An algorithm-independent burst-free adaptive hybrid

J. FranklinInst. Vol. 333(B), No. 5, pp. 687-705, 1996

~ Pergamon

S0016-0032(96)00046M

Copyright © 1996 The Franklin Institute Published by Elsevier Sci. . . . Ltd Printed in Great Britain 00164)032/96 $15.00+0,00

An Algorithm-independentBurst-freeAdaptive

Hybrid b y M. A. K H A S A W N E H

and

T. F. H A D D A D

Department o f Electrical Engineering, Jordan University of Science and Technology, Irbid 221 10, Jordan (Received 26 November 1994," accepted 14 March 1996)

ASSTRACT: This paper presents a structural solution to the bursting phenomena in adaptive hybrids. An algorithm-independent burst-free adaptive echo canceler is developed by introducing a stand-by adaptive filter in a single adaptive hybrid system. The purpose of this filter is to cancel out the pole(s) of the closed-loop characteristic equation, which, generally, lead to the bursting phenomena in adaptive systems with feedback. Several simulations examples are presented in this paper to demonstrate the superiority of the new configuration under the difJbrent conditions that would normally cause bursting, including practical situations where we have actual speech signals. Copyright © 1996 Published by Elsevier Science Ltd L Introduction

The use of adaptive filters over telephone networks has been of great advantage at reducing echoes generated in these networks. Generally, the presence of adaptive filters in closed-loop systems enhances the possibility of forcing the system poles out of their stability region, which is a direct reason for the bursting phenomena in a telephone network as addressed in (1). Recently, considerable research efforts have investigated the bursting phenomena in adaptive systems (1--4). Some of these efforts formulate heuristic interpretations as to the nature of bursting, and establish a fundamental understanding of this phenomena, by exploring its features as well as the conditions which cause it to happen (1, 2). Current solutions to the bursting problem in adaptive hybrids utilize either Leaky-type LMS algorithms (2), or some kind of correlation measures to cease the coefficients drift by stopping the adaptation process (3, 4). These methods are not only algorithm-dependent solutions, but may also impose limitations on the overall performance of the echo canceler, either by the adverse effect of leakage in producing bias in the prediction error, or by stopping the adaptation process itself. Unlike existing solutions, in this paper, a new algorithm-independent adaptive echo canceler is developed. As shown in Fig. 1, the new adaptive hybrid is configured by introducing a stand-by adaptive filter in parallel with the conventional echo canceler. This stand-by filter is supposed to completely identify the feedback path of the closedloop adaptive system, thereby, eliminating its effect and resulting in a burst-free closedloop adaptive system. The idea behind this new configuration is similar to the one 687

688

M. A. Khasawneh and T. F. Haddad

U(n) FIG 1. The new single adaptive hybrid. proposed by Zinser et al. (5), where a new crosstalk resistant adaptive noise canceler is introduced. Finally, simulation results of the proposed adaptive hybrid of Fig. 1 show immunity against the occurrence of bursting under different test conditions. IL The Statement of the Bursting Phenomena Bursting is defined as periodically oscillating weight trajectories with long periods of successful adaptation. It is considered as an unpredicted abnormal behavior usually associated with under-excited adaptive feedback systems (6). In the subspacc of narrowband excitation signals, in which the signals are not rich enough to provide persistent excitation to all modes of the adaptive filter, the filter coefficients are forced to drift away from their optimal values (7). Consequently, this parameter drift enhances the possibility for poles of the adaptive closed-loop system to cross the unit circle. At such instants, the dynamics of the adaptive filter start to drive the poles back inside their stability region, by producing a large prediction error sequence (1). Then, the adaptation process is pushed back into the previous cycle to produce a whole series of periodic oscillations, which characterize the bursting phenomena. A symptomatic direct consequence of feedback is a high correlation between the excitation sequence and the predication error of the adaptive filter, which is considered to be a strong indication of parameter drift that normally causes bursting in closed-loop systems (3). In this paper, we will adopt the model developed in (1), shown in Fig. 2, to investigate the bursting phenomena in adaptive hybrids. Referring to Fig. 2, bursting is very likely to happen in situations where the far-end signal F(n) is narrowband, while at the same time, the near-end signal is significantly large (1). One special case is the single tone or constant near-end signal with zero or quiescent far-end signal. In such a case, it is shown in (1) that the filter coefficients start to drift away forcing the system poles out of their stability region, at which instant, bursting begins reflecting on weight convergence. In the subsequent sections we will introduce a new adaptive hybrid configuration, which effectively prevents the occurrence of bursting under different burst-invoking conditions.

