GB2476930A - Estimating Channel Impulse Response by cross correlating received signal with weighted taps also applied at the transmitter - Google Patents

Abstract

The invention concerns digital radio systems and features waveforms enabling the channel impulse response (CIR) to be measured free from distortion so that a Rake processor may be programmed so as to implement the matched filter to the multipath radio. The data signal is fed through a tapped delay line, multiplied by a set of tap weighting factors and thence summed to produce the real and imaginary transmission signals (Fig. 2). At the receiver the signal is cross correlated with the same tap weights in the real and imaginary paths. The tap weights are selected such that a correlation peak is produced for each multipath in the CIR. In a further embodiment of the invention, there are multiple transmitters and receivers. transmitting and receiving waveforms which feature low levels of mutual. The low levels of mutual interference are reduced further in their effects by using time hopping, forward error correction and soft decision decoding.

Description

BROADBAND WIRELESS COMMUNICATION SYS-

TEM

Introduction and Background

This invention is concerned with a robust wireless communication system which en-ables high data rate information to be transmitted and received reliably using a wireless transceiver up to 1km from the source of information which may be any source of digital information. The invention may be used at any wireless frequency but will find most ap-plications in the unlicenced Instrument Scientific Model (ISM) and Short Range Devices (SRD) frequency bands which feature a wide bandwidth. Short range, low power wireless links, particularly when received within a building feature high attenuation, shadow-ing, and propagation exhibiting many multipaths with wide variations in signal strength.

The invention is tolerant to these propagation characteristics, makes efficient use of the available received power and allows several users to operate simultaneously in the same frequency band.

A transmitted radio signal will reach the receiver by way of multiple paths and in circum-stances, such as when the transmitter or receiver is located within a building where the direct path is obstructed or has considerable attenuation, multipath signals have to be O used for communication 1, 2]. Within a building, the total delay spread of the multipath signals is typically 100 nS, and individual paths are resolvable down to 5 p5 {2, 3]. In Q narrowband digital communications, the signalling rate is low and the symbol period typ- ____ ically extends over several S with the result that the receiver filter averages the received multipath signals. In this process, since multipath signals have effectively a random phase L.C) relative to each other, some signal cancellation takes place between the multipath signals and necessarily not all the received power is able to be utilised in the subsequent data demo dulat or.

In broadband digital communications, in contrast, the signalling rate is high and it is fea-sible to combine the received multipath signals together using a Rake receiver [4] without incurring the loss experienced by narrowband communications. This principle is utilised in Ultra Wide Band (UWB) communications where narrow pulses are transmitted peri-odically with the period chosen so as to exceed the delay spread of the multipath signals and in these circumstances the fingers of the Rake receiver may be chosen to maximise the received power 5]. Effectively the narrow pulses resemble impulses enabling the impulse response of the channel to be measured automatically with each transmission. Conse-quently the Rake receiver becomes the matched filter for the channel [1].

Description of the invention

The problem with the transmission of narrow pulses in the original UWB system 5] is that the transmitter has to transmit a high level of peak power relative to the average power.

One answer is to use binary sequences, such as the Barker sequences 8] to modulate a carrier and use a cross correlator in the receiver to produce an impulse like output. How-ever, with Barker sequences the cross correlation function around the main peak output is not zero and so an inexact channel impulse response is measured leading to a degradation in the Rake receiver.

The invention consists of transmitting wideband signals that enable a receiver using cross correlation to measure the impulse response of the radio channel free from distortion, so that a Rake processor, may be progranrmed to implement the matched filter to the multipath radio channel in the receiver. In this way the peak signal to noise ratio at the output of the Rake processor will be maximised prior to data detection. In another embodiment of the invention there are simultaneous. multiple transmitted signals using the same radio carrier frequency, as well as being used to measure the channel impulse response, the signals are chosen such that only relatively low levels of mutual interference are experienced in the cross correlators in the receivers. Examples of suitable waveforms for transmission are also described.

