GB2388503A - Channel estimation - Google Patents

Abstract

A method for producing a modified impulse response, which may be used in an equalizer to improve e.g. DFE is disclosed where a first impulse response (22) is produced e.g. from a received signal (20) by a correlator (10). The impulse response (22) is analysed in analyser (12), which determines a characteristic of the response with which to determine a threshold value. Modifier (16) then compares portions of the impulse response (22) with the threshold value, and reduces the magnitude of such portions that fall below the threshold value. The amount of reduction depends on the portion being examined; the mount of reduction may be smaller if the portion has a magnitude close to the threshold value, or if the portion is adjacent another portion having a magnitude above the threshold value.

Description

1 2388503

Channel Estimation s This invention relates to channel estimation. It is particularly, but not exclusively, related to improved channel estimation for a high frequency tHF) equalizer.

Traditionally HF radio frequencies provide a 10 relatively poor transmission channel (compared to VHF and UHF frequencies). One reason for this is that the characteristics of the channel vary rapidly over time and with frequency for a number of reasons, such as reflections from the ionosphere.

15 It is usual to apply some form of channel equalization to correct for as much or as many of these distortions as possible.

A channel response at any particular time is defined by an impulse response. In theory, this may be determined 20 by sending an impulse over the channel and recording what is received.

The impulse response received is often composed of more than one pulse and will be affected by noise associated with the channel.

Most current systems do not operate by actually 5 sending a single impulse to determine the response, but instead analyse received real signals and determine the impulse response from their known characteristics.

Once an estimate of the impulse response of the channel has been obtained, the receiver can attempt to 10 correct for the distortion that has been imposed on the received signal; this process is termed equalization. An equalizer may also be able to perform the function of demodulation, i.e. determining the most likely data sequence that was transmitted. Many systems currently use 15 a form of decision feedback equalization (DEE), in particular block decision feedback equalization (BDFE).

Whilst recent developments in this field have been

directed to improving the performance with changing channels and complexity reduction, there is still a need 20 for a system which achieves optimum bit error rate (BER) performance over a wide range of channel conditions, including multipath fading and additive white Gaussian noise (AWGN).

Therefore, at its broadest' the present invention 25 provides a method for reducing the influence of noise on

a measured impulse response, and an apparatus for carrying out that method.

According to one aspect of the present invention there is provided a method of producing a modified 5 impulse response including the steps of receiving a first impulse response; determining whether the magnitude of any portion of said first impulse response is to be reduced; and producing a modified impulse response by reducing the magnitude of at least one portion of said 10 first impulse response identified in the determining step, wherein the amount of reduction varies according to one or more characteristics of at least part of the first impulse response.

The part of the first impulse response that is used 15 to vary the amount of reduction need not be the portion of the first impulse response that is being reduced.

However, the part and the portion may be the same.

The determining step may identify any portion of the first impulse response having a magnitude below a 20 predetermined threshold value.

Alternatively, the method may include calculating the average magnitude of portions of the first impulse response using a history of at least one previously recorded response, and the determining step may identify 25 any portion of the first impulse response having an average magnitude below a predetermined threshold value.

f Preferably the method includes the steps of analysing a plurality of first impulse responses to determine one or more characteristics of each of said first impulse responses and determining said threshold 5 value from one or more of those characteristics.

Particular examples of the characteristics that can be used to determine the threshold value are the maximum magnitude of the first impulse response or the total energy of the first impulse response.

10 The threshold value can be determined from the characteristics of the impulse response that is being modified, or from the recent history of that characteristic from previous first impulse responses (such as an average over a predetermined number of 15 previous first impulse responses or the maximum value of that characteristic over a predetermined number of previous first impulse responses).

Alternatively or additionally, the threshold value may be determined from other pre-defined parameters such 20 as the type of modulation used for the signal to be demodulated. The modiried impulse response produced by the method of the invention may then be used as the estimate of the channel impulse response by means of which the channel 25 can be equalized by any standard technique.

When determining a channel impulse response, the result may be corrupted by noise introduced in the

1. channel. The longer the period over which the impulse response is measured, the more influence the noise will have. For the portions of the impulse response that are small in amplitude, the degradation in performance caused 5 by adding the noise can outweigh the improvement that their inclusion has in producing an accurate representation of the channel. Therefore, by modifying the impulse response that is to be used by the equaliser so as to reduce those portions for which the degradation 10 due to the noise outweighs the improvement in channel representation, the signal-to-noise ratio after equalization can be improved and the bit error rate reduced. Whilst this improvement can be obtained by reducing 15 the magnitude of the portions in question, it may in some cases be preferable that the magnitude of at least some of those points in the modified impulse response is reduced to zero. Likewise, it is possible that some points will not be reduced at all. In other words, the 20 amount of reduction may be any value from (and including) 0S to loot of the magnitude of the point(s) in question.