An Alyorithm-independent Burst-free Adaptive Hybrid

689

x(n)

F(n

hi r(n)

'+ v(n)

FIG 2. The conventional single adaptive hybrid.

IlL

The N e w

Adaptive Hybrid

A reliable and effective remedy to the bursty behavior in adaptive hybrids requires a thorough investigation of the root cause of the problem. Figure 2 illustrates the block diagram commonly used to model the feedback effect in adaptive hybrids (1). The study of the system diagram of Fig. 2, in which a feedback loop is included to model the source of bursting, suggests the introduction of an additional block within the system. This new block will serve to identify the dynamics of the feedback path. In particular, we propose that this added block maintains the required degrees of freedom to perfectly match the echo path; this is achieved by making this block adaptive. As shown in Fig. 1, the proposed block is used to adaptively self-optimize its parameters, such that the excitation signal e(n) is proportional only to the far-end signal, F(n). Eventually, by subtracting the portion related to r(n) from x(n), this new configuration highly reduces the correlation between x(n) and r(n); thus significantly suppressing a symptom indicant of bursting. From another perspective, the characteristic equation of the single adaptive hybrid system shown in Fig. 2 is 1-~ffz -~ (1), where ~ = h - w . As ~ff starts to exceed its unity bound of stability, the filter coefficients begin to oscillate about their stability bound. However, the characteristic equation of the system shown in Fig. 1 is 1 - ( ~ - b)v~z- 1; thus as b converges to its optimal value ~, the pole of the characteristic equation converges to zero. Consequently, the proposed adaptive filter will cancel out the pole(s) of the closed-loop system characterizing a given telephone network, which means that there is no possibility of having more bursting. In the next section we will present different simulation examples to demonstrate the burst-free behavior of the new single adaptive hybrid under different conditions. IV. Simulation Results

To evaluate the performance of the proposed configuration, a comparison with the single adaptive hybrid model in (1) is performed by means of the following four cases.

M. A. Khasawneh and T. F. Haddad

690

System Pole 1.4

1.2

1.0

-~

0.8

i

i

//

i

/

/ / / /j /

/

!

/

!

/

e~ ca

0.6

0.4

0.2

0.0

I

I

I

I

1000

2000

3000

4000

5000

Iteration # FIG 3. The pole of the conventional adaptive hybrid system of case 1, with dc near-end signal.

Case 1: Typical burst-invoking conditions Bursting evidently occurs in adaptive hybrids whenever we have a quiescent far-end speaker, while the near-end speaker is active (1). To satisfy this requirement, let the signals F(n) and N(n) shown in Figs 1 and 2 be equal to 0 and 1, respectively. Both models of Figs 1 and 2 were implemented using the conventional LMS algorithm with step size p = 0.03, a feedback factor ~ = 0.25 and a hybrid with a single weight h = - 0 . 1 . Figure 3 represents the trajectory of the pole, I ~ l , of the model shown in Fig. 2, where the reader can identify bursting from the periodic oscillations of the pole around its unity bound of stability, which causes a periodic signal growth as shown in Fig. 4. On the other hand, the results of simulating the new adaptive hybrid of Fig. 1 show that the system is in the normal mode of operation; that is, x(n) = aN(n) = 0.25, and e(n) = F(n) = 0, which are the values that x(n) and e(n) have converged to in Figs 5 and 6. As expected, the weight b(n) of the proposed filter scheme, Fig. 1, converges to its optimal value ~ = 0.25 as shown in Fig. 7. The behavior of the standard filter weight can be studied using the LMS recurrence equation w(n + 1) = w(n) + 21~r(n)e(n).

