GB2458880A - Beamforming in wireless communication - Google Patents

Abstract

Beamforming for use in wireless communication involving apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal. The approach involves determining a beamforming vector on the basis of a channel matrix to a given receiver. The approach involves determining an eigenbeamformer vector from the channel matrix, and rotating the eigen-beamformer vector into a reference direction in vector space such that application of said rotated eigenbeamformer vector would result in peak radiation being directed in the reference direction. A radiation pattern associated with the rotated eigen-beamformer vector is then sampled with respect to transmission direction, and the resultant samples are compressed to reduce spatial directivity induced by the eigen-beamformer. From this, a rotated candidate beamformer is developed on the basis of the compressed samples and the rotated candidate beamformer is returned to the orientation of the eigen-beamformer vector before the previous rotation.

Description

1 2458880 Wireless Communications Apparatus The present invention concerns wireless communications apparatus, and particularly transmit beamforming for use in arrangements wherein there is an equivalent isotropic radiated power (EIRP) restriction. It is particularly suited to applications involving ultra wideband (UWB) but is not restricted thereto.

Apparatus such as UWB apparatus is, in many regulatory environments, restricted by an EIRP restriction. This means that transmitted power over the whole angular range of an antenna should not exceed a particular value. In general, transmitted power should not exceed a particular level in any particular direction.

Multiple antenna configurations are of potentially significant use in the delivery of multiple input multiple output (MIMO) technology. This has the potential to deliver high data rate and/or robust communication, by exploiting the additional degrees of freedom and diversity afforded by the spatial domain, in addition to the frequency and/or time domains.

It will be appreciated that many problems arise when data is transmitted from multiple antennas simultaneously. For example, a signal received at a corresponding receiver comprises a superposition of the transmitted signals. This results from the nature of transmission over a wireless medium. The superposed signals must be separated by a MIMO detector of the receiver. Some MIMO apparatus aim to use knowledge of the wireless channel at the transmitter to precondition the transmitted message so as to facilitate detection at the receiver. This conditioning is known as beamforming or precoding. In order to be effective, this generally requires a degree of knowledge at the transmitting device of the characteristics of the wireless channel between the transmitting device and the receiving device. This channel knowledge can be ascertained either from a feedback channel dedicated to the transmission from the receiver to the transmitter of such channel knowledge, or by using channel reciprocity, particularly if the communication arrangement between the transmitter and receiver uses time division duplexing.

Whereas optimal precoding algorithms are known, these need to be placed in the context of other performance constraints imposed on MIMO apparatus. In particular, systems such as UWB are restricted by EIRP constraints. This imposes greater restrictions on performance than would a conventional total transmit power constraint.

Any beamforming scheme applied at the transmitter for such systems would need to be compliant with regulatory EIRP restrictions.

One particularly useful and commonplace type of beamforming is known as antenna selection. This is investigated in "Performance analysis of combined transmit-SC/receive-MRC," (S. Theon, L. V. Perre, B. Gyselinckx and M. Engels, IEEE Transactions on Communications, vol. 49(1), January 2001).

In that approach, the transmitter consists of multiple antennas, and knowledge of the prevailing condition of the wireless channel is used to determine from which antenna a message should be transmitted. Antenna selection can be applied in wideband systems by using orthogonal frequency division multiplexing (OFDM). In an OFDM system, antenna selection can be performed on the basis of selecting per subcarrier or per groups of subcarriers. Consequently, on any given subcarrier, a particular antenna may be chosen for transmission, whereas another antenna may be chosen for transmission on a different subcarrier. In that way, transmission may be optimised across the bandwidth according to some specified cost (or utility) function. Examples of such functions include instantaneous receive signal-to-noise ratio (SNR), capacity, and uncoded bit error rate (BER). In EIRP constrained systems, such as UWB, it transpires that per subearrier antenna selection can maximise system capacity in many practical cases, such as where there are only two transmit antennas. This also implies that transmit antenna selection can be, for example, the received SNR optimising scheme when there is only one receive antenna and two transmit antennas. t.

