshold 3.

If, for example, 30 (in which case the combining vector rk is always to be the maximal singular vector of Hk as set out above) the singular value decomposition of the user's channel Hk is performed according to: 11k = UkDkVkH (22) The precoding vector k and the combining vector rk can then be determined according to: rk Uk(:,1)H T -rkP and k (23) Alternatively, if, for example, 3=1 the singular value decomposition of the user's channel Hk is performed taking into account interference from other channels by performing singular value decomposition of PK defined above in equation (21) according to: Pk=UkDkV (24) The precoding vector k and the combining vector r can then be determined according to: rk = Uk(:,1)" = rkP and k Ic (25) f L k [lcD In the most general case, where 0 <13 < 1 a determination need to first be made of whether or not the correlation between a precoding vector determined according to equation (23) and a precoding vector determined according to equation (25) exceeds the predetermined threshold value 13. For this purpose singular value decomposition of both P< and Hk are performed according to: kk'kTk and (26) Il/c UkDk7 The correlation between the maximum singular vectors of K and HK can then be determined according to: a = Uk (:, )H * k (:, 1) (27) If a �= /3 the receiver combining vector r is determined as the maximum singular vector of 11k according to: rk = (28) Otherwise the receiver combining vector rk is determined as the maximum singular vector of K according to: rk = Uk (:, 1)" (29) Based on the appropriate choice of receiver combining vector r the precoding vector k can then be determined according to: fk-rkPk and fk=j[ (30) Once all of the precoding vectors f1to k and all of the receiver combining vectors r1 to rk have been determined the precoding matrix F" and the receiver combining matrix R can be generated according to:

H

FF = "2 (31) r1 0 0 0 Or 0 0 R=0 (32) O 0 0 rK Example 2: Number of receivers> number of transmitter antennae The above described method can also be extended according to the Gram-Schmidt process to the more general case where the number of receivers/users (here the receiver can be called as user without loss of generality) is larger than the number of transmitter antennae. In this case users that are permitted to participate in the network need to be selected from among the group of available users. In this case the overall number of potential users is defined to be N and the number of users that can simultaneously use the transmission system is K. Thus K users need to be selected from amongst the N potential users. The K users are given indices &r(1) ... ir(I -1)) and the N users are given indices f12, .., N). The channels of the N users are: [ll'. (33) The above described method can be extended to form the basis for user selection by selecting, during step k of the Gram-Schmidt process, a user 7rOc) from among the set of users k(1), ...,it(k -1))c that remain unselected at the start of this step k. The user selected is the user that has the maximal norm of where receiver combination vector r Is generated based on above analysis. It will be appreciated that again the receiver combination vector rk may be chosen to be the maximum singular vector of the channel matrix Hk if it is determined that the correlation between the maximum singular vector of the channel matrix Hk and the maximum singular vector of Hk(I-f7fJ.) exceeds a predetermined threshold value 13.

In the following the method according to the second example is set out step-by-step. In a first step the overall channel matrix is defined as shown in equation (33). The threshold value $3 is then set/initialised to a value between 0 and 1 in a second step. In the third step singular value decomposition of all channel matrices Hk fork {1, 2, ..., N} is performed according to: Hh=U&DhVK (34) The matrices U for all N users are then analysed according to: ir(1)= ary iax,llUk(:1)'Rkll (35) to identify the user with the channel matrix having the maximum singular vector with the largest norm. This user is given user index ir(1), as indicated by equation (35).

The receiver combining vector r(1) as well as the precoding vector f(1) for this use can then be determined according to: r7,(1) -UZ(I)(.,1) f(j) r)Rfl.�) and (36) -tjr(a)

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IJwC1) Identification and optimisation of the first user's performance can be considered in isolation as the first user does not suffer from interference from other user's channels. The method then proceeds to a selection of the remaining K-i users and to the computation of the receiver combination vectors rk and precoding vectors k to be used for the selected K-i users. In practice this can be achieved by setting up a loop that repeats K-I times, as is shown as step 6 in Figure 3.