(1)

Given that ~(n) = h - w ( n ) , Eq. (1) can be written as v~(n+ 1) = v~(n)-- 21~(v~(n)e(n) + N(n))e(n) or equivalently

(2)

An Algorithm-independentBurst-free Adaptive Hybrid

691

x (n) 1.5

i

!

i

1000

2000

3000

I

1.0

¢,

0.5

eo

0.0

-0.5

-1.0

i

0

4000

5000

Iteration # FIG 4. Bursting in the received signal

x(n).

x (n) 0.30

0.25

0.20

"2 0.15

0.10

0.05

0.00

I

I

i

|

1000

2000

3000

4000

Iteration # FIG 5. The received signal

x(n)

using the new configuration.

5000

M. A. Khasawneh and T. F. Haddad

692

e (n) 0.30

0.25

0.20

•z

0.15

oa

0.10

0.05

0.00

~

~

'

1000

2000

3000

4000

5000

Iteration # FIG 6. The excitation o f the adaptive hybrid with the new configuration.

0.30

.

w (n) = b (n) . .

.

w=b 0.25

0.20

0.15

0.10

0.05

0.00

i

I

i

i

1000

2000

3000

4000

Iteration # FIG 7. The trajectories o f w(n) and b(n) o f the new configuration.

5000

An Alyorithm-independent Burst-free Adaptive Hybrid

693

System Pole

//

1.2

1.0

0.8

0.6

0.4

0.2

0,0

0

I

I

I

1

1000

2000

3000

4000

5000

Iteration # FIG 8. The pole of the c o n v e n t i o n a l adaptive hybrid system with sinusoidal n e a r - e n d signal.

x (n) 0.8

i

I

0.6 0.4 0.2 "~

0.0 -0.2 -0.4 -0.6 -0.8

-1.0

I

I

I

1000

2000

3000

Iteration # FI~ 9. Bursting in the received signal

4000

x(n).

5000

M . A. Khasawneh and T. F. Haddad

694

x (n) 0.5 0.4 0.3 0.2

:

0.1

i,

, :

ii

!

i i' i, J :;'

0.0 -0.1 -0.2 -0.3 -0.4 -0.5

1000

2000

3000

4000

5000

Iteration # F~G 10. The received signal

x(n)

using the new configuration.

e (n) 0.5 0.4 0.3 0.2 0.l 0.0 -0.1 -0.2 -0.3 -0.4 -0.5

0

'

'

~

1000

2000

3000

'

4000

Iteration # FIG 11. The excitation o f the adaptive hybrid in the new configuration.

5000

An Algorithm-independent Burst-free Adaptive Hybrid

695

x (n)

-I

,ill,.,li,,ihi.dh ,Jii,,JJil.,]iJ.llii,,lJl.li[h,ili,,Jll...ili, ,lii,,iiil.lJi,.lJli.liii.lili,,J]i.u}il.iiil,,Jh.~iih,Ill,:,llJ,

-2

-3

i

I

I

I

1000

2000

3000

4000

5000

Iteration # FIG 12 The received signal x(n), using the new configuration with a sinusoidal far end signal vP(n4- 1) = (1 - 2#e 2(n))v~(n) - 2pe(n)N(n).

(3)

Solving for the steady-state point at which ~* = v~(n+ 1) = v~(n) (1), gives

N(n) w*

-

e(n)

"

(4)

On the other hand

e(n 4- 1) = (c~-- b(n) )( ff:(n)e(n) - N(n) ).

(5)

Substituting for ~'(n) in the above equation by ~;;*, results in zero steady-state e(n). As the model in Fig. 2 is concerned, e(n) in the above equations has to be replaced by x(n), and it is well established in (1) that the zero stationary point of x(n) leads to the bursting phenomena in adaptive hybrids; see model of Fig. 2. On the other hand, in the new model proposed in Fig. 1, zero steady-state value of e(n) means that there is no excitation input to the hybrid itself, and since the prediction error of one adaptive filter in the new system is an excitation to the other, the filter weight trajectory w(n) will match that of b(n), which is clearly evident in Fig. 7. Another case of interest is where F(n) = 0 with a single-tone near-end signal. For the same previous system parameters, the results of simulating the system of Fig. 2 are shown in Figs 8 and 9, where we note the behavior that characterizes the bursting phenomena. However, Figs 10 and 11 represent the signals x(n) and e(n), which show that the new adaptive hybrid is smoothly functioning under the conditions that normally exhibit bursting.

