GB2400000A - Iterative frequency domain equalizer for a MIMO system receiver - Google Patents

Abstract

An iterative frequency domain equalizer 28 for a Multiple Input Multiple Output (MIMO) system receiver uses an estimated initial solution and then makes a semi-hard decision 34 based on the knowledge that there is a finite possible date set. A regularization method, e.g. the Tikhonov Regularization algorithm, is then used to form an updated soft estimate. The process is repeated until a stoppage criterion is met. The initial soft estimates may be determined using a Minimum Mean Square Error (MMSE) detection process. The equaliser may be used for OFDM or SC-FDE (Single Channel Frequency Domain Equalization) signals. In a second embodiment, once a predetermined number of iterations has been reached the outputs are sent to a channel decoder (70, Fig. 3) instead of directly to the semi-hard decision blocks.

Description

1 2400000 Method and Apparatus for Signal Detection

Technical Field of the Invention

The present invention relates to Multiple Input - Multiple Output (MIMO) telecommunications systems, especially Wideband MIMO systems, and in particular to signal equalization and detection in receivers.

Description of Related Art

Multiple Input - Multiple Output (MIMO) telecommunications systems have been proposed for use in order to provide capacity improvements in wireless communications systems. A MIMO system has multiple antennas at the transmitter and at the receiver. The multiple antennas at the receiver will therefore each detect multiple versions of the transmitted signal, depending upon the exact channel characteristics between the set of transmitting antennas and the set of receiving antennas. The optimal receiver can in principle detect the transmitted signal from amongst the signals detected by the multiple antennas at the receiver using the maximum likelihood detection principle. However, the detection in most practical cases is not feasible due to the enormous computational burden.

Different MIMO systems have been proposed. For example, Orthogonal Frequency Division Multiplexing (OFDM) has been proposed in an attempt to reduce the required receiver complexity. Further, the document "Frequency Domain Equalization for Single Carrier Broadband Wireless Systems", Falconer et al, IEEE Communications Magazine 2002, pp58-66 describes a system in which the equalization is performed in the receiver in the frequency domain.

For synchronized transmissions, it can be shown that the MIMO equalization/detection problem for MIMO-OFDM and MIMO Single Carrier Frequency Domain Equalization (MIMO-SCFDE) can be expressed as a set of linear problems.

It is known from the document "On the Choice of the Regularization Parameter for Iterated Tikhonov Regularization of Ill-Posed Problems", Engl, Journal of Approximation Theory 49, 55-63 (1987), that iterated Tikhonov Regularization (also known as Ridge Regression in statistical literature) can be used for solving ill- posed linear equations. Specifically, it is known that Tikhonov Regularization can be used iteratively to find successive approximate solutions to such equations.

Summary

According to a first aspect of the present invention, there is provided a method for detecting transmitted signals, in a receiver of a telecommunications network operating in a multiple input-multiple output system, from multiple samples of received signals, the method comprising the steps of: (i) transforming the received samples into the frequency domain; (ii) determining an initial set of soft estimates of the frequency domain transformed transmitted signals; (iii) transforming the set of soft estimates from the frequency domain into the time domain; (iv) modifying one or more soft estimates from the set of soft estimates if said one or more soft estimates meets a confidence criterion; (v) transforming the modified soft estimates into the frequency domain; (vi) obtaining an updated set of soft estimates of the transmitted signals, by operating on the samples of the received signals and the modified estimates obtained in step (v), using a regularisation algorithm; (vii) transforming the set of updated soft estimates from the frequency domain into the time domain; and (viii) repeating steps (iv) to (vii) if a stoppage criterion is not met.

According to a second aspect of the present invention, there is provided a signal detector, operating in accordance with the method as defined in the first aspect of the present invention.

This has the advantage that the increasingly accurate estimated solutions to the MIMO equalization/detection problem can be obtained efficiently.

In some embodiments of the invention, this can be achieved without requiring an external device to provide prior information about the transmitted signal.

The method can also be used in conjunction with an external device such as a soft-in-soft-out channel decoder. In this case, the channel decoder is used to obtain a proposed solution.

Brief Description of the Drawings

For a better understanding of the present invention, and to show how it may be put into effect, reference will now be made, by way of example, to the accompanying drawings in which: Figure 1 is a block schematic diagram showing a receiver in accordance with an aspect of the present invention.

Figure 2 is a flow chart illustrating a detection technique in accordance with an aspect of the present invention.

Figure 3 is a block schematic diagram showing an alternative receiver in accordance with an aspect of the present invention.

Figure 4 is a flow chart illustrating a second detection technique in accordance with an aspect of the present invention.

