GB2478360A

GB2478360A - Optimal pilot symbol design/placement in spatial and delay correlated MIMO OFDM channels

Info

Publication number: GB2478360A
Application number: GB1003743A
Authority: GB
Inventors: Cheran Malsri Vithanage
Original assignee: Toshiba Research Europe Ltd
Current assignee: Toshiba Europe Ltd
Priority date: 2010-03-05
Filing date: 2010-03-05
Publication date: 2011-09-07
Also published as: GB201003743D0

Abstract

Prior art systems tend to assume uncorrelated channels which result in equispaced pilots being optimal. The invention acknowledges that real world channels are often correlated and presents an efficient sub-optimal formula for determining pilot positioning and symbol type. The formula (see Figure) utilises channel statistics, in particular the space delay channel correlation matrix Rh(aka channel covariance matrix) and noise variance No. This formula is suitable for low SNR situations. For high SNR situations the alternative formula of Fig. 6 is used which omits the need for the noise variance. In practical systems both formulae can be used and the best pilots selected from the two results (see Fig. 7). Since only channel statistics are used the signalling is reduced compared to transmitting the full channel estimate.

Description

MIMO-OFDM system utilising a method of frequency domain pilot symbol optimisation based on channel statistics The present invention is concerned with communication systems using orthogonal frequency division multiplexed (OFDM) transmissions. It is particularly, but not exclusively, concerned with such communications involving apparatus with multiple transmit and receive antennas.

A multiple input, multiple output (MIMO) transmission channel can be considered to be a plurality of channels defined by a single transmit antenna and a single receive antenna. To facilitate coherent detection at a receiver, the channels from each of the transmit antennas to each of the receive antennas need to be estimated. For this purpose, it is usual to transmit pilot symbols, which are known both at the transmitter and the receiver. By detection of these pilot symbols at the receiver, on each of the channels, channel estimation can be achieved.

An example of such pilot symbol placement in amongst the data carrying subcarriers is shown in figure IA. Figure IA is a graphical representation of transmit antennas versus subcarriers, in accordance with a prior art example. A transmitter with two antennas is considered and the number of subcarriers defined for transmission (and reception) in the system is 16. The pilot symbols are indicated as shaded regions of the frame, with unshaded regions being available for carriage of data symbols.

In the illustrated arrangement, a conventional method of pilot symbol insertion, is illustrated. In this arrangement, pilot symbols are placed equidistantly in the range of subcarriers.

Different methods of pilot symbol placement will generally lead to variation in the performance of channel estimation at the receiver. Also, the nature of the pilot symbols transmitted on the selected subcarriers will again affect the accuracy of channel estimation at the receiver.

An aspect of the invention focuses on subcarrier selection for the carriage of pilot symbols, and the nature of the pilot symbols to be so transmitted on the se'ected subcarriers.

In addressing this, an assumption is made in this disclosure that that there is knowledge at the transmitter of channel statistics to the receiver. This is a more relaxed requirement than exact channel knowledge, since channel statistics vary more slowly over time than specific channel information, thus enabling their estimation and tracking at the transmitter.

Optimal pilot symbol design for OFDM systems has been considered, for example, in: R. Negi and J. Cioffi, "Pilot tone selection for channel estimation in a mobile OFDM system,' IEEE Transactions on Consumer Electronics, vol. 44, August 1998, pp. 1122-28; X. Cai and G. B. Giannakis, Error probability minimizing pilots for OFDM with M-PSK modulation over Rayleigh-fading channels," IEEE Transactions on Vehicular Technology, vol. 53, January 2004, pp. 146-1 55; and I. Barhumi, G. Leus and M. Moonen, "Optimal training design for MIMO OFDM systems in mobile wireless channels,' IEEE Transactions on Signal Processing, vol. 51, no. 6, June 2003, pp. 1615-1624.

In particular-, Barhumi et al. considers the general case of having multiple transmit/receive antennas (i.e. MIMO -multiple input multiple output systems), as is the case in the present disclosure. However, all of these prior disclosures focus upon scenarios in which the underlying channels are subject to uncorrelated scattering, both in space and time (i.e. when there are no antenna correlations nor delay domain correlations).

It is correctly concluded in those works that, for such channels, the optimal method of pilot symbol placement is to place them such that there is an equal spacing between one another (as illustrated in figure 1A). For MIMO systems, Barhumi et al. finds that the transmission of phase shift orthogonal sequences on the subcarriers (which were in turn selected as mentioned) is optimal. Thus, for uncorrelated channels, the problem of pilot design and allocation has been solved.

On the other hand, more recent experimental investigations into wideband short range indoor channels conclude that there exist scenarios where the underlying channel impulse responses are subject to correlated scattering in time (i.e. delay domain correlations exist in practice). Examples of this include R. Saadane, A. Menouni, R. Knopp and D. Aboutajdine, "Empirical eigenanalysis of indoor UWB propagation channels," IEEE Globecom conference, pp. 3215-19, 2004, and U. G. Schuster and H. Bolcskei, "Ultrawideband channel modelling on the basis of information theoretic criteria", IEEE Transactions on Wireless Communications, vol. 6, pp. 2464-75, July 2007.

