MIMO wireless communication systems

Abstract

A wireless communication system is described which includes a transmitter operable to transmit a transmitted signal, the transmitter having one or more transmitting antennae, a receiver operable to receive a received signal, the receiver having one or more receiving antennae, wherein lattice reduction is used in obtaining, at the receiver, an estimate of the transmitted signal based on the received signal, characterized in that the lattice reduction utilizes a lattice reduction matrix, a decomposed representation of which is transmitted between the transmitter and the receiver.

Claims

1. A wireless communication system comprising: a transmitter operable to transmit a source signal, the transmitter having one or more transmitting antennae, wherein the source signal is multiplied by a channel matrix before being transmitted by the transmitter; and a receiver operable to receive a received signal, the receiver having one or more receiving antennae; wherein the transmitter comprises a calculating unit for calculating a lattice reduction matrix for transforming the channel matrix into a form in which rows and columns are more orthogonal, the transmitter being operable to obtain a decomposed representation of the lattice reduction matrix and to transmit said decomposed representation of the lattice reduction matrix to the receiver, wherein the decomposed representation of the lattice matrix is represented by fewer bits than the lattice reduction matrix, and wherein the receiver is further operable to receive the decomposed representation of the lattice reduction matrix, to reconstruct the lattice reduction matrix therefrom, and to obtain an estimate of the source signal utilizing the lattice reduction matrix.

2. The wireless communication system according to claim 1, wherein the transmitter is a transmitter of a base station, the receiver is a receiver of a user station, the lattice reduction matrix is calculated at the base station and the decomposed representation of the lattice reduction matrix is transmitted from the base station to the user station.

3. The wireless communication system according to claim 1, wherein an identifying index is assigned to each totally unimodular matrix in a set of totally unimodular matrices, and in transmitting the decomposed representation of the lattice reduction matrix, which comprises one or more of the totally unimodular matrices in the set, indices for one or more relevant totally unimodular matrices, the product of which is the lattice reduction matrix, are transmitted instead of transmitting the one or more relevant totally unimodular matrices themselves or elements thereof.

4. A transmitter for use in a wireless communication system, the transmitter comprising: one or more transmitting antennae operable to transmit a source signal to a receiver which has one or more receiving antennae operable to receive a received signal, wherein the source signal is multiplied by a channel matrix before being transmitted by the transmitter; a calculating unit for calculating a lattice reduction matrix for transforming the channel matrix into a form in which rows and columns are more orthogonal; and wherein the transmitter is further operable to obtain a decomposed representation of the lattice reduction matrix and to transmit said decomposed representation to the receiver, wherein the decomposed representation of the lattice reduction matrix is represented by fewer bits than the lattice reduction matrix.

5. The transmitter according to claim 4, wherein the transmitter is a transmitter of a base station, the receiver is a receiver of a user station, the lattice reduction matrix is calculated at the base station and the decomposed representation of the lattice reduction matrix is transmitted from the base station to the user station.

6. The transmitter according to claim 4, wherein the lattice reduction matrix is a unimodular matrix and the decomposed representation thereof comprises one or more totally unimodular matrices the product of which is the lattice reduction matrix, the one or more totally unimodular matrices being taken from a set of totally unimodular matrices, wherein the one or more totally unimodular matrices are determined by initially defining that a current intermediate matrix equals the lattice reduction matrix and then iteratively repeating the following until obtaining a calculated matrix, or the calculated matrix when pre- or post-multiplied by one of the totally unimodular matrices in the set, equals (or equals a scalar multiple of) one of the totally unimodular matrices in the set: for each of the totally unimodular matrices in the set which perform column and row additions: calculating an intermediate matrix by post-multiplying the current intermediate matrix by a totally unimodular matrix; calculating a norm of the intermediate matrix and if the norm is a smallest norm calculated so far, remembering the norm as the smallest norm calculated so far, storing the totally unimodular matrix as a current totally unimodular matrix, and redefining the intermediate matrix as the intermediate matrix for the next iteration; calculating the intermediate matrix by pre-multiplying the current intermediate matrix by the totally unimodular matrix; and calculating the norm of the intermediate matrix and if the norm is the smallest norm calculated so far, remembering the norm as the smallest norm calculated so far, storing the totally unimodular matrix as the current totally unimodular matrix, and redefining the intermediate matrix as the intermediate matrix for the next iteration.