M. A. Khasawneh and T. F. Haddad

696

e (n)

i,I,¸ i'll' ~'1i "!' i~'~I' ~ll' ~,rl,¸ ,Tr,Lit lp, 'rl' '!, ll' 'r i, !,1,~rv ,jr 'T' 'rTI'"rl'" T' 'rl' 'r':( 'rr',",[,,: "~

0

-I ,, ,I 1, ,~lJ,,I I, )t, ,~lJ,,111,,11, ,Lll~.,ll, ~iL~,,ih ,ll. ,~h, ,It, ,lli, ,~lJ,,lil, ,It, ,~ll, ,11,~lJ, ,~ll,.,li, ,k ,IJL~11

-2

-3 0

' 1000

20'00

' 3000

40'00

5000

Iteration # FIG 13. The excitation of the adaptive hybrid with the new configuration, with a sinusoidal farend signal.

Case 2: The new configuration under normal conditions In this case study, we will examine the behavior of the new adaptive hybrid under normal conditions. Let the far-end signal F(n) = sin(2rcfn), and let the near-end signal N(n) = 0,/~LMS = 0.03, ~ = 0.25, with h = - 0 . 1 . Simulation results are shown in Figs 12-15, where it is clear that a complete echo cancellation has been achieved. It is noteworthy to point out that under the conditions of active far-end speaker and a quiescent near-end speaker, the weight(s) of the introduced pole(s) canceler filter b(n) will converge to the stationary values of w(n), which is clear in Fig. 15; that is, because r(n) converges to zero with a quiescent near-end speaker.

Case 3: Burst-free adaptive hybrid with a speech signal Simulation results presented under this case study are meant to illustrate the optimal performance of the new configuration of Fig. 1, as compared with the conventional system of Fig. 2, in a practical situation. The speech signal shown in Fig. 16 was applied at the far-end inputs of the two systems of Figs 1 and 2, with unity dc as the near-end signal in both models. The two systems were simulated using the LMS algorithm with /~ = 0.03, • = 0.25 and the hybrid model h = - 0 . 1 . Figure 17 represents the signal x(n) after simulating the system of Fig. 2, where the periodic signal growth, the bursting, has started following the first quiescent period in F(n). In Figs 18 and 19, we observe a successful cancellation of the echo by the new adaptive hybrid. Note that the signal x(n) in Fig. 18 is a dc-shifted version of F(n) by ~ N(n) = 0.25, and e(n) is very close to F(n), which means that our system has satisfactorily achieved its objective.

An Algorithm-independent Burst-free Adaptive Hybrid

697

r (n) 0.06

I

I

i

i

0.04 0.02

0.00

t~

-0.02 -0.04

-0.06 -0.08 -0.10 0

I

I

i

i

1000

2000

3000

4000

5000

Iteration # FIG 14. The prediction error o f the single adaptive hybrid.

w (n) = b (n)

0.00

I

I

!

I

-0.02

-0.04

"r, -0.06

-0.08 b = (w)

-0.10

-0.12

1 00

2000

3000

4000

Iteration # FIG 15. The trajectories o f

w(n) and b(n) o f the

new configuration.

5000

698

M . A. Khasawneh and T. F. Haddad Speech Signal

3I I

",~

0

-1

-2

-3

2000

4000

6000

8000

10,000

12,000

Iteration no. FIG 16. The speech signal.

x (n) 2.5

I

i

i

i

2000

4000

6000

8000

I

2.0 1.5 1.0 0.5 ~

0.0 -0.5 -1.0 -l.5 -2.0 Iteration no. F i e 17. Bursting in the received signal x(n).

10,000

12,000

An Algorithm-independentBurst-freeAdaptiveHybrid

699

x (n)

31

I

i

i

i

i

-1

-2

i

-3 0

2000

i

4000

i

i

I

6000

8000

10,000

12,000

Iteration no. FIG 18. T h e received signal x(n), using the new configuration.

e (n) i

i

i

i

i

2000

4000

6000

8000

10,000

"6

-1

-2

-3

0

Iteration no. FIG 19. The excitation of the adaptive h y b r i d with the new configuration.