Also, practical multiple antenna implementations (either at the transmitter or the receiver) are subject to spatial correlations, since design and space considerations mean that antennas cannot be spaced sufficiently apart to avoid such correlations. For such scenarios, an equal spacing between the pilot carrying subcarriers and the transmission of phase shift orthogonal sequences may no longer be optimal.

It is apparent that no algorithms currently exist which provide near optimal pilot symbol designs and placements for such general scenarios, given that pilot symbols need to be distributed among data symbols.

An aspect of the invention provides a method of determining pilot symbols to be transmitted, and the subcarriers to transport them. The intention is to use the method to provide near optimal minimising of channel estimation error at the receiver.

An exactly optimal method should be considered, of selecting a set ofF subcarriers out of a total set of N subcarriers and the transmission of optimal pilot symbols on this selected set, as will be illustrated in due course. However, such an approach would (N N! incur a complexity in the order of I I = which is clearly unattractive for P) P!(N-P)! practical implementation for usual values of N. It would be desirable to have a method which exhibited performance close to the optimal method, while avoiding the complexity incurred by using the optimal method.

Design of pilot symbols in MIMO-OFDM systems with spatial correlations has also been considered in the field of the invention. For example, H. Zhang, Y. Li, A. Reid and J. Terry, "Optimum training symbol design for MIMO OFDM in correlated fading channels," IEEE Transactions on Wireless Communications, vol. 5, pp. 2343-2347, 2006, and H. D. Tuan, V. J. Luong and H. H. Nguyen, Optimization of training sequences for spatially correlated MIMO-OFDM," IEEE ICASSP Conference, pp. 2681- 84, 2009 illustrate such techniques.

However, those disclosures are only concerned with the situation in which pilots are to be transmitted on the full set of subcarriers of the system. Thus, the effect of pilot symbol placement is not taken into account. Also, those disclosures are restricted to a particular type of spatial correlation (those which separate into correlations at the transmit antennas and correlations at the receive antennas) and do not consider the case of delay domain correlations.

A. Y. Panah, B. Nosrat-Makouei and R. G. Vaughan, "Non-uniform pilot-symbol allocation for closed-loop OFDM," (IEEE Transactions on Wireless Communications, vol. 7, July 2008) discusses pilot symbol allocation in an OFDM channel, but relies on perfect channel knowledge to do so. Perfect channel knowledge is not always available, and provision of this at the transmitter will inevitably affect channel capacity, as some transmission opportunities will be committed to provision of this perfect channel knowledge to the transmitter.

The design of pilot symbols is considered in D. Hu, L. Yang, Y. Shi and L. He, "Optimal pilot sequence design for channel estimation in MIMO OFDM systems," IEEE Communications Letters, vol. 10(1), January 2006. This is in the context of non equally-spaced pilot placement. However, the disclosure of that document does not extend to the manner in which non-uniform pilot placement is addressed. Also, that work does not consider the channel statistics to optimise their pilot symbol design.

To coherently detect transmissions, the intermediate channels need to be estimated at the receiver. For this purpose, pilot symbols are transported in some of the subcarriers. This invention presents a method of optimising the pilots: in terms of the symbols as well as the subcarriers selected to transport them. Optimality is judged by the performance of channel estimation at the receiver. It is well known that if the underlying channel impulse responses constitute of uncorrelated taps, then an optimal placement is spacing them with an equal spacing between successive pilot symbols.

Also, use of pilot symbols such as phase shift orthogonal sequences, is optimal.

However in practice, it is possible to observe channel correlations both in the spatial domain as well as in the delay domain. For such correlated scenarios, conventional pilot transmissions may no longer be optimal.

This invention gives a near optimal method of pilot design, which is applicable for arbitrary correlations in the channels. Advantages over conventional approaches are observed when the channels are subject to significant correlations.

An aspect of the invention comprises a method of preparing a signal for transmission on a multi antenna OFDM communication channel, the channel defining a plurality of subcarriers each being suitable to support communication of an OFDM symbol, comprising selecting one or more pilot symbols to be transmitted and at least two pilot subcarriers from said subcarriers for carriage of a pilot symbol, said selecting of said pilot symbol and said selecting of said subcarriers being performed on the basis of channel statistics for the communication channel.

Another aspect of the invention provides a signal processing apparatus operable to determine pilot information for a transmission of a multi antenna OFDM signal across a communication channel, comprising pilot selection means operable to select a pilot symbol to be transmitted, and pilot subcarrier selection means operable to select at least two of said subcarriers for transmission of said selected pilot symbol, wherein said pilot selection means and said pilot subcarrier selection means are operable on the basis of channel statistics for said communication channel.

One or more of these aspects of the invention can be incorporated into a wireless communications apparatus comprising a plurality of antennas.

The invention, in accordance with any above aspect, can be provided in electronic form, either by way of discrete components or one or more integrated circuits. In conjunction with this, or alternatively, one or more elements of the invention may be provided by way of computer executable instructions, to be executed on a suitable computer apparatus, possible with the intercession of an operating system and/or software based tools, libraries and so on. Such computer executable instructions can be provided in the form of a download, such as borne on a computer receivable signal, or by way of introduction through use of a computer readable medium, or a mass storage device such as Flash memory. The reader will appreciate that the invention is not limited to any particular embodiment, and can be provided by one or other of hardware or software components, or a combination of the two.