7. The transmitter according to claim 6, wherein matrix inversion is performed if necessary in order to obtain the one or more totally unimodular matrices the product of which is the lattice reduction matrix.

8. The transmitter according to claim 4, wherein, if there is an error in, or a problem associated with, a data packet received by the receiver, the transmitter is adapted to transmit the decomposed representation of the lattice reduction matrix to the receiver thereby enabling the receiver to re-decode the data packet using the lattice reduction matrix, instead of re-transmitting the data packet.

9. The transmitter according to claim 4, wherein the lattice reduction matrix is a unimodular matrix and the decomposed representation thereof comprises one or more totally unimodular matrices the product of which is the lattice reduction matrix.

10. The transmitter according to claim 9, wherein an identifying index is assigned to each totally unimodular matrix in a set of totally unimodular matrices, and in transmitting the decomposed representation of the lattice reduction matrix, which comprises one or more of the totally unimodular matrices in the set, indices for one or more relevant totally unimodular matrices, the product of which is the lattice reduction matrix, are transmitted instead of transmitting the one or more relevant totally unimodular matrices themselves or elements thereof.

11. The transmitter according to claim 10, wherein if a totally unimodular matrix is multiplied by itself one or more times in the decomposed representation of the lattice reduction matrix, a power m is transmitted (where m-1 is the number of times that the totally unimodular matrix is multiplied by itself) instead of transmitting the index for the totally unimodular matrix a required number of times.

12. A method for use in a wireless communication system which incorporates a transmitter for transmitting a source signal using one or more transmitting antennae and a receiver for receiving a received signal using one or more receiving antennae, the method comprising, at the transmitter: transmitting the source signal from the transmitter to the receiver, wherein the source signal is multiplied by a channel matrix before being transmitted by the transmitter; calculating a lattice reduction matrix for transforming the channel matrix into a form in which rows and columns are more orthogonal; and finding a decomposed representation of the lattice reduction matrix, wherein the decomposed representation of the lattice reduction matrix is represented by fewer bits than the lattice reduction matrix; transmitting the decomposed representation of the lattice reduction matrix to the receiver, the method further comprising, at the receiver: receiving the decomposed representation from the transmitter; and reconstructing the lattice reduction matrix and using it to obtain an estimate of the source signal based on the received signal.

13. The method according to claim 12, further comprising feeding back channel state information (CSI) from the receiver to the transmitter, wherein the channel state information is used in calculating the lattice reduction matrix at the transmitter.

14. The method according to claim 12, wherein, in the wireless communication system, the transmitter is a transmitter of a base station and the receiver is a receiver of a user station, the finding of the decomposed representation of the lattice reduction matrix comprising finding one or more totally unimodular matrices the product of which is the lattice reduction matrix.

15. The method according to claim 14, wherein an identifying index is assigned to each totally unimodular matrix in a set of totally unimodular matrices, and transmitting the decomposed representation of the lattice reduction matrix, which comprises one or more of the totally unimodular matrices in the set, involves transmitting the indices for relevant totally unimodular matrices.

16. The method according to claim 15, wherein if a totally unimodular matrix is multiplied by itself one or more times in the decomposed representation of the lattice reduction matrix, then transmitting the decomposed representation of the lattice reduction matrix involves transmitting a power m (where m1 is the number of times that the totally unimodular matrix is multiplied by itself) instead of transmitting the index for the totally unimodular matrix a required number of times.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The drawings associated with this specification help to explain the background of the invention. They also help to explain certain features and aspects of the invention. However, it will be clearly understood that the drawings are given for the purposes of explanation and to assist understanding only, and the invention is not necessarily limited to or by any of the background information, features or aspects shown in, or described with reference to, the drawings. In the drawings:

(2) FIG. 1 is a schematic representation of a simplified 32 MIMO system and the individual SISO channels between the respective transmitter and receiver antennae.

(3) FIG. 2 is a conceptual diagram of a more generalized MIMO system in which the transmitter has N.sub.t transmitting antennae, and the receiver has N.sub.r receiving antennae. FIG. 2 also schematically represents the introduction of noise into the signals received by the receiving antennae.

(4) FIG. 3 is a schematic representation system similar to that given in FIG. 1, but relating to a more generalised MIMO system.