Detailed Description of Embodiments

Figure 1 is a block schematic diagram of a receiver 20 in accordance with an aspect of the present invention.

The receiver may be used for example in a mobile radio communications network. The system can be used for example as a physical layer backbone for wireless local area networks, digital video broadcasting, personal area networks, etc. The receiver is adapted to operate in a Multiple Input - Multiple Output (MIMO) communications system. More specifically, the receiver is adapted to operate in a MIMO system, using Single Carrier Frequency Domain Equalization (SCFDE). Still more specifically, in the preferred embodiment the receiver is adapted to receive zero tailed SCFDE signals. That is, the transmitted data is formed into packets, which have silent periods between packets. The silent periods should be long enough to handle any expected channel delays between the transmitter and receiver.

In an alternative embodiment, the receiver may be adapted to receive SCFDE signals with a cyclic prefix.

That is, the last part of each block of data is repeated cyclically before the block to form a prefix.

Again, the duration of the cyclic prefix should be long enough to handle any expected channel delays.

As in a conventional MIMO system, signals are transmitted from a transmitter having multiple antennas. The receiver 20 similarly has multiple receive antennas 22. The received signals from each of the antennas 22 are applied to respective circularity induction (CI) blocks 24, and then to respective fast Fourier transform (FFT) blocks 26, so that the equalization can be performed in the frequency domain.

The receiver 20 is therefore a Multiple Input - Multiple Output (MIMO) single channel Frequency Domain Equalization (SC- FDE) receiver.

The outputs from the FFT blocks 26 are passed to an iterative equalization block 28, which performs the frequency domain equalization as will be described in more detail below, and the detected signals are passed to processing circuitry (not shown), which operates on them in any conventional manner.

It can be shown that the MIMO equalization/detection problem reduces to a set of linear problems. For a data vector of length K, there is a set of K linear problems. For each k, with O < k < K-1, there is a linear problem: Yk =Gkxk +nk (1) where xk is a column vector of the stacked kth elements from the frequency domain representation of the transmitted signals from all transmit antennas, G is the mixing matrix, and Yk is an equivalent frequency domain representation of the stacked kth elements from the received signals at all receive antennas, and n represents the noise.

More specifically, the elements of each mixing matrix G represent the frequency responses of the channels from each of NT transmit antennas to each of NR receive antennas. Thus:

3 04,1 2 À À k) Gk= Ask) 2(k) , i(k) (2) 4(k) 2(k) \(k) _ NR I NR, I NR NT The iterative equalization block 28 operates in accordance with an algorithm which is illustrated in Figure 2, in order to produce successive estimated solutions to the linear problems, until some stoppage criterion is met. One particular difficulty is that, depending on the values of the elements in the mixing matrices G. the linear problems may be ill-conditioned, leading to significant noise amplification when deriving solutions to the problems.

In step 40, the iterative equalization block 28 receives the frequency domain samples from the FFT blocks 26, and, in step 42, the bootstrap equalizer/detector blocks 30 act on the frequency domain samples to form initial soft estimates of the signals.

In this preferred embodiment of the invention, the initial soft estimate is generated by means of a conventional MMSE algorithm.

In step 44, the soft estimates obtained in step 42 are supplied to respective inverse fast Fourier transform (IFFT) blocks 32, for reconversion from the frequency domain to the time domain.

The resulting time domain soft estimates are then acted on in step 46 using respective tuneable semi-hard decision devices 34. The tuneable semi-hard decision devices use the fact that the transmitted information signals have values which must be chosen from a finite set of available values.

Then, for any of the soft estimates which meets some specified confidence criterion, a modified estimate is produced. More specifically, in this illustrated embodiment of the invention, a modified estimate is produced in respect of each sample which lies within a predetermined distance of one of the available values for the information symbols. Still more specifically, in this illustrated embodiment of the invention, each soft estimate which lies within the predetermined distance of one of the available values is modified to take that available value.

Thus, any soft estimates, which are sufficiently close to one of the available values, are replaced by hard decisions. Meanwhile, soft estimates lying outside these decision boundaries are left unchanged because a hard decision cannot be made on them. Put another way, some of the estimated values are rounded to values which form part of the set of valid signals, dependent upon the level of confidence (either 'high' or 'low') associated with the estimated values.

Proximity to an available value can be used as a confidence criterion because the distribution of each estimated symbol is well approximated by a Gaussian distribution, and so a proximity to an available value corresponds to a posterior probability of an error.

