WO2007113511A1

WO2007113511A1 - Signal-to-noise ratio estimation for digital signal decoding

Info

Publication number: WO2007113511A1
Application number: PCT/GB2007/001169
Authority: WO
Inventors: Thushara Hewavithana; David Michael Brookes; Stewart Hamish Bell
Original assignee: Matsushita Electric Industrial Co. Ltd.; Imperial College Of Science
Priority date: 2006-03-31
Filing date: 2007-03-30
Publication date: 2007-10-11
Also published as: GB0606532D0

Abstract

An initial noise estimation is determined using received DPQSK values rounded to the nearest, permitted value in the encoding scheme. The estimate is improved in an iterative process or using a look up table of the relationship between the estimate and the actual SNR or using a polynomial or other formula approximation. In an alternative method the previously proposed moment ration is used as the starting point.

Description

Signal-to-Noise Ratio Estimation for Digital Signal Decoding

The present invention relates to decoding of digital signals that have been encoded using phase shift keying (PSK). The invention has been particularly developed for use in decoding differential PSK symbols used in Digital Audio Broadcasting but has other applications in digital signal processing.

1. Introduction

In many soft decision algorithms the soft decision outputs require either knowledge or an estimate of the signal to noise ratio (SNR). This is, in particular, true of the expressions derived for DQPSK soft decisions. Therefore it is necessary to estimate the signal and noise power using a priori knowledge and the signal available at the receiver. If there are no pilots available to assist the estimation process, then the receiver has to rely on blind techniques for the estimation. For example, in the DAB system, apart from the phase reference symbol, which appears only once every 96 ms at the start of each DAB frame in transmission mode I, there are no regularly spaced pilot symbols in frequency and time domain [6].

We propose a set of SNR estimation algorithms that can be used in a DPSK modulated system that require no pilot symbols for the estimation process. Although πlA DQPSK modulation is assumed in the derivation of the SNR estimation algorithms, it is straightforward to generalize this to any DPSK system. We also show that an approach previously given in [5] for QPSK systems can be extended to MPSK modulation schemes which we refer to as the moment ratio algorithm (MR_Algorithm).

2. Literature Review on SNR Estimation

Most of the SNR estimators found in the recent literature are formulated in the context of iterative decoding of turbo codes using MAP₅ Log-MAP, and Max-Log-MAP algorithms. Some authors claim, however, that in this context- the 'accuracy of SNR estimation does not have a large influence on the BER performance [57, 58]. ^; ..

For a QPSK modulated signal, the noise variance can be estimated using the following: conventional method [59], . ^• ■ ^• .

where X ~ N(±α,σ^) is the amplitude of the signal. Here X is a real quantity representing either the I or Q component of the received signal. An important point to note is that this estimator is a biased estimator even when a large number of data samples are used. A good estimate of the noise power is only obtained for high SΝR values as shown by the ratio of estimated and true noise power vs true SΝR graph for BPSK shown in figure 1. Noise power ratio here is defined as the ratio between the estimated arid the true noise power given by 5.2.

. _ . _π „ . Estimated noise power

Noise Power Ratio (5.2)

True noise power

We can generalize the method given above for any constant modulus type signals. However, as the modulation order increases, so does the lower bound for SNR for which the estimated noise variance is accurate. Figure 1 also shows the noise variance ratio graph for the π 14 - DQPSK used in DAB. As evident from the two graphs of the Figure 1, the minimum SNR for getting accurate noise variance is increased to 20 dB for π / 4 -DQPSK compared to 10 dB in BPSK case.

The noise variance estimator given in [58] uses decoded hard bits at the output of the turbo decoder to estimate the signal and uses the estimated signal to estimate the noise. Therefore there is a delay of one frame in the estimation of noise variance. In the DAB case, the delay would be 15 common interleaved frames (CIFs) due to the time interleaver placed between the DQPSK demodulator and the Viterbi decoder. The algorithm given in [5] estimates the SNR for BPSK signal using the ratio- between, the second moment estimator of the signal and the average of the absolute- value of the signal, :

)/ ii{]x|}². An apparent disadvantage of this method is that it can only be applied to

BPSI< over AWON channels. The method given in [5] is extended in [60] to Nakagami fading channel models and [61] further extends this to a Nakagami fading with diversity combining for multiple receiver antennas. However, all these methods are still restricted to BPSK modulation.