(5) FIG. 4 is a schematic representation illustrating certain important functional components of a MIMO-OFDM transmitter.

(6) FIG. 5 is a schematic representation illustrating certain important functional components of a MIMO-OFDM receiver.

(7) FIG. 6 is a graphical illustration of the principle of lattice reduction, using as an example a simple two-dimensional lattice.

(8) FIG. 7 is a block diagram illustrating a MIMO wireless communication system according to the mathematical model of equation (I), and also illustrating some further processing performed by the receiver. The MIMO wireless communication system in FIG. 7 is of a kind to which the present invention may be applied.

(9) FIG. 8 is a graph illustrating Bit Error Rates (BER) vs Signal to Noise (SNR) results obtained using lattice reduction according to the present invention in a channel with low spatial correlation.

(10) FIG. 9 is a graph illustrating Bit Error Rates (BER) vs Signal to Noise (SNR) results obtained using lattice reduction according to the present invention in a channel with high spatial correlation.

DETAILED DESCRIPTION OF ASPECTS AND EMBODIMENTS OF THE INVENTION

(11) It will be recalled from the background section above that the relationship between the signal y received by the receiver and the signal x transmitted by the transmitter in a typical MIMO system may be modelled using the basic mathematical model given in equation (I) (which is repeated below):
y=Hx+n(I)

(12) FIG. 7 is a block diagram illustrating a MIMO system according to this mathematical model, and also illustrating some further processing performed by the receiver. The MIMO wireless communication system in FIG. 7 is of a kind to which the present invention may be applied. However, it should be noted that the invention is not necessarily limited to implementation in systems corresponding to this representation.

(13) In FIG. 7, the source signal x is transmitted from (the multiple antennae) of the transmitter over the air (as described above), and the effect of this is represented in the model by pre-multiplying the source signal vector x by the channel matrix H to give the quantity Hx shown in FIG. 7. The noise component n is then added, thus giving the signal y received by the (multiple antennae of the) receiver, as per the model in equation (I).

(14) It will also be recalled from the background section above that, in LR-MIMO systems, the purpose of lattice reduction is to transform the channel matrix H into a form in which the rows and columns are more nearly orthogonal (i.e. so that the rows and columns are, in effect, more nearly linearly independent). This helps to minimise the detrimental effects (such as impeded receiver performance) of correlation in the MIMO channel, which is represented in the mathematical model (I) by correlation between the rows and columns of the channel matrix H. As explained above, the matrix by which this transformation of the channel matrix H is affected is generally called the Lattice Reduction Matrix P.

(15) One of the major complexities associated with practical implementations of LR-MIMO lies in the calculation of the Lattice Reduction Matrix P. However, the method used to calculate the Lattice Reduction Matrix P is not critical to the present invention. Therefore, for the purposes of the present invention, the Lattice Reduction Matrix P may be obtained using any suitable technique. One known algorithm which is suitable for this purpose is commonly referred to as the LLL algorithm. This algorithm is well documented, and the following document is a good reference for it: L. Lovasz, An Algorithmic Theory of Numbers, Graphs and Convexity, Philadelphia, USA: Society for Industrial and Applied Mathematics, 1986.

(16) Whilst the Lattice Reduction Matrix P may be obtained using the known LLL algorithm, or alternatively any other suitable algorithm (it being recalled that the means by which it is obtained is not critical to the present invention), nevertheless finding the Lattice Reduction Matrix P (irrespective of which algorithm or technique is used) generally requires an iterative process. The calculation of the Lattice Reduction Matrix P therefore requires considerable power and computational resources. To address this issue, in some embodiments of the present invention, and in particular the embodiments described in detail here, the calculation of lattice reduction matrix P is performed at the base station (which generally has far greater power, processing and transmission/reception resources than a mobile station) and then transmitted to the user station (which could be a mobile station or a fixed subscriber station etc). Consequently, the embodiments described here relate primarily to downlink transmissions. However, as explained above, no limitation should be implied from this, and the present invention may be applicable to downlink or uplink.