It is a feature of one embodiment of the invention that a carrier is modulated with a sequence of carefully chosen phase shifts such that at the output of the corresponding cross correlators in the receiver, an impulse like output is produced with a zero response around the main peak output. The outline system of the wireless transmitter and receiver arrangement of the invention is shown in Figure 1. The system features a data source comprising an asymptotically, semi-infinite sequence of information symbols s(n'r) where 0 y is the symbol period and n is an integer with values 0, 1,. . oc. In general the data symbols may he m-ary Pulse Amplitude Modulation (PAM), unipolar or bipolar [1], with complex values such that s(ni) +jsy(nT) (1) Each data symbol is convolved with a complex sequence of finite length r(iT)+jy(iT) 0 for 1 0 to vT to form an encoded complex sequence e(t) given by 00 T e(t) s(t -1T)(xi + jyi) (2) n=0 1=0 The duration of each complex sequence is (r + l)T and is chosen to he less than the symbol period so that the encoded data consists of repetitive complex sequences with the data impressed on each complex sequence. The data modulated complex sequence stream is used in turn, to modulate using Quadrature Amplitude Modulation (QAM) a carrier, on a centre frequency fo to produce a modulated signal m(t) given by m(t) (s(t --iT) s(t -lT))xicos(2fot) n=0 1=0 -(s(t -ny -IT) + s(t -nr -lT))y1sin(2fot) (3) This embodiment of the invention is firstly described by way of example for the case where the waveform used to measure the channel impulse response consists of 7 complex symbols. Each complex symbol is represented by two real values and so the 7 complex symbol sequence is represented by two sequences of length 7 symbols, each symbol having two real values. Each complex symbol is referred to as a zymbol in the following text to avoid confusion with data symbols.

The detailed arrangement for the modulation of the complex sequence on the data and subsequent modulation using QAM is shown in Figure 2 for this example where the sequence is of length 7 zymbols, The symbols from the Data source shown in Figure 2 are input to the two tapped delay filters, each consisting of 7 taps. In the tapped delay filters, each tap is separated from the next by a delay T. Each data symbol input to the upper tapped delay filter is multiplied firstly by yl, then secondly by y2, then thirdly by y3, and so on until on leaving the tapped delay filter, the input is multiplied by y7, as is shown in Figure 2. All of the results of the 7 multiplications are summed by snrn of the upper tapped delay filter shown in Figure 2. In Z transform terminology 1] the impulse response of the upper tapped delay filter is y(z) yl +y2z + y3z2 +y4z3 +y5z+ y6z +y7z6 (4) Similarly each input data symbol to the lower tapped delay filter is multiplied firstly by xl, then secondly by x2, then thirdly by 3, and so on until on leaving the tapped delay filter, the input is multiplied by 7, as is apparent in Figure 2. All of the results of the 7 multiplications are summed by smn of the lower tapped delay filter shown in Figure 2.

0 In Z transform terminology the impulse response of the lower tapped delay filter is x(z) xl + x2z + a'2 + x423 + x5z + x6z5 + x7z6 (5) The coefficients of (z) and y(z) are defined in terms of the coefficients of a phase poly-nomial, 0(z) 0(z) 0 + 02z + 03z2 + 04Z + 05z4 + 05z5 + 67z (6) where x(z) cos(O+1)z (7) and y(z) sin(0*i)z (8) The two outputs of the Local Oscillator shown in Figure 2 are identical and represented mathematically as cos(2irfot). The upper output shown in Figure 2 is phase shifted by to produce -sin(2irfot) and is multiplied by the outpnt of the upper tapped delay filter, using the mixer (the upper one shown) to produce 00 V --IT) + .s(t --lT))y(siu(2f0t) ii=O (=0 The lower output of the Local OscIlator shown in Figure 2, represented mathemati-cally as cos(2irf0t) is multiplied by the output of the lower tapped delay filter, using the mixer (the lower one shown) to produce 00 r (s(t -ni -iT) -s(t -in--1T))x1co.s(2rrfot) n=0 1=0 The two mixer outputs are summed together as shown in Figure 2, to produce mathe-matically 7n(t) the QAM signal given by Equation (3). The QAM signal is amplified in the Tx Amp prior to being radiated by the antenna.