The semi-hard decision devices 34 are tuneable in the sense that the decision boundaries around the value of each information symbol are adaptable. In each iteration, different decision boundaries may be selected according to some optimality criterion. Where the decision boundaries are positioned exactly half the distance between information symbols, then a hard decision will always result. Thus, in this special case, the semi-hard decision device reduces to a purely hard decision device.

Apart from in this special case, the output of the tuneable semi-hard decision devices 34 are therefore made up of hard decisions for some symbols and soft estimates for other symbols. The outputs of the tuneable semi-hard decision device comprise both hard decisions and soft estimates.

In step 48, the outputs of the semi-hard decision devices are supplied to respective fast fourier transform (FFT) blocks 36, for reconversion into the frequency domain. The frequency domain estimates are then supplied back to the bootstrap equalizer/detector blocks 30 in step 50, together with the original frequency domain samples, and are used in a regularization algorithm, to obtain an updated soft estimate of the transmitted signals.

In this illustrated embodiment of the present invention, the regularization algorithm which is used utilises Tikhonov Regularization (TR), which is a conventional method for solving ill-conditioned linear inverse problems. This method involves introducing additional side constraints, which the desired solution needs to fulfil, into the least squares (LS) optimization constraint. TR is well suited to solve problems containing a smooth decay in a design matrix spectrum. In contrast, decomposition based methods are better suited to solve problems in which there is a distinct 'jump' in the magnitude of the singular values (thus, indicating some effective rank). TR does not necessitate decomposition to be performed on a design matrix.

An additional side constraint in the TR method is: JTR(X)=II(Y-GX)II2 + QCX) The side constraint helps to narrow the set of possible solutions which satisfy the LS constraint, provided the former is consistent with the problem. The side constraint also needs to be a sufficiently simple criterion if an analytical solution to equation (3) is required. A general choice for box) which is suitable for providing an analytical solution is: QCX)=) IIL XII2 (4) where L is some linear operator acting on the solution.

In many problems L represents the discrete derivative (of some order) operator in which case the solution is known to fulfill certain smoothness conditions. \2 is a smoothing regularization parameter whose value dictates the smoothness of the filtering function which is imposed on the spectrum of the design matrix by the side constraint. As \2 00, no weighting is imposed on the singular values of G and the TR solution coincides with the LS one. By contrast, as \2 -em, an excessively smooth function is applied on the spectrum of G. and information about the solution in the observation is lost in the attempt to over-suppress noise. In practice, optimal selection of \2 is difficult and many methods have been proposed in the

literature in this field (e.g. Cross Validation,

Generalised Cross Validation, Graphical methods).

In the case where knowledge about an initial-default solution x is known for the problem, then equation (4) can be further generalized as: Q(x)=72. ||L.(x-x'2 (5) In this case \2 controls the bias in the estimator towards the default solution. As 2_=, the estimator will coincide with the default solution and no useful information will be extracted from the observations.

This is not necessarily bad as the default solution might already be close to the true one (in which case the observation will have a negative effect on the quality of the estimator) although this is not easy to verify in practice.

Starting from the general formulation of TR criterion: JTR(X)=II(Y-GX)I2 + > AIL (X-X)2 (6) A solution can be found by setting -t2.(x - x)H LHL(x x)+ (y - Gx)H (y - Gx)= 0 ( 7)

MAXI

which leads to the following solution: 2.2.LHL(x-x)-2.GH. - Ox)= 0 =' TR =(7.L L+GHG) (2LHL GH) (8) It can be seen that the Tikhonov estimator has similarities with the structure of the MMSE one.

Indeed by setting L=I,x=0 and 72= o2, we get the MMSE solution for the case when the noise is zero mean with covariance o2.I and is uncorrelated with x. This indicates that using the MMSE solution (in step 42 described above) is a good choice for producing an initial soft estimate of the signal, and that it is not necessary to solve a computationally intensive optimization problem.

Thus, in step 50, the bootstrap equalizer/detector blocks 30 calculate updated soft estimates from the semi-hard estimator output and the original samples, namely: xk= IN +GHG. xi l+GHy (9 t! z k k) for 0 < k < K-1, and 1 i < N. where x is the soft estimate output after regularization, x is the output from the semi-hard decision block 34, transformed back into the frequency domain, k is the index of the solution, and i is the index of the iteration.

Once the updated soft estimate has been produced by the regularisation process, the procedure passes to step 52, in which the outputs are passed to the IFFT 32, and transformed back into the time domain. Thereafter, in step 54, it is determined whether some stoppage criterion has been met. For example, in the embodiment described above, the stoppage criterion is that a predefined number of iterations, N. has been performed, but equally, as is conventional, the stoppage criterion may be that some predefined solution quality criterion (for example, relating to the Quality of Service of the MIMO system, or relating to the incremental change in the outcome since the preceding iteration) has been met. ! Where the stoppage criterion has been met, the block 28 outputs the latest updated soft estimates for further processing.