(17) In order for the transmitter to calculate the lattice reduction matrix P it must have knowledge of the channel seen by the receiver. In the FDD (Frequency Division Duplex) systems mentioned above where uplink transmissions (user to base station) and downlink transmissions (vice-versa) employ different carrier frequencies, this may be achieved by feeding channel state information (CSI) back from the receiver to the transmitter (i.e. transmitting information pertaining to the channel H back to the transmitter). Alternatively, in so-called TDD (Time Division Duplex) systems, the uplink and downlink are transmitted in two adjacent time slots on the same frequency. If the two time slots are within the channel coherence time (i.e. the channel does not change) then the channel state information need not be fed back. Therefore, in TDD systems, channel reciprocity may be exploited in order to calculate the lattice reduction matrix P at the transmitter.

(18) In FIG. 7, the dashed box represents the receiver, and the contents of the dashed box represent the processing of the signal after it has been received by the receiver. It should be noted from FIG. 7 that the receiver receives from the transmitter not only the signal y, but also the Lattice Reduction Matrix P which is calculated at the transmitter (as explained above). After the signal y is received by the receiver, it is equalized. In FIG. 7, a particular form of equalization known as Zero Forcing is illustrated which involves pre-multiplying the received signal y by the quantity (HP).sup.1. It will be recognised that, implicit in this equalization, is the assumption that the channel characteristics can be represented by the channel matrix H when transformed by the lattice reduction matrix P (i.e. it is assumed that the channel can be represented by the quantity HP). Whilst FIG. 7 illustrates the use of Zero Forcing equalization, it is to be understood that other equalization methods might also be used such as, for example, Minimum Mean Square Error (MMSE) and Successive Interference Cancellation (SIC). The particular form of equalization is not therefore critical to the present invention. The result of the zero forcing equalization shown in FIG. 7 (i.e. the result of pre-multiplying the received signal y by the quantity (HP).sup.1) is as follows. Given that y=Hx+n from equation (I), and defining that n=(HP).sup.1n (i.e. n is simply a convenient notation for the resultant noise vector transformation), it follows that the result of the zero forcing is given by:
(HP).sup.1y=(HP).sup.1(Hx+n)=(HP).sup.1Hx+(HP).sup.1n=P.sup.1x+n

(19) After the zero forcing equalization, the signal is then passed through a slicer. The slicer quantizes each entry of the equalized signal to the nearest constellation symbol and obtains a hard estimate of {circumflex over (z)}, where {circumflex over (z)}=P.sup.1x. Finally, the receiver obtains an estimate {circumflex over (x)} of the source signal (i.e. {circumflex over (x)} is an estimate of the original signal x transmitted by the transmitter) by pre-multiplying the estimate {circumflex over (z)} by the lattice reduction matrix P; i.e. {circumflex over (x)}=P{circumflex over (z)}. One of the specific reasons why lattice reduction provides performance improvements in correlated MIMO channels is because transforming the channel matrix H into a form in which the rows and columns are more nearly orthogonal improves the performance, and in particular the decision boundaries, of the slicer. This is explained in further detail in the following document which is a good reference: H. Yao and G. W. Wornel, Lattice-Reduction-Aided Detectors for MIMO Communication Systems, Proc. Global Commun. Conf. (GLOBECOM-2002), Taiwan, November 2002

(20) One of the benefits that the present invention may desirably achieve is that, for a given transmission, the demands placed on the systems' limited reception resources can be reduced by the way in which the lattice reduction matrix P is transmitted from the transmitter to the receiver. Specifically, by transmitting a decomposed representation of the lattice reduction matrix P from the transmitter to the receiver, rather than transmitting the full lattice reduction matrix itself, the present invention may reduce the demands placed on the systems' reception resources. This may be particularly important for the receiver where the receiver is a user station (e.g. a mobile handset or the like) which may have relatively very limited reception and power/data processing resources.

(21) Decomposing the lattice reduction matrix P reduces the number of bits required to represent the matrix (compared with the number of bits required to represent each individual entry in the un-decomposed matrix), and therefore it reduces the number of bits required to be transmitted from the transmitter to the receiver. In other words, rather than quantizing the individual entries of the lattice reduction matrix P for transmission from the transmitter to the receiver, the present invention decomposes the matrix P to reduce the number of bits required to be transmitted.