The two noise variance estimation algorithms for multicarrier systems given in [62] could be used in OFDM systems using coherent modulation methods. The decision directed method given in [62] is similar to the EC_Algorithm proposed in section 4, but is only applicable to pulse amplitude modulated signals. It could however be straightforwardly extended to coherent QAM systems by considering the quadrature and in phase components of the symbols separately. The second algorithm described in [62] is based on the EM (Expectation Maximization) [63] algorithm, and assumes knowledge of channel information in order to estimate the noise variance. The algorithms given in [64] extends those in [62] to a multicarrier improving the estimate is based on the realisation that, subject to certain assumptions, the relationship between an system with multiple users. However, the extended algorithms are still applicable for only synchronous systems.

Summary of the Invention

The present invention provides a method of decoding a digital signal as described in claim 1. Thus the basis of the invention is the determination of an initial noise estimate by rounding received differential phase values to the nearest permitted value in the encoding scheme. This initial estimate can be improved in an iterative process to be described below but a more computationally efficient method of improving the estimate is based on the realization that, subject to certain assumptions, the relationship between an initial SNR estimate obtained in this way and the actual SNR do not depend to any major extent on other factors. Thus the initial estimate of noise or SNR can be refined using a look-up table or a formula approximating the actual relationship. . ^'. . , ^• . ^■ . ^•

The iterative method of improving the noise or SNR estimate uses calculations of symbol probabilities. These are straightforward mathematical calculations and do not form part of this invention.

Another aspect of this invention is described in claim 13. This is based on using the unique relationship between the moment ratio, to be described below, and actual SNR to determine actual SNR. Again this can be achieved using a look-up table or computation using a suitable formula.

The invention will now be described in detail by way of specific examples with reference to the drawings in which:

Figure 1 is an estimated and true noise power ratio vs. true SNR graph for BPSK and π I A - DQPSK signals;

Figure 2 is a graph of true SNR vs. initial SNR estimation for an EC_Algorithm;

Figure 3 is a graph of true SNR vs. moment ratio for an MR_Algorithm;

Figure 4 is a graph of normalized bias of SNR estimate for L=IO;

Figure 5 is a graph of normalized MSE of SNR estimate for L=IO; Figure 6 is a graph of normalized bias of SNR estimate for L=IOO;

Figure 7 is a graph of normalized MSE of SNR estimate for L=I 00;

Figure 8 is a graph of normalized bias of SNR estimate for L=IOOO;

Figure 9 is a graph of normalized MSE of SNR estimate for L=IOOO;

Figure 10 is a graph of normalized bias of SNR estimation for L=IO; Figure 11 is a graph of normalized variance of SNR estimation for L=I 0;

Figure 12 is a graph of normalized bias of SNR estimation for L=50;

Figure 13 is a graph of normalized variance of SNR estimation for L=50;

Figure 14 is a graph of normalized bias of SNR estimation for L=IOO;

Figure 15 is a graph of normalized variance of SNR estimation for L=IOO; Figure 16 is a graph of BER comparison for estimated and perfect SNR values; Figure 17 is a graph of noise power estimation for TUl 5; . .. ^■

Figure 18 is a graph of signal power estimation for TUl 5;

Figure 19 is a true SNR vs. initial SNR estimation, graph for EG_Algorithm using numerical integration and Monte Carlo methods; ^• . Figure 20 is a true SNR vs. moment ratio graph for MR_Algorithm using numerical integration and Monte Carlo methods; and

Figure 21 is a block diagram of the proposed, estimation procedure for SNR estimation of a DQPSK signal according to a preferred embodiment of the present invention.

