GB2406758A

GB2406758A - Updating filter coefficients for multi-path equalisation

Info

Publication number: GB2406758A
Application number: GB0322908A
Authority: GB
Inventors: Carlo Luschi; Charl Andries Cilliers
Original assignee: Ubinetics Ltd
Current assignee: Aeroflex Cambridge Ltd
Priority date: 2003-09-30
Filing date: 2003-09-30
Publication date: 2005-04-06
Anticipated expiration: 2023-09-30
Also published as: GB2406758B; GB0322908D0

Abstract

The performance of multi-path equaliser coefficients are measured S3 and a decision is made as to whether the coefficients should be updated by adjusting the existing coefficients S4, or by direct calculation of a fresh set of coefficients for the equaliser S1. The computationally less intensive process of coefficient adjustment is chosen if the channel variations are within the tracking capabilities of the adaptive algorithm. Preferably the coefficient adjustment comprises treating the coefficients as a vector and adapting the vector to approximately minimise a cost function. The direct calculation of a fresh set of coefficients preferably involves determining a solution for the vector that minimises the cost function. The measurement of coefficient performance may involve assessing the mean squared error in the output of the equaliser. Application is to a wide-band code division multiple access (WCDMA) mobile radio receiver.

Description

EQUALISATION TECHNIQUES

The invention relates to methods of; and apparatus for, performing equalisation techniques.

When a telecommunications signal is transmitted wirelessly between a transmitter and a receiver, the signal can propagate from the transmitter to the receiver by various routes.

These routes, apart from the direct route between the transmitter and the receiver, usually involve the reflection of the signal from objects in the environment. Thus, different versions of the transmitted signal arrive at the receiver by different routes and the various versions of the signal can interfere with one another at the receiver making it more difficult to recover the information that was contained in the signal sent out by the transmitter. The transmitted signal is therefore said to suffer from multi-path propagation effects. One way of overcoming such effects is to use an equaliser in the receiver.

In brief, an equaliser operates by filtering the composite signal, comprised of the versions of the transmitted signal travelling along the various paths, that is obtained by the receiver.

The filtering performed by the equaliser ideally removes the distortion due to multipath reception. Since it is possible that the transmitter, the receiver and/or one or more objects creating a multi-path component may be mobile, it is apparent that an equaliser will need updating from time to time to take into account variations over time that occur in the number and nature of the multi-path components that are present.

The invention concerns an improved technique for updating an equaliser.

According to one aspect, the invention provides a method of updating equaliser filter coefficients, the method comprising measuring the performance of the coefficients in the equaliser to decide whether the coefficients should be updated by adjusting the existing coefficients or by direct calculation of a fresh set of coefficients for the equaliser.

The invention also consists in apparatus for updating equaliser filter coefficients, the apparatus comprising means for measuring the performance of the coefficients in the equaliser to decide whether the coefficients should be updated by adjusting the existing coefficients or by direct calculation of a fresh set of coefficients for the equaliser.

The invention thus provides an equalization technique in which the filter coefficients can be updated using a selected one of a group of available techniques. For example, the direct calculation technique mentioned above may be significantly more computationally- intensive than the technique based on adjusting the existing coefficients such that it is desirable to use the adjustment approach rather than the direct calculation approach unless the former approach is likely to degrade the performance of the equaliser to a significant degree.

In one embodiment, the technique of adjusting the set of existing equaliser coefficients involves treating the existing equaliser coefficients as a vector and adapting the vector in order to minimize a cost function that has the vector as an argument. This can be achieved by calculating, e.g., the gradient, with respect to the vector, of a cost function which has, as an argument, the vector and updating the vector with a scaled version of the gradient.

In one embodiment, the direct calculation of a fresh set of equaliser coefficients comprises treating the equaliser coefficients as a vector and determining the solution for the vector that minimises a cost function that has the vector as an argument.

In one embodiment, the performance of the equaliser coefficients is measured by assessing the mean square error in the output of the equaliser.

The invention also relates to a signal receiver, such as a mobile telephone, arranged to perform equalization and to update its equaliser coefficients using the technique according to the invention.

From another perspective, the invention also relates to a program for causing data processing apparatus to perform the equaliser coefficient updating technique according to the invention. Such a program may be conveyed by a suitable data carrier.

