GB2372653A - Adaptive filters - Google Patents

Abstract

A method of estimating accurately normalised initial filter coefficients in an adaptive filter, such as a decision feedback equaliser in a communications system, includes the step of initialising a set of normalised filter coefficients in accordance with a channel estimate and a calculated channel matched filter model. Use of such normalised initial filter coefficients allows the use of an adaptive training algorithm with a larger step size than previously possible, leading to rapid convergence with the use of a short training sequence.

Description

s ADAPTIVE FILTERS The present invention relates to adaptive filters and

more specifically to new methods of achieving fast and accurate filter initialization, training and tracking.

10 BACKGROUND OF THE PRESENT INVE'<TION

Modern communication systems utilising wideband communication paths can suffer from a multipath phenomenon known as ISI (inter symbol interference), which reduces the received signal quality. For example, in a mobile 15 communication system, schematically shown in Figure 1, the base station 1 transmits an RF signal to a mobile station 2. If the communication is over a direct path, 3, there is no ISI. However, in a practical system reflections will occur from buildings etc. (illustrated by the reflective paths 4 in the figure). These reflections will cause multiple signals to be received by the receiver. Since direct and 20 reflected path lengths are different, a signal representing a single transmitted symbol (a single bit of data) can arrive at different times. This will result in a time spreading of the signal for that symbol, referred to as inter-symbol-interference (ISI), which potentially causes difficulty in detecting the symbol.

2s Figure 2 illustrates an equivalent effect in a wired or fixed communication system where two nodes 5 and 6 are linked. If an intermediate node 7 exists (which connects the path to another node 8) multiple paths 10 and 11 can result. An example of this is communication through cable networks that involve the mains local area network (M-LAN), which can be used in a home-based application. The 30 mains power cables are used to implement a local network in a frequency-isolated area, for example a home or office department. The observed multipath propagation is similar to that shown in figure 2, but the interference level could be

- - 5 much higher for high-speed data communications. This type of communication system is new, but has a very wide application area.

Multipath propagation or time dispersion can also occur, as illustrated in figure 3, in an optical cable 12 with reflection paths 14 causing inter-symbol-interference on the centre trace beam 13.

The multipath channel can be modelled by a tapped delay line filter, as shown in figure 4, where Ts represents the symbol period. The resulting signal vk is made up of the combination of the input symbols ok, xk I, xk 2, Xk multiplied by filter coefficients It,, hi, he and a noise component Ok, as shown in Eq. 1, 5 where L+1 is the number of taps in the channel model (or the symbol storage capacity of the channel).

Vk = h;Xk-i + ilk (l) i=0 20 The power delay profile of the channel is shown in figure 5. It can be seen that the channel signal can be modelled as a series of time spaced samples. Since the received signal is spread over a number of symbol periods, then symbols can interfere with one another, giving the phenomenon known as inter-symbol-

interference (ISI). This results in the received signals badly defining the original 2s transmitted symbol stream. In the past, various methods have been employed to remove this ISI.

A channel matched filter, such as that shown in figure 6, can be used to convert the channel signals into a waveform, such as that shown in figure 7. The channel 30 matched filter CMF receives the channel waveform from the channel model, and combines the received signals with the complex conjugates of the tapped delay line filter model coefficients. The output of the CMF is calculated as,

L Yk = h _ iVk- i (2) i=o The output ISI profile of the CMF is calculated according to the following equation: L+j dj = hjh j j = -L -1 (3) =o L dj = hjh' j = 0 (4) i=o L-j dJ = hjh,+j j = I,,L (5) i=0 15 Equations (3), (4) and (5) can be expanded for a 5 tap channel profile (L+1=5) as d 4 = hoh4 d3=h,h4+hoh3 d-2 = h2h4 + h h3 + hoh2 d = h3h4 + h2h3 + h,h2 + hoh; o = h4h4 + h3h3 + h2h2 + h,h; + ho ho (6) d, = h4h3 + h3h2 + h2h, + h ho d2 = h4h2 + h3h, + h2ho d3 = h4h; + h3ho d4 = h4ho The profile (Figure 7) from the CMF has the advantage of being symmetrical and 20 exhibiting a large real valued centre tap. It has been shown in several publications that the CMF f lter provides the optimum symbol-synchronisation point and multipath diversity at the centre tap, do. The output of the CMF can then be fed as

an input to a decision feedback equaliser (DEE) filter to remove side lobes calculated by equations (3) and (5). For this type of equalisation a novel direct coefficient calculation method has been developed in the University of Bristol and presented in the MoMuC-2 and VTC'98 conferences. The method calculates the equaliser coefficients directly from the channel profile and produces the best lo performance for an equaliser filter. However, the required extra unit for running the CMF filter, the feedback data gain adjustment problem and more importantly the need for a DSP to execute the required Teoplitz Matrix inversion make the method too expensive and complex for most low-cost, low-power applications.

