Experimental Analysis

The block for system parameter identification shown in Fig.5.1 was simulated.

The signal of the desired response was obtained by bringing noise with normal distribution and unit power to the input of a ninth-order FIR filter, with the parameters H¼ 0:1; 0:2; 0:3; 0:4; 0:5; 0:4; 0:3; 0:2; 0:1f g: Independent noise with normal distribution and a fixed variance was added to the filter output signal so that the signal-to-noise ratio is SNR¼ 30dB before the start of impulse contamination. Impulse noise was generated according to the model n kð Þ ¼ a kð ÞA kð Þ; P a kð ð Þ ¼ 1Þ ¼ 0:01; P a kð ð Þ ¼ 0Þ ¼ 0:99 and var A kf ð Þg ¼ 10⁴

=12:^b1ð Þ:k

0 500 1000 1500 2000 2500 3000

0.8 0.85 0.9 0.95 1

ρ^(k)

0 500 1000 1500 2000 2500 3000

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

λ(k)

0 500 1000 1500 2000 2500 3000

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15

(a)

(c) (b)

broj iteracija Number of iterations

Fig. 5.13 Estimation of time-variable parameter using the RRLS algorithm with a variable forgetting factor q and an outlier detector without impulse contamination. (a) value of variable forgetting factor, (b) estimated value of variable parameter b1and the parameter k which detects the presence of impulse noise, (c) additive noise

The length of the sliding window nH; applied for the determination of the parameter k; was chosen to be nH¼ 5 to minimize the probability of occurrence of more than one outlier in the window simultaneously and at the same time to decrease the number of iterations when the algorithm for the forgetting factor update is inactive. Based on experimental results we adopted a value of 10 for the constant c as a sufficiently good to follow the phenomena of impulse contami-nation. The changes of the b₁ parameter of the FIR filter, as defined in Fig.5.14, includes sudden drops and surges, as well as linear growth with larger or smaller inclination.

Figure5.13 shows the estimated value of the variable parameter for the case when no impulse contamination is present in additive noise. The parameter k has a value of 0 during the whole estimation, which is expected since no outliers occur, so that the leading role in the estimation is assumed by the PA-RLS algorithm. The adequate estimation of the forgetting factor in accordance with the variation of the estimated parameters is obvious.

Figure5.14shows the results obtained for the case when impulse contamina-tion is present in additive noise (Fig.5.14d). The parameter k successfully detected each occurrence of impulse contamination (Fig.5.14c) and thus pre-vented the update of the variable forgetting factor in the interval after the impulse disturbance occurred. Due to the appearance of impulse disturbances around 1,200 and 2,300-th iteration one notices insignificant deviations in the estimation of the parameter values, (Fig.5.14b), however they did not influence significantly the total result of the parameter estimation.

At the end, let us note the following. It is possible to solve the problem of the estimation of the time-variable parameter in the presence of impulse disturbances in additive noise using a robust recursive least squares algorithm with variable forgetting factor and a detector of impulse disturbances (outliers). The proposed algorithm is basically a two-step one, since depending on the detection of impulse

0 500 1000 1500 2000 2500 3000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Fig. 5.14 Variation of the 0.5

b₁parameters of an FIR filter of the order M = 9

disturbances it functions either as a robust recursive least squares algorithm or as a recursive least squares algorithm with a strategy for the forgetting factor choice based on parallel adaptation. The obtained results show a satisfactory detection of the appearance of impulse disturbances using the so-called median filter, which ensures correct following of parameter variations, with simultaneous prevention of propagation of errors caused by impulse disturbances (Fig.5.15).

Naturally, it is possible to utilize some other algorithm to determine the variable forgetting factor in the estimation of the filter parameters in nonstationary intervals instead of the PA-RLS algorithm. The latter algorithm was chosen because it represents a satisfactory tradeoff between numerical complexity and efficiency in various applications.

0 500 1000 1500 2000 2500 3000

-0.2 0 0.2 0.4 0.6

0 500 1000 1500 2000 2500 3000

0.8 0.85 0.9 0.95 1

ρ(k)

0 500 1000 1500 2000 2500 3000

0 0.5 1

λ(k)

0 500 1000 1500 2000 2500 3000

-60 -40 -20 0 20 40

broj iteracija Number of iterations

(a)

(b)

(c)

(d)

Fig. 5.15 Estimation of the time-variable parameter using the RRLS algorithm with variable forgetting factor q and with a detector of outliers if impulse contamination is present: (a) the value of the variable forgetting factor, (b) estimated value of the variable factor b₁, (c) parameter k which detects the presence of impulse disturbances (d) additive noise

Application of Adaptive Digital Filters for Echo Cancellation in Telecommunication Networks

Echo is a phenomenon we meet almost every day. During conversation, one may hear echo of speech that occurs because of the reflection of the sound signal from the walls, floor or some other surrounding objects. Echo always appears when there is reflection, but is often imperceptible if the time difference between the appearance of the original signal (speech) and the arrival of the reflected signal (echo) is small.