Referring to Figure 21, a received RF signal is processed to resolve the DQPSK symbol stream. QPSK symbols are extracted using a differential decoder 10 which receives the current symbol and. the previous symbol via a delay element 11. The QPSK symbols as well as the current and delayed DQPSK are supplied to noise estimation algorithm 12, to be described in more detail below. From this the average noise power 13 is obtained and together with the original symbol stream used to obtain average signal power 14 to then obtain an SNR estimate.

3. SNR Estimation for DQP SK

π

In this section, we derive an iterative algorithm for the estimation of SNR in DQPSK

4 modulated signal. We initially make no assumptions about the propagation channel model, but later show how to apply the algorithm to a specific propagation environment. We denote by

d_t —_j and d_t two consecutive complex- valued faded received DQPSK symbols, without

the noise. We assume that the channel is slowly varying with respect to the symbol duration and therefore there is negligible relative phase rotation or amplitude variation in successive symbols due to the propagation channel. We also assume that we have perfect carrier recovery at the receiver and therefore no relative phase rotation in successive DQPSK symbols due to carrier frequency offset. However, the carrier phase can be arbitrary. These assumptions lead to,

However, since the transmitted value of ki. is not exactly known at the receiver, an estimate of

Assuming, that we have an initial estimate of the signal and noise powers, we can .calculate the posteriori probability for the transmitted QPSK symbols, denoted by the indices /c; , given, two consecutive received DQPSK symbols, S_n and S_n^ . In a real receiver, assuming that the signal and noise power remain stationary for L DQPSK symbols, the ensemble averages in (5.9) and (5.10) may be replaced with the time averages Therefore, given L consecutive DQPSK symbols, S₁ for 0< i < L — 1, the noise variance estimate is given by,

Similarly, using the time average version of (5.10), the estimated signal power is given by,

The initial estimate of the noise power needed for the first iteration can be obtained using the hard decoded QPSK symbols as given below.

where corresponds to the hard decoded QPSK symbols obtained by rounding the phase of to the nearest QPSK phase.

Calculation of the a posteriori probabilities has to be done according to the propagation model. In a time invariant scenario, we calculate the probabilities as follows,

for k_n e / . For a Rayleigh fading propagation model, obtain the a posteriori probabilities as,

Now we can use these new a posteriori probability values to estimate the SNR more accurately. The above iterative SNR estimation (IE_Algorithm) process is summarized in Table 5.1

Table 5.1: Summary of Iterative SNR estimation Algorithm - IE-Algorithm

(1) Initialization Step:

Initialize the noise and signal power estimates using (5.13) and (5.12)

(2) Iteration Step: Calculate the QPSK symbol probabilities, for i = 1...L — 1 and Jc₁ e l , in time invariant channels, use (5.14) in fading channels, use (5.15) Calculate the new estimate of the noise power:

Calculate the new estimate of the signal power:

(3) Termination Repeat Step (2), for a fixed number of iterations or shold

When the hard decoded QPSK symbols, w^k' , are accurate, the initial estimate of the signal and noise powers can also be expected to he accurate. Therefore the number of iterations need would be lower. It is also possible to use methods such as multiple symbol differential detection (MSDD) [50-52] to improve the accuracy of w^k" and therefore improve the accuracy of the initial SNR estimate and therefore reduce the number of iterations. However, this will lead to an increase in the complexity of the algorithm.

4. Non-iterative SNR Estimation Algorithms for DQPSK.

The complexity of the SNR estimation algorithm described in the aforementioned Section 3 depends on the actual SNR of the signal. For a high SNR signal, our initial SNR estimate can provide us with an accurate a posteriori symbols probabilities and therefore one or two iterations lead to an accurate estimate of SNR. However, in a low SNR situation, the initial estimate of the SNR could be quite inaccurate since it is more likely to make an error inw*' , and therefore need more iterations to get an accurate SNR estimate. In practice, the iteration step of the algorithm could be run until the relative change of signal power estimates for successive iterations fall below certain threshold value as shown in Table 5.1.