For more conventional systems which are subject to transmit power constraints, the received SNR optimal beamforming method is the transmission of signals on the principal right singular vector of the channel matrix. If the channel matrix is M by the term "principal right singular vector", we refer to an eigenvector corresponding to the largest eigenvalue of MUM, where the superscript H denotes the conjugate transpose.

This is observed in "Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems," (M. Kang and M. S. Alouini, IEEE Journal on Selected Areas in Communications, vol. 2 1(3), pp. 4 18-426, April 2003).

Such a beainforming method can be described as eigen-beamforming. Eigen-beamforming increases the directivity of spatial radiation and thus, when implemented in EIRP constrained systems, the transmit power needs to be backed off such that the regulatory EIRP constraints are not violated. This issue is illustrated in Figure 1, which plots the radiation patterns due to three beamforming schemes. It is assumed that the EIRP should be restricted to be below one unit.

Plots 101 and 102 represent beamforming schemes which transmit the same amount of power. However, the spatial directivity of plot 101 is higher. Thus while plot 102 represents a transmitter which is allowed to transmit at that power, that of plot 101 is required to have its transmit power reduced at least to that shown by plot 103. Thus, any transmission scheme leading to a spatially non-isotropic radiation can incur a transmit power penalty in EIR.P constrained systems. This will lead to the result that, with the proper scaling, the eigen-beamforming solution cannot be considered the optimal transmission scheme. The eigen-beamforming vector, when scaled to satisfy the EIRP restrictions, will be called the "scaled eigen-beamforrning vector" through this disclosure. Although the use of scaled eigen-beamforming is evidently sub-optimal for EIRP constrained systems, it has been considered as a possible low-complexity beamforming method, for instance in "Performance of multiple-receive multiple-transmit bearnforming in WLAN-type systems under power or EIRP constraints with delayed channel estimates" (P. Zetterberg, M. Bengtsson, D. McNamara, P. Karisson and M. A. Beach, Proceedings of the IEEE Vehicular Technology Conference, 2002).

A method of optimising transmit beamforming for received SNR in EIRP constrained systems is presented in Zetterberg et al. However, this optimal method has a high implementation complexity since it involves an optimisation in a complicated multi-dimensional space.

While transmit antenna selection can be optimal for transmitters with only two antennas, both transmit antenna selection and scaled eigen-beamforming are sub-optimal in general. This is unfortunate since many UWB systems operate in low SNR situations where the loss in received signal power due to the use of a sub-optimal beainforming method can significantly affect system performance.

Aspects of the invention provide a method and apparatus for transmit beamforming, which improves the SNR at reception compared with both of the sub-optimal methods described above. The implementation complexity of resultant algorithms when performed on a suitable computer apparatus can be shown to be much less than the optimal method given in Zetterberg et al. Another aspect of the invention comprises a method of determining a beamforming vector for use in wireless communication involving apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal, including determining said beainforming vector on the basis of a measure of transmission channel to a given receiver, said measure being expressible in the form of a channel matrix, the determining including determining an eigen-beamformer vector from said channel matrix, rotating said eigen-beamformer vector into a reference direction in vector space such that application of said rotated eigen-beam former vector would result in peak radiation being directed in said reference direction, sampling a radiation pattern associated with said rotated eigen-beamformer vector with respect to transmission direction, compressing resultant samples to reduce spatial directivity induced by said eigen-beamformer, developing a rotated candidate beamformer on the basis of said compressed samples and returning said rotated candidate beamformer to the orientation of said eigen-beamformer vector before said rotating.