However, when the location of the reflection is sufficiently far from the speaker, as is the case in large empty rooms, then the time delay of the reflected signal is larger and echo may thus be significantly more marked in comparison to the original signal.

Echo is also generated in telecommunication networks. In this case the term of echo implies a delayed and distorted version of the original acoustic or electrical signal which moves towards its own source due to reflection or some other reason.

From the point of view of transmission quality, echo represents a disturbance causing a decrease of intelligibility in speech transmission, and an increase of error probability in data transfer. The origins of echo should be sought in specific requirements regarding the type of transmission, diversity of terminals and requirements for maximum exploitation of the available transmission systems.

Although data transfer, in the form of telegraphy, preceded speech signal transmission, speech communication became dominant with time and determined the development of telecommunication networks. The contemporary trend of the development of computers, which are becoming omnipresent due to their low cost, imposes an increasing need for data transfer. It is natural that there is a tendency to use the existing telephone networks for this type of transmission too. However, these networks are optimized for the transmission of analogous speech signals and thus introduce various distortions in data transfer. The most marked distortions are the linear ones, which include echo.

On the other hand, regardless if one deals with data or speech transmission, due to specific requirements in the use of communication equipment (like for instance acoustic and video teleconferences, satellite transmissions and similar) several different types of echo signal are generated.

The causes, modes and origins of echo in telecommunication networks may be different, but their common trait is that they decrease the quality of communica-tions. Thus there is an interest for a practical use of echo cancellers.

B. Kovacˇevic´ et al., Adaptive Digital Filters, DOI: 10.1007/978-3-642-33561-7_6,

 Academic Mind Belgrade and Springer-Verlag Berlin Heidelberg 2013

187

The theoretical basis for echo cancellation is in the field of adaptive digital filtering. This filed has been intensively researched in the last several decades, and the first practical implementation of an echo canceller appeared during 1960-ties.

However, because of the requirements connected with complex digital signal processing, a wider usage had to wait for the advent of the (LSI) Large scale integrated technology. The first echo canceller in (VLSI) Very large scale inte-grated technology was implemented in 1980 and this opened new possibilities for the improvement of characteristics and functionalities of echo canceller, as well as for their downsizing and cost decrease.

Following the technological development, the usage of echo cancellers also evolved, from the original concept of echo cancellation on very long distance lines to the application in full-duplex systems for data transfer, as well as in cancellation of acoustic feedback (acoustic echo) in electro-acoustic, tele-audio and video conferences.

As a rule, modern communication systems contain subsystems for local echo cancellation based on the principles of adaptive filtering. The technology of digital signal processors (DSP) ensures new possibilities for the implementation of complex algorithms for local echo cancellation, optimized with regard to adap-tation speed and accuracy. This is also a reason for an increasing interest for the improvement of the existing and the generation of new algorithm for more efficient solution of the echo cancellation problem.

The goal of this Chapter is to explain the concept of adaptive echo cancellation based on adaptive digital filtration, with a special emphasis on local echo, to represent the theoretical background, the possibilities and the limitations of this approach, as well as to present some of the achieved original results contributing to the improvement of the existing solutions.

The further text presents the basic types of echo signals, their causes and origins. It points out some conventional ways for the cancellation of this phe-nomenon, considers their drawbacks and outlines the principles of adaptive echo cancellation.

Several classes of recursive adaptive algorithms for local echo cancellation are analyzed from the point of view of accuracy, training speed, adaptation and the complexity of their implementation. Special care has been dedicated to the analysis of the influence of training sequences to the performance of the adaptive local echo canceller. The adjustment of the frequency range to the given parameters of the adequate communication channel was considered, as well as the statistical-correlation properties of the training sequences. The performed analysis encom-passes a novel approach based on the possibility of the ‘‘on-line’’ generation of optimal input signals, taking as the synthesis criterion the classes of functionals used in the field of optimal experiment planning. The algorithms of this type are con-sidered in detail inChap. 4. Besides that, we proposed the use of robust recursive algorithms in the case when echo signal is contaminated by additive impulse noise of by Gaussian noise with ‘‘weighted tails’’. An exhaustive experimental and theo-retical analysis of robust adaptive digital filters is given inChap. 5.