The set of users under consideration is then limited to the users that have not yet been selected according to: k = ..., -(37) indicating that the previously selected user no longer forms part of the set of users under consideration. In keeping with above discussed equations (16) and (21) matrices K consisting of the channel matrix Hk and also taking into account interference from other channels are subsequently formed according to: k H{I -(fg(0 fTr(O)} (38) for each user and singular value decomposition is performed for each of the matrices K in step 10 of Figure 3 according to: Hk{I_ > (f0 fi())J Ilk iht (39) As described above for the first example with regard to equation (26), singular value decomposition is also performed for the matrix Hk itself. In this example, however, singular value decomposition is performed for each of the remaining users k. This can be expressed as: (40) Similar to the steps taken with regard to equations (28) and (29) in the first example above, it is then decided for each of the remaining users k if the correlation of the maximum singular vector of K with the maximum singular vector of Hk is below threshold 13 according to: Ojk(:,1)11Uk(:,1)ll<p (41) If statement (41) is true for a particular user, then the maximum singular vector of matrix Hk is not considered sufficiently accurate to be useful as an approximation of the maximum singular vector of the matrix K for the particular user. The maximum singular vector for this user therefore is defined to correspond to the maximum singular vector of the matrix K according to: Uk(:,l)Uk(:1) (42) Otherwise the maximum singular vector of matrix Hk is considered a sufficiently accurate approximation of the maximum singular vector of the matrix P. The maximum singular vector for this user therefore is defined to correspond to the maximum singular vector of the matrix Hk according to: 1) U:, 1) (43) Once all maximum singular vectors for the users k have been determined, the user it(I), having the maximum singular vector with the largest norm (be that the maximum singular vector of the matrix PK or of the matrix Hk according to the selection mode as described above) is identified according to: ir(1) = arg (:, 1) 1t (44) For this user ir(t),the precoding vector 1r, and the receiver combining vector r), can then be determined according to: f) = r@P,l([) and

II

ilfirco nI Once this procedure has been repeated K-i times K users will have been selected from the N overall available users and the precoding vectors k and the receiver combining vectors rk will have been determined for all selected users.

Based on the so determined precoding vectors k and receiver combining vectors r the overall receiver combining matrix R can be generated according to: r,ô 0 0 = 0... 0 (46) 0 0 r(4) It will be appreciated that for at least some of the selected users the receiver combining vector rk corresponds to the maximum singular vector of the channel matrix Hk. As set out above, for such users it is not necessary for the receiver combining vector r to be communicated from the transmitter to the receiver, thus reducing the amount of forward overhead required during operation of the system.

The overall channel matrix for the selected users can be defined according to: _IT T... TiT 47 lhhIir(J()Mir(K_i) and the precoding matrix F can then be determined based on: RH = SF (48) It will be noted that in equations (46) to (48) the order of the users is opposite to the order in which the users have been selected. As a result of the above described selection process the first user selected will provide the best BER, with the worst BER being provided by the last selected user. This affects the average BER of the system negatively. By reversing the order of the users, the BER of the first half of the users is degraded, while the BER of the second half of the users is improved. The average BER achieved by the reversal of the order of the users is, however, improved.

The above described examples require that the transmitter has knowledge of the properties of all of the receiver's channels. Channel properties can be fully estimated in TDD systems due to channel reciprocity. For FDD system, the receivers can feedback channel information to the transmitter for the above described selection of users and for calculating the receiver combination vectors for the selected users.

Once a set of users has been selected those users among the selected users having a receiver combining vector corresponding to the left singular vector corresponding to the maximum singular value of the channel matrix Hk only need to transmit the maximum singular value to the receiver. The amount of information required to be transmitted for these particular users is thus greatly reduced, giving rise to an overall reduction in the amount of transmission overhead on the system. A transmission system operating based on the above principles can nevertheless achieve excellent performance as will be discussed in the following with regard to Figures 4 and 5.

Figures 4 and 5 illustrate the average BER achieved by a transceiver operating in accordance with the above examples depending on signal to noise ratio and relate to a system comprising a transmitter equipped with four antennae communicating simultaneously with four receivers, each having four antennae and receiving one data stream.

Figure 4 explores the dependence of BER on the chosen threshold 13 for the extreme cases 13 = 1 and 13 = 0 and on the number of users of the system. It can be seen from Figure 4 that, if only a small number of users use the system there is a considerable difference between the BER achievable at higher SNR, indicating that, through an appropriate choice of 13 considerable BER performance improvements are achievable, albeit at the cost of increased forward overheads for the transmission of receiver combination data to the receivers.

