WO1999053658A1

WO1999053658A1 - Initialisation of coefficients for decision feedback equalisers

Info

Publication number: WO1999053658A1
Application number: PCT/GB1999/001081
Authority: WO
Inventors: John David Porter
Original assignee: Adaptive Broadband Limited
Priority date: 1998-04-08
Filing date: 1999-04-08
Publication date: 1999-10-21
Also published as: GB2336277A; GB9807600D0; GB2336277B; AU3431299A; EP1070411A1

Abstract

A decision feedback equaliser is preloaded with filter coefficients for training purposes. A data signal is received which includes a training sequence. A sample value of the training sequence is correlated with a stored equivalent training sequence and the peak correlation value is determined. A first set of correlation values is preloaded into a feedforward portion of the DFE for use as initial feedforward filter coefficients before training and the outputs of a feedforward filter are used as initial feedback filter coefficients in a feedback portion of the DFE.

Description

INITIALISATION OF COEFFICIENTS FOR DECISION FEEDBACK EQUALISERS

Field of the Invention

The invention relates to a preloading technique for adaptive equalisers of the type used in radio modems where the equaliser taps are preloaded before equalisation begins .

Background to the Invention

The invention has been developed in the context of a wireless Asynchronous Transfer Mode (ATM) networking infrastructure which is capable of supporting multi-media data traffic at high bit rates in local and wide areas, but the invention could also be used with other networking infrastructures . In radio communications systems, the transmitted signal travels from transmitter to receiver over a channel consisting of a number of different paths, known as multipaths. The transmitted signal component travelling along a particular path experiences absorption, reflection or scattering by any objects located in that path. This causes the signal components arriving at the receiver to have different amplitudes, phases and delays so that they interfere with one another. This interference is known as multipath fading, and results in Intersymbol Interference (ISI) at baseband. ISI describes the spreading out of the data symbols so that components of past and future symbols are superimposed on the current symbol, thus causing symbol errors.

A well-known technique for reducing the effects of ISI is adaptive equalisation. Equalisation is a process which uses filters to remove ISI caused by distortion in the channel. Adaptive equalisation makes use of filters which adapt to follow any changes in the channel distortion. For channels with severe distortion, a Decision Feedback Equaliser (DFE) is often used, which attempts to remove ISI due to previously detected symbols.

In a conventional data communications system, each data unit or packet contains an equaliser training sequence, which is included in a preamble as shown in

Figure 1. The preamble is used for synchronisation and for training of the filter coefficients in the equaliser before data detection begins. The preamble is required to have a certain minimum length to ensure that the equaliser coefficients are properly trained. The minimum length of the training sequence depends on factors such as the length of the filters used in the equaliser, the severity of the channel distortion and the type of training algorithm used. The training sequence represents an overhead in terms of transmission rate, since it uses up symbols which would otherwise be used for data symbols. Furthermore, the time taken for the equaliser to train causes a delay in the detection of each data packet, which is an overhead in turnaround time for each packet. High bit rate radio communication systems such as wireless ATM transmit short data packets and require delays in detecting data to be as low as possible. In wireless ATM systems, both the data overhead and the detection delay caused by the use of a training sequence impose severe limitations on performance. Therefore, there is a need to reduce the length of the training sequence and also to reduce the delay in training the equaliser.

Preloading the equaliser taps allows an initial estimate of the tap coefficient values to be made which is as close as possible to the final converged values. Provided that. the initial estimate is reasonably accurate, the tap coefficients will be almost converged before equalisation begins. This results in reduced convergence time, which means that shorter training sequences may be - 3 -

used without degrading the performance of the equaliser. However, existing methods for calculating the initial tap coefficient values are computationally intensive, which makes these methods unsuitable for applications requiring short turn-around times. Therefore, there is a need for a simple method for calculating the initial equaliser coefficient values.