The amount of reduction may vary as a function of the relative magnitude of one or more characteristics of the first impulse response and the threshold value.

/ Alternatively, it may vary as a function of the time separation between the portion of the first impulse response in question and the nearest part of the first impulse response that exceeds the threshold value. A 5 combination of these methods may be used. These methods are explained in detail below.

In another alternative, the amount of reduction may vary according to the history of measurements recorded; the more a response occurs at a particular value, the 10 more likely it is that it is part of the signal response rather than noise. An average of the characteristic measured may be calculated over a number of received signals, and the point(s) to be modified may be only those where the average measurement at that point is 15 below the threshold.

In one embodiment, the first impulse response that is to be modified according to the invention is produced by correlating known parts of a received signal against local data.

20 The step of determining the channel impulse response may be followed by, or combined with the step of determining the most likely data sequence contained in the signal from which the channel impulse response was determined.

According to another aspect of the present invention, there is provided a circuit for modifying a first impulse response including means for reducing the magnitude of those portions of the first impulse response 5 which have a magnitude below a predetermined threshold value, wherein the amount of reduction varies according to one or more characteristics of at least part of the first impulse response.

Suitable methods for determining the threshold value 10 include those described above in relation to the first aspect of the present invention, and the circuit preferably includes means for analysing one or more impulse responses and determining the threshold value according to characteristics of one or more of the 15 analysed impulse responses.

The circuit of the invention may also include a correlator for producing the first impulse response from a received signal. The first impulse response thus produced is then used as the input to the modifier 20 circuit of the invention.

Preferably said correlator produces the impulse response of the channel at various points in time by correlating a part of the received signal for which the data is known against a local replica of that part of the 25 received signal.

The circuits described above may also be incorporated with an equaliser, which uses the modified impulse response as an estimate of the channel impulse response. The equaliser, or a separate circuit, can then S use that channel impulse response to compute the most likely data sequence contained in the received signal from which the channel impulse response was determined.

A further aspect of the invention provides a modem incorporating a circuit according to the invention as 10 described above.

In many cases, the impulse response will be a discrete function, and so may be described as having a number of "points", and the invention acts to reduce the magnitude of those points that have a magnitude below the 15 threshold value. However, the method of the present invention is equally applicable to continuous impulse responses where a portion of the response that is below the threshold value is reduced.

In an alternative aspect of the invention, there is 20 provided a method of producing a modified impulse response including the steps of: receiving a first impulse response; determining whether any portion of the first impulse response has a magnitude below a predetermined threshold value; and producing a modified

impulse response by setting to zero at least some of the portion(s) that have a magnitude below the predetermined threshold value, wherein the threshold value is determined using a characteristic of the first impulse 5 response other than the maximum magnitude of the impulse response to be modified. A circuit implementing this method may also be provided. Further details of this aspect may be derived from the details of the other aspects explained above.

10 Embodiments of the invention will now be described with reference to the attached drawings, in which Figure 1 is a schematic diagram of a channel equalizer according to the present invention; Figures 2a, 2b and 2c show how a potential channel 15 impulse response may be affected by noise, and may be modified according to the invention; and Figures 3a, 3b, 3c and 3d show how the history of measurements is used to calculate an average of the impulse response, whereby the average is used to affect 20 the amount of reduction of the impulse response.

One embodiment of the present invention is as part of an equalizer for an HE radio channel, such as that used in an HE modem. Whilst the description of this

embodiment will refer specifically to an HE channel, the

. invention is considered to be equally applicable to other wavebands or frequencies.

An HF propagation channel is characterized by time-

varying multipath propagation, with typical delay spreads 5 of several milliseconds. Current modulation techniques use phase shift keying (PSK) or quadrature amplitude modulation (QAM) constellations of various sizes, often at a symbol rate of 2.4 ksps (kilosymbols per second).

Therefore, equalization is necessary prior to 10 demodulating them.

Examples of well--known equalization techniques include decision feedback equalization (DFE) and block decision feedback equalization (BDFE). For both of these techniques, as for most equalization techniques, the 15 receiver must form an estimate of the impulse response of the channel, which can then be used in the equalizer.