For larger number of users the dependence of BER on the choice of 3 is less severe. This suggests that there is scope for choosing a threshold value 13 that allows a reduction in the forward overhead required for communicating receiver combination information in the system. As 13 can be dynamically chosen, the system can cater for a scenario where only a small number of users attempt to operate in the system as well as situations where the presence of a larger number of users could be exploited to reduce system overheads. It can, for example, be envisaged that 13 is altered when the number of users on the system changes by a predetermined amount, so that the receiver combining vectors and the precoding vectors can be updated to cater for changing operating conditions.

Figure 4 shows the dependence of average BER on SNR and 13 for a system in which four users are chosen from among eight potential users. Also illustrated is the amount by which the forward overhead has been reduced for the threshold value 13 presented alongside the reduction value. Unsurprisingly the best system performance is achieved if a 13 value of'1' is chosen. This is because in this case receiver combination information is transmitted for each user, allowing for the most accurate receiver combination achievable with the present system. Remarkably and surprisingly, however, a reduction of 13 by only 10% to 0.9 brings about a 60% reduction in the amount of forward overhead while the system achieves a BER performance that is near identical to the performance of the system for 13 = 1.

For comparison purpose Figure 5 also shows the performance of a THP system with antenna selection. Three kinds of antenna selection mechanisms are illustrated. The graph labelled RX-MAS relates to a system in which antenna selection is performed at the receiver, wherein the receiver selects one channel based on the maximal norm of the channel vectors. The graph labelled RX-RAS relates to a system in which the receiver randomly selects a channel and in which the transmitter selects the user based on the selected channel. In both RX-MAS and RX-RAS, the receiver feeds the selected channel back to the transmitter. The transmitter bases THP on the feed back channel. The graph labelled TX-AS relates to a system where channel selection is performed in the transmitter. In TX-AS, the transmitter has full knowledge of each receiver's channels and select the best K channel to proceed THP.

Figure 5 indicates that the present system consistently outperforms the systems in which antenna selection is performed at the receiver (RX-MAS and RX-RAS) in terms of BER over the entire width of the investigated SNR band. It is moreover clear that the present system outperforms the system in which the transmitter selects the channels to be used for all of the investigated values of 13 above 0.3. As can be seen, the minimum reduction in forward overhead for these case is 89%. In these case a considerable reduction in forward overheads is thus achieved, while BER performance is also improved. In light of this it is clear that, by introducing the threshold 13 BER performance comparable to that of prior art systems can be achieved while at the same time a considerable reduction in the forward overhead is achieved.

It will be appreciated that, while the above described second example determines the correlation between the maximum singular vector of the channel matrix Hk and the maximum singular vector of the matrix K to determine whether or not the maximum singular vector of the channel matrix Hk is a sufficiently accurate representation of the maximum singular vector of the matrix user selection according to another example may not use this comparison and simply select the user that has the maximum singular vector of the associated matrix K with the highest norm.