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Another aspect of the invention comprises wireless communications apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal, and beamforming means operable to apply a beamforining defined by a beamforming vector on a signal to be transmitted from said antennas, including beamforming vector determining means for determining said beamforming vector on the basis of a measure of transmission channel to a given receiver, said measure being expressible in the form of a channel matrix, the beamforming vector determining means including eigen-beamformer determining means for determining an eigen-beamformer vector from said channel matrix, vector rotation means for rotating said eigen-beamformer vector into a reference direction in vector space such that application of said rotated eigen-beamformer vector would result in peak radiation being directed in said reference direction, sampling means for sampling a radiation pattern associated with said rotated eigen-beamformer vector with respect to transmission direction, data compression means for compressing resultant samples to reduce spatial directivity induced by said eigen-beamformer, data transformation means for developing a rotated candidate beam former on the basis of said compressed samples and rotation reversion means for returning said rotated candidate bearnformer to the orientation of said eigen-beamformer vector before said rotating.

Another aspect of the invention comprises an approach to beamforming, for use in wireless communication involving apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal. The approach involves determining a bearnforming vector on the basis of a channel matrix to a given receiver. The approach involves determining an eigen-beamformer vector from the channel matrix, and rotating the eigen-beamformer vector into a reference direction in vector space such that application of said rotated eigen-beamformer vector would result in peak radiation being directed in the reference direction. A radiation pattern associated with the rotated eigen-beamformer vector is then sampled with respect to transmission direction, and the resultant samples are compressed to reduce spatial directivity induced by the eigen.

beamformer. From this, a rotated candidate beaniformer is developed on the basis of the compressed samples and the rotated candidate beamformer is returned to the orientation of the eigen-beamformer vector before the previous rotation.

Aspects of the invention may comprise a computer program product comprising computer executable instructions operable to cause a computer to become configured to perform a method in accordance with any of the above identified aspects of the invention. The computer program product can be in the form of an optical disc or other computer readable storage medium, a mass storage device such as a flash memory, or a read only memory device such as ROM. The method may be embodied in an application specific device such as an ASIC, or in a suitably configured device such as a DSP or an FPGA. A computer program product could, alternatively, be in the form of a signal, such as a wireless signal or a physical network signal.

Specific embodiments of the invention will now be described with reference to the accompanying drawings, in which: Figure 1 is a graph of transmission power profiles exemplifying isotropic and non-isotropic radiation profiles from a multi-antenna transmitter; Figure 2 is a schematic diagram of a wireless communications apparatus incorporating a communications unit in accordance with a specific embodiment of the invention; Figure 3 is a schematic diagram of a communications unit of the specific embodiment of the invention; Figure 4 is a flow diagram illustrating a method of computing beamformer attributes for use by the apparatus in Figures 2 and 3; Figure 5 is a graph illustrating objective function plotted against compressor parameter, for various implementations including that of the specific embodiment; and Figure 6 is a graph illustrating packet error rate performance for a specific embodiment of the invention in comparison with other approaches The wireless communication device 100 illustrated in Figure 2 is generally capable of being used in a MIMO context, to estabLish a MIMO communications channel with one or more other devices and, in accordance with a specific embodiment of the invention, to take account of channel information so as to derive a pre-coding (or otherwise described as beamforming) scheme appropriate to the quality of the channel. The reader will appreciate that the actual implementation of the wireless communication device is non-specific, in that it could be a base station or a user terminal.

Figure 2 illustrates schematically hardware operably configured (by means of software or application specific hardware components) as a wireless communication device 100.

The wireless communication device 100 comprises a processor 120 operable to execute machine code instructions stored in a working memory 124 and/or retrievable from a mass storage device 122. By means of a general purpose bus 130, user operable input devices 136 are capable of communication with the processor 120. The user operable input devices 136 can comprise, in this example, a keyboard and a mouse though it will be appreciated that any other input devices could also or alternatively be provided, such as another type of pointing device, a writing tablet, speech recognition means, or any other means by which a user input action can be interpreted and converted into data signals.