5 Alternatively, a minimum mean square decision feedback equaliser (MMSEDFE) can be used. The MMSE-DFE does not require the CMF filter but suffers from a feedback data gain adjustment problem. This gain problem is present in many previous DEE based equalization methods and prevents accurate adaptive filter training and/or tracking. The MMSE-DFE method has a higher bit-error-rate and 20 greater complexity than the CMF-DFE. In these studies the training method is not adaptive and the training is not suitable for a hardware filter implementation due to the difficulty of matrix inversion.

The least mean square (LMS) algorithm is preferred for most adaptive filter 2s applications that require simple implementation and is also more stable than any other technique. The LMS algorithm suffers when the channel has a null point close to the centre of the unit circle in the zdomain. This results in a slow convergence speed and thus a long training sequence is required to achieve full convergence. In the standard LMS algorithm, if the training step size is large then so the LMS training becomes unstable. If the step size is small then the algorithm may not converge completely by the end of the training sequence.

5 Although the fast initialization, normalization and adaptive training/tracking technique presented here is explained using the EMS algorithm, the initialization and normalization processes are valid for all training algorithms. It is important to stress that the initialization approach is just a first step towards the calculation of the final filter co-eff cients. Following inhialisation, a unique normalization lo process is applied to produce gain balanced feedforward and feedback filter coefficients. This normalization is key to achieving fast and accurate training and tracking following feedforward and feedback filter initialization. In many applications the accuracy of the initialization process may well enable the feedback filter (FBF) coefficients to be excluded from the adaptive process, with 15 training restricted to the feedforward filter (FFF) coefficients.

DECISION FEEDBACK EQUALISER (DFE)

Figure 8 shows a decision feedback equaliser incorporating a feedforward filter 20 (FFF) (16) and a feedback filter (FBF) (17). +i is the number of feedforward i coefficients (18) and to, is the number of feedback filter coefficients (19). The variables xk (24) and x-k (25) represent the estimated data of the DEE and the detected data from the estimated data respectively. The feedforward filter (16) comprises a delay line (15) from which signals are tapped, the tapped signals 25 represent the samples in figure 4. The feedback filter (17) also comprises a delay line (20), which has as its input the output of the equaliser x-k (25), or the reference training symbols, xk (21). This output is the estimate from the filter of the symbol concerned. The feedback filter also has a number of taps, which represent the precursor samples.

The tapped signals from both the feedforward and feedback filters are scaled by respective coefficients c A, to co(18) and c, to clp (l9), and are then added

-6- 5 together to provide the output (24). The expression for the DEE operation is given by: O (hb Xk = Cjvk_; + CiXk-i i=-LJ,. i=I The output of the equaliser is then detected (normally using a hard threshold) to lo determine its level (25). During a training period, often at the start or in the middle of the data transmission, the coefficients of the filter can be adjusted so that the output of the equaliser has the expected value. The error, ilk iS calculated for use in the training and tracking algorithm as: i5 Ok = Xk-Xk (8) The coefficients can be obtained in various manners using so-called adaptive training techniques. These adaptive training techniques use a known training sequence of symbols, which allow the receiver to compare the detected symbol 20 sequence with the expected. sequence, as shown in Eq.(8). Ihe equaliser coefficients can then be adjusted until the detected symbols have an error rate within the required tolerance (or until the end of the training sequence is reached).

As mentioned above, the coefficients can be calculated in several ways. The 25 various methods can be grouped into linear (such as least mean squares) and non-

linear (such as recursive least squares RLS) techniques. The least mean squares (LMS) algorithm is the simplest method for equaliser training. However, the performance of conventional EMS algorithms is quite poor and its convergence rate is slow. The recursive least squares algorithm provides very high performance 30 but is complex to implement. It is also possible to directly calculate the equaliser coefficients. Examples of direct calculation methods include the minimum mean square error and channel matched filter equaliser.