In a low SNR case, by approximating the QPSK to the nearest QPSK phase, we can expect an under estimate of the noise power as a result of hard decision process wrapping the noise contributions into a single quadrant, which leads to an over estimate of the SNR. Provided this over estimation of the SNR is well quantified, we can make a correction to the' SNR estimate. It is interesting to examine whether we can make a one time correction to the initial SNR estimate to obtain an accurate SNR from the initial estimate. In Appendix E, we have shown that the true SNR is a one-to-one function of the initial SNR. Therefore, we propose a simpler two step SNR estimation algorithm as described in Table 5.2. We refer to this algorithm as the EC_Algorithm (Estimation and Correction Algorithm) in the rest of the thesis. In contrast to the iterative algorithm described in the previous section, this non-iterative algorithm does not require estimation of QPSK symbol probabilities and is therefore computationally more efficient. Appendix A also shows that we can extend the SNR estimation method given in [5] for a

Table 5.2: Summary of the non-iterative SNR Estimation Algorithm - EC_Algorithm

(1) Initial Estimation Step:

Make an initial estimate of SNR

(2) Correction Step: Use the table given in Appendix E or a polynomial approximation to map Initial SNR estimate to the True SNR

MPSK modulation system. More specifically, it is shown that the moment ratio, — / Tf~ _> *^{s a}

function of only the true SNR. We have derived an expression for this function, which is repeated here for convenience, and evaluated it using numerical integration techniques.

(5.16)

Therefore the SNR estimation problem reduces to one of estimating the above moment ratio and then mapping it to 'the SNR using a polynomial or table implementation of the above function. We will refer to this method as the MR_Algorithm (Moment Ratio Algorithm) and uses it to compare the performance of the two proposed methods in the results and discussion section.

Figure 2 shows a graph of look up table data for EC_Algorithm calculated using the numerical integration method derived in Appendix E. As seen from the figure 2, the required correction to the estimate becomes very large for true SNRs below 0 dB but no correction at all is needed at high SNRs. Figure 3 shows a graph of look up table data for the MR_Algorithm algorithm calculated using numerical integration methods. An important observation about the above look up tables is that both mappings are non-linear, for all SNR values in the case of MR_Algorithm, and for low SNR values in the case of EC_Algorithm.

5. SNR Estimation when the Noise is Correlated with known Correlation

In this section we extend the Iterative Estimation algorithm derived in the aforementioned section 3 to the scenario where the noise in successive DQPSK symbols is correlated. We assume that the correlation of the noise is known. An example of this situation is when a channel equalizer is used at the receiver. If we assume a baud spaced equalizer and the post equalizer ISI to be negligible, then the noise correlation at the output of the equalizer is given by the following formula, given that the input noise to the equalizer is white.

(5.17) where f is the equalizer weight vector and η.. is the noise corrupting the. i'^h- post equalizer DQPSK symbol. We have normalized the noise correlation with respect to the post equalizer noise variance, 2 σ^ . The a posteriori probabilities of the QPSK signal depend on signal and noise variance as well as of the noise correlation. In the following section, we generalize the iterative algorithm given in the previous section to noise with known correlation. For the case of correlated noise,

Since k. is a function of the transmitted data, it is independent of the noise, so

where k. is the a priori probability of QPSK symbols. Assuming all the QPSK symbols are equally likely, the correlation components in the above equations average to zero. Therefore, the post-equalizer noise power is given by,

Using a posteriori probabilities in (5.8), we get an alternative expression fo using

equation (5.9). Therefore, the iterative algorithm given in Table 5.1 can be slightly modified to estimate the post-equalizer noise power and the and the post equalizer signal power as given in Table 5.3. For this algorithm the a posteriori probabilities for the time invariant channel scenario are given by,

where is the post equalizer noise power, a is the signal amplitude after the equalizer, and

a_π is a normalizing factor to ensure that We have assumed that all the

QPSK symbols are equally likely and therefor

. For Rayleigh fading channels, the a posteriori probabilities are given by,

(5.22) . wher s the post-equalizer noise power, the post-equalizer signal power, and a_Ray

is a normalizing factor such that ^In equation (5.21) and (5.22) the noise

correlation is calculated using (5.17)

If an adaptive equalizer is used in the receiver, then the noise correlation has to be updated according to the current values of the equalizer impulse response.