Specific embodiments of the invention will now be described, with reference to the accompanying drawings, in which: Figure 1A is a schematic drawing of a pilot symbol placement in accordance with an

example of the prior art;

Figure 1 B is a schematic drawing of a pilot symbol placement in accordance with an example of a described specific embodiment of the invention; Figure 2 illustrates schematically an OFDM transmitter in accordance with a specific embodiment of the invention; Figure 3 illustrates schematically an OFDM receiver in accordance with a specific embodiment of the invention; Figure 4 illustrates a flow diagram of a process of determining pilot symbol placement and pilot symbols in accordance with the specific embodiment of the invention; Figure 5 illustrates pseudo code of a routine for determining pilot symbol placement in accordance with a first approach of the specific embodiment of the invention; Figure 6 illustrates pseudo code of a routine for determining pilot symbol placement in accordance with a second approach of the specific embodiment of the invention; Figure 7 illustrates a flow diagram for selection of the first or the second approach as illustrated in figure 5 and 6; Figure 8 illustrates an example outcome of use of the specific embodiment of the invention in a first simulation; and Figure 9 illustrates an example outcome of use of the specific embodiment of the invention in a second simulation.

The invention is illustrated by way of a specific embodiment, based upon a generic model of a multiple antenna equipped OFDM based communication system.

Figure 2 illustrates an OFDM transmitter while Figure 3Error! Reference source not found, illustrates an OFDM receiver. At transmission, a frame of data symbols (which contains the information to be conveyed) exist. These data symbols are to be transmitted as separate streams from the r transmit antennas. Taking a "vector pilot symbol" to consist of the set of signals to be transmitted by the r antennas at an particular subcarrier, it is assumed that the transmitter is permitted to transmit P vector pilot symbols.

At stage 204, a set of P vector pilot symbols is interspersed with the data streams to build up a frame of N symbols to be transmitted from each antenna. Such a frame is illustrated in Figure 1 B. As shown, N is the number of subcarriers defined in the channel on which transmission of either data or pilot symbols is permitted. In practice, such a pilot symbol insertion is required only when the channels need to be estimated at the receiver. Once channel estimation has taken place, pilot symbol insertion can be avoided, as long as the intermediate channels remain static.

These N symbols in each stream are then serial-to-parallel converted in 205-n (here "n" is the index of the transmit antenna). The inverse fast Fourier transform of the result is taken in stage 206-n. The output of stage 206-n is taken to stage 207-n where a guard interval (in the form of a cyclic prefix, zero padding or otherwise) is added and the result is parallel-to-serial converted. The resultant baseband signal is digital-to-analogue converted in 208-n and thereafter upconverted to the transmission frequency and transmitted via the antenna 210-n.

In such a transmitter, in stage 204, it is necessary to determine the pilot symbols to be transmitted, and the identity of the subearriers to transport them. The focus of this disclosure is thus on the unit 211, in which this determination is made. This unit requires the channel statistics as the basis for its determination via a procedure to be described in detail in due course.

A straightforward method of obtaining these channel statistics is to estimate them at the receiver and feed them back to unit 211. It may be possible, on the other hand, to exploit channel reciprocity to estimate these statistics directly at the transmitter. That approach can become feasible when the forward and reverse transmissions from one communication device to another occupy the same frequency bandwidth.

The pilot symbol placement, to be decided upon by unit 211, is denoted by the set P {i,2,...,N}. For example if 1 and 16 are elements of P, then the 1st and 16th subcarriers are used to transmit pilot symbols. Also the matrix X denotes the actual pilot symbols to be transmitted on these subcarriers. X will be defined more precisely in due course. The unit 211 is configured to determine X and P such that the accuracy of estimating the channels at the receiver is optimised.

It is necessary, for differentiation between pilot carrying and data carrying subcarriers, for the receiver to know the positions of the pilot symbols. It is also necessary, for subsequent channel estimation, for the receiver to have knowledge of the identity of the pilot symbols themselves. Thus the data {P, x} can be fed forward to the receiver as shown by the thick line at the bottom of Figure 2. As determined in the specific embodiment, {P, x} is dependent on the channel statistics rather than the individual channel realisations. Thus, the required rate of transfer of such information (represented by the thick lines in figure 2) is considerably lower than the rate of information transfer enabled by the OFDM transmission.

Referring to figure 3, the receiver 300 captures the wireless transmission through its receiving antenna 309-rn (here, "m" stands for the receive antenna index), down-converts the result to baseband in 301-rn and converts the resultant analogue signal into a digital signal in 302-rn. The guard interval, inserted at transmission, is removed in stage 303-rn and the result is serial-to-parallel converted. The output of 303-rn is fast Fourier transformed in stage 304-rn and the result is parallel-to-serial converted in stage 305-rn. At this point, the receiver is in possession of noise corrupted versions of the transmitted streams of data and pilot symbols. Then in stage 306, the pilot information {, X} is used to estimate the channels between the baseband of the transmitter and the baseband of the receiver. This information, in this embodiment, is fed forward by the transmitter 200 as described earlier and as illustrated by the thick line at the top of Figure 3. The estimated channels are thereafter utilised in stage 307 to detect the data symbols, transmitted on the data carrying subcarriers.