Audio/video output hardware devices 138 are further connected to the general purpose bus 130, for the output of information to a user. Audio/video output hardware devices 138 can include a visual display unit, a speaker or any other device capable of presenting information to a user.

A communications unit 132, connected to the general purpose bus 130, is connected to a plurality of antennas 134. In the illustrated embodiment in Figure 1, the working memory 124 stores user applications 126 which, when executed by the processor 120, cause the establishment of a user interface to enable communication of data to and from a user. The applications in this embodiment establish general purpose or specific computer implemented utilities that might habitually be used by a user.

Communications facilities 128 in accordance with the specific embodiment are also stored in the working memory 124, for establishing a communications protocol to enable data generated in the execution of one of the applications 126 to be processed and then passed to the communications unit 132 for transmission and communication with another communications device. It will be understood that the software defining the applications 126 and the communications facilities 128 may be partly stored in the working memory 124 and the mass storage device 122, for convenience. A memory manager could optionally be provided to enable this to be managed effectively, to take account of the possible different speeds of access to data stored in the working memory 124 and the mass storage device 122.

On execution by the processor 120 of processor executable instructions corresponding with the communications unit 132, the processor 120 is operable to establish communication with another device in accordance with a recognised communications protocol.

The communications unit 132 will now be described in further detail. As illustrated in figure 3, baseband and multiple subcarrier versions of the communications unit 132 are exemplified.

In figure 3, data (x) to be transmitted is input to a beamformer 202, which is configured by a beamformer vector computation unit 204. The beamformer vector computation unit 204 is itself governed by channel state information (H) which is derived from whatever available source. In many circumstances, a channel estimate will be available from an assumption of channel reciprocity, as the unit will itself be operable as a receiver as well as being a transmitter, or the receiver at the other end of the channel might transmit, for instance on another lower capacity channel, channel information.

Such channel information could be transmitted in full, or in a compressed format.

The beamformer produces multiple streams, one for each antenna 134. Each stream is passed to a digital to analogue converter 208, a frequency upconverter 210 and a power amplifier 212. The output of each power amplifier 212 is suitable to be passed to a respective antenna 134.

There now follows an explanation of the function of the beamforming vector computation unit illustrated in figure 3. A generic model (for the purpose of illustration of the invention) of a baseband communication system can be described as follows.

With R denoting the number of receive antennas, the communication system employs n transmit antennas. H, which is an x ji matrix, denotes the equivalent channel between the transmitter and the receiver. To demonstrate use of the system, it is supposed that, at a particular time instant, the transmitter intends to transmit the scalar symbol x, pre-multiplied by a n. x I beamforming vector v. Using the R xl vectors ii and y to denote the additive noise manifesting at the receiver and the resultant total signal at the receiver, respectively, y = Hvx + n.

It will be noted that the elements of the vectors and the matrix above are complex numbers for a baseband representation.

Design of the beamforming vector v is addressed herein. Such design can be made according to various criteria such as maximising the received SNR, maximising the resultant system capacity or minimising the decoded error rates at the receiver. While maximisation of received SNR will be considered from here onwards, it will be apparent to the skilled reader that other objectives could also be considered. Also, the focus will be on transmissions which are constrained by their equivalent isotropic radiated power (EIRP). A signal normalisation will be considered for the system such that its EIRP needs to be constrained below one unit.

The presently described embodiment provides a method of beaxnforming for EIRP limited systems which is intended to perform more effectively than current sub-optimal methods and at a complexity much less than that of the optimal method given in Zetterberg et al. The method is based on perturbing the scaled eigen-beamformer such that the peak-to-average power ratio (PAPR) of its radiation is reduced.

The method of the implementation can be summarised in terms of the following steps, in which a compressing function is used to achieve the spatial PAPR reduction.

1. Given a channel matrix H, compute the scaled eigen-beamforming vector and the beamforming vector representing transmit antenna selection.