6. Algorithm Implementation Issues

In a time invariant propagation channel with stationary noise, all three algorithms described in section 3 can be expected to give better performance for larger length DQPSK symbol sequences. However, in a time varying channel or a non-stationary noise, scenario, an SNR estimate can only be representative of a. single or short sequence of DQPSK compared to the coherence time of the channel. It is advantageous to have a. recursive version of tile algorithm, so that the SNR estimate for tile previous estimate can be used to estimate the SNR for the current symbol. This eliminates the need for storing the previous DQPSK symbols and therefore reduces time memory requirements of the algorithm.

Table 5.3: Summary of Iterative SNR estimation Algorithm for Correlated Noise- IEC_Algorithm

(1) Initialization Step:

Initialize the signal and noise power estimates using (5.13) Estimate the Noise correlation using (5.17)

(2) Iteration Step:

Calculate the QPSL symbol probabilities, p(k_i^s. s_i_₁), for i = 1...L - 1 and k. e /, in time invariant channels, use (5.21) in fading channels, use (5.22)

Calculate the new estimate of the post- equalizer noise power:

Calculate the new estimate of the signal power:

^{■ i=0}

averaging by N,. = -l/ln(a). For example, for a channel with coherence time of 30 symbol periods, a = 0.9672 corresponding to N_r = 30 would lead to an SΝR estimate which is representative of the current symbol.

Table 5.4: Realtime Implementation of the EC_Algorithm

(1) Initialize the signal and noise Powers:

Use a finite length of DQPSK symbol sequence with (5.13) and (5.12) For each DQPSK symbol, (2) Update the signal and noise powers:

Use equations (5.23) and (5.24) respectively

(3) Correct the Estimated SΝR:

Use the look up table to map the initial SΝR estimate to the True SΝR

7. Performance Evaluation and Discussion

We use Monte Carlo simulations to compare the performance of the proposed SΝR estimation algorithms using the π / 4 -DQPSK modulation scheme. Performance measures used are the estimation bias, which is normalized with respect to the true SΝR, and the mean square error (MSE), which is normalized with respect to the square of the true SΝR. We first have to establish how many iterations would be reasonable for the IE_Algorithm before the performance comparisons are done. Therefore initial experiments were conducted to compare time performance of the IE_Algorithm for different numbers of iterations.

7.1 Performance Evaluation for the Iterative SΝR Estimation Algorithm

In this section we analyze the performance of the IE_Algorithm using different number of iterations for different lengths of DQPSK sequence, L. Zero iterations means just the initial estimate of the SΝR using the hard decisions for QPSK and is estimated using the noise and signal powers calculated using (5.13) and (5.12) respectively. For higher numbers of iterations we perform the iteration step given in Table 5.1 for the specified number of iterations.

Figure 4 and 5 show the bias and MSE performance for the IE_Algorithm for L = 10. According to the MSE and the Bias graphs, we get a significant performance gain at low SNR values from using larger number of iterations. However, the additional gain from using more than 5 iterations seems to be insignificant.

The non zero bias of the estimates is due to the nonlinear dependency of QPSK symbol probabilities on the SNR value. Because of this nonlinear dependency, any variance in the SNR estimate translates into a bias in the estimate. Estimation variance is a direct result of having a finite number, L, for the length of the input DQPSK sequence. Therefore, as the value of L increases, we can expect the value of estimation bias to decrease along with time estimation variance. This in fact is what we observe when the simulation is repeated for larger values of L as shown in Figure 4 to 9.

For time wide range of L values tested, the additional performance gained using more than 5 iterations seem to be insignificant. Therefore, we use 5 iterations for IE_Algorithm when comparing its performance with time other proposed algorithms.

7.2 Performance Comparison for Different SNR Estimation Algorithm

We now compare time performance of proposed SNR estimation algorithm for different DQPSK sequence lengths. We used 5 iterations for the IE algorithm. Time mappings between the estimated SNR to true SNR in EC_Algorithm, shown in Figure 2, and the moment ratio to true SNR in MR_Algorithm, shown in Figure 3, are done using look up tables. An important observation about the above look up tables is that both mappings are non-linear, for all SNR values in the case of MR_Algorithm, and for low SNR values in the case of EC_Algorithm. Therefore we expect both algorithms to produce a biased estimate of SNR even when the initial SNR estimate in the case of EC_Algorithm and moment ratio in the case of MR_Algorithm are unbiased.