A channel statistics estimation unit 308 is illustrated to estimate the channel statistics at the receiver. The input to such a unit can include the channel estimates provided by channel estimator 306. The estimated channel statistics can then be fed back to the transmitter 200, to facilitate unit 211 to determine the identity and placement of pilot symbols.

Estimation of channel statistics needs to be performed (or updated) only periodically since such statistics are static for a longer duration than the actual channels themselves. For this reason it can reasonably be expected that this feedback of channel statistics needs to be performed at a much lower rate than the rate of information transfer. On the other hand, if the transmitter is exploiting channel reciprocity to obtain the channel statistics, such a feedback can be avoided altogether.

Finally, it should be noted that the thick lines in Figure 2 and Figure 3 denote transfer of control parameters between the two communicating devices. In practice, these control signals themselves need to be multiplexed with the information bearing signals arid transmitted and received via the antennas of the devices. As with existing systems, control information will need to be exchanged before harnessing the approach used in accordance with the described embodiment of the invention. Thus, prior to information transfer, there should necessarily be a stage for passing some control information. For example, the receiver needs to know which modulations, channel codes, etc. are being used in the transmissions. So, some control information will always be conveyed to establish a good connection, It will be understood by the reader that such initial control information transfer can be effected via channels not optimised to fully exploit the available resources. Furthermore, it might be the case that these pilots are not used at the beginning of the data transmission. After transmitting a certain amount of data, where conventional pilots, with below optimal performance, are used, the transmitter can start to employ the near-optimal pilot symbols and placements given by this specific embodiment of the invention.

In another embodiment, a receiver could be configured both to collect channel statistics and to compute pilot information{P, X} itself by running the algorithm presented later on. In such a case, of course, the feeding forward of {, x} from the transmitter to the receiver can be avoided -instead, the receiver would feed {, X} back to the transmitter and the need for feedback of the channel statistics would be eliminated.

Notation To explain the specific embodiment in further detail, certain notation will now be introduced for the benefit of the reader. As previously noted, N is the number of subcarriers and P c{1,2,...,N}denotesthe indices of the subcarriers selected to transmit pilot symbols. In this example, at each transmit antenna, the same subcarriers are utilised for pilot signal transmission (c.f. Figure 1).

The number of vector pilot symbols is denoted P Throughout this disclosure, in accordance with convention, vectors are denoted by bold faced lower case letters and are generally represented as column vectors. Matrices are denoted by bold faced upper case letters, and scalars are denoted by regular lower case letters.

For a matrix M, MT, M, M" M1 and Tr(M) denote, respectively, the transpose, conjugation, conjugate transpose, inverse and trace of the matrix.

For a vector v, diag(v) denotes a matrix with v as the diagonal.

E5denotes expectation with respect to the probability distribution of x.

I is the s x s identity matrix.

2ir(n-I)(!-1) With L <N, 0 is an N x L matrix with each Iement (n,l) being e N for fl = 1,2,...,N and 1,2,...,L. For a set P ç {1,...,N}, a matrix O1 is composed of the set of rows of 0 indexed by P. The Kronecker product between matrices is a11 a121 [a11B a12B denoted by the symbol ®. Forexample, fA=: I thenA®B= a21 a22j La21B a22B Considering an OFDM system employing n7. transmit antennas and R receive antennas, and taking the maximum delay spread of the time domain channel impulse responses to be L, the channel impulse response from transmit antenna n to receive antenna m is defined as hmn =(hmnl,hmn2,...,hmnL)T Vector h is defined as h = (br1hr2 h * h1h2 h)T To cater for arbitrary spatial and delay domain correlations subject to Rayleigh fading, h is assumed to be distributed as CJV(O,Rh). That is, it is a zero mean complex Gaussian distribution with covariance matrixRh. The following derivations can be easily modified to the scenario where the mean is non zero.

The nTnRL x nTnRL matrix Rh = Eh (hW") is termed the space-delay channel correlat ion matrix in the following. In some literature, such matrices are also called covariance matrices. Either term is appropriate in the context considered here. As mentioned previously, it is assumed that P («= N) subcarriers are reserved for the transmission of pilot symbols. The length-P frequency domain pilot symbols on transmit antenna n are x,, = . The pilot symbols are to be transmitted on the set of subcarriers P. The frequency domain received signals corresponding to the pilot symbols at receive antenna m are defined as ym = (ym,I,Ym2,,Ym,p)T and (as for the vector h discussed above) Y(YrYYR) X is defined as the p x n.i matrix[diag(x1)diag(x2). . .diag(x)]. That is, it is a matrix with n. matrix blocks concatenated horizontally, with each matrix block being a diagonal matrix.

Due to the use of conventional ODFM transmission either with a cyclic prefix or zero padding, the received signal can be modelled as follows: y =[i ®x][i ®0]h+n.

In this model, it can be assumed that n CA1(o,N0I). For signal normatisation, it is assumed that Tr(Rh) = land Trace(XX")-,1,,p* The operating SNR is taken to

I be-. N0

Now, Rh lEb (hhH) is a positive semi definite matrix. Thus, this matrix can be decomposed in the form ofRh UDUH. Assuming the rank of Rh is r(«=nTnRL), D can be assumed to be an r x r diagonal matrix with positive real diagonal elements and U to be an nrnRL x r matrix with orthonormal columns. With such a description, an nTnRL x r matrix square root can be defined forRh, which is denoted Rh2 such that ! Rh2).