The receiver arrangement for measuring the channel impulse response is shown in Fig-ure 3. The Local Oscillator in Figure 3, has two equal outputs represented mathematically as cos(2irfot + ), which is arranged, by design, to be equal to the output of the Local Oscillator shown in Figure 2 plus an arbitrary phase shift q. The received QAM sig-nal which is equal to the transmitted QAM signal convolved with the channel impulse response, pius interference plus noise, is quadrature downconverted by the upper mixer and lower mixer shown in Figure 3. The input to the upper mixer is the Local Oscillator output phase shifted by, represented mathematically as -sin(2rrfot + b). Ignoring the noise and interference, the output is -sin(2rrfot + )(rn(t) * c(t)), where * represents convolution and c(t) is the channel impulse response. Similarly the output of the lower mixer, ignoring the noise and interference, is cos(2rfot + ç)(m(t) * c(t)).

a The mixer outputs are each input to the tapped delay filters respectively shown in Fig- ____ ure 3. These tapped delay filters are the matched filters to those tapped delay filters used in the transmitter, that is they are the matched filters to the tapped delay filters shown in Figure 2. In Z transform terminology the matched filter to y(z) is denoted by (z) and is given by (z) y6z1 y5z2 -y4z3 -y3z4 -y2z5 y1z6 (9) O It will be noticed that the coefficients of y(z) and (z) are the same, but of opposite sign and in reverse order of each other. The matched filter to x(z) is denoted by I'(z) and is given by (z) x7 + x6z1 + x52 + x4z + x3z + x2z5 + x1z6 (10) Similarly, the coefficients of x(z) and (x) are the same hut in reverse order of each other.

To avoid excessively tedious mathematical expressions, it is convenient to use the pre-envelope complex model, the analytic signal 1, 9] to describe the outputs of the tapped delay filters shown in Figure 3. The two real outputs are represented in complex form and denoted denoted by q(t), which is given by: q(t) (s(t -nr) + js(t -in-)) * (x(t) + jy(t)) * e(t) * e3(t) -j(t)) (11) As convolution can be carried out in any order q(t) is given by q(t) (Sr(t -/n-) + js(t -nT)) * c(t) * &(x(f) + ±()) * ((t) -jQ(t)) (12) which simplifies to q(t) (s(t-in-) +js(t-in-))*e'c(t)((x(t) *(t) +y(t) *(t)) +j(y() *(t) -x(t) *(t))) (13) It is clear from Equation (13) that the complex output, q(t), is equal to the complex data convolved with the channel impulse response c(t), phase shifted by ç5, and convolved with a real part (x() * (t) + y(t) * (t)) and an imaginary part (y(t) * (t) x(t) * (t)). Since the channel impulse response c(t) is complex anyway, the simplest way to deal with the phase shift q is to absorb it into the channel impulse response by defining a new channel impulse response. â(t) c(t)e and Equation (13) then becomes q(t) (14) It is helpful to give an example for the 7 tap version of (t) and y(t) and the convolution that results in (:r(t) * (t) + y(t) * (t)) and (y(t) * (t) -x(t) * x(t) is given by its Z transform coefficients ad to x7: x() 1 + 1z' + O.25z2 -O.688z3 + O.688z4 + O.531z5 + O.054z6 (15) and y(t) is given by its Z transform coefficients yl to yT: y(z) -O.968z2 + O.726z O.726z1 + O.847z5 + O.998z (16) The sequence of 7 phase shifts, in degrees, producing the coefficients of x(z) and y(z) 0 above are: 0, 0, 284.5, 133.4, 313.5, 57.9, 86.9 The convolution result (x(f) * (t) + y(t) * )) is shown plotted in Figure 4 using 8 samples per zymbol. The convolution result (y() * (t) -x() * (t)) is shown plotted in Q Figure 5, also using 8 samples per zymbol. The important point is that the convolution result for the real part corresponds to an approximation to an impulse, plus and minus 24 samples around the peak output and the imaginary output is zero over the same time interval of 48 samples. Consequently provided the duration of the channel impulse response ê(t) is less than 24 samples, it will he present undistorted at the output of the tapped delay filters shown in Figure 3 and will input to Channel Impulse Response Estimation shown in Figure 3 in the form of (s(t -nr) + js(t -aT)) * â(t). from Equation 14. The first term (s(t aT) + js(t -ar)) is the periodic complex data and so the channel impulse response (i)is not available directly. It can he made available directly by setting the periodic data equal to constant l's, with imaginary part zero. This case corresponds to constant data which may be inserted in a pre-amble training period for measuring the channel impulse response.