Figure 10 and 11 show the comparative performance of proposed SNR estimation algorithms for L = 10. The EC_Algorithm and IE_Algorithm have a better MSE and Bias performance compared to the MR_Algorithm. This agrees with the theory since MR_Algorithm only uses the amplitude information of the DQPSK symbols in the estimation process whereas the other two algorithms use both the received DQPSK symbol data and prior knowledge about time symbol constellation in the estimation process. Figure, 12 and 13 show the comparative performance of proposed SNR estimation algorithms for L = 50. As we expected, the both the bias and variance of the estimates are reduced from that of time X = IO experiment. This trend is further confirmed by time performance figures for L = 100 given in Figure 14 and 15.

Since we intend to use the proposed SNR estimation algorithms in soft decision de-coding algorithms it is important to establish whether the error of the SNR estimates using time proposed algorithms have any adverse effect on time performance_of a DAB receiver. It is mentioned in the literature [57,58] that the accuracy of the SNR estimators are not that important as far as the BER performance of the turbo codes are concerned. We conducted several simulations to examine the performance degradation due to using the estimated SNR instead of the true SNR in a DAB receiver model. In the example shown in Figure 16, the EC_Algorthim is used to calculate the SNR in the soft decision algorithms. In the DAB receiver the soft decision outputs from the DQPSK using the estimated SNR are fed into a convolution decoder to decode into hard bits. These post-Viterbi BER results were compared with those obtained using the soft decisions calculated assuming perfect signal and noise power values [65]. It can be seen from the graph that using the SNR knowledge in soft decisions gives improved performance equivalent to IdB for BER up to 10^"4 (Note: BER 10^"4 is considered to be an edge of service target for DAB [I]). Furthermore the BER degradation due to using the estimated SNR in the soft decision algorithm rather than the true SNR is less than 0.3 dB for BER up to 10^"4, but at high SNRs, errors in SNR estimate mean that it is better to use a simpler soft decision method that does not require the SNR. In the above simulations, an AWGN propagation channel is assumed. Figure 17 and. 18 show an example of signal and noise power estimation for the TU15 [21] propagation model at 7dB overall SNR in DAB L Band where the noise is assumed to be colored over the spectrum. Here the signal is generated according to the DAB standards [6] and therefore consist of an OFDM signal with each subcarrier been modulated with τr/4-DQPSK. The noise corrupting each subcarrier can still be considered to be white and Gaussian distributed. According to the Figures 17 and 18 the noise signal power estimates are greatly improved by the correction technique. The estimates still have substantial variation, which can be reduced either by integrating over more symbols or, if the SNR can be assumed to be smooth over the frequency band, averaging over adjacent carriers. However, in general, the assumption of smooth variation of SNR over the DAB band is not accurate due to narrowband interferences. Therefore it is not recommended to do the averaging in the frequency direction.

In fading channel scenarios it is difficult to define the true power of the signal and the noise since some of the channel variations also have a similar effect to noise on DQPSK decoding.

Therefore, a better way to assess the performance of the SNR estimation algorithms in fading channels is to use them in a soft decision decoding algorithms and use the BER as the performance measure. We have used the EC_Algorithm extensively in our soft decision algorithms and the BER results show a significant performance gain over soft decision algorithms not using the SNR information;

8. Conclusions

We have proposed a set of novel SNR estimation algorithms for DPSK modulated signals. The bias and the MSE of the SNR estimates are examined using MATLAB simulations. We have also presented recursive implementations of the algorithms which make them suitable for realtime receives needing SNR estimates for soft decision decoding.