Summary of the Invention

A preferred embodiment of the present invention provides a method for preloading equaliser taps comprising the steps of: obtaining first estimates for the equaliser feedforward tap coefficients from the output of a correlator; reshaping the first estimates to give improved estimates; and generating feedback tap coefficients by feeding the output of the correlator as data samples through the preloaded feedforward filter. This and other aspects of the invention are defined with more precision in the appended claims, to which reference should now be made.

A preferred embodiment of the invention will now be described in detail by way of example, with reference to the figures in which:

Figure 1 shows the structure of a data packet and preamble model;

Figure 2 shows a block diagram of a typical radio channel model; Figure 3 shows a typical channel impulse response;

Figure 4 shows a block diagram of a correlation and symbol timing extract circuit for use together with an equaliser. Note: only the baseband signal processing is 4 -

considered here. Frequency conversion and filtering are omitted for clarity;

Figure 5 shows a block diagram of a known decision feedback equaliser; Figure 6 shows the reshaping profiles to be used in an embodiment of the present invention;

Figure 7 shows a block diagram of an equaliser embodying the invention;

Figure 8 shows a flow diagram of the operation of the circuit of Figure 7; and

Figure 9 shows a flow chart of the method for performing reshaping on feedforward taps in an embodiment of the invention.

Detailed Description of Preferred Embodiments Radio data communications systems transmit data symbols grouped together in packets. The packet usually includes a short preamble sequence which is known to both transmitter and receiver (see Figure 1) . The preamble sequence is used for frame and bit synchronisation as well as equaliser training at the receiver.

A sequence of symbols x is transmitted over a radio communications channel of the type shown in the model of Figure 2 with sampled impulse response . The channel model has a transmitter 2, a channel 4, additive noise 8 and a receiver 6. The channel has a sampled impulse response of the type shown in Figure 3. Channel impulse response is given by:

h = [ h_{l f L}]

The sampled received signal at time t = kT:

L -l y_k " Σ∑ (=0^χ _k-r^h, ^{+ n} _k where

T = the period of the transmitted symbols y_k = the sampled received signal at time t = kT i , k = integers x_k = the transmitted symbol at time t = kT h = the sampled channel impulse response vector h₁ = the ithe sample of the vector n_k = noise sample at time t = kT

[ ]^τ = matrix transpose.

The channel impulse response is characterised by leading echoes (precursors), the main pulse (cursor), and following echoes (postcursors ) as shown in Figure 3. A channel where there is a direct, or line-of-sight (LOS) path between the transmitter 2 and receiver 6 is known as a line-of-sight (LOS) channel, and will have a dominant main pulse, but no precursors in the channel impulse response. A channel having no line-of-sight path between the transmitter and receiver is known as an obstructed or non-LOS channel, and may have large precursors in the channel impulse response.

At the receiver (as shown in Figure 4), the data is sampled by an analog-to-digital (A/D) converter 60 and passed into a correlator 62. The correlator 62 computes the complex correlation product between the data sequence and a stored copy of the known preamble sequence.

The magnitude of the correlator output at time t is:

A (t) = R_xyR_xy ^* where

Σ- w [cross correlation of received data ι =l samples with preamble sequence)

X_j = ith symbol of the preamble sequence y_∑ = ith sample of the received signal p = length of the preamble sequence * = complex conjugate operator.

The peak value of the output A (t) is used to extract frame synchronisation and symbol timing for the data packet by a timing extract circuit 64 whilst the data is stored in buffer 66. As shown in Figure 4, once symbol timing is established, the data is passed into a Decision Feedback Equaliser (DFE) 68 of the type shown m Figure 4. The DFE shown m Figure 5 consists of a Feedforward filter (FF filter), detector, Feedback Filter (FB filter), associated adders, and shift registers. Both the FF filter and FB filter consist of tapped delay lines 10 along which input signal samples y_k are passed.

The input samples are fed from the input to each delay 10 to a respective multiplier 12 where they are weighted by a coefficient c_λ and then summed in an adder 14 whose output is denoted z_k .

The purpose of the FF filter is firstly to approximate a matched filter for the received signal, and secondly to move non-minimum phase zeros inside the unit circle. This ensures that the cascaded channel and FF filter have a combined impulse response d which is minimum phase .