The preceding paragraphs have mentioned the minimization of a cost function. It will, of course, be understood that minimisation is often a question of degree in that a determined minimum is commonly, to a greater or lesser extent, an approximation.

By way of example only, certain embodiments of the invention will now be described with reference to the accompanying figures, in which: Figure 1 is a block diagram illustrating some of the elements involved in handling a signal received at a mobile telephone; Figure 2 is a block diagram focussing on the elements involved in the calculation of equaliser coefficients of the mobile telephone shown in Figure 1; and Figure 3 is a flow chart of the equaliser coefficient update process used in Figure 2.

Figure 1 is a block diagram illustrating some of the key elements of a mobile telephone 10.

The telephone 10 operates according to a wide-band code division multiple access (W- CDMA) standard. Signals received at an antenna (not shown) are supplied to an analogue to digital converter (ADC) 12 after suitable frequency down-conversion and filtering (again, not shown). The digitised samples produced by the ADC 12 are then filtered once more by the RX filter 14 and supplied to an equaliser 16. The equaliser processes the multi-path components that are present in the signal that it receives from the RX filter 14.

The equalised signal produced by the equaliser 16 is then provided, in parallel, to each of several despreading units, for example units 18 and 20. Each of the Respreading units employs a different spreading code to despread a different information stream contained within the signal that issues from the equaliser 16.

The equaliser 16 is essentially a digital filter with a series of taps, each tap having a corresponding coefficient. See, for example, J. G. Proakis, Digital Communications, New York: McGraw-Hill, 1993. In order to ensure that the equaliser 16 is tracking changes in the multi-path environment to which the telephone 10 belongs, the filter coefficients in the equaliser 16 are periodically recalculated by a processor 22. Such a construction will be well known to the skilled person. The process by which the filter coefficients of equaliser 16 are calculated and recalculated will now be described in more detail.

Consider a synchronous CDMA transmission, and assume the received discrete-time signal model r, =dnh, nM An,, (1) n where r, = r(iTc I M) are the received complex signal samples taken at rate Tc I M, with Tc denoting the chip interval, he = h(I TC I M) are the rate Tc I M samples of the complex equivalent channel impulse response (including the transmit pulse shaping filter and the receive pulse matched filter), dn represents the complex multi-user transmitted chip sequence, and n, = n(iTc IM) are complex additive Gaussian noise samples with zero mean and variance cry, which model thermal noise and inter-cell interference. Also assume that the channel impulse response samples he are appreciably different from zero only for (=O,...,LM-1. The oversampled sequence r, can be decomposed into M chip- rate subsequences relative to M distinct subchannels. In vector notation, we define for each chip interval irk [rkM+m r(k+)M+m rk+N-)M+m] m 0,. . ., M 1 (2) where the index k denotes the k-th chip interval, index m indicates the subchannels and ( )T indicates transpose. From (1) and (2) we also write rid = H( )dk +nk i, m = 0, ,M-1, (3) where, letting h'm) = h'M+m hi, ht 2''' hi) O O O him) ... him) him) ,, O }I'm)= . . . . . m=O, ,M-1, (4) O O O O h m) dk = [dk-+] dk-+2 dk+N-! ] ( ) nk [nkM+ml n(k+l)M+m n(k+N-I)M+m] , m 0,. . ., M 1. (6) Denoting by wkm) the N-dimensional vector of the equalizer coefficients relative to the m -th subchannel, wk = [WkM+m w(k+'M+m w(k+N)M+m] m 0, , equalizer output at time k is Yk = Wk rk( ) + .. + W(M-)Tr(M-) Then, letting wk = [w( )7 w(M-') ]T (8) r = [r(0)7 r(M-)T]T H d + n (9) H = [H( )7... H(M-I)T] (10) nk = [n( ) ... nkM-I)T]T (11) the output of the linear equalizer can be expressed as

T

Yk =Wkrk. (12) The signal model described refers to a chip-level, fractionally-spaced, linear equaliser.

However, the signal model described above, and the following discussion, could be modified in a straightforward manner for application to the cases of chip-level, chip or fractionally spaced, decision-feedback equalisation and symbol-level, symbol of fractionally spaced, linear or decision-feedback equalisation. It should also be noted that the model described above also applies when all or some of the M chip-rate subchannels correspond to signal samples obtained from multiple receive antennas.