The second approach is to use data decision feedback to produce (t) from q(t): (t) q(t)((t -ar) + j(t -nr)) (17) -nr)((:r(t) * (t) + y(t) * (t)) + j(y(t) * It) -x(t) * where ((t -ni) + j(t -ni)) is the estimated sequence of the transmitted data. In this way with a period of r, a repetitive estimate of the channel impulse may be obtained from the outputs of the tapped delay matched filters shown in Figure 3.

0 0 25.7 1.2 79.7 100.5 106.1 56.8 346.3 293.8 288.4 293.3 94.2 164.6 245.2 332.2 170.3 59.4 60.0 216.8 295.0 111.2 46.0 270.0 172.1 21.6 184.9 282.1 81.9 290.8 134.5 318.2 Table 1: Sequence of 32 phase values, 0 to 032 in degrees, which define x(z) and y(z) of length 32 zymbols Longer sequences than 7 zymbols may be used in order to increase the duration over which the channel impulse response may be estimated for longer delay spread multipath radio channels. Table 1 shows a sequence of 32 phase values, 9 to 032 which may be used to define the Z transform polynomials x(z) and y(z) each having 32 zymbols: where now x(z) cos(0ji)z (18 and (19) Using these 32 zymbol sequences, the corresponding outputs of the tapped delay filters shown in Figure 2 (but now the 7 taps, tapped delay filters are replaced with tapped delay O filters having 32 taps), are given in Figures 6 and 7 respectively with 8 samples/zymbol and a single input symbol of data equal to 1+jO.

The consequent two outputs of the matched 32 tap, tapped delay filters in the receiver, for the case where 0, are equal to the real part and imaginary part respectively of the 0 autocorrelation function of the transmitted 32 zymbol phase sequence, having 8 samples per zymbol, and these outputs are shown in Figures 8 and 9 respectively, It will be noticed from Figure 8 that the real part has a zero response around the main peak amplitude of 32, for 64 samples on either side of the main peak. Similarly the imaginary part from Figure 9 has a zero response over the entire corresponding interval. Provided the channel impulse response (t) has a duration of less than 64 samples (8 zymbols) then it will be presented undistorted at the input of the Channel Impulse Response Estimation shown in Figure 3.

As an example, consider that the channel impulse response â(t) is 0.25(t + 2T) + j/t) -0.5/t -3T) (20) where S(t) is the standard Kronecker delta function, or equivalently stated the channel impulse response in Z transform form as the polynomial, c(), 0.25z2 +jz° -0.5z (21) Now the two outputs of the matched tapped delay filters in the receiver will be as shown in Figure 10 for the real part and in Figure 11 for the imaginary part. It can be seen that the real part, shown in Figure 10, has a positive peak of 8, arising from the 0.25(t + 2T) part of the channel impulse response and has a negative peak of 16, arising from the -0.5(t -3T) part of the channel impulse response. Similarly the imaginary part shown in Figure 11 has positive peak of 32, arising from the j(t) part of the channel impulse response.