Rather than repeatedly sending an impulse over the channel, one standard approach to determine the channel impulse response is to correlate a received signal 20 against a local copy of what was transmitted. This is only possible if the receiver has knowledge of at least part of the transmitted data. However, standard modulation formats include periods of such data, often termed "training sequences" or "preambles".

When an input signal is corrupted by noise, the result of the correlation will also be corrupted.

Assuming that the "training sequence" in question is S:, and the noise samples are Ni, then the output of the 5 correlator will be M Rj =(Si +Nj) S,) i=0 where the correlation is over M samples and * denotes the complex conjugate.

Normally the signal S is defined so that it has a 10 perfect autocorrelation (i.e. for a single-path channel with no noise, Rj is zero for all j 0), or a close approximation to this. However, when noise is present, the correlator output R is corrupted by noise at every point, even if only one of the original points contains 15 the necessary information for demodulating the data. If the total number of points is large (as will generally be the case for an HE equalizer), the effect of the noise will be to degrade the performance of the equaliser significantly. 20 Although the above example has been given for a single path channel, this result is obviously applicable to any channel where the actual number of paths is significantly less than the number of possible paths (i.e. the number of correlation points computed).

The present invention improves the performance of the equaliser by discriminating between correlation points that are considered to contain only noise and those which are considered to contain a signal component, 5 on the basis of their magnitude.

An improvement in the BER As Eb/No performance of the order of l dB can be achieved. The best improvement occurs on AWGN channels and at low Eb/No, and therefore at moderate data rates (e.g. 3200 bps at HF). At higher 10 data rates a very high Eb/No is required for acceptable performance, and therefore on a channel that can support such communication there is less noise present. As a result, the improvement that may be obtained is lower.

Figure l shows a schematic diagram of an equaliser 15 according to the present invention, for use in, for example, an HE modem.

A received signal 20 is passed through a correlator lo, which measures a first impulse response of the channel at various points in time by correlating one or 20 more parts of the received signal for which the data is known against a local copy of the corresponding data.

This produces a first impulse response 22. In general, this impulse response will be complex-valued.

The first impulse response 22 then passes through analyser 12, which determines one or more characteristics of the first impulse response 22 such as the its largest magnitude, or the total energy of all points of the 5 response. Alternatively, the analyser may use characteristics from a predetermined number of previous first impulse responses, for example by taking the average value of a characteristic, or the maximum of a characteristic. A combination of these features may also 10 be used.

The impulse response 22 and the data 24 from the analyser are then passed to threshold setter 14, which determines a threshold below which points in the impulse response will be removed or ignored. In the simplest 15 implementation of the invention, this threshold will be a fraction of the largest magnitude of the impulse response 22. The impulse response 22 and the threshold data 26 are then passed to the modifier 16, which reduces the 20 values of all points in the impulse response with a magnitude lower than that of the threshold to zero, and in doing so produces a modified impulse response 28.

Since low magnitude points with any phase angle can have equal detrimental effects to the signal-to-noise ratio,

the modifier 16 may set all points in the impulse response which have an absolute value lower than the threshold to zero.

Any point in the impulse response 22 whose magnitude 5 exceeds the threshold is considered to contain a valid signal component and is retained unmodified. Any point in the impulse response 22 whose magnitude does not exceed the threshold is assumed to only contain noise and so is reduced or set to zero. If the threshold has been 10 chosen correctly, the improvement resulting from the elimination of noise in the impulse response will on balance exceed the degradation resulting from reducing the effect of points which might contain a small signal component. 15 For a discrete first impulse response consisting of a number of points in the time domain, the values of each point (relative time, magnitude and phase angle) are stored in a memory or register.

When the modified impulse response is output, each 20 point is read from the memory or register, and for those that have a magnitude of less than the threshold value, a magnitude of e.g. zero is output. This threshold value may be used as a hard limit, with all impulse response points (or portions) having a lower magnitude than it

being set to zero and all impulse response points (or sections) having a higher value being left unchanged.

However, the likelihood that an impulse response point is predominantly the result of noise does not 5 change abruptly according to whether the magnitude of the point is just above or just below the threshold.

Therefore, alternatively, the impulse response points (or sections) having a magnitude below the threshold may be reduced in magnitude rather than all set to zero, with 10 those points having the lowest magnitude being reduced the most, and those having a magnitude just below the threshold being reduced only slightly. Assuming that the measured impulse response is RI, the modified impulse response R'I and the threshold is T. this can be expressed 15 mathematically as: R. IR,I27

( T) I I

where f (x) is a monotonically increasing function of x, that is if y > x then f (y) f (x), with f(1) = 1. Note that this does not preclude setting some impulse response 20 points to zero.