For π/4-DQPSK, which is the modulation scheme . used in DAB, it is observed that all three algorithms give a good estimate of the SNR of the signal without having prior knowledge of the transmitted pilot symbols. The IE_Algorithm and EC_Algorithm consistently outperform the MR _Algorithm for SNR values higher/than 5dB. For. the SNR values between 0 and 5,- all three algorithms have similar performances. Although the results presented hereinbefore mainly use time invariant channel models, we have successfully used these algorithms in the soft decision decoding of DQPSK and they were found to perform well under various fading channel scenarios. Our simulations also confirm that the BER performance degradation due to using the estimated SNR instead of the true SNR in soft decision algorithms in the DAB receiver is less than 0.3dB.

APPENDIX A

Derivation of the SNR Estimation Algorithms

A.I Dependency of the True SNR on the estimated SNR

Noise power is estimated using the following expression,

(A.I)

whe the differential angle between the two consecutive DQPSK symbols and r;

and ^_-1 are the amplifiers of Sj and S_1-1 respectively. If the value of s estimated according to

the value o hen the value o is estimated as follows,

From (5.5), the joint of PDF of the amplitude and the phase of a DQPSK symbol can be written as,

Assume the channel to be time invariant. Without the loss of generality, we assume the signal power is unity in each real and imaginary dimension. Therefore we have and

and A.3 reduces to the following:

Assuming the noise in two adjacent DQSPK symbols to be independent, the join PDF of two consecutive DQPSK symbols can be written as,

(A.8) Changing the range of integration for different portions of integration,

(E.9)

Therefore the estimated signal to noise ratio, SNR , is a function of only the true signal to noise ratio, SNR.

A.2 Derivation of Moment Ratio (MR) SNR Estimation Algorithm

For this derivation, we use the general PDF function given in (A.5) when calculating the moments. The expected value of the amplitude of the DQPSK signal, s. can be written as follows,

(A.16)

Therefore the moment ratio is a function of true SNR. We can use either numerical integrati on of Monte Carlo techniques to create a table of true SNR vs the moment ratio and use that to estimate the SNR from the estimated moment ration at the receiver. Figure 19 shows a graph of the look up table for mapping the initial SNR estimate to the true SNR. Figure 20 shows a graph of the look up table for mapping the moment ratio estimate to the true SNR.

List of Acronyms

ACGN Added Coloured Gaussian Noise

ADC Analogue to Digital Converter

APA Affine Projection Algorithm AWGN Added White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

BU Bad Urban Propagation Environment

CE Convolution Encoder Ch_2TapA Two Tap Channel With Relatively Strong ISI

Ch_2TapB Two Tap Channel With Relatively Weak ISI

CIF Common Interleaved Frame

CMA Constant Modulas Algorithm COFDM Coded Orthogonal Frequency Division Multiplexing CP . Cyclic Prefix DAB Digital Audio Broadcasting DAC Digital to Analogue Converter : DeMUX Demultiplexer

DFT Discrete Fourier Transform

DMT Discrete Fourier Transform

DQPSK Differential Phase Shift Keying

EDS Energy Dispersal Scrambler EM Expectation Maximization Algorithm

FFT Fast Fourier Transform

FIB Fast Information Block

FIC Fast Information Channel

FIR Finite Impulse Response HT Hilly Terrain Fourier Transform

IDFT Inverse Discrete Fourier Transform

IF Intermediate Frequency

IFFT Inverse Fast Fourier Transform

IPNLMS Improved Proportionately Normalised Least Mean Square ISCI Inter Sub-Carrier Interference

ISI Inter-Symbol Interference

LMS Least Mean Square

LNA Low Noise Amplifier

LOS Line of Sight MAP Maximum Aposteriori

ML Maximum Likelihood

MMSE Minimum Mean Square Error

MPSK M-Ary Phase Shift Key

MSC Main Service Channel MSDD Multiple Symbol Differential Detection MSE Main Service Channel MUX Multiplexer ;

MVU . . Minimum Variance Unbiased

NLMS Normalised Least Mean Square OFDM Orthogonal Frequency-Division Multiplexing PDF Probability Density PNLMS Proportionately Normalised Least Mean Square QPSK Quadrature Phase Shift Keying RA Rural Area Propagation Environment RiceChLD1.5A Time varying long delay channel with an early arrival path and long Delay of 1.5 times the Guard Interval