Now, assuming the receiver knows the channel statistics, which is essentially the knowledge of the parametersRandN0, the linear minimum mean squared error channel estimator is: h_R2RII R -h y7,h, YpYp 7' where =1E{y?y} = [i ® X][IflTfl ® &]Rh [flTflR ® ]J1 [mR ®X]H + NOIflRP and RYh _IE{yphr} = [in,, 0 X1[InTnR ® Furthermore, the error due to such an estimator, can be shown to be distributed as a Gaussian distribution with mean zero and covariance matrix:

I H I H

R6 =Rh2 [Ir+_!_Rh2 [inn IIH[ (xHx)][I ®OP1RJ R, The corresponding mean squared error (MSE) in the channel estimation at the receiver is given byTr(R3. This MSE is a good measure of channel estimation accuracy at the receiver and the present embodiment seeks to minimise it. The MSE is clearly determined by the subcarriers selected for pilot transmission P and the actual pilot symbols X. Therefore, it will be seen by the reader that an objective for this embodiment of the invention is to select a set Pc {1,2,...,N} with P elements and an P x nP matrix X of the form [cieag(x)diag(x2)...diag(xfl)] with Trace(XX")-_nP, in order to minimise the resultant MSE in the channel estimationC =Tr(Re).

I I

Definition of the matrix square root Rh2 = UD2 enables the simplification of this objective function as: _Tr[D +UH {IflR �[(i ®e;)(XHx)(IflT The exhaustive search based optimal method The subcarriers for pilot transmission and the pilot symbols (i.e. {P, x}) can be decided upon optimally, simply by considering all the possible subsets of the set {1,2,...,N} of size P numerically optimising the objective function over the space of pilot symbols X for each such subset, and then by selecting the subset and the pilot symbols which minimises. Although optimal, such an approach requires the evaluation of I ") N! possible subsets, along with a numerical optimisation LP) P!(N-P)! for the pilot symbols in each subset.

Thus such an approach is clearly not feasible for practical implementation, even for (N moderate valFes of N. For example, with N = 128, P = 8 the number > 1010. In due course, the performance of the specific embodiment of the invention is compared with this naïve optimal approach for an illustrative example.

Specific embodiment The procedure employed by the specific embodiment of the invention, to obtain the pilot information, {P, x} is illustrated in Figure 4. Essentially it consists of two central functional steps. Firstly, at initialisation (in step Sstart), the pilot symbols X are taken to be the same as the phase shift orthogonal sequences proposed in Barhumi et al. Given this X, an attempt is made in step Si to minimise the MSE to find a good pilot placement P. The method of this embodiment of the invention provides a greedy algorithm for this optimisation. This algorithm is summarised in due course.

It will be noted by the reader that a naïve optimal approach to find the best pilot placement P requires an evaluation of all the size P subsets of the set {1,2,...,N}.

This implies a prohibitive complexity for a naïve approach. The algorithm summarised in the next section avoids such a complexity but performs near optimally.

Next, in step S2, it is assumed that the set T', which was derived in Si, is fixed and then the MSE C is numerically optimised over the possible pilot symbols to find a good candidate X. For this numerical optimisation, standard algorithms could be utilised such as disclosed in D. P. Bertsekas, "Nonlinear programming," Athena Scientific, 1995. Another suitable algorithm can be that described in J. P. Coon and M. Sandell, "Constrained optimization of MIMO training sequences," EURASIP journal of applied signal processing, vol 2007(1). These standard algorithms are essentially iterative algorithms, which seek to reduce the objective function at each iteration, and continue such iterations until the differences between successive values are below some predetermined low value. Of course, in the present case, the objective function is Since these algorithms are designed not to increase the value of the objective function at each iteration, they are guaranteed to find at least a local minimum, with a sufficient number of iterations.

The procedure is now completed (in step Sfinish) by producing the recent values for P and X as the set of pilot carrying subcarriers and the actual pilot symbols.

The reader will appreciate that there are possible variations to this general procedure.

In some instances, it might be useful to iterate the steps Si and S2 to obtain better placements and pilots. Also, as will be illustrated by demonstrations of numerical simulations later on, at certain scenarios, step S2 can be avoided altogether. In other words, the phase shift orthogonal sequences can be taken as the pilot symbols and only their placement optimised by the methods described in the next section.

Step Si: detailed description

Given a set of candidate pilot symbols, X the overall procedure for the computation of their placement, P is described in the pseudo code set out in Figure 5. The algorithm represented by that pseudo code will now be described. Along with X, the inputs required for the procedure are the space-delay channel correlation matrix Rh, noise variance N0, and the number of pilot symbols to be placed among the subcarriers P. In the initialisation stage, the channel correlation matrix is eigen-decomposed to derive the nTnRL x r matrix U with orthonormal columns and the r x r diagonal matrix D with positive real diagonal elements. Here, r is the rank of Rh and its maximum value is nTnRL. The sets 7j and V0 are initialised to be the empty set and the full set {1,2,...,N} respectively. TheLxN matrix �uI and matrix U are then partitioned into the forms 0' = [0102. . . ON] and U = [ur u. . . U]. Here, each O is an L xl vector and eachU5 is annTLxr matrix.