2. Induce a rotation to the scaled eigen-beaniformer such that in an n. -point inverse discrete Fourier transform (IDFT), the first sample gives the peak of the radiation due to that vector. Obtain the n. -point IDFT of this rotated vector.

3. Perturb the resultant IDFT samples such that their PAPR is reduced. In particular, this can be achieved by sending these through a compressing function. Furthermore, a family of compressing functions can be used, from which a member can be selected to optimise the received SNR. Compress the n IDFT samples produced in Step 2 using the best compressing function selected to maximise the received SNR.

4. Take the discrete Fourier transform (DFT) of the compressed samples, scale it to satisfy the EIRP restrictions and remove the pre-rotation which was initially induced in Step 2. This produces the new candidate for a beamforming vector.

5. Select the best performer out of the resultant candidate and the transmit antenna selection method, as the beamforming solution.

This algorithm will now be described in further detail. To do this, the reader will be informed by mathematical notation which will be used in the description.

The transpose operation is denoted by (.)T and the conjugate transpose operation by (Sr.

For a vector v, IlviL denotes the largest magnitude of its components, IlII2 denotes the Euclidean norm /V H v and (v), denotes its I th element. For v = (1, , * U)r the K �= n length inverse discrete Fourier transform (IDFT),

I

r=IDFTK(v)=rJ,rZ,...,rK) 2z(1-l)(m-I) is taken to be given as rm = K for m = l,2,...,K.

0Kxn is taken to be the representative DFT matrix such that r = 0Kxfl The n,. length vector e, consists of all zeros except at the k th position, the k th position being 1.

For a complex number C, denotes its magnitude and Lc, its phase.

Having regard to the above, a more detailed description of the beamforming algorithm, as implemented by the beamforming vector computation unit, will now be given with reference to the flow chart of Figure 4.

In Step 302, the beamforming vector computation unit 204 is fed the channel matrix H, for which the beamforming vector is to be designed.

The beamforming vector computation unit 204 computes the beamforming vector due to transmit antenna selection, in Step 303. Mathematically, this beamforming vector can be identified as ek where k = argmaxJHe. In other words, k is the largest norm column of the channel matrix.

In Step 304, the beamforming vector computation unit 204 computes the scaled eigen-beamforming solution. Firstly, v, , which denotes a principal right singular vector of the channel matrix LI is computed. It should be noted that the term principal right singular vector of H refers to an eigenvector corresponding to the largest eigenvalue of H11H. This vector needs to be scaled to satisfy the EIRP constraints.

For a transmitter equipped with a linear array of n. isotropic antennas using the beamforming vector v, it can be shown that the emitted radiation is determined by the IDFT of v and that its peak radiation is determined by the largest magnitude component of its IDFT, or by 1° Kxn,. vii. This is explained in "Antenna Theory" (C. A. Balanis, John Wiley, 1997).

In this example, K is a suitably large integer value much greater than ni.. For example it can be 64. Thus, when the E1RP is restricted to one unit, the EIRP scaled eigen-beaniformer can be derived as v = V1 In Step 305, v is rotated such that n -point IDFT operation (rather than a K > point IDFT) is able to capture the peak radiation. This can be achieved by firstly computing 7= arg rnaxl(e Kxflr v SB) which corresponds to the direction of peak radiation. 1 0 2,rT J-j;-

With D, = 2(n. -1)1 0 e K rotation is achieved by letting v,01ç, = This ensures that, in an n. -point IDFT of v,0, the first component represents the peak radiation due to v SB* This rotation helps in preserving the direction of peak radiation by the operations in the subsequent steps.

In Step 306, an n. -point IDFT of v,,,,8 is taken. The result of this is denoted r. As a result of the rotation induced in Step 305, the peak radiation due to VSBiS captured by the first component of r.