-7- The main limitations of direct coefficient calculation are the need to estimate the required channel accurately and the problem of estimating the required feedback data gain in order to adapt the incoming data level to the detector output level. No optimum solution to this latter problem has been reported in the public domain lo and this prevents accurate high speed training and tracking after the initialization process. Both problems require powerful high-speed microprocessors to execute the required matrix inversion within realistic timescales.

SUMMARY OF THE PRESENT INVENTION

A method is provided to accurately estimate correctly normalised feedforward and feedback equaliser filter coefficients using an estimate of the channel impulse response. The normalization process ensures that an optimum gain balance can be achieved between the feedfor vard and feedback filters and is unique to this 20 method. Given that accurate feedfor vard and feedback filter normalization has been achieved in this embodiment, fast and accurate channel training can be performed post- initialisation using a training algorithm. In this embodiment, the EMS training algorithm is used, and given the accuracy of the normalised initialization, large feedforward and feedback step-sizes can be used to achieve us rapid feedforward and feedback filter convergence. Once training is complete, a set of equaliser coefficients is achieved that successfully remove all pre- and post-

cursor ISI from within the filter span of the equaliser. Without such training, the feedforward filter will simply act as a channel matched filter and will not equalise any of the pre-cursor ISI, resulting in a high residual mean squared error and a 30 sub-optimum bit error rate performance. In cases with severe pre-cursor ISI, without postinitialisation training, the equaliser filter may be incapable of achieving correct decisions. Once training is complete, data derived tracking can

-8- s then be supported to track changes in the channel due to conditions such a frequency offset and/or rapid motion (such as that experienced in GSM).

BRIEF DESCRIPTION OF THE DRAWINGS

Figures 1, and 3 illustrate multi-path signal transmission in communication lo systems; Figure 4 is a block diagram illustrating a model of the multi-path signal transmission channel of figures 1, 2 and 3; Figure 5 illustrates the power delay profile of the channel and sampling points for the channel coefficients modelled in figure 4; 5 Figure 6 illustrates a channel matched filter (CMF); Figure 7 illustrates the output power delay profile or ISI profile of the CMF; Figure 8 illustrates the decision feedback equaliser (DFE); Figures 9 and 10 illustrate the relative performance characteristics of known equalization techniques and an equalization technique incorporating a method 20 embodying the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Embodiments of the present invention are concerned with the fast and accurate 2s calculation of feedforward and feedback equaliser coefficient values in a decision feedback equaliser. The method uses a combination of channel estimation, normalised feedforward and feedback filter initialization, and feedforward and feedback filter training and tracking using an adaptive algorithm. The method can also be applied to the FFF in a Linear Transversal Equaliser (LTE).

In the particular embodiment to be described, the technique used for actually estimating the coefficients is the least means squares algorithm, however any

-9- 5 appropriate estimation algorithm can be used with the initialisation and normalization method embodied in the present invention.

As discussed previously, the decision feedback equaliser is typically Rained using a training sequence at the start or in the middle of a communications packet. The lo Raining data is known at the receiver allowing the actual detected symbol stream to be compared with the required symbol stream. The equaliser can then adapt to the particular communication path concerned.

In the ordinary case, the strongest path ( h, illustrated in figure 4) of the channel is 15 chosen for symbol synchronization. Pre-cursor path (only hOin fig. 4) symbols are cancelled by the feedforward filter (FFF) and post-cursor path (h2,h3,h4) symbols are cancelled by the feedback filter (FBF). The FFF is an anti-causal, finite impulse response (FIR) filter. For a good solution, a filter size equal to or bigger than the length of the channel model is chosen. The FFF works in order to 20 combine the power delay profile in its targeted window. The FBF is causal and normally implemented using L-1 taps, it cancels the received signal energy for it's targeted window. Therefore, energy in the vicinity of the synchronization symbol should be reserved in the feedfor vard filter ISI cancellation window to obtain more multipath diversity.

In order to do this, the least delayed transmit symbol (ok) at the cenke tap data ( ok in figure 8) should be used for symbol synchronization. All received power for symbol xk is represented in the feedforward filter and other interfering symbols are shared by the feedforward and feedback filters. Figure is arranged to obtain 30 the symbol synchronization at symbol xk, which is received through the first tap of the channel ho as it appears in the centre-tap data Vk. Then, subsequent interference symbols Xk+ lo ok++_ and previous interference symbols Xk lo ok_ are targeted as interference components by the FFF and FBF

-10 5 respectively. Since the FBF is causal, there is no need to employ more than L-1 taps. When this kind of symbol synchronization is applied, all adaptive training algorithms (RLS, LMS etc.) approximate the equaliser coefficients slowly and lo require many Gaining iterations. If the convergence speed is increased by either incrementing the training step size of the EMS algorithm or by decrementing the forgetting factor of the RLS algorithm then the algorithms become unstable with this type of symbol synchronization. When symbol synchronization is performed on the strongest path of the channel, ISI cancellation is easy and training becomes 15 stable hence the ISI components have lower energy than the targeted symbols.