The combined impulse response is:

d = h ø c

where ® represents convolution.

The purpose of the FB filter is to remove Inter- Symbol Interference (ISI) due to previously detected symbols . It comprises a set of delays 10 which receive the output samples of the DFE. These samples are weighted in respective multipliers 16 by coefficients b then summed in an adder 18.

When the vector of sampled data y is input to the DFE, M samples are processed to produce one output symbol, where M is the number of taps in the FF filter. The number of taps in the FB filter is B .

The outputs of adders 14 and 18 of the FF and FB filters are combined in a further adder 20 before passing to a detector 22. The detector uses the output sample z_k of the adder to make a decision on the transmitted symbol at time t -kT. This decision is £,.. An error signal e_λ = St_t - z_k is generated by subtracting the equalised value z_κ from the output of the training sequence 26 during the training mode and from the output of the detector 22 during decision-directed mode.

The known preamble training sequence is placed at the beginning of each data packet, to provide perfect values for _A instead of using the detector output decisions. This is known as the training mode, and allows the equaliser taps to at least partially converge before the actual data begins.

In training mode, a switch 24 switches the output, and hence the input of the FB filter to a training sequence store 26 which stores values equivalent to those received in a data packet preamble.

Once the preamble sequence is finished the detector 22 decisions are used for _k . This is known as decision- directed mode. The error signal is used to update the tap coefficients of the FF and FB filters using an update algorithm such as Least Mean Squares (LMS) or Recursive Least Squares (RLS) . The time taken for the coefficient taps to settle within a specified range of their optimum values is known as the convergence time. The convergence time is critical in packet data transmission systems since longer convergence times necessitate longer preamble sequences .

The circuitry of the preferred embodiment is shown in Figure 7, and the operation of the preferred embodiment is illustrated in the flow chart of Figure 8. The operation of the circuitry in Figure 7 is as follows for each data packet .

The received signal y(t) is sampled and converted into digital values y_k by the Sampler and Analog-to- digital Converter 30. The values y_k are passed into Buffer A 32, and also into the correlator 34. The correlator 34 computes the correlation product A_k between sample vector y_k and the known training sequence, and outputs the values A_k to the Timing Extract Circuit 36. The Timing Extract Circuit 36 searches for the largest peak of A_k and outputs a timing marker value t₂ both to the correlator 34 and to Buffer A 32 to mark the position of the largest peak in the data stream. Once the timing marker t₃ is received by the correlator 34, it outputs a set of values A_k - R_yyR*_xy and R_xy to a Tap Reshape Circuit 38, and outputs the set of values R*_xy to Buffer B 40. The Tap Reshape Circuit 38 uses the values of A_k to calculate the power in leading and following echoes, and then uses an appropriate reshaping profile to reshape the values R_xy to produce initial values for the FF filter taps c ' = [c₁ ' , . . . , c_M' ] , as described in the flow chart of Figure 9.

The values c ' = [c₁ ' , . . . , c_M' ] are then loaded into the taps of the FF filter 42 from the Tap Reshape Circuit 38. Switch A 44 is then moved into position p2 and Switch B 46 is moved into position pi. The values R*_xy are shifted out of Buffer B 40 through Switch A 44 and through the FF filter 42 in the same way as data samples. The output from the FF filter 42 resulting from input values R*_xy are the values b= [b₁ , . . . , b_B] , which are loaded into the taps of the FB filter 48 through Switch B 46 in position pi. Switch A 44 is then moved to position pi, and Switch B 46 is moved to position p2. At this point, both the FF filter 42 and the FB filter 48 are preloaded and the equaliser is ready to accept data. The sampled received signal y_A is then shifted out of Buffer A 32 and through the Modified DFE 50, and equalisation continues from this time onwards as in a conventional DFE for the rest of the data packet.