By way of this example for the channel impulse response, the procedure for programming the Rake processor is as follows. The measured channel impulse response is 8(t + 2T) + j32(t) -16S(t -3T) (22) The Rake processor is programmed such that its impulse response, Rk(t), is the complex conjugate of the time reverse of the measured channel impulse response â0(t). In this way it presents the matched filter to the channel reponse maximising the peak signal to noise.

ratio at the Rake processor output. Consequently Rk(t) is given by: Rk(t) -16a(t + 3T) -j326(t) + 8(t -2T) (23) The peak signal output of the Rake processor, PRke (t) for each data symbol transmitted is given by Ppke(t) -16l(t + 3T -n) x -16S(t -3T -nv-) +j32l(t -m-) x -j32S(t -n) o + 8(t 2T n) x 8(t -2T -T)(r(t -n) +js(t - (s( -i) + s(t -n))(256 + 1024 + 64)ö(t n) O (s(t -n) +js(t -n))1344(t -n) (24)

I

The peak signal output has a value of 1344 due to Rake processing and the peak signal to noise ratio is N(64+io24+256) where N, is the average noise power of each time sample. Without Rflke processing the peak signal to noise ratio which corresponds to the highest value radio path would only be Consequently the Rake processing improves the peak signal to noise ratio for this example by 1.2 dB.

This was a simple example to aid clarity in the diagrams and in practice there are usually a higher number of multipath signals received. A 5 dB to 10 dB improvement in the peak signal to noise ratio due to Rake processing is commonplace.

In a simpler embodunent of the invention, the carrier frequency is amplitude modu-lated, using a suppressed carrier with a sequence of real oniy zymbols corresponding to Pulse Amplitude Modulation (PAM) 10]. Instead of a complex sequence, each data bit is convolved with a real sequence of finite length c(iT) for 1 0 to vT to form an encoded real sequence c(t) given by e(t) s(t-ny-IT)x1 (25) n=O 1=0 In Z transform terms, in this simpler embodiment of the invention, y(z) 0, and (z) alone defines the sequence used to measure the impulse response of the channel. An example of a suitable sequence of real values for a length 32 sequence is given in Table 2.

1 1 -1 -0.02 0.18 0.76 1 0.55 0.24 0.72 0.32 0.40 -0.56 -0.82 -0.42 0.39 -0.17 0.51 0.89 -0.69 0.57 -0.36 -0.31 0 -0.14 0.7 -0.88 0.21 0.42 0.39 -1 0.68 Table 2: Sequence of 32 real values which define x(z) of length 32 zymbols A plot of this sequence is shown in Figure 12. It will be seen that the sequence takes multiple values between 1 and -1. Asy(z) 0, only the tapped delay filter implementing x(z) is required in the transmitter arrangement of Figure 2, and only the single mixer is required in the modulator, However in the receiver, the QAM downconverter is still required because the channel impulse response (t) is complex. The receiver arrange-ment is simpler because only two matched tapped delay filters are required instead of four matched tapped delay filters. This is because y(z) is zero and does not need to be implemented.

The output of the matched tapped delay filter corresponding to the real output for an ideal channel using the sequence given in Table 2 is shown in Figure 13. It can be seen that on each side around the peak output of approximately 12 there is a zero response for a total of 64 samples (8 zymbols). As before, provided the impulse response of the 0 channel has a delay spread corresponding to less than 8 zymbols then it will be present undistorted at each output of the two matched tapped delay filters (referring to Figure 3) for the real and imaginary components respectively of the impulse response of the channel.

In a further embodiment of the invention, there are multiple transmitters and receivers, IC) each using the same carrier radio frequency with each transmitter attempting to convey data to its respective receiver independently of the other transmissions. As before, each transmitter transmits a repetitive waveform consisting of a sequence of carrier phase values designed to produce a zero response around the correlation peak seen at the receiver for the case where the channel impulse response consists of a single impulse. As well as having good correlation properties, the sequences of carrier phase values are chosen such that relatively low values of interference are experienced at the outputs of the matched tapped delay filters in the other receivers, apart from the intended receiver. As an example, the sequence of phase values of length 32 already given in Table 1 are used to define all of the sequences.

Denoting the sequence of phases as B for i 1 to 32, as before, the real and imaginary sequences for the transmitter with index rn are defined by the Z transform polynomials (z) and y (z) given by 31.

(fl x 360\ . Inn x 360\ -.