However, their approximation does not maximise the multipath diversity in the channel. When the channel power delay profile is estimated during the frame 20 synchronization process the channel coefficients are used to initialise a CMF filter in the FFF of the DEE, which are expressed in equation (9).

Cj - h j where j=-L, O Cj = 0 where -Lit j < -A (assuming Lay 2 L) (9) Then the FFF filter coefficients for a 6 tap FFF and 5 tap channel model appear as

-11 c-s = o C_4 =h4 C 3 =h3 s * (10) C-2 = h2 C_l =hl c0 = ho (centre tap) These coefficients initialise the FFF to act as a CMF filter. While the FFF does not correctly equalise pre-cursor ISI, such initialization removes training sensitivity to the eigenvalue spread in the radio channel. This initialization also lo optimises the signal to noise ratio prior to training. As mentioned above, the CMF extends the interference profile as shown in Figure 7 and presents all the multipath energy for the desired symbol at the centre ISI component do. The above initialization secures all the received signal energy about the target symbol xk in the feedforward filter. This is a unique starting point for a linear transversal 5 equaliser (LTE) and is not dependent on any particular adaptive training algorithm. When the operation of the DEE is considered, the feedback coefficients can be initialized according to the ISI profile of the CMF. The FBF works as a 20 substructure of the target interference component and the previous symbols ISI components should be subtracted from the estimate of the DEE by the FBF.

According to this phenomena, the FBF coefficients would be given as shown in equation (1 1) 25 cj = -dj where j= 1, - L (l l) and the FBF coefficients for a 5-tap channel profile would be as

-12 cl = -d, C3 = -d3 C4 = -d4 Although the above initialization is valid for a theoretical unit-valued received signal level, in all practical scenarios the received signal will have a non-unity lo level and will not be compatible with the unit-valued hard detected data in the FBF. The feedforward initialization must therefore be normalized to ensure successful equalization and post-initialisation training and tracking. In this patent the unique use of the CMF's centre tap, do' is used to achieve optimum normalization, as shown in equation ( 13).

s Cj,N012M4LlSED = d where j =-L, -1,O,l, L (13) Therefore, in a particular embodiment using a (6,4) DEE, a 6 tap FFF and a 4 tap FBF would be used. This structure would ideally equalise a channel with delay lo spread spanning up to 5 symbol periods. Assuming the symbol spaced channel estimate taps are denoted by ho..h4. The DEE should be initialised as shown in equation 14.

C_5 =0

C 4 = hi C 3 = h;/ c = h:2/ c hi/ co = h'/o - d,/ _ - d;/ c = - din c din (14) When the initialization is optimally normalised in accordance with equation (14), the training will start with complete ISI cancellation for previously detected symbols. However, ISI components from subsequent symbols will still exist and must be removed via adaptive training to accurately complete the equalization

-l< s process. If this additional training is not implemented, significant ISI will remain and performance will be poor is channels will significant pre-cursor ISI. The resulting power delay profile after normalised initialization and before adaptive training is shown in Figure 7. It is possible to keep the FBF coefficients fixed and simply adapt the FFF coefficients to force the required ISI cancellation according 10 to the pre-determined FBF settings. However, including the FBF in the adaptive training process will increase performance since the updated FFF filter coefficients require new FBF filter coefficients to achieve an optimum solution.

Simulations have shown that the FBF coefficients do not change significantly since the error function does not have a large effect on the FBF given that the FBF 5 operation is initially correct. It should be stressed that the adaptive training process is only effective after the initialization feedforward filter coefficients are normalised using the centre tap of the CMF response, do Failure to optimally normalise the initial coefficients will result in the adaptive training failing to improve, or even worsen in some cases, the resulting performance.

The correctly normalized initial match filter values of the FFF coefficients combined with the pre-converged FBF coefficients results in a stable training algorithm allowing the adaption algorithm to use a larger step size (EMS), or a smaller forgetting factor (RLS) when calculating the FBF and/or FFF coefficients.