Often, as a result of the characteristics of the filters contained in HE radios, each multipath component appears spread over a number of adjacent impulse response

points rather than at a single point. In this case, it may be beneficial to include a number of adjacent impulse response points, even though only the central ones may have a magnitude that exceeds the threshold. Therefore, a 5 further alternative approach is for the amount by which impulse response points with magnitude below the threshold are reduced to be determined by their separation in time from points with magnitude above the threshold. Thus, points adjacent to those that are above 10 the threshold would be reduced only slightly, whereas those at a greater separation would be reduced more.

Using the same notation as before, this may be expressed mathematically as: R. |R,I>T

R. = l R. |R | T 15 where tmin is the minimum time separation between the impulse response point under consideration and an impulse response point whose magnitude exceeds the threshold, and f(x) is again a monotonically increasing function; hut in this case f(O) = 1. Note that this does not preclude 20 setting some impulse response points to zero.

It is frequently the case that the impulse response changes comparatively little between successive measurements, whereas the noise present on each

( measurement is independent. Thus, by taking account of a number of consecutive measurements, it is possible to obtain an improved discrimination between signal and noise. One common algorithm that may be used is a running 5 average, defined by: fat (I) N f (i) i=-(N-! jr where f(t) is the measurement of a particular impulse response point at time t, N is the number of measurements to average, and the interval between 10 measurements is T. An alternative approach is exponential averaging, defined by: fAv() (1)fAv(-r)+J(t) a<c1 where the notation is the same as above, and the averaging time constant is approximately -by. Other 15 standard averaging techniques may also be used.

The three preceding techniques can be used separately or in combination.

In an alternative embodiment, the magnitude of each point is read before the values are stored in the memory 20 or register, and only those points with a magnitude above the threshold value are stored as non-zero values.

The modified impulse response 28 is then passed to the equaliser lS, which uses it as an estimate of the

channel impulse response in compensating for the distortion of the received signal 20. The equaliser 18 may also compute the most likely data sequence 30 contained in the received signal.

5 The effect of the invention is illustrated in Figures 2 and 3, with the impulse response being shown as real rather than complex for clarity purposes. The impulse response is shown as a number of discrete "points". In the majority of circumstances for an HE 10 channel, the impulse response will be a discrete function, however, the method of the present invention is equally applicable to continuous impulse responses where a portion of the response that is below the threshold value is reduced.

15 Figure 2(a) shows a possible channel impulse response, showing two paths. Figure 2(b) shows this response (solid black dots 1), overlaid with the response actually measured by the correlator (grey dots 2). The difference between each pair of dots represents the 20 effect of noise in the channel (N). The horizontal dotted lines 3 and 4 show the threshold chosen by the receiver, in this example at one fifth (0.2) of the maximum magnitude of the received impulse signal. Figure 2(c) shows the modified impulse response after the points

( with magnitude below the threshold value have been set to zero except for those adjacent to points above the threshold. It is clear that in Figure 2(c), the total contribution of the noise to the impulse response has S been greatly reduced whilst little (in this particular example, no) signal component has been lost.

Figure 3(a) shows a possible channel impulse response, showing two paths. Figure 3(b) shows this response (solid black dots l), overlaid with the 10 responses actually measured by the correlator at two successive points in time (grey dots 2 and white dots 3).

The difference between each of these and the channel impulse response represents the effect of noise in the channel (N), and is of course different for the two 15 measurements. The horizontal dotted lines 4 and 5 show the threshold chosen by the receiver, in this example at one fifth (0.2) of the maximum magnitude of the received impulse signal. Note that there are two occasions 6 where the impulse response exceeds the threshold for one 20 of the two measurements even though there is no signal component present, and one occasion 7 where the impulse response fails to reach the threshold for one of the two measurements even though a signal component is present.

Figure 3(c) represents the effect of averaging the two

( 20 measurements for each impulse response point. It can be seen that this removes the anomalies (6 and 7) referred to above, and hence provides better discrimination between signal and noise. The points whose averaged 5 magnitude is below the threshold are then set to zero or modified in any of the manners already described; as an example, Figure 3(d) shows the modified impulse response after the points with an average magnitude below the threshold value have been set to zero except for those 10 adjacent to points with an average magnitude above the threshold. Thus, only modifying points based on their averaged magnitude provides a better result because anomalies are likely to be ironed out by the averaging process. 15 The invention may include any variations, modifications and alternative applications of the above embodiments, as would be readily apparent to the skilled person without departing from the scope of the present invention in any of its aspects.