Where it is determined in step 54 that the stoppage criterion has not been met, the procedure returns to step 46, in which the latest updated soft estimate is used in the semi-hard decision device 34, and after transformation by the FFT 36 to step 50, which again applies the regularisation to the semi-hard estimate.

The regularisation parameter \2 is increased before each application of the regularisation step 50, to recognise an increasing degree of confidence in the latest semi- hard proposal solution x. Again, the resulting soft estimate of the symbols is used in determining whether the stoppage criterion is met, and steps 46, 48, 50, 52 and 54 continue to be iterated until the stoppage criterion is met.

Since the value of the regularisation parameter \2 is increased in successive iterations of the process, it is necessary to recalculate the term

_

(' IN + GHG, which appears in equation (9) above. Preferably, this recalculation can itself be performed using an iterative algorithm, based on the matrix inversion lemma IL, whereby, given the inverse M1 of a matrix M, it is possible to recompute (M+D)-1 efficiently when D is a diagonal matrix.

Firstly, D is decomposed as: D = s,s, + 5252 + - + BEST ( 1 O) where si is the all-zero vector except for the ith element which is Audi. The matrix inversion lemma then computes (M+ wT)-1 from M1 and v, as: MIL(M-' ,v) (M + wT)-I = M-' _ M W M (11) Using the decomposition of D given in (10) above, the matrix inversion lemma can be applied iteratively N times in order to compute (M+D)-1 given and D. In particular, by setting an initial value for A = M-1, then, for i = 2... N-1: Ai = AIL (Ai1, si1).

The fact that s has a single non-zero element reduces the number of computations required.

Figures 3 and 4 relate to a second embodiment of the present invention. The second embodiment is closely related to the embodiment shown in Figures 1 and 2, and features which are common to the two embodiments are indicated by the same reference numerals, and will not be described further herein.

In particular, the second embodiment of the invention is applicable to a situation in which the transmitted data is encoded before transmission.

In the circuit of Figure 3, and the process of Figure 4, after step 52, in which the updated soft estimates have been transformed back into the time domain by the IFFT blocks 34, the completed number of iterations is counted and, in step 90 of the process, it is decided whether a predetermined number of iterations has been reached. If not, the process returns to step 46, as described with reference to Figure 2, with the outputs from the IFFT blocks 32 returned to the semi-hard decision blocks 34. However, if a predetermined number of iterations has been reached, the process passes to step 92, and the outputs from the IFFT blocks 32 are sent not directly to the semi-hard decision blocks 34, but instead to a channel decoder 70.

The channel decoder 70 produces two outputs, namely a possible final output signal, to which the stoppage criterion is applied in step 54 of the process, and so called extrinsic information, which is passed back to the semi-hard decision blocks 34 in the event that the stoppage criterion is not met. If the extrinsic information is passed back to the semi-hard decision blocks 34, it is used to form a new proposal solution in the same way as described above, except that the semi-hard decision blocks 34 use a direct probabilistic criterion rather than a comparison with a decision boundary, when determining whether to modify one of the soft estimates.

The "predetermined number" mentioned with reference to step 90 in Figure 4 is applied such that, in a process which may for example have 10 or more iterations, the outputs of the IFFT blocks 32 are passed through the channel decoder on each fifth iteration, so the "predetermined number" would be 5.

Although Figure 3 shows switches 72, which connect the outputs of the IFFT blocks 34 either to the semi-hard decision blocks 34 or to the channel decoder 70, it will be appreciated that all of the data flows in Figure 3 are under software control, and that data is routed either to the semi-hard decision blocks 34 or to the channel decoder 70 under software control rather than through a physical switch.

In preferred embodiments of the present invention, based either on the first or second embodiment described above, a first predetermined number of applications of the Tikhonov regularisation algorithm are performed using a first value of the smoothing regularisation parameter. These applications are performed with the decision boundaries at successively increasing distances from the available values. After resetting the decision boundaries to their original positions, a second predetermined number of applications are performed using a second value of the smoothing regularisation parameter. Again, these applications are performed with the decision boundaries at successively increasing distances from the available values. This may be repeated as many times as required.

It can therefore be seen that the present invention provides a method and apparatus for providing an improved estimate of transmitted signals in a MIMO system. Therefore, the present invention has significant advantages over conventional systems for improving performance.

The skilled person will also be aware that the present invention may be implemented in respect of any ill conditioned linear inverse problem where a finite solution set is identified and there is some knowledge about the statistics of the solution.