In the foregoing, the element x, denotes the symbol transmitted by the ith antenna on the j th pilot carrying subcarrier, given in the input matrix X. Thereafter the algorithm enters a P stage recursion. At each stage of this recursion, an attempt is made to allocate the k th vector pilot symbol to the best possible subcarrier. Dk_l ={dI,d2,...,dNk+I} is the set of candidate subcarriers from which a selection is made. The algorithm parses through these candidates in the first inner "For" loop ("For t=1:(N-k+1)"). For each of these candidates, indexed byd,, the matrix E, is built up using the steps given in the pseudo code. Out of these, the best subcarrier is selected so as to minimise Tr(E,). The selected subcarrier d1 is included in the set of pilot carrying subcarriers and removed from the set of candidates for selecting more pilots.

After completing the P stage recursion, the set P, is output as the set of pilot carrying subcarriers The order by which the set was generated needs to be preserved here, since the k th vector pilot symbol needs to be allocated to the subcarrier that was selected at the k th stage of the above recursion.

Improving numerical stability of step Si at hicth SNR, and its all SNR' variation For some scenarios, when the SNR becomes large, it can be seen that the quantities dealt with in the pseudo code of Figure 5 can become small and hence can lead to numerical issues. This is especially so with finite precision implementations, as would be required in practical hardware. One simple solution to this is the use of the alternative algorithm of Figure 6. The only difference between the two embodiments is that the algorithm of figure 6 does not utilise the matrix of eigenvalues D and the noise variance N0. The fixed matrix Irand value 1 are used instead. This algorithm is not sensitive to these particular values. For example, there is no strict requirement to use the exact value I instead of the noise variance. What is required is to use alternatives, which do not depend on the SNR and which will lead to better numerical stability.

Since this variation of the algorithm does not depend on the noise variance (i.e. the operating SNR), it does not possess SNR related numerical stability issues.

Furthermore, the actual channel statistics utilised by this new algorithm is just the nTnRL x r matrix U. Thus the overhead needed to communicate channel statistics to the transmitter for the purpose of generating the pilot symbol placement may also be reduced by following this procedure (the original algorithm requires the knowledge ofnTnRLxnrnRL matrixRh,where nTnRL»=r, in addition to the operating SNR).

The pseudo codes of figure 5 and figure 6 essentially give two algorithms that are suitable for low SNR and high SNR operations, respectively. An algorithm that is suitable for all SNR operations is one which selects the best placement out of these two algorithms at each SNR. This procedure is summarised in Figure 7.

As shown in Figure 7, subroutines 500 and 600 are executed to find and respectively, with resultant calculation of MSEs M1 and Mhjgh. A decision is taken on the basis of comparison of M,0 and Mh,gh -if M10 is lower than Mhjgh then pilot placement 1, is adopted as 7'; otherwise is adopted. Thus, the pilot placement which leads to the lower MSE is taken as the output.

It should be noted that no provision is made in the flow diagram for the case when M, and Mhjgh are equal. In that event, an arbitrary selection of one or other can be made. In such cases, both versions will lead to the same performance.

The basic goal here is to ensure that the better of the "low SNR" and high SNR" algorithm is used to find the placement.

Conventional approaches to pilot symbol placement only involve equispacing. Also, concerning the identity of the pilot symbols, it has been firmly established in the field of the invention that sequences such as phase shift orthogonal sequences should be used. As will be described with reference to simulation examples, when correlations exist in the channels (in space and/or delay domains), such conventional approaches may not always be optimal.

In this embodiment, a procedure is described for optimising the pilot symbols and the subcarriers for their transmission, given arbitrary correlations in the space and delay domains. This improvement can be utilised to reduce the pilot overhead in certain environments subject to significant channel correlations, which would in turn improve the overall throughput of the communication system.

As will be shown via examples later, the proposed scheme of pilot symbol design is able to achieve near optimal channel estimation performance at the receiver. This is despite the significantly lower complexity compared to a naive optimal approach, which requires an exhaustive search.

As mentioned earlier, the resultant improved channel estimation performance could be used to reduce the amount of pilot symbols that needs to be transmitted. This reduction can in practice be achieved via transmitting a reduced number of pilot symbols per each OFDM frame where channel estimation will be made at the receiver, or by transmitting pilot symbols less frequently (i.e. by spacing the OFDM frames that carry interspersed pilot symbols, further apart in time).

Simulations Simulation results are provided for an embodiment of the invention in an n,. = 2 system, where the transmissions are into channels with L =2 taps. Following the approach described in E. Yoon, J. Hansen and A. Paulraj, "Space-frequency precoding with space-tap correlation information at the transmitter," (IEEE Transactions on Communications, vol. 55, no. 9, September 2007) it is assumed that the space-delay channel correlation matrix Rh is such that the correlations separates into independent correlations at the transmitter (denoted by RTX), at the receiver (denoted by R) and in the delay domain (denoted by RL).

These correlations are set as: [ 1 -O.5618+jO.73811 R 1 land Tx L-0.5618-i0.7381 1] [ 1 O.7389+j0.4485 R =1 [0.7389-jO.4485 1 For RTX, this corresponds to a two antenna transmitter where the antennas are spaced apart by half a wavelength with a mean angle of departure of 450 and a variance in the cluster angle spread of 25°. This is as per H. Bolcskei, "Principles of MIMO-OFDM wireless systems," in CRC handbook on signal processing for communications, M. lbnkahla, Ed., 2004.