2s An adaptive training algorithm that achieves convergence using a shorter training sequence is obviously more desirable than one that requires a long training sequence and is non-adaptive. Previous, nonadaptive DEE implementations cannot be used in rapidly changing channels or channels exhibiting large degrees of frequency offset. The embodiments presented here can reduce the required 30 training sequence length dramatically. This occurs since the normalised initial filter coefficients are close in the FBF to the final values achieved after iterative training. Also, FFF initialization based on the norrnalised time reversed conjugate

-15 5 of the channel estimate removes adaptive training sensitivity to channel shape and eigen-value spread.

The features of this new adaptive training approach are now studied in a particular embodiment using the LMS algorithm, which is a member of the stochastic lo gradient-based algorithms. The LMS uses an estimate of the gradient of the error function and as such does not require a measurement of the pertinent correlation functions (nor does it require matrix inversion, which is not well suited to ASIC application). The LMS algorithm is simple and robust and performs well under a wide range of channel conditions and input signal powers.

In order to determine the values of the tap coefficients required for a given channel, a training sequence of data bits is supplied to the receiver. In a typical LMS system this can be anything up to 800 bits of information. Since the receiver knows the training sequence, the output from the DEE can be compared with the 20 expected output and the coefficients adjusted accordingly. The update equation for the ordinary LMS algorithm is given as: Ci,k+ = Ci,k +.k.Vk i when i =-L',.. 0 (15) c, k+ = c.k + A. ek. ok i when i = I,..

2s where k is the time index, is the step-size of the LMS algorithm and of the error as calculated at the k-th internal (equation (8)). () represents the complex conjugate of the variable. It has been suggested in several textbooks that the step size for the LMS in adaptive equaliser training should lie in the range 0.005 to 0.1, with a value of 0.045 often quoted as providing stable training. The standard LMS 30 algorithm normally converges within 400-800 training iterations. When the normalised initialization described in this document is applied to the LMS algorithm, the update equation becomes:

-1c- s C,k+l = Cjk + ^p.Sk.Vk_j when i =-L, O (16) Cj,k+l = Ci.k + 6.Sk Xk-, when i = 1, - L where the step sizes for the FFF and FBF?respectively, Aff and bib, differ from the original update equation. The same DEE filter structure is used. Simulation lo studies have shown that the FFF step-size, 6, can be increased to a value of 0.2 without resulting in instability. This result would not be possible without the unique normalization process described in this patent application. Extensive computer simulation results have shown that the feedback filter step size, An,, should lie in the range O to 0.1, with a typical value is 0.01. When the FBF step 5 size,6'b, is set to zero it implies the FBF filter is removed from the adaptive training process. Results in static channels have shown that this does not result in any major performance degradation and the error performance is still better than the ordinary EMS algorithm, as shown in the performance curves of figures 9 and 10. The larger step size in the FFF (typically a value of 0.2), dramatically reduces 20 the number of iterations required for complete convergence. Training sequence lengths of 100-150 symbols have been shown to produce low and very reasonable levels of mean square error, as shown in Figure 9.

The above describes sub-optimal adaptive training of the feedfonvard filter using 25 fixed initial coefficients in the feedback filter to reduce complexity. Alternatively, it is possible to adaptively train and track the feedback filter coefficients using fixed normalised initial coefficients in the feedforward filter. Given that the training of the feedback filter is far simpler when implemented in dedicated hardware (since hard values in the feedback filter convert tradition multiplications 30 to shifts and adds), this latter approach can significantly reduce training and tracking complexity.

-17- 5 Figures 9 and lO are graphs illustrating the relative performance of the training algorithms. It can be seen that the unique normalised initialization technique followed by fast LMS adaptive training, as described in the patent application, results in greatly improved convergence speed, as well as a significantly reduced bit-error-rate. It is clear from figure 9 that the equaliser starts with a low mean lo square error value (the error coming from pre-cursor ISI components that are not corrected until the adaption process is complete) and reduces further after training with 100-150 iterations. Given an accurate normalised initialization, the training process enables full pre and post cursor ISI cancellation to be performed, resulting in an optimum ISI-free result. The performance curves have been produced 5 assuming a fixed training step-size. Variable step size techniques could also be applied, as mentioned in several patent applications, to further reduce the mean square error after training, thus reducing the bit-error-rate (BER). In figure 9 the FBF step size is kept constant at =0.02 and the FFF step size An is varied to determine an optimum fixed value. Larger step sizes for the FFF noticeably reduce 20 the mean square error and do not cause instability.