Claims

Claims: 1. A method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding comprising determining receiver combining vectors based on the interrelationship between the Gram-Schmidt process and LQ decomposition.
2. A method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding comprising determining receiver combining vectors as being the vector maximising the square of the norm of a diagonal element of a triangular matrix generated by the Gram-Schmidt process when performing LQ-decomposition of a matrix comprising for each channel of the MIMO system the products of the receiver combining matrix and a channel matrix.
3. A method according to Claim 1 or 2, wherein each said receiver combining vector is jointly determined with an associated precoding matrix.
4. A method of determining receiver combining vectors in a MIMO system employing Tomlinson-Harashima precoding and supporting K data streams associated with K receivers, each receiver comprises a plurality of antennae, the method comprising: performing singular value decomposition of a channel matrix H1 associated with the first receiver to determine a first receiver combining vector r1 as the left singular vector associated with the maximum singular value of the channel matrix H1; and sequentially determining receiver combining vectors r2 to rK for the second to Kth receivers by performing singular value decomposition of matrices P2 to k defined by: k _Hk(11ifIJ for 2 �= k �= K, the receiver combining vectors r2 to r being the left singular vectors of the respective matrices P2 to k that are associated with the maximum singular value of the respective matrix P2 to P, wherein Hk is the channel matrix associated with the k-th receiver, I is the identity matrix, r1H1. r.P.f= forilandf.= forl<i�=k-1.V
5. A method according to claim 4, further comprising, when determining a said receiver combining vector r2 to rK further performing singular value decomposition of the channel matrix Hk associated with the receiver for which the receiver combining vector is to be determined to determine the left singular vector associated with the maximum singular value of the channel matrix Hk; determining the correlation of the said left singular vector of the matrix k with the said left singular vector of the channel matrix and if said correlation exceeds a predetermined value, setting the receiver combining vector for the receiver to the said left singular vector of the channel matrix k
6. A method according to claim 4 or 5, further comprising determining new receiver combination vectors if it is determined that the number of receivers in the system has changed and changing the predetermined value based on the detected change in the number of receivers.
7. A method of estimating a receiver combining vector for use in a MIMO system based on a channel matrix associated with a receiver in the system, the method comprising: estimating a receiver combining vector taking into account likely interference between signals transmitted to the receiver and signals transmitted to other receivers; determining a receiver combining vector based solely on the receiver's channel matrix; determining a correlation between the estimated and determined receiver combining vector and, if the correlation exceeds a predetermined threshold, selecting the receiver combining vector determined based solely on the receiver's channel matrix as the receiver combining vector for the receiver.
8. A method of selecting a receiver from among a number of available receivers for participation in a MIMO system employing Tomlinson-Harashima precoding and arranged to support K data streams, each of said available receivers comprising a plurality of antennae and each of said available receivers associated with a channel matrix, the method comprising: selecting one or more receivers for participation in said system and determining a receiver combining vector for each selected receiver; selecting a k-th receiver for participation in the system by performing singular value decompositions of a number of matrices k associated with unselected receivers to determine a corresponding number of left singular values associated with the maximum singular values of the respective matrix k' and selecting as the k-th receiver the receiver having the left singular value with the highest norm; wherein the matrices k are defined as: 1k =Hk[I-_fI"fIJ wherein Hk is the channel matrix of a receiver under consideration, I is the identity matrix and: rH f, for =1 lirilEli IF = r1P for 1 <i �= k-i II'.II wherein H1 is the channel matrix associated with the first previously selected receiver and r1 is the receiver combining vector of the first selected receiver, r is the receiver combining vector of the i-th previously selected receiver and P1 are the matrices k associated with the respective previously selected receivers.
9. A method according to Claim 8, wherein the first receiver is selected by performing singular value decompositions of the channel matrices of all available receivers, determining the left singular vector associated with the maximum singular value of each channel matrix and selecting the receiver having the maximum singular vector with the highest norm as the first receiver.
10. A method according to Claim 9, further comprising sequentially selecting the second to K-th receivers, wherein k = 2 in the fiist sequential selection step and wherein k is incremented for each sequential selection step.
11. A method according to Claim 8, 9 or 10, further comprising determining a receiver combining vector for a selected receiver by performing a singular value decomposition of the matrix k of the selected receiver to determine the left singular vector associated with the maximum singular value of the matrix k' performing a singular value decomposition of the matrix 11k of the selected receiver to determine the left singular vector associated with the maximum singular value of the matrix tk' determining a correlation between the two left singular vectors and, if said correlation exceeds a predetermined value, defining the receiver combining vector as being the left singular value of the matrix Hk that is associated with the maximum singular value of the matrix Hk.
12. A method according to Claim 11, wherein, if said correlation does not exceed the predetermined value, defining the receiver combining vector as being the left singular value of the matrix k that is associated with the maximum singular value of the matrix
13. An apparatus for use in a MIMO system employing Tomlinson-Harashima precoding, the apparatus arranged to determine receiver combining vectors based on the interrelationship between the Gram-Schmidt process and LQ decomposition.