For R1, this corresponds to a two antenna receiver where the antennas are spaced apart by half a wavelength with a mean angle of arrival of 800 and a variance in the cluster angle spread of 25°. This is also as per Bolcskei referenced above.

Finally, the delay domain correlations for this example are represented by the matrix: [ 1.0582 0.5291-jO.8466

RL H

[0.5291+10.8466 0.9418 This matrix, although of dimensions 2 x 2, is a rank I matrix, signifying a highly correlated scenario. A 16 subcarrier system is considered, with the problem of placing 4 vector pilot symbols among these subcarriers such that the channel estimation at the receiver is optimised.

MSE performances of different pilot placements for the above correlations in are illustrated in figure 8. For the actual pilot symbols, phase shift orthogonal sequences (PSOS) are used as given in Barhumi et al. It is apparent that, for this example, by optimising the placement of the given 4 vector pilot symbols, it is possible to perform about 3dB better than a simple equispaced placement. In this simulation, the "all SNR" version of the algorithm as set out in figure 7 is employed, and this is demonstrated to achieve near-optimal performance, even though the complexity of that algorithm is much less than that of the optimal method, which requires an exhaustive search.

In figure 9, results are illustrated of considering the overall problem of optimising the pilot symbols as well as pilot placement. The line labelled "MSE due to equispaced placement of PSOS" is the performance achieved by conventional systems.

As shown earlier, optimising the placement of these pilots offers improvement for all SNRs, for this example. It will be of interest to the reader to note that optimising the pilot symbols themselves, in addition to the placement, results in further gain at low SNRs. The performance due to the "optimal pilot sequences" is the best possible achievable MSE, but at the cost of high complexity -for the computation of these optimal sequences, an exhaustive search must be undertaken, thus their computation is prohibitive for real time implementation.

The line labelled "proposed pilot sequences" gives the MSE due to pilots obtained by the described method. Again, for step SI described above, the all SNR' version of the algorithm was employed in the simulation. This procedure avoids performing any exhaustive search, but it can be seen that the resultant MSE is near optimal.

From the foregoing, the reader will appreciate that a method is provided which can be implemented in suitable apparatus for enhancement of existing techniques for placement of pilot symbols, and for selection of suitable pilot symbols for particular conditions.

The above example performs close to an optimal approach. In addition, and importantly, the prohibitive complexity of the exhaustive search is avoided. The embodiment is thus able to handle arbitrary correlations within the underlying channels and still decide on the pilot symbols and their placement to optimise channel estimation at the receiver, in a practically feasible manner.

The examples provided above are but a selection of the range of implementations that can be achieved, as the reader will appreciate. No limitation is to be implied from the above description to the scope of the invention put forth herein, which is to be discerned from the following claims. The claims may be read in the light of (but not limited by) the description, and with reference to the accompanying drawings.