Figure 10 shows the bit-error-rate analysis of the standard LMS technique compared with the fast adaptive Supervised LMS (SLMS) approach described here. In figures lO.a, lO.b and lO.c both the ordinary and supervised LMS 2s algorithms are trained using 200 and 450 iterations. There is no noticeable benefit from the use of a longer training sequence when the SLMS algorithm is used. In all cases the performance of the SLMS is much higher than the ordinary LMS.

When the training of the FBF is ignored there is no significant increase in the resulting bit-error-rate (this is especially true for static channels). Hence, to reduce 30 complexity, cost and power consumption, in low mobility applications ordy the feedforward filter coefficients may be adapted in practice.

-18 5 If another training algorithm with much faster convergence is used for adaptive training, i.e. the RLS algorithm, then the speed improvement would be expected to be similar to the LMS, i.e. a minimum of improvement of three times in convergence speed. A performance improvement, in teens of bit-error-rate, will also be observed s nce the adaptive training is no longer sensitive to Eigen value lo spread or the shape of the ISI profile prior to equalization.

Ignoring the training of the FBF would dramatically reduce the complexity and speed problems of the RLS algorithm and thus enable it to be implemented and applied at far lower processing rates.

In any mobile data transmission system (such as GSM) the mobile terminal will often transmit and receive data while in motion. Under such conditions, each multipath component will experience a Doppler shift. After the vector summation of the many multipaths, the resulting channel will experience considerable 20 fluctuation with time. More precisely, the co-efficients of the channel estimate, ho..h4, will vary significantly with time. Hence, the initial values for the feedback and feedforwardfilter coefficients are only valid for a short period of time. Adaptive training must converge the filter coefficients rapidly well within the coherence time of the channel. Failure to converge within the coherence time 2s of the channel will result in a failure to equalise the ISI present in the radio channel. Using the methods described in this patent application, the convergence properties of any training algorithm can be enhanced by a factor of three or more.

Enhancements of this type (i.e. fully converged training in just 100-150 iterations instead of 450 iterations) using the LMS training algorithm were demonstrated 30 earlier for a particular embodiment of the patent. Similarly, if the RLS adaptive training algorithm were used, rapid convergence well within a 26 symbol period window would be achieved. It is well know that the maximum Doppler frequency that can be tolerated prior to equalization is directly proportional to the

5 convergence speed of the adaptive training algorithm. Using the SLMS approach, training is improved by a factor of three or more. This results in an equalisation technique that can tolerate more than three times the maximum Doppler frequency for a standard training algorithm.

0 In practical radio modems, frequency offset is a common problem at the receiving unit. Frequency offset causes the received signal constellation to spin, resulting in incorrect decisions at the decision device. It is well known that adaptive training algorithms can tolerate a degree of frequency offset while training. Once again, the degree of frequency offset tolerance is proportion to the time required to 15 achieve fully converged equaliser coefficients. In the case of the SLMS algorithm, since the adaptive training time is reduced by a factor of three or more, the amount of frequency offset that can be tolerated prior to adaptive equalization is increased by a factor of three or more. For practical embodiments, this is an important result that can greatly simplify the resulting radio design.

Having acquired a fully converged set of equaliser coefficients as described previously in the document, in a time varying channel it is then necessary to ensure that these coefficients continue to track any changes in the channel. As discussed earlier, using the SLMS algorithm it is possible to convergence in the 25 presence of far higher (relative to standard adaptive training algorithms) frequency offsets and Doppler frequencies. Using any standard form of data derived tracking algorithm (such as the LMS or RLS algorithm) in the data mode, it is possible to track these far higher values of frequency offset and Doppler. In a standard embodiment, the degree of tolerable frequency offset and the slower 30 training process would limit Doppler. The SLMS algorithm reduces the time required for channel training and channel tracking by a factor of three or more (as demonstrated in a particular embodiment). Use of the SLMS also enables equaliser training and tracking to operate in the presence of far higher frequency

-20 5 offsets (again more than three times the value that can be tolerated in the standard algorithm). As will be readily appreciated, embodiments of the present invention can result in a low cost, high-speed and high performance technique for adaptive equalisation lo and channel tracking. The only additional processing required compared to the standard LMS algorithm is the calculation of equations (4), (5) and (14), a single real-valued division (since the centre tap of the CMF do is real) , and a number of extra multiply-accumulate operations (15 for L=5 and 21 for L=6). Although these appear as extra system complexity, equations (4) and (5) can be executed by 5 the same autocorrelation filter used for bit synchronization. The division operation in equation (14) is a data normalization process and can be implemented using a data shifting operation. Hence, the normalized initialization method is suitable for either DSP or hardware filter implementations.