The preferred embodiment of the invention comprises a preloading technique for adaptive equalisers for use in radio modems as described with reference to Figure 7 above . The equaliser taps are preloaded before equalisation begins, using the following method: first estimates for the feedforward tap coefficient values are obtained using a channel estimate from the correlator of Figure 4 as it acts upon the training sequence; the first estimates for the feedforward tap values are reshaped to give improved estimates of their optimum values; feedback tap values are generated by running the correlator output through the preloaded feedforward taps. This suboptimum approximation is sufficiently accurate to reduce the equaliser training time, yet computationally simple enough to allow high speed operation. Accordingly, the convergence time is reduced by preloading the equaliser tap coefficients with initial values which are obtained using a simple approximation method.

In an alternative implementation only the feedforward coefficients are preloaded using the reshaped estimates. The feedback coefficients are then derived in - 10

the usual manner using the training sequence. This is not as good a method but may be used if the small time delay required to calculate the FB filter taps is unacceptable.

Suboptimum Approximation for the FF Filter Taps Existing methods in the art calculate the FF filter tap coefficients c from an estimate of the channel impulse response using Fourier Transform or matrix inversion methods, which are computationally intensive. However, the optimum values for the FF filter tap coefficients c may also be considered to be the combination of a matched filter with impulse response h* (-t) , followed by a reshaping filter g.

The matched filter response is derived from the correlation outputs as follows:

R*_xy - h = channel impulse response estimate;

R _y = h * = matched filter response estimate;

A_k = R_xyR*_xy = jc ² = echo power estimate for tap i.

These estimates are reliable provided the autocorrelation function of the training sequence used is flat around the central peak.

Simulation results have shown that the reshaping filter may be approximated by a scaling factor applied to each coefficient of the matched filter. The scaling factors can be divided into two groups: scaling factors for a LOS channel and scaling factors for a non-LOS channel. The vector of scaling factors f_£ may be used for any LOS channel having no significant precursors in its channel impulse response. The vector of scaling factors f may be used for any non-LOS channel having significant precursors in its channel impulse response.

There are a set of heuristic rules that are used to derive the reshaping profiles. However, they are only 11 -

general rules and therefore do not give a unique solution for the reshaping profiles. The rules are summarised here :

(a) The FB filter of the DFE can only cancel ISI from past symbols (this corresponds to postcursors in the channel impulse response) . Therefore, we do not wish to have any precursors in the combined response of the channel and FF filter d = h ® c. This can be achieved by forcing all the FF filter taps before the reference tap to zero, thus all taps of the reshaping profiles before the reference tap are zero.

(b) The reference tap should be a scalar multiple of the largest tap of the matched filter response, which is achieved by setting the reference tap of the reshaping profile to a value of unity (although this value may be scaled if necessary) .

(c) For a non-LOS channel, it is desirable to capture signal energy from precursors of the channel.

It is obvious that for any particular channel the initial values found using these reshaping profiles will not be exact. However, on the average, the initial tap values are close enough to the final converged values to significantly reduce the training time.

The exact values chosen for the scaling factor vectors f_f may vary slightly according to the particular equaliser configuration, but once chosen they remain constant. Examples of scaling factor vectors f_f and f₂ for an equaliser with nine feedforward taps are given below:

LOS CHANNEL f_f = [0.0, 0.0, 0.0, 0.0, 1.0, 0.2, 0.2, 0.2, 0.2]

Accordingly, the reference (centre) tap is multiplied by a scale factor of 1.0, taps before the reference tap 12

are multiplied by a scale factor of 0.0 and taps after the reference tap are multiplied by a scale factor of 0.2.