Claims

CLAIMS: 1. A method of preparing a signal for transmission on a multi antenna OFDM communication channel, the channel defining a plurality of subcarriers each being suitable to support communication of an OFDM symbol, comprising selecting one or more pilot symbols to be transmitted and at least two pilot subcarriers from said subcarriers for carriage of a pilot symbol, said selecting of said pilot symbol and said selecting of said subcarriers being performed on the basis of channel statistics for the communication channel.
2. A method in accordance with claim 1 and including establishing an initial set of candidate pilot symbols for transmission, and performing an optimisation to determine a set of suitable subcarriers for transmission of said candidate pilot symbols.
3. A method in accordance with claim 2 wherein said optimisation to determine a set of suitable subcarriers comprises recursively allocating possible symbols to possible subcarriers, to obtain, in each recursion, a best subcarrier to be used and then to be eliminated from further recursions, until the desired number of pilot subcarriers has been identified.
4. A method in accordance with claim 2 or claim 3 and including, after determining said set of suitable subcarriers, performing an optimisation to determine pilot symbols to be transmitted on said determined set of suitable subcarriers.
5. A method in accordance with any preceding claim and including receiving channel statistics from a device in receipt of a transmission on said communication channel.
6. A method in accordance with any one of claims 1 to 4 and including determining channel statistics at a point of receipt of a communication on said communication channel, wherein said selecting is performed at said point of receipt, and communicating information identifying said pilot subcarriers back to a point of transmission on said communication channel.
7. A method in accordance with any one of said preceding claims wherein said selecting of said pilot subcarriers comprises applying a sub-optimal algorithm to determine a suitable selection of pilot subcarriers based on said initial set of pilot symbols, and determining, on the basis of said suitable selection, applying a further sub-optimal algorithm to determining suitable pilot symbols to be transmitted in said selected pilot subearriers.
8. A signal processing apparatus operable to determine pilot information for a transmission of a multi antenna OFDM signal across a communication channel, comprising pilot selection means operable to select a pilot symbol to be transmitted, and pilot subcarrier selection means operable to select at least two of said subcarriers for transmission of said selected pilot symbol, wherein said pilot selection means and said pilot subcarrier selection means are operable on the basis of channel statistics for said communication channel.
9. A signal processing apparatus in accordance with claim 5 and including channel statistics receiving means operable to receive channel statistics from a device in receipt of a transmission on said communication channel.
10. A signal processing apparatus in accordance with claim 5 and including OFDM signal receiving means operable to receive an OFDM signal on said communications channel, channel statistics determining means for determining said channel statistics, and pilot information transmission means operable to transmit, to a multi-antenna transmitter, pilot information to be used by said transmitter to condition an intended OFDM transmission on said communications channel.
11. A signal processing apparatus in accordance with any one of claims 5 to 7 wherein said pilot subcarrier selection means is operable to select said pilot subcarriers by applying a sub-optimal algorithm to determine a suitable selection of pilot subcarriers based on said initial set of pilot symbols, and to determine, on the basis of said suitable selection, a further sub-optimal algorithm to determining suitable pilot symbols to be transmitted in said selected pilot subcarriers.
12. A wireless communications apparatus comprising a plurality of antennas and a signal processing apparatus in accordance with any one of claims 8 to 11.
13. A computer program product comprising computer executable instructions which, when executed by a suitable computer, cause said computer to perform the method in accordance with any one of claims 1 to 7.
14. A computer program product in accordance with claim 13 wherein said product comprises a computer readable storage medium.
15. A computer program product in accordance with claim 13 wherein said product comprises a computer receivable signal bearing said instructions.
16. An OFDM signal comprising pilot symbols placed in subcarriers of said signal, by way of a method in accordance with any one of claims 1 to 7.Amendments to the Claims have been filed as follows: CLAIMS: 1. A method of preparing a signal for transmission on a multi antenna OFDM communication channel, the channel defining a plurality of subcarriers, said channel being suitable to support communication of an OFDM symbol, comprising selecting one or more pilot symbols to be transmitted and at least two pilot subcarriers from said subcarriers for carriage of a pilot symbol, said selecting of said pilot symbol and said selecting of said subcarriers being performed on the basis of channel statistics for the communication channel.2. A method in accordance with claim I and including establishing an initial set of candidate pilot symbols for transmission, and performing an optimisation to determine a set of suitable subcarriers for transmission of said candidate pilot symbols.3. A method in accordance with claim 2 wherein said optimisation to determine a set of suitable subcarriers comprises recursively allocating possible symbols to possible subcarriers, to obtain, in each recursion, a best subcarrier to be used and then to be eliminated from further recursions, until the desired number of pilot subcarriers has been identified.4. A method in accordance with claim 2 or claim 3 and including, after determining said set of suitable subcarriers, performing an optimisation to determine pilot symbols to be transmitted on said determined set of suitable subcarriers.S..... * 25* *...* * e 5. A method in accordance with any preceding claim and including receiving channel statistics from a device in receipt of a transmission on said * . . * ** communication channel.6. A method in accordance with any one of claims ito 4 and including determining channel statistics at a point of receipt of a communication on said I....* communication channel, wherein said selecting is performed at said point of receipt, and communicating information identifying said pilot subcarriers back to a point of transmission on said communication channel.7. A method in accordance with any one of said preceding claims wherein said selecting of said pilot subcarriers comprises applying a sub-optimal algorithm to determine a suitable selection of pilot subcarriers based on said initial set of pilot symbols, and determining, on the basis of said suitable selection, applying a further sub-optimal algorithm to determining suitable pilot symbols to be transmitted in said selected pilot subearriers.8. A signal processing apparatus operable to determine pilot information for a transmission of a multi antenna OFDM signal across a communication channel, comprising pilot selection means operable to select a pilot symbol to be transmitted, and pilot subcarrier selection means operable to select at least two of said subcarriers for transmission of said selected pilot symbol, wherein said pilot selection means and said pilot subcarrier selection means are operable on the basis of channel statistics for said communication channel.9. A signal processing apparatus in accordance with claim 5 and including channel statistics receiving means operable to receive channel statistics from a device in receipt of a transmission on said communication channel.10. A signal processing apparatus in accordance with claim 5 and including OFDM signal receiving means operable to receive an OFDM signal on said communications channel, channel statistics determining means for determining said channel statistics, and pilot information transmission means operable to transmit, to a multi-antenna transmitter, pilot information to be used by said transmitter to condition an intended OFDM transmission on said communications channel.11. A signal processing apparatus in accordance with any one of claims 5 to 7 wherein said pilot subcarrier selection means is operable to select said pilot subcarriers by applying a sub-optimal algorithm to determine a suitable selection of pilot subcarriers based on said initial set of pilot symbols, and to determine, on the basis of said suitable selection, a further sub-optimal algorithm to determining suitable pilot symbols to be transmitted in said selected pilot subcarriers.12. A wireless communications apparatus comprising a plurality of antennas and a signal processing apparatus in accordance with any one of claims 8 to 11.13. A computer program product comprising computer executable instructions which, when executed by a suitable computer, cause said computer to perform the method in accordance with any one of claims 1 to 7.14. A computer program product in accordance with claim 13 wherein said product comprises a computer readable storage medium.15. A computer program product in accordance with claim 13 wherein said product comprises a computer receivable signal bearing said instructions.16. An OFDM signal comprising pilot symbols placed in subcarriers of said signal, by way of a method in accordance with any one of claims 1 to 7.