20 The SLMS technique described above uses a unique combination of normalized initialization followed by adaptive training and tracking to enhance the performance of an adaptive filter. In the particular embodiments described previously, equalization filters in general and the DEE in particular have been used as examples. However, the SLMS concept may be applied to any adaptive filter 2s structure. To clarify this point, the following paragraphs explain the application of the SLMS in the area of adaptive antenna arrays. More specifically, adaptive antenna arrays applied to systems suffering from frequency selective fading will be considered. In this case a two dimensional filter structure is generated with filter taps present in both the time and space domain. The time taps are used to 30 remove the presence of ISI in the time domain and to equalise the frequency response in the frequency domain. The space taps are used to adapt the spatial pattern of the antenna array's far field to enhance signal power and reduce

interference and ISI effects. It should be noted that the methods described here

-21 5 also apply to the traditional narrowband adaptive antenna case using the special case of a single time domain tap per antenna element.

The SLMS technique can be used as a method to initialise and then fast adaptively train the filter coefficients for an individual antenna element in a diversity 10 structure or a combination of antenna elements in a fully adaptive antenna array.

This latter case results in the algorithm being applied to a twodimensional filtering process. The equalization process on each antenna element may use any filter based equaliser structure (such as the LTE or the DEE) and any adaptive training algorithm (such as the LMS or RLS).

For the specific embodiment of a DEE filter on each element of an antenna array, it is well known that a single feedback filter can be used for all antenna elements to reduce complexity. Using the methods described previously, it is possible to uniquely initialise the single set of feedback filter coefficients using the sum of the 20 optimally normalised initialization coefficients for each branch. This approach has not been reported in the public domain and results in a number of significant benefits. The unique normalization process described in this patent application enables the summation of feedback filter initialization values to result in perfect and accurate ISI cancellation. The individually normalised CMF coefficients are 25 used on each individual antenna branch with subsequent training being used to either adapt the feedforward, the feedback or both sets of filter coefficients as desired. When the techniques described above are applied to an antenna array (either so narrowband or wideband), the resulting training and tracking processes are dramatically simplified in terms of implementation complexity and enhanced in terms of convergence and tracking time. Particular embodiments based on a single time tap and N (N<6) space taps have demonstrated that accurate array

-22 5 training is possible using the LMS algorithm in the presence of interference with just tens of training iterations. Again, for many practical antenna applications, reduced implementation complexity and rapid training and tracking are essential.

Finally, the methods described in this application make use of an accurate and lo stable starting point that can be used for subsequent fast adaptive coefficient training with no instability or sensitivity to eigen value spread or channel profile shape.

Claims (1)

1. -23 5 CLAIMS:

   1. A method of estimating accurately normalised initial filter coefficients in an adaptive filter, the method including initialising a set of normalised coefficients in an equaliser filter in accordance with a channel estimate and a calculated lo channel matched filter model.

   2. A method as claimed in claim 1, wherein the received signal is modelled using a tapped delay line filter model and wherein the channel matched filter output signal has an inter-symbol-interference profile modelled according to the 15 following expressions: L+j dj= hjh, jj--L,-,- 1 i=0 L dj = Thjh; i=0 J=0 20 where d represents the intersymbol interference components after processing through the channel matched filter. hi represents the i-th time sample of the complex channel impulse response and hi represents the complex conjugate of the i-th sample. L+1 equals the number of taps in the filter model of the channel and wherein the preselected coefficients of the feedforward filter (in an LIE) are 25 initialised and normalised prior to training and tracking according to the following expressions: Cj= hj wherej=-L,--O Cj,nOR S5D = d where j =- L, 0.

   -2d- 5 Cj, j=.,....o representing the equaliser feedforward f Iter coefficients before normalization and C j NORM, S D j=_t o the corresponding coefficients after normalization. Accurate normalization is required in an LTE to ensure an optimal relationship between the error signal (which is generated assuming a unit values training sequence) and the magnitude of the feedfor vard filter samples. Failure to lo normalise correctly will negate the advantages of training and tracking and render the equaliser inoperable in a time-varying channel.