Returning to the telephone 10 and the signal model described above, the equaliser 16 has an operating cycle comprising two phases. First, a phase in which the coefficients in the vector wk are determined by processor 22. Second, a phase in which the signal samples arriving at the equaliser 16 undergo linear filtering according to equation (12) above.

The processor 22 has two techniques available for calculating the coefficients Wk. The processor 22 can either adapt an existing set of equaliser coefficients or it can abandon the existing equaliser coefficients and directly calculate a replacement set of coefficients.

Hereinafter, the former technique will be referred to as the "adaptive algorithm" and the latter technique will be referred to as the "block algorithm". Figure 2 focuses on the operation of the processor 22 and includes a selector 24 to denote that either the block algorithm 26 or the adaptive algorithm 28 is used to determine an updated set of coefficients for the equaliser 16. The block algorithm and the adaptive algorithm will now be described in more detail.

A common strategy (in both the block and adaptive algorithms) for the design of the MN equalizer coefficients of the vector wk is based on the minimization of a suitable cost function J(wk). The optimum coefficients vector wk according to the selected cost cutenon Is wk = argminJ(wk) (13) wk Denote by Vw the (stochastic) gradient with respect to the vector wk.

In the case of the block algorithm, the optimum coefficients vector wkis directly computed as Wk = Wk: VWk J(wk) O (14) The cost function J (W k) can take several forms. For example, the cost function may be based on the mean-square error (MSE) between the transmitted data dk and the equaliser output Yk such that: (Wk) E {|yk dk+D| }= E { |Wk rk -dk+D| } (15) Where D is a delay parameter.

When the adaptive algorithm is used to determine the equaliser coefficients, the cost function J (w k) can take the same form that is used in the block algorithm. Given a set of filter coefficients w k for chip k, then the adaptive algorithm calculates the set of equaliser coefficients Wk+ for the next chip interval as: we+ = wk -y Vwk J(wk) (16) Where y>0 and is a step size parameter which controls the convergence rate of the equaliser coefficients.

The use of the block and adaptive algorithms by processor 22 will now be explained with the aid of Figure 3, which shows process steps S1, S2, S4 and S4. Step Sl is the calculation of equaliser coefficients by the block algorithm using equation (14) and step S4 is the calculation of equaliser coefficients by the adaptive algorithm using equation (16).

Step S2 is the process of conducting equalization using a set of equaliser coefficients that have been produced by the prevailing one of the block and adaptive algorithms. Step S3 is the determination, when the adaptive algorithm is in use, of whether the adaptive algorithm can continue to be used to determine new coefficients.

At initialization, a set of equaliser coefficients is calculated using step S1. These coefficients are then used in equalization in step S2. Next, step S4 is used to determine new equaliser coefficients that are put to use in step S2. Then, the output of the equalization process is tested by step S3 to determine whether the adaptive algorithm remains suitable for use in the next update of the equaliser coefficients. The test that is used to make this decision will be described later. If the test of step S3 indicates that it is inappropriate to continue to use the adaptive algorithm, then the process flow returns to step S I and the process recommences from S 1 in the same manner as at initialization.

The update of the equaliser coefficients is performed periodically using step S1 or S4. It will be apparent that, whenever possible, the adaptive algorithm is used to update the equalization coefficients since the adaptive algorithm is considerably less computationally intensive than the block algorithm. For example, the block algorithm is usually required to calculate the inverse of large matrices, whereas the calculations of the adaptive algorithm involve less expensive operations. Thus, the average time needed to perform an equaliser coefficient update may be reduced facilitating the operation of the telephone in an environment in which the multi-path propagation conditions are changing rapidly such that equalization coefficient updates need to be performed frequently. Furthermore, the way in which the block and adaptive algorithms are positioned in the process of Figure 3 provides a synergy between the use of the two algorithms, as will now be explained.

Consider the case where conditions are such that the process of Figure 3is in the regime where the test in S3 indicates that continued use of the adaptive algorithm is appropriate.