14. An apparatus for use in a MIMO system comprising receivers and employing Tomlinson-Harashima precoding, the apparatus arranged to determining receiver combining vectors as being the vector maximising the square of the norm of a diagonal element of a triangular matrix generated by the Gram-Schmidt process when performing LQ-decomposition of a matrix comprising for each channel of the MIMO system the product of the receiver combining matrix and a channel matrix.
15. An apparatus according to Claim 13 or 14, further arranged to jointly determine each said receiver combining vector with an associated precoding matrix.
16. An apparatus arranged to determine receiver combining vectors for use in a MIMO system employing Tomlinson-Harashima precoding and capable of supporting K data streams associated with K receivers, each receiver comprises a plurality of antennae, the apparatus arranged to obtain channel matrices H1 to HK; to perform singular value decomposition of a channel matrix H1 associated with the first receiver to determine a first receiver combining vector r1 as the left singular vector associated with the maximum singular value of the channel matrix H1; and to sequentially determine receiver combining vectors r2 to rK for the second to Kth receivers by performing singular value decomposition of matrices P2 to k defined by: k HkI-f"f for 2 �= k �= K, the receiver combining vectors r2 to r being the left singular vectors of the respective matrices P2 to k that are associated with the maximum singular value of the respective matrix P2 to k' wherein Hk is the channel matrix associated with the k-th receiver, I is the identity matrix, rH. r.P.f fori=landf.= I forl<i�=k-1. un II17. An apparatus according to claim 16, further arranged to, when determining a said receiver combining vector, further perform singular value decomposition of the channel matrix associated with the receiver for which the receiver combining vector is to be determined to determine the left singular vector associated with the maximum singular value of the channel matrix of the receiver; to determine the correlation of the said left singular vector of the matrix k with the said left singular vector of the channel matrix; and if said correlation exceeds a predetermined value, to set the receiver combining vector for the receiver to the said left singular vector of the channel matrix.18. An apparatus according to claim 16 or 17, further arranged to determine whether or not the number of receivers in the system has changed, and, if so, to change the predetermined value based on the detected change in the number of receivers.19. An apparatus arranged to estimate a receiver combining vector for use in a MIMO system based on a channel matrix associated with a receiver in the system, the apparatus arranged to: estimate a receiver combining vector taking into account likely interference between signals transmitted to the receiver and signals transmitted to other receivers; determine a receiver combining vector based solely on the receiver's channel matrix; determine a correlation between the estimated and determined receivel combining vector and, if the correlation exceeds a predetermined threshold, to select the receiver combining vector determined based solely on the receiver's channel matrix as the receiver combining vector for the receiver.20. An apparatus arranged to select a receiver from among a number of available receivers for participation in a MIMO system employing Tomlinson-Harashima precoding, the MIMO system arranged to support K data streams, each of said available receivers comprising a plurality of antennae and each of said available receivers associated with a channel matrix, the apparatus arranged to: select one or more receivers for participation in said system and determine a receiver combining vector for each selected receiver; select a k-th receiver for participation in the system by performing singular value decompositions of a number of matrices k associated with unselected receivers to determine a corresponding number of left singular values associated with the maximum singular values of the respective matrix k' and select as the k-th receiver the receiver having the left singular value with the highest norm; wherein the matrices P are defined as: Pk wherein Hk is the channel matrix of a receiver under consideration, I is the identity matrix and: = rH1 for i1 riIIi V = rP1 for 1 <i k-i Jr1PV wherein H1 is the channel matrix associated with the first previously selected receiver and r1 is the receiver combining vector of the first selected receiver, r1 is the receiver combining vector of the i-th previously selected receiver and P are the matrices k associated with the respective previously selected receivers 21. An apparatus according to Claim 20, arranged to select the first receiver by performing singular value decompositions of the channel matrices of all available receivers, determine the left singular vector associated with the maximum singular value of each channel matrix and select the receiver having the maximum singular vector with the highest norm as the first receiver.22. An apparatus according to Claim 21, further arranged to sequentially select the second to K-th receivers, wherein k = 2 in the first sequential selection step and wherein k is incremented for each sequential selection step.23. An apparatus according to Claim 20, 21 or 22, further arranged to determine a receiver combining vector for a selected receiver by performing a singular value decomposition of the matrix k of the selected receiver to determine the left singular vector associated with the maximum singular value of the matrix k' perform a singular value decomposition of the matrix "k of the selected receiver to determine the left singular vector associated with the maximum singular value of the matrix Hk, determine a correlation between the two left singular vectors and, if said correlation exceeds a predetermined value, defining the receiver combining vector as being the left singular value of the matrix Hk that is associated with the maximum singular value of the matrix Hk.24. An apparatus according to Claim 23, arranged to define the receiver combining vector as being the left singular value of the matrix k that is associated with the maximum singular value of the matrix k if said correlation does not exceed the predetermined value.25. An apparatus according to any of Claims 13 to 24, wherein the apparatus is a base station or an access point.26. A computer program product comprising computer executable instruction which, when executed by a computer, cause said computer to perform a method in accordance with any one of claims 1 to 12.27. A computer readable carrier medium comprising a computer program product in accordance with claim 26.