RiceChLD1.5B Time varying long delay channel without arrival paths and long Delay of 1.5 times the Guard Interval

RiceChLD3A Time varying long delay channel with an early arrival path and long Delay of 3 times the Guard Interval RF Radio Frequency RSC Recursive Systematic Convolutional Codes

SFN Single Frequency Networks

SINR Signal to Interference and Noise Radio SMSE Square root Mean Square Error

SNR Signal to Noise Ratio

SOVA Soft Output Viterbi Algorithm

TU Typical Urban Propagation Environment

WSSUS Wide Sense Stationary Uncorrelated Scattering

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Claims

CLAIMS:

1. A method of decoding a signal which has been modulated with digital data using phrase shift keying and transmitted over a communication channel, in which the signal to noise ratio (SNR) is estimated and the estimate is used in the decoding process, characterised in that the estimation of the SNR includes: a) obtaining differential phase shift values from the signal, b) deriving hard decoded phase shift keyed (PSK) symbols by rounding the differential values obtained in a) to the nearest permitted value in the encoding scheme, and c) estimating the amount of noise in the signal by comparing the values derived in step b) with the values obtained in step a).

2. A method as claimed in claim 1 in which the estimate of the amount of noise is used to estimate probabilities for each of the permitted values, and the probabilities are used in the calculation of an improved estimate of the amount of noise.

3. A method as claimed in claim 2 in which the probability estimation involves the use of a channel propagation model.

4. A method as claimed in claim 2 or 3 in which the improved estimate of the amount of noise is used to calculate improved probability values which I turn are used to calculate a further improved estimate of the amount of noise.

5. A method as claimed in claim 4 in which the steps of calculating improved probability values and calculating a further improved estimate of the amount of noise are repeated until the difference between successive estimates of the amount of noise is below a predetermined threshold.

6. A method as claimed in any of claims 2 to 5 in which the noise is known to be correlated between successive symbols in which an estimate of the relationship between the noise amounts in successive symbols is used in the calculation of probabilities. . ■

7. A . method as claimed in claim 1 including the additional step of applying a correction factor to the amount of noise estimated in step c) based on a precalcualted relationship between the estimated amount of noise and the actual amount of noise in the signal.

8. A method as claimed in claim 7 in which the correction factor is obtained from a look up table.

9. A method as claimed in claim 7 in which the correction factor is calculated using a formula approximating the pre-calculated relationship.

10. A method as claimed in claims 7, 8 or 9 in which the pre-calculated relationship is based on SNR values obtained from the estimated and actual amounts of noise.

11. A method as claimed in any preceding claim in which the amount of noise is estimated in step c) is based on comparison of values averaged over a predetermined number of symbols, and in which the estimate is updated for each successive symbol using a weighted sum of the previous estimate and an estimate obtained with the new symbol.

12. Use of a method as claimed in any preceding claim for decoding DQPSK symbols.

13. A method of decoding a signal which has been modulated with digital data using differential phase shift keying and transmitted over a communication channel, in which the signal to noise ratio (SNR) is estimated and the estimate is used in the decoding process, characterised in that the estimation of the SNR includes: calculating the moment ratio of the received symbols as the ration of: the square of the mean of the magnitude of received noise corrupted symbols and the mean of the square of the magnitude of the received noise corrupted symbols, and determining the amount of noise or the signal to noise ratio based on a pre-calculated relationship between the moment ratio and the actual amount of noise or actual signal to noise ratio.

14. A method as claimed in claim 13 in which a look-up table is used for determination of the amount of noise or the signal to noise ratio.

15. A method as claimed in claim 13 in which the amount of noise or the signal to noise ratio is determined using a formula approximating the pre-calculated relationship.

16. Use of a method as claimed in any preceding claim in soft decision decoding.

17. A method or use as claimed in any preceding claim in which the noise estimate is used to calculate SNR and the SNR is supplied to a Viterbi decoder.

18. A digital signal processor programmed to process digital signals according to a method as claimed in any preceding claim.

19. A digital audio broadcast receiver having a signal processor as claimed in claim 18.