Given an initial set of equaliser coefficients, the process may have to perform the cycle of steps S4-S2-S3 several times in order for the equalisation coefficients deduced by the adaptive algorithm to track the most appropriate set of equalization coefficients as the propagation conditions vary. It is possible to improve this tracking capability by increasing the step size y in equation (16). However, a large step size y may introduce an unacceptable level of adaption noise, also known as tap noise, and degrade the equaliser error performance. In regard to the issue of the tracking capability of the loop S4-S2-S3, it will be noted that, ultimately, the adaptive algorithm is always operating on a set of equaliser coefficients that stem from an iteration of the block algorithm. Thus, the loop S4-S2-S3 is usually provided, unless there has been a relatively large change in the prevailing multi-path conditions, with a set of equaliser coefficients from the block algorithm that provide a good starting point for the loop S4-S2-S3, thereby facilitating tracking of the time-varying channel.

A possible test performed at step S3 of Figure 3 will now be discussed in greater detail.

Step S3 may perform an MSE calculation to quantify the difference between a set of transmitted data values and the corresponding outputs of the equaliser 16. This process can be performed using data from a pilot sequence, since the intended values of such data will be known a priori to the telephone 10. If the MSE result is low then the current set of equalization coefficients can reasonably be regarded as close to the ideal set of equalization coefficients. This indicates that the adaptive algorithm is able to satisfactorily track the channel variations. On the other hand, if the MSE result in Step S3 is higher, then the adaption of the loop S4-S2-S3 does not perform satisfactorily, and the decision is made in step S3 to calculate the next set of equalization coefficients using the block algorithm in S1.

Claims

1. A method of updating equaliser filter coefficients, the method comprising measuring the performance of the coefficients in the equaliser to decide whether the coefficients should be updated by adjusting the existing coefficients or by direct calculation of a fresh set of coefficients for the equaliser.

2. A method according to claim 1, wherein the existing coefficients were obtained by direct calculation thereby providing a starting point for forming the coefficient update by adjusting the existing coefficients.

3. A method according to claim 1 or 2, wherein the step of adjusting the set of existing coefficients comprises treating the equaliser coefficients as a vector, and adapting the vector in order to at least approximately minimise a cost function that has the vector as an argument.

4. A method according to claim 3, wherein the step of adapting the vector comprises calculating the gradient of the cost function with respect to the vector and combining the vector with a scaled version of said gradient.

5. A method according to any one of claims 1 to 4, wherein the direct calculation of a fresh set of equaliser coefficients comprises treating the equaliser coefficients as a vector and determining a solution for the vector that minimises a cost function that has the vector as an argument.

6. A method according to any one of claims 1 to 5, wherein the step of measuring the performance of the existing coefficients comprises assessing the mean squared error in the output of the equaliser.

7. Apparatus for updating equaliser filter coefficients, the apparatus comprising means for measuring the performance of the coefficients in the equaliser to decide whether the coefficients should be updated by adjusting the existing coefficients or by direct calculation of a fresh set of coefficients for the equaliser.

8. Apparatus according to claim 7, wherein the existing coefficients were obtained by direct calculation thereby providing a starting point for performing the coefficient update by adjusting the existing coefficients.

9. Apparatus according to claim 7 or 8, wherein the adjustment of the set of existing coefficients comprises treating the equaliser coefficients as a vector, adapting the vector in order to at least approximately minimise a cost function that has the vector as an argument.

10. Apparatus according to claim 9, wherein the adaption of the vector comprises calculating the gradient of the cost function with respect to the vector and combining the vector with a scaled version of said gradient.

11. Apparatus according to any one of claims 7 to 10, wherein the direct calculation of a fresh set of equaliser coefficients comprises treating the equaliser coefficients as a vector and determining a solution for the vector that minimises a cost function that has the vector as an argument.

12. Apparatus according to any one of claims 7 to 11, wherein the measuring means is arranged to measure the performance of the existing coefficients by assessing the mean squared error in the output of the equaliser.

13. Radio signal receiving equipment comprising the apparatus of any one of claims 7 to 12.

14. A program for causing data processing apparatus to perform the method of any one of claims 1 to 6.

15. A method of updating equaliser filter coefficients, the method being substantially as hereinbefore described with reference to Figures 1 to 3.

16. Apparatus for updating equaliser filter coefficients, the apparatus being substantially as hereinbefore described with reference to Figures 1 to 3.