(22) In the preferred embodiments of the invention explained hereafter, the lattice reduction matrix P is decomposed by exploiting the fact that the matrix P is a unimodular matrix. Those skilled in the art will recognise that a unimodular matrix is defined as a matrix that has a determinant or +1 or 1 and which has only integer entries (although the entries may be real or complex integers). Furthermore, in these preferred embodiments, the unimodular matrix P is decomposed into one or more (typically multiple) totally unimodular matrices. Again, those skilled in the art will recognise that a totally unimodular matrix is defined as a matrix for which every square non-singular submatrix is unimodular. From this definition, it follows that a totally unimodular matrix need not be square itself, but any totally unimodular matrix has only 0, +1, 1, i, or i, entries.

(23) One particular benefit of these preferred embodiments is that only a limited number of totally unimodular matrices are required to decompose the original matrix P. These totally unimodular matrices may be referred to as decomposition matrices. The limited number of decomposition matrices may be considered to comprise a set of decomposition matrices.

(24) The operation of certain aspects of the invention will be described below with reference to a simplified example 22 MIMO system (i.e. a system in which there are two transmitting antennae and two receiving antennae, and in which the channel could hence be represented by a 22 channel matrix H). It will, of course, be understood that the principles described with reference to this simple example may be extended to systems having a far greater number of degrees of freedom (i.e. having a greater number of transmitting and/or receiving antennae).

(25) The totally unimodular decomposition matrices listed in the table below may be used to decompose a 22 lattice reduction matrix P by performing elementary row and column operations. Specifically, matrices D.sub.0 to D.sub.3 perform column and row permutations, while matrices D.sub.4 to D.sub.11 perform column and row additions. Note that the decomposition matrices shown in the table below are not unique, and it would be possible to use other decomposition matrices to perform elementary row and column operations.

(26) TABLE-US-00001 Decomposition Totally Unimodular Matrix Index Decomposition Matrix D.sub.0 $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ D.sub.1 $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$ D.sub.2 $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$ D.sub.3 $\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$ D.sub.4 $\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$ D.sub.5 $\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$ D.sub.6 $\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]$ D.sub.7 $\left[\begin{array}{cc}1& 0\\ -1& 1\end{array}\right]$ D.sub.8 $\left[\begin{array}{cc}1& i\\ 0& 1\end{array}\right]$ D.sub.9 0$\left[\begin{array}{cc}1& 0\\ i& 1\end{array}\right]$ D.sub.10 $\left[\begin{array}{cc}1& -i\\ 0& 1\end{array}\right]$ D.sub.11 $\left[\begin{array}{cc}1& 0\\ -i& 1\end{array}\right]$

(27) As an illustration, consider a lattice reduction matrix P given by:

(28) $P=\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]$

(29) In this example, the given lattice reduction matrix P can be decomposed using decomposition matrices from the table above as follows:

(30) $P=D_5{D}_4\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$

(31) Therefore, in the above example, instead of signalling the individual entries of the lattice reduction matrix P, indices associated with decomposition matrices D.sub.5 and D.sub.4 can be signalled. Those skilled in the art will recognise that the receiver must have knowledge of the indices associated with each decomposition matrix, as used by the transmitter, in order to be able to reconstruct the lattice reduction matrix from the received indices. Therefore, after the receiver has identified (from the received indices) the totally unimodular matrices that form the matrix decomposition (it also being appreciated that the order in which the totally unimodular matrices appear in the decomposition is also transmitted by the transmitter, either by sending the relevant indices in their correct order or by some other means), the receiver can then reconstruct the lattice reduction matrix P by multiplying the said totally unimodular matrices together.

(32) It is also necessary to signal the number of decomposition matrices in the overall decomposition of the lattice reduction matrix because, depending on the lattice reduction matrix, a varying number of decomposition matrices may be required. Even so, this approach significantly reduces the signalling overhead associated with transmitting the lattice reduction matrix from the base station transmitter to the user station receiver, as described further below.

(33) In cases where there is significant correlation in the MIMO channel (i.e. significant correlation between individual SISO channels, this being represented by correlation in the rows and columns of the channel matrix H), the decomposition of the lattice reduction matrix P can result in repeated multiplications of the same decomposition matrix. As an example, if the lattice reduction matrix P is given by

(34) $P=\left[\begin{array}{cc}1& 1\\ 2& 3\end{array}\right]$
then a resultant decomposition would be:

(35) $P=D_5{D}_5{D}_4=D_5^2{D}_4\left[\begin{array}{cc}1& 1\\ 2& 3\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]={\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]}^2\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$

(36) In cases such as this (and even more so in instances where more than one of the decomposition matrices is multiplied by itself one or more times in the overall decomposition), additional savings in terms of signalling overhead may be achieved by signalling the indices associated with the relevant decomposition matrices (D.sub.5 and D.sub.4 in the example above), and additionally signalling a power for each or some of the decomposition matrices (in the example above that power 2 is signalled for D.sub.5 and the power 1 is signalled for D.sub.4).