   3. A method as claimed in claim 2, wherein any remaining feedforward filter coefficients beyond the effective time span of the channel estimate are set to zero.

   4. A method as claimed in any one of claims 1 to 3, wherein feedback filter coefficients of the filter equaliser are initialised before training and tracking in accordance with the intersymbol interference profile of the output of the channel matched filter and normalised feedforward filter values as described in the 20 following expression, cj = -dj where j = I, where Cj j= I, represent the feedback filter coefficients concerned.

   5. A method as claimed in any one of claims l to 4, wherein the initialised feedforward coefficients are accurately normalized to ensure gain balance between the initial feedforward and feedback filter coefficients.

   30 6. A method as claimed in claim 5, wherein normalization of the coefficients is performed according to the following relationship:

   -25- 5 Cj NOR 4Lls6D=dj where j=-L, -l,O,l, L 7. A method as claimed in any one of claims 1 to 6, in which adaptive LMS training for an LTE filter is performed using a single step-size greater than 0.05.

   8. A method as claimed in any one of claims 1 to 6, in which adaptive RLS lo training for an LTE filter is performed using a single forgetting factor less than 0.985.

   9. A method as claimed in any one of claims 1 to 8, in which an EMS algorithm is used with large and independently optimised feedforward and feedback step-sizes.

   5 10. A method as claimed in any one of claims 1 to 4 and 6 to 9, wherein accurately normalised feedback and/or feedforward filter initialization is performed in conjunction with the channel matched filter thereby avoiding subsequent training sensitivity to channel profile shape and eigen-value spread in severe channels.

   20 11. A method as claimed in any one of claims 1 to 10, wherein post initialisation adaptive training is applied to the feedforward filter and wherein fixed initial values based on the channel estimate and the CMF profile are used for the feedback filter in a Decision Feedback Equaliser.

   12. A method as claimed in any one of claims 1 to 11, wherein post 25 initialization and adaptive training is applied to a feedback filter, for training and channel tracking, and fixed feedforward filter coefficients after the initial training using the channel estimate, the CMF profile, and the claimed fast training technique are used during equalization over a data sequence.

   -26 s 13. A method as claimed in any one of claims 1 to 12, wherein fast adaptive training can be accurately performed in the presence of high speed Doppler in a mobile terminal. Accurate training in the presence of Doppler is enabled due to the accuracy of the normalised initialization and the fast convergence achieved by the use of larger step sizes (LMS) or smaller forgetting factors (RLS) in the lo subsequent post- initialisation training process.

   14. A method as claimed in any one of claims l to 13, wherein fast adaptive tracking can be accurately performed in a data derived mode after training in the presence of high speed Doppler in a mobile terminal. Accurate tracking in the presence of Doppler is enabled due to the accuracy of the normalised initialization 5 and the fast converge achieved by use of larger step sizes (LMS) or smaller forgetting factors (RLS) in the subsequent post-initialisation training process.

   15. A method for fast initializing, training and tracking spatial and temporal multipath in a radio channel using multiple baseband equalisers on each antenna element in a diversity or antenna array unit.

   20 16. A method as claimed in claim 15, wherein the feedforward filters of any individual antenna in an antenna diversity or adaptive antenna array are initialised and adaptively trained in accordance with a method as claimed in any one of claims 1 to 14.

   17. A method as claimed in claim 15 or 16, wherein initial normalized 2s coefficients for a single feedback filter are calculated for all antennas in an antenna diversity or an adaptive antenna array, the feedback filter being initialised using coefficients obtained as the sum of the normalized initialization coefficients for each element, normalization being in accordance with the method as claimed in claim 7.

   5 18. method as claimed in claim 15, 16 or 17, wherein training and tracking speed and convergence accuracy is improved in beam forming, beam steering and ISI cancellation for narrowband or wideband antenna arrays using a method as claimed in claim 7.

   19. A method as claimed in any one of claims 15 to 18, to accurately initialise lo and train at high speed a traditional narrowband antenna array using a single adaptive feedforward time tap per spatial antenna element.

   20. A method as claimed in any one of claims 1 to 19, in which bit accuracy in the coefficients and error generation and update process can be minimised as a result of accurate normalization and low mean square error at start up, the 15 resulting reduction in the number of bits required to represent these signals reducing power consumption and gate count.