Claims (26)

1. A method of producing a modified impulse response including the steps of: 5 receiving a first impulse response; determining whether the magnitude of any portion of said first impulse response is to be reduced; and producing a modified impulse response by reducing the magnitude of at least one portion of said first 10 impulse response identified in the determining step, wherein the amount of reduction varies according to one or more characteristics of at least part of the first impulse response.

15

2. A method according to claim l, wherein the determining step identifies any portion of the first impulse response having a magnitude below a predetermined threshold value.

20

3. A method according to claim l including calculating the average magnitude of portions of the first impulse response using a history of at least one previously recorded response, wherein the determining step identifies any portion of the first impulse response

( having an average magnitude below a predetermined threshold value.

4. A method according to either one of claims 2 or 3 5 including the steps of analysing a plurality of first impulse responses to determine characteristics of each of said first impulse responses and determining said threshold value from one or more characteristics of at least one of said first impulse responses.

5. A method according to claim 4, wherein the characteristic from which said threshold value is determined is the maximum magnitude of the first impulse response from which said modified impulse response is to 15 be produced.

6. A method according to claim 5, wherein said threshold value is determined as a predetermined fraction of said maximum magnitude.

7. A method according to claim 4, wherein the characteristic from which said threshold value is determined is the total energy of the first impulse response from which said modified impulse response is to

be produced.

8. A method according to any one of claims 5 to 7, wherein said threshold value is determined from the 5 recent history of said characteristic from a predetermined number of previous first impulse responses.

9. A method according to claim 8, wherein said threshold value is determined from the average of said 10 characteristic.

10. A method according to claim 8, wherein said threshold is determined from the maximum of said characteristic.

11. A method according to any one of the preceding claims, wherein said reducing includes setting the magnitude of at least some of the portion in question to zero.

12. A method according to any one of claims 2 to 11, wherein the amount of reduction varies as a function of the relative magnitudes of the one or more characteristics of the first impulse response and the

threshold value.

13. A method according to any one claims 2 to 12, wherein the amount of reduction varies as a function of 5 the time separation between the portion of the first impulse response in question and the nearest part of said first impulse response that exceeds said threshold value.

14. A method of determining a channel impulse response 10 of a communications channel including the steps of: producing a modified impulse response by a method according to any one of the preceding claims from a first impulse response produced by said channel; and equalizing said modified impulse response.

15. A method according to claim 14, wherein said equalising is performed using block decision feedback equalization. 20

16. A method of producing a modified impulse response from a received signal wherein a first impulse response is produced by correlating known parts of said received signal against local data, and said modified impulse response is produced by a method according to any one of

claims 1 to 13.

17. A method of determining the most likely data sequence from a received signal transmitted through a 5 communications channel, including the steps of: producing a modified impulse response according to claim 16; equalising said modified impulse response to determine the channel impulse response) 10 using said channel impulse response to determine the most likely data sequence contained in said received signal.

18. A circuit for modifying a first impulse response to 15 produce a modified impulse response including: means for reducing the magnitude of those portions of the first impulse response that have a magnitude below a predetermined threshold value, wherein the amount of reduction varies according to one or more 20 characteristics of at least part of the first impulse response.

19. A circuit according to claim 18, including:

means for analysing a plurality of first impulse responses to determine characteristics of each of said first impulse responses; and means for setting said threshold value according to 5 one or more characteristics of at least one of said first impulse responses.

20. circuit for producing a modified impulse response of a communications channel from a received signal, 10 including: a correlator for producing a first impulse response by correlating parts of said received signal against known data; and a circuit for modifying said first impulse response 15 according to either one of claims 18 or 19.

21. A circuit for determining a channel impulse response for a communications channel from a received signal, including: 20 a circuit for producing a modified impulse response according to claim 20i and an equalizer for correcting for the channel impulse response using said modified impulse response.

(

22. A circuit for receiving data in a signal transmitted through a communication channel, including: a circuit for determining a channel impulse response according to claim 21; and 5 means for computing the most likely data sequence contained in said signal using said channel impulse response.

23. A modem incorporating a circuit according to any one lO of claims 18 to 22.

24. A method of modifying an impulse response substantially as herein described, with reference to the accompanying drawings.

25. A method of determining a channel impulse response substantially as herein described, with reference to the accompanying drawings.

20

26. An equalizing device substantially as herein described, with reference to the accompanying drawings.