In Step 307, the components of r are compressed to reduce their dynamic range. This is, in effect, a reduction of the PAPR of the spatial radiation. Furthermore, in this algorithm, a family of possible compressing functions I',, are considered, wherein the compressing functions are parameterised by the real scalar parameter p. One possible example is given by (f (r)), = tanh(uf(r) )exp(jz(r),).

When compressed through a particular compressor f,,, the value of the target objective function, representative of the received SNR, can be shown to be given by: IlD,0x f, (r Kxn x,,,. (r p(u) is a function of the real scalar,u as shown by an actual example in Figure 5. This function can be numerically optimised over 1u to find the best value p maximising the objective function. A numerical method suitable for this one dimensional optimisation is the Nelder-Mead simplex method as disclosed in "Nonlinear programming" (D. P. Bertsekas, Athena Scientific, 2003).

It should be noted by the reader that, in a practical implementation, such optimisations can be simplified by considering a set of possible values for p and then evaluating the values of the objective function for this set. The result due to compressing r with the compressor f,, is denoted 1. In other words, (jr), = tth(u0,I(r),l)expUZ(r),) for i = In Step 308, the DFT of? is taken and scaled to satisfy the EIRP restrictions, producing the beamforming solution This vector needs to be adjusted to remove the rotation which was induced earlier in Step 305. The adjusted beamforming vector v is produced by v = Finally, in Step 309, the better approach between application of v and transmit antenna selection is selected, depending on that which produces the largest received SNR.

It will be appreciated that, while not essential to the delivery of the present embodiment, the computational complexity of computing the DFTs and IDFTs can be reduced by using fast Fourier transforms (FFT).

Also, while the use of DFTs and IDFTs to convert from one domain to another is useful in this context, this is taking advantage of an assumption that the transmit antennas form an equispaced linear array. If this is not the case, then a further matching will need to be carried out to transform from beamforming vectors to the spatial radiation and vice versa.

This arrangement renders up the beamforming vector which improves link performance subject to EIRP restrictions at the transmitter, when there is a linear array of transmit antennas. Previous work of Zetterberg et a!. had given a computationally intensive solution, involving a multi dimensional optimisation, to obtain the optimal vector. The algorithm of this invention gives a much simpler algorithm, which involves an optimisation only over a real scalar variable. The error rate performance of the invention is much better than conventional sub-optimal solutions such as transmit antenna selection and scaled eigen-beamforming.

Furthermore, it will be apparent to a skilled person that the proposed compression based scheme can be generalised by considering compressing functions which are parameterised by more than one variable. Such generalisations would offer improved performance at the cost of an increase in complexity due to the need to optimise over more than one variable.

Figure 6 gives an illustration of the packet error rate (PER) performance due to the use of the proposed beamforming algorithm as implemented in the specific embodiment.

Simulations were made in conformity to the OFDM based WiMedia specifications for UWB systems. Since the EIRP restrictions apply per subcarrier for such systems, the beamforming was also applied per subcarrier. For the simulations, the number of receive antennas, tiR was set to be 1. Four transmit antennas were spaced apart by 5cm.

The packet error rate is plotted in figure 6 against the ratio between the EIRP at transmission to the noise power at the receiver.

Although the above described embodiments of the invention are intended to inform the reader as to the possibilities for implementation of the invention, the invention is not limited to such embodiments. Indeed, the reader will appreciate that many alternative embodiments, and modification, replacement or omission of individual features of the illustrated embodiments are possible within the scope of the invention. The invention should instead be read as being defined by the appended claims, which can be read in conjunction with, but should not be considered limited by, the present description and accompanying drawings.