NON-LOS CHANNEL f₁ = [0.0, 0.0, 0.0, 0.0, 1.0, 1.8, 1.8, 1.8, 1.8]

Accordingly, the reference (centre) tap is multiplied by a scale factor of 1.0, taps before the reference tap are multiplied by a scale factor of 0.0, and taps after the reference tap are multiplied by a scale factor of 1.8. Simulation results have shown that the scale factor vectors f_f and f as listed above, give good performance for a range of different radio channels. The justification for choosing the scale factor vectors f_f and f₂ is as follows. In its standard form, the DFE can only remove ISI due to previously detected symbols. Thus, the FB taps can only remove postcursors of the combined impulse response d = h ø c . This means that for radio channels which exhibit severe phase and amplitude distortion, the matched filter is not the optimum setting for the FF filter tap coefficients. To remedy this, the scale factor vector should attempt to reshape the matched filter in such a way as to minimise the magnitude of the precursors in the combined impulse response d. For a LOS channel with a dominant main pulse, it is necessary to increase the magnitude of the main pulse of the matched filter, and to decrease the magnitude of both precursors and postcursors of the matched filter. This leads to the numerical values given above for the scale factor vector f_f . For a non-LOS channel with significant power in the precursors of the channel impulse response, it is necessary to increase the magnitude of precursors of the matched filter, and to decrease the magnitude of postcursors. This leads to the numerical values given above for f₁. The scale factor vectors f_f and r^" ₂ may be 13

thought of as reshaping profiles for the matched filter as shown in Figure 6.

Preloading the initial values for the equaliser tap coefficients takes place at the start of every received burst of data. However, the values of the reshaping profiles f_f and f₂ are fixed. The equaliser selects the appropriate reshaping profile, either f_f or f_{l t} on a burst- by-burst basis.

A simple method for realising this reshaping is to start with the matched filter response R_> ( -t) = h* ( -t) . The correlator output R_xy gives reliable estimates of h* provided that the autocorrelation function of the training sequence is flat in the region of interest around the central peak. The next task is to classify the channel into one of two groups, LOS or non-LOS. Using the estimated matched filter values measured by the correlator. This is done by calculating the power in each matched filter tap coefficient value where:

Power₁ = |c ² for i = 1 , . . . , M

Note that the values of |c₂|² are immediately available since they are equal to the correlator output values A (t) , and therefore the values lc ² need not be calculated. Denote the largest tap as c_m , where 1 < m < M. The tap c_m is referred to as the reference tap, or main tap. The correlator should usually adjust the bit timing so that the reference tap is positioned at the centre of the FF filter. However, the reference tap may alternatively be moved to a position offset from the centre of the FF filter if it is required to minimise the number of FF filter taps.

Now sum the power of the coefficient taps occurring before the largest tap, which is the estimated power due to leading echoes (precursors) : 14 -

m-\

Power in leading echoes _frrf , = / \c \

; = 1

Then sum the power of the coefficient taps occurring after the largest tap, which is the estimated power due to the following echoes (postcursors) :

Power in following ³ echoes P f ,ol ,l,owing = i }—J \lc/\1 ι=m*\

Preloading FB Filter Taps

The FB filter taps should converge to Jb - h ® c which is the convolution of the channel impulse response with the FF filter. It is possible to calculate an estimate for vector Jb by preloading the FF filter tap values [c ' , ..., c_M'] and then running the set of conjugated matched filter tap values [Cj*, ..., c_M*] (which is the same as the estimated channel impulse response h) through the FF filter in the same manner as data samples. The output values of the FF filter will then be estimates of the FB filter tap coefficients [b_lf ..., b_B] . This procedure is realised very simply by attaching the conjugated matched filter tap values [c₁* , ■■., c_M*] at the front of the data packet and running them through the FF filter taps. These estimates for the FB taps are then used to preload the FB filter tap vector ib = [b_lf ..., b_B] before equalisation begins .

Algorithm for Finding Initial FF and FB Tap Values

The following algorithm summarises the procedure for finding the initial values of the FF and FB filter taps:

1. calculate Pι_eaζj_ing and Pfoii_ow_mg

2- IF (P_leadιng > P_followιng) AND (P_leadιng > Threshold)

THEN channel = non-LOS (leading echo)

ELSE channel = LOS (following echo) 15

3. non-LOS (leading echo channel) : multiply the matched filter taps [ c_{l r} . . . , c_M] by the vector of leading echo scale factors f₁ = [ f , . . . , f_1M] to obtain

C = [ C Σ_{1 Λ t} • • • r C_M Ii_Ml LOS (following echo channel) : multiply the matched filter taps [ c , ■ . . , c_M] by the vector of following echo scale factors f₁ = [ f_fl , . . . , f_fM] to obtain

C — [ C_j 1 _fl , • • • r C_M L f_M\

4. preload FF filter taps with the reshaped values c ' = [c'j, ... , c '_M]

5. pass the values R*_xy = [ c* , . . . , c *_v] through the FF filter. Output Jb = [£>,, ..., b_B]

6. preload FB filter taps using calculated values b = [ b_{l f} . . . , b_B] .