(37) The examples above illustrate how the present invention enables significant savings to be made in terms of the signalling overhead associated with transmitting the lattice reduction matrix from the transmitter to the receiver. However, in order to realise these advantages, means must be provided for determining a decomposition of a given lattice reduction matrix. Strictly speaking, the means by which the decomposition of the lattice reduction matrix is obtained is not critical to the invention, and therefore any suitable means or method could be used. One method for determining a decomposition of the lattice reduction matrix is explained below. However, it is to be understood that the invention is not necessarily limited to this particular method, and other methods might alternatively be used.

(38) In general terms, the presently described method involves an iterative process of pre- or post-multiplying the lattice reduction matrix P with all candidate decomposition matrices in order to perform elementary row or column operations. In each iteration, the decomposition matrix D, which yields the smallest Frobenius norm when pre- or post-multiplied with the lattice reduction matrix is chosen. Those skilled in the art will be familiar with matrix and vector norms, of which the Frobenius norm is simply one example. The Frobenius norm has been chosen in the particular method presently described, although a range of other norms might alternatively be used. The process terminates when the resulting matrix equals (or alternatively equals a scalar multiple of) one of the decomposition matrices.

(39) The process discussed in general terms in the previous paragraph may be more fully understood with reference to the following pseudo code. The operation of each line in the pseudo code is explained on the right.

(40) TABLE-US-00002 1. Define norm.sub.min = infinity; n = 0;P.sub.1 = P Initialise the minimum norm, iteration number n, and LR transform matrix P.sub.n respectively 2. REPEAT Continue iterating until condition in 3 below is met (A). n = n+1 Update iteration number (B). FOR all D.sub.i = {D.sub.4,D.sub.5,...,D.sub.11} Try all candidate decomposition matrices (I). P= P.sub.nD.sub.i Calculate an intermediate matrix by post- multiplying the LR transform matrix by the current decomposition matrix (II). IF P < norm.sub.min If the norm of the intermediate matrix is the smallest so far, proceed with (i), (ii) and (iii) below (i). norm.sub.min = P Store the norm of the intermediate matrix (ii). D.sub.n = D.sub.i Store the decomposition matrix for iteration n (iii). P.sub.n+1 = P Store the intermediate matrix for the next iteration END IF (III). P = D.sub.iP.sub.n Calculate the intermediate matrix by pre- multiplying the LR transform matrix by the current decomposition matrix (IV). IF P < norm.sub.min If the norm of the intermediate matrix is the smallest so far, proceed with (i), (ii) and (iii) below (i). norm.sub.min = P Store the norm of the intermediate matrix (ii). D.sub.n = D.sub.i Store the decomposition matrix for iteration n (iii). P.sub.n+1 = P Store the intermediate matrix for the next iteration END IF V. P.sub.n = P.sub.n+1 Update the LR transform matrix END FOR 3. UNTIL P.sub.n k {D.sub.1,D.sub.2,...,D.sub.11}

(41) In the above pseudo code, . denotes the Frobenius norm and k is a scalar factor. It will be recognised that the process represented by the pseudo code above produces a decomposition of the form, for example:
D.sub.6P=D.sub.2

(42) This can easily be transformed into the desired decomposition format by performing matrix inversion. For example:
D.sub.6.sup.1D.sub.6P=D.sub.6.sup.1D.sub.2

(43) From the above table it will be noted that, in this example, D.sub.6.sup.1=D.sub.4. Therefore
P=D.sub.4D.sub.2

(44) This illustrates one example of a process by which the lattice reduction matrix P may be decomposed into a series of one or more totally unimodular decomposition matrices. As noted above, other processes for achieving this purpose are possible.