:rm(z) (cos(O11)c'os 32) -sn(O11)srn 32)) (26) and rrn x 360 irn x 360 y(z) (s1n(O1*i)cos( 32) +cos(01*i)sin( 32))z (27) In the above cosine and sine functions, as before, the arguments are in terms of degrees not radians. Up to 32 different waveforms are defined by Equations (26) and (27) for in 0 to 31 corresponding to up to 32 transmitters each transmitting different waveforms. In practice, it is not expected that all transmitters will be transmitting simultaneously as the total level of interference experienced at each receiver will then he quite high. However interference can be mitigated by using forward error correction and soft decision decoding as described below.

A plot of the real seqnence, for transmitter. m3, corresponding to x3(z) is shown in Figure 14. A plot of the imaginary sequence, for m3, corresponding to y3(z) is shown in Figure 15. In comparison, the sequences for the transmitter, m0 are the earlier plots Figures 6 and 7. The real part of the autocorrelati n function for the sequences obtained with n3 is shown in Figure 16. It will be noticed from Figure 16 that the real part has a zero response around the main peak amplitude of 32, for 64 samples on either side of the main peak as was obtained before, for m0, in comparison to Figure 8. However it will be noticed that the sidelobes in Figure 16 are not the same as those in Fignre 8.

Similarly the imaginary part shown in Figure 17, for m3, is similar to Figure 9 which is obtained with m0, and also has a zero response over the central corresponding interval of 136 samples.

The level of interference experienced by the receiver for m0, when the transmitter for 0 m3 is transmitting (or vice versa) is shown in Figure 18 for the real part and in Figure 19 for the imaginary part. The worst case interference level is -10.2 for the real part and Q 8.2 for the imaginary part hut these do not occur at the same time. In practice, the interference values will be modulated by the data, also by the channel impulse responses, (the channel impulse from the transmitter causing interference will usually be different IC) from the channel impulse from the transmitter of the wanted signal) and by the relative timing of the wanted signal correlation. In order to average out the effects of interference, time hopping may be employed in which each transmitted waveform is subject to a pseudo random timing offset controlled by a pseudo random number generator in the transmitter.

A training sequence can be used to enable the receiver to synchronise an identical pseudo random generator A suitable forward error correction coding technique is to use a Low Density Parity Check (LDPC) error correcting code and soft decision, iterative decoding 11].

Figure 20 shows the performance results of computer simulations using the 32 zymhol waveforms defined above in Equations (26) and (27) with phase values given in Table 1.

Figure 20 shows plots of Frame Error Rate, with 528 information bits per Frame, as a function of the ratio of the energy per information bit to the noise spectral power density in dB () and the number of simultaneous transmitters. The LDPC code used, is the WiMax (1056, 528) LDPC code {12. It can be seen from Figure 20 that 5 simultaneous, equal power, transmitters can operate using the same radio centre frequency at a cost of only 1.5 dB degradation compared to a single transmitter with each of the 5 receivers independently measuring the channel impulse response and programming its respective Rake processor to optimise the peak signal to noise ratio as described above. Furthermore, based on the worst case interference level between users, given above of 10.2, and with no forward error correction, for 5 simultaneous users, the total interference level would be 40.8, and with random binary data this would cause an error rate of arising from the probability of 4 users happening to send the same data this event coinciding with the 5th user transmitting the opposite data. This error rate will occur regardless of how high the signal to noise ratio is in the receiver. It can be seen from Figure 20 that the combination of time hopping and forward error correction is an effective countermeasure for peak levels of interference and produces much better error rate performance.

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[8] R. H. Barker, Group synchronizing of binary digital systems, Communication Theory, pp. 273-287, Butterworth, London [9] D. Gabor, Theory of Communication. J.IEE, vol. 93, pp. 429-457, 1946.

[10] L.W. Couch, Digital and Analog Communication Systems, 5th ed.. Prentice Ball, 1997 11] S. Lin and D.J. Costello, Jr., Error Control Coding, 2nd ed., Pearson Prentice Hall, 112] WiMax Standard, IEEE Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, 2005