Claims (20)

1. CLAIMS: 1. A method of determining a beamforming vector for use in wireless communication involving apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal, including determining said beamforming vector on the basis of a measure of transmission channel to a given receiver, said measure being expressible in the form of a channel matrix, the determining including determining an eigen-beamformer vector from said channel matrix, rotating said eigen-beamformer vector into a reference direction in vector space such that application of said rotated eigen-beamfonner vector would result in peak radiation being directed in said reference direction, sampling a radiation pattern associated with said rotated eigen-beamformer vector with respect to transmission direction, compressing resultant samples to reduce spatial directivity induced by said eigen-beamformer, developing a rotated candidate beamformer on the basis of said compressed samples and returning said rotated candidate beamformer to the orientation of said eigen-beamformer vector before said rotating.
2. 2. A method in accordance with claim I and further comprising scaling said resultant candidate vector to comply with an imposed restriction on transmitted power.
3. 3. A method in accordance with claim I or claim 2 wherein said eigen-beamfonner vector is a scaled eigen-beamformer vector.
4. 4. A method in accordance with any one of the preceding claims wherein said compressing comprises applying a compression algorithm to the samples.
5. 5. A method in accordance with claim 4 and including selecting a compression algorithm on the basis of effectiveness thereof to increase received SNR.
6. 6. A method in accordance with claim 5 wherein said selecting comprises optimising a parameter defining a compression algorithm on the basis of effectiveness thereof to increase received SNR..
7. 7. A method in accordance with claim 6 wherein said compression algorithm comprises a tanh compression.
8. 8. A method in accordance with any one of the preceding claims wherein said sampling of the radiation pattern comprises obtaining a discrete Fourier transform of said beamforming vectors.
9. 9. A method in accordance with any one of the preceding claims wherein said developing of a rotated candidate beamformer comprises obtaining an inverse discrete Fourier transform of said compressed samples.
10. 10. Wireless communications apparatus comprising a plurality of antennas, each being suitable for emitting a wireless signal, and bearnforming means operable to apply a beamforming defined by a beamforming vector on a signal to be transmitted from said antennas, including beaniforming vector determining means for determining said beamforming vector on the basis of a measure of transmission channel to a given receiver, said measure being expressible in the form of a channel matrix, the beamforming vector determining means including eigenbeamformer determining means for determining an eigen-beamformer vector from said channel matrix, vector rotation means for rotating said eigenbeamforifler vector into a reference direction in vector space such that application of said rotated eigen-beam former vector would result in peak radiation being directed in said reference direction, sampling means for sampling a radiation pattern associated with said rotated eigen-beamformer vector with respect to transmission direction, data compression means for compressing resultant samples to reduce spatial directivity induced by said eigen_beamformer, data transformation means for developing a rotated candidate beamformer on the basis of said compressed samples and rotation reversion means for returning said rotated candidate beamformer to the orientation of said eigen-beamformer vector before said rotating.
11. 11. Apparatus in accordance with claim 10 and further comprising scaling means for said resultant candidate vector to comply with an imposed restriction on transmitted power.
12. 12. Apparatus in accordance with claim 10 or claim 11 wherein said eigen-beamformer vector is a scaled eigen-beamformer vector.
13. 13. Apparatus in accordance with any one of claims 10 to 12 wherein said data compression means is operable to apply a compression algorithm to the samples.
14. 14. Apparatus in accordance with claim 13 and including compression algorithm selection means for selecting a compression algorithm on the basis of effectiveness thereof to increase received SNR.
15. 15. Apparatus in accordance with claim 14 wherein said compression algorithm selection means comprises parameter optimisation means for optimising a parameter defining a compression algorithm on the basis of effectiveness thereof to increase received SNR.
16. 16. Apparatus in accordance with claim 15 wherein said compression algorithm comprises a tanh compression.
17. 17. Apparatus in accordance with any one of claims 10 to 16 wherein said sampling of the radiation pattern means is operable to apply an inverse discrete Fourier transform to said beamforming vectors.
18. 18. Apparatus in accordance with any one of claims 10 to 17 wherein said data transformation means is operable to obtain a discrete Fourier transform of said compressed samples.
19. 19. 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 9.
20. 20. A computer readable carrier medium comprising a computer program product in accordance with claim 19.