It will be apparent to the skilled person that the above specified embodiment of a zero-tailed SC-FDE MIMO and the algorithm disclosed are not exhaustive, and variations may be employed to achieve a similar result whilst employing the same inventive concept. For example, this concept may be utilised in any MIMO system. Also, the regularisation algorithm utilized may be, for example, a truncated singular value decomposition regularisation algorithm, or a steepest descent iterative formulation of the Tikhonov regularisation algorithm, or a subspace search iterative formulation of the Tikhonov regularisation algorithm.

Claims (20)

1. Claims 1. A method for detecting transmitted signals, in a receiver of a

   telecommunications network operating in a multiple input-multiple output system, from multiple samples of received signals, the method comprising the steps of: (i) transforming the received samples into the frequency domain; (ii) determining an initial set of soft estimates of the frequency domain transformed transmitted signals; (iii) transforming the set of soft estimates from the frequency domain into the time domain; (iv) modifying one or more soft estimates from the set of soft estimates if said one or more soft estimates meets a confidence criterion; (v) transforming the modified soft estimates into the frequency domain; (vi) obtaining an updated set of soft estimates of the transmitted signals, by operating on the samples of the received signals and the modified estimates obtained in step (v), using a regularisation algorithm; (vii) transforming the set of updated soft estimates from the frequency domain into the time domain; and (viii) repeating steps (iv) to (vii) if a stoppage criterion is not met.
2. 2. A method as claimed in claim 1, wherein the regulari sat ion algorithm i s a Tikhonov regulari sat ion algorithm.
3. 3. A method as claimed in claim 2, wherein the Tikhonov regularisation algorithm utilised is an iterative formulation of the Tikhonov regularisation algorithm.
4. 4. A method as claimed in claim 1, wherein the regularisation algorithm is a truncated singular value decomposition regularisation algorithm.
5. 5. A method as claimed in claims 2 or 3, wherein each application of the Tikhonov regularisation algorithm uses a smoothing regularisation parameter, and wherein a value of said smoothing regularisation parameter is increased in successive applications of the Tikhonov regularisation algorithm.
6. 6. A method as claimed in claim 5, comprising performing a first predetermined number of applications of the Tikhonov regularisation algorithm using a first value of the smoothing regularisation parameter, and subsequently performing a second predetermined number of applications of the Tikhonov regularisation algorithm using a second value of the smoothing regularisation parameter.
7. 7. A method as claimed in any preceding claim, wherein the transmitted signals have values selected from a finite set of values, further comprising, in step (ii), modifying one or more soft estimates from the set of soft estimates if said one or more soft estimates is within a predetermined distance of a value selected from said finite set of values.
8. 8. A method as claimed in claim 7, wherein the predetermined distance is adaptable.
9. 9. A method as claimed in claim 8, when dependent on claims 6 and 7, comprising performing the first predetermined number of applications of the Tikhonov regularisation algorithm with successively increasing predetermined distances.
10. 10. A method as claimed in claim 7, comprising modifying the one or more soft estimates to be equal to the respective value selected from said finite set of values.
11. 11. A method as claimed in any preceding claim, wherein step (i) comprises determining the initial set of soft estimates from the received samples by means of a minimum mean square error detection process.
12. 12. A method as claimed in one of claims 1 to 11, wherein the stoppage criterion relates to a number of iterations performed.
13. 13. A method as claimed in one of claims 1 to 11, wherein the stoppage criterion relates to a quality measure of the updated set of soft estimates.
14. 14. A method as claimed in any preceding claim, wherein the signals are transmitted using SCFDE or OFDM.
15. 15. A method as claimed in claim 14, wherein the signals are transmitted using zero-tailed SCFDE or OFDM.
16. 16. A method as claimed in claim 14, wherein the signals are transmitted using SCFDE or OFDM with a cyclic prefix.
17. 17. A method as claimed in any preceding claim, wherein the set of updated soft estimates, transformed into the time domain, are passed to a channel decoder, and the stoppage criterion is applied to the channel decoder output.
18. 18. A method as claimed in claim 17, wherein the set of updated soft estimates, transformed into the time domain, are passed to the channel decoder on only some iterations of steps (iv) to (vii), while steps (iv) to (vii) are automatically repeated on other iterations.
19. 19. A method as claimed in claim 18, wherein the set of updated soft estimates, transformed into the time domain, are passed to the channel decoder on one iteration of steps (iv) to (vii), out of a successive predetermined number of iterations.
20. 20. A MIMO receiver, operating in accordance with a method as defined in any preceding claim.