(45) Discussion of Performance Results

(46) The effectiveness of the efficient signalling provided by the present invention in transmitting the lattice reduction matrix P has been assessed with link level simulations in a 22 MIMO system. For the purposes of overhead calculation, the following amounts of data were assumed:

(47) TABLE-US-00003 Signalling According to the Present Standard Signalling Invention per complex valued matrix per decomposition matrix 4 bits. The element 8 bits (3 bits actual overhead depends on the number of resolution + 1 sign bit, for matrices required for the decomposition of each of the real and the lattice reduction matrix P. In order to imaginary parts) signal the number of matrices an additional 4 bits were assumed.

(48) The overhead results summarized in the table below were obtained by averaging over 2000 random Rayleigh flat fading channels with either low (=0.1) or high (=0.9) spatial channel correlation, where is the channel correlation coefficient. The number of bits using decomposition includes a 4 bit overhead which indicates the number of totally unimodular matrices used in the decomposition.

(49) TABLE-US-00004 Channel Channel correlation low correlation high ( = 0.1) ( = 0.9) Number of bits required according 9.76 18.64 to the present invention Number of bits required with 32 32 standard signalling Relative overhead reduction using 69.5% 41.75% signalling according to present invention

(50) From the results shown in the table above, it will be seen that the efficient signalling provided by the present invention can reduce the overhead by about 40% in highly correlated channels and by about 70% in channels with low-level correlation.

(51) The graphs in FIGS. 8 and 9 illustrate Bit Error Rates (BER) vs Signal to Noise (SNR) results that were obtained with a linear MMSE receiver using lattice reduction according to the present invention, and using the same settings as for the overhead results given in table above. Specifically, FIG. 8 plots BER vs SNR performance in a channel with low spatial correlation, and FIG. 9 plots BER vs SNR performance in a channel with high spatial correlation. The graphs illustrate that, in correlated MIMO channels, lattice reduction and signalling according to the present invention enabled significant gains to be made over traditional linear MMSE receiver performance. In fact, performance approaches the performance of the optimal but computationally complex Maximum Likelihood (ML) receiver, as shown FIG. 9.

(52) Possible Applications of the Present Invention

(53) Various aspects and embodiments of the invention, and various aspects pertaining to its implementation, have been discussed above. By way of further explanation, the following list provides some examples of possible applications of the invention. It will be understood that these applications are suggested solely to assist further understanding of the invention by placing it in the context of possible applications. However, the invention is in no way limited to or by any of these particular possible applications, and indeed, a range of other applications is possible. MIMO schemes where the computation of the lattice reduction matrix at the receiver would be a large computational burden. This is generally the case in wireless cellular systems where the mobile station has limited computational power. Other application areas might include low-cost receivers such as those used in wireless sensor networks. Multicast transmissions, where the transmitter sends a single message to multiple receivers. In this case the transmitter can send the individual lattice reduction matrix to each of the receivers. Alternatives to lattice reduction such as precoding or beamforming cannot be used since each receiver has an individual channel, which would require an individual pre-code or beamforming weight per receiver at the transmit side. Data repetition for erroneously received data packets. In wireless cellular systems, Hybrid Automatic Repeat Request (HARQ) mechanisms are typically used when a data packet is received erroneously. In HARQ the transmitter re-transmits the erroneously received data packet, thereby consuming valuable resources. With the scheme proposed by the present invention, instead of re-transmitting the erroneously received data packet, the transmitter could send the lattice reduction matrix to the receiver. The receiver could subsequently attempt a re-decode the data packet using the lattice reduction matrix. The benefit of this comes from the fact that only the lattice reduction matrix needs to be signalled from the transmitter to the receiver instead of re-sending the entire data packet.

(54) In any of the aspects or embodiments of the invention described above, the various features may be implemented in hardware, or as software modules running on one or more processors. In particular, aspects of the invention may be implemented as software which, when executed by a processor of a transmitter, causes the transmitter to implement any of the methods described above. Similarly, aspects of the invention may be implemented as software which, when executed by a process of a transmitter, provides a transmitter in accordance with the invention as described above. Features of one aspect may be applied to any of the other aspects.

(55) The invention also provides a computer program or a computer program product for carrying out any of the methods described herein, and a computer readable medium having stored thereon a program for carrying out any of the methods described herein.

(56) A computer program embodying the invention may be stored on a computer-readable medium, or it could, for example, be in the form of a signal such as a downloadable data signal provided from an Internet website, or it could be in any other form.

(57) Those skilled in the art will recognise that various changes and alterations may be made to the various aspects and embodiments of the invention described herein without departing from the spirit and scope of the invention.