The values of Threshold, and components of f_t and f_f are small real numbers, which are chosen for the particular equaliser configuration, and remain constant thereafter .

Sampling Rate The embodiment described herein includes, but is not limited to, symbol-spaced sampling (where the sampling period is equal to the symbol period) . Fractionally- spaced sampling may also be used where Q samples are taken per symbol period, and where Q is an integer.

Computational Complexity

In order to quantify the computational advantages of the present invention over existing techniques, the number of multiplications and additions are totalled for each method. In all cases, the number of operations listed is that required to calculate the initial values for the FF taps only, where M is the number of FF taps. For purposes of comparison, it is assumed that the number of FF taps M - 16

is equal to the length of the channel impulse response L . In the suboptimum approximation method of the present invention, M additions are required to sum the power in the leading and following echoes, and M multiplications are required to multiply each matched filter coefficient value by its associated constant scaling factor (reshaping profile value) .

Method for finding Complex Multiplies Complex Adds initial tap values

Matrix inversion AM² + AM + 2 AM² + 5W +2 (Levinson method)

Back substitution method M² M² - 2M + 1

Fourier Transform method M + Mloq₂M 2M(l+log₂W)

Suboptimum approximation M M method of the present invention

Table 1: Comparison of the number of arithmetic operations required to calculate initial values for the FF taps ,

It can be seen from Table 1 that the suboptimum approximation method of the present invention requires many fewer arithmetic operations than the matrix inversion (Levinson method) , the back substitution method and the Fourier Transform method. Furthermore, the M multipliers required by the suboptimum approximation method may be simplified into shift registers and adder trees because the scale factor vectors f_t and f₁ which are used in the multiplications consist of constant, real numbers.

Claims

17 -CLAIMS :

1. A method for preloading filter coefficients in a decision feedback equaliser (DFE) comprising the steps of: receiving a data signal which includes a training sequence for the DFE; correlating sample values of the training sequence with a stored equivalent training sequence; detecting the peak correlation value derived by the correlation; and loading a first set of correlation values into a feedforward portion of the DFE for use as initial feedforward filter coefficients before training begins.

2. A method according to claim 1 including the further steps of: passing a second set of correlation values through this loaded feedforward portion of the DFE; and loading the output values of the feedforward filter into a feedback portion of the DFE for use as initial feedback filter coefficients before training begins.

3. A method according to claim 1 or 2 including the step of reshaping the first set of correlation values before loading them into the feedforward portion of the DFE.

4. A method according to claim 3 in which the reshaping step comprises weighting the first set of correlation values in dependence on the amount of energy in the received signal.

5. Apparatus to preload filter coefficients in a decision feedback equaliser (DFE) comprising: - l

means for receiving a data signal which includes a training sequence for the DFE; means for correlating sample values of the training sequence with a stored equivalent training sequence; means for detecting the peak correlation value derived by the correlation means; and loading a first set of correlation values into a feedforward portion of the DFE for use as initial feedforward filter coefficients before training begins.

6. Apparatus according to claim 5 further including : means for passing a second set of correlating values through the thus loaded feedforward filter portion; and loading the output values of the feedforward filter into a feedback portion of the DFE for use as initial feedback filter coefficients before training begins .

7. Apparatus according to claim 5 or 6 comprising means for reshaping the first set of correlation values before loading them into the feedforward portion of the DFE.

8. Apparatus according to claim 7 in which the reshaping means weights the first set of correlation values in dependence on the amount of energy in the received signal.