12,000

M. A. Khasawneh and T. F. Haddad

700

w (n) 0.18 0.16 0.14

i

!

i

i

i

i

i

S

0.12 0.10 e~ ca0

0.08 0.06 0.04 0.02 0.00 -0.02

i

I

500

1000

i

i

i

i

1500

2000

2500

3000

i

3500

4000

I t e r a t i o n no.

FIG 20. The trajectory of w(n), using the new configuration with a single tone near-end signal. e (n) i

1.5

i

1.0 0.5

o.o~-0.5 I

I

I

1000

1500

2000

-1.0

0

500

I

2500

I

I

3000

3500

4000

I t e r a t i o n no. x (n)

r (n)

2 1

=

0

-1 -_

-2

0

1000

2000

3000

I t e r a t i o n no.

4000

0

1000

2000

3000

I t e r a t i o n no.

FIG 21. The sequences labeled on Fig. 1, with single tone near-end signal.

4000

An Algorithm-independentBurst-free Adaptive Hybrid

701

w (n)

0.25

I

I

I

I

i

i

2;00

3000

0.20

0.15

=

eu)

0.10

0.05

0.00

I

-0.05 0

500'

10'00

FIG 22. The trajectory o f

15100

2000

3;00

4000

Iteration no. using the new configuration with a d c near-end signal.

w(n),

e (n)

1.5 1.0 ~-

0.5

0.0 -0.5

I

I

500

I

1000

I

1500

I

2000

I

2500

I

3000

3500

4000

Iteration no. 1.5

i

x (n) ;

r (n)

1.22:

i

i

i

i

1.0 .~

1.0

=

0.5

0.8 0.6 ctt

0.4

0.0 0.2

-0.5

1000

~

2000

~

3000

4000

0.0

0

,

1000

,

2000

,

3000

Iteration no. Iteration no. FIG 23. T h e sequences labeled o n Fig. 1, with dc n e a r - e n d signal.

4000

M. A. Khasawneh and T. F. Haddad

702

w (n)

1.4

i

jI

1.2 1.o •~

0.8

0.6

i

i

i

!

/

/

f

I

0.4 0.2 0.0

0

500 '

1000 '

15'00

2000 '

2; 00

30; 0

3500 '

4000

Iteration no. FIG 24. The trajectory of w(n), using the conventional configuration with a single tone near-end signal.

Case 4: The new adaptive hybrid with a multi-tap feedback path Here, we consider a single adaptive hybrid with the following 5th order FIR bandpass channel Q = [-0.0362

0.01913

0.7837

0.01913

-0.0362].

The performance of the proposed system in Fig. 1 is compared with that of Fig. 2, with dc and single tone near-end signals, independently, accompanied with a quiescent farend signal. A single-tap hybrid is used with a 5th order stand-by adaptive filter for the same value of/~ = 0.012. Simulation results for Fig. 1 are depicted in Figs 20 and 21 for the single tone case, and in Figs 22 and 23 for the dc near-end single case. In these figures it is evident that the 5th order stand-by adaptive filter has successfully eliminated the effect of the bandpass channel, thereby, resulting in a stable single adaptive hybrid. On the other hand, Figs 24~27 illustrate the results of implementing the system in Fig. 2; an oscillatory behavior in the filter weight as well as the signal in the return path is noted. However, due to the effect of the multi-tap channel, this oscillatory behavior decays with time, since the overall closed-loop adaptive hybrid is a multi-pole closedloop system; thus the bursty behavior is controlled by the location of more than one pole. Nevertheless, it can still be considered as an abnormal bursty behavior.

V. Concluding Remarks A new adaptive hybrid configuration was presented in this paper, in which an alogrithm-independent burst-free echo canceler was introduced. This filter is used to

An Alyorithm-independent Burst-free Adaptive Hybrid

703

x (n) i

i

i

i

i

I

..= ,-

0

-1

-2

-3

0

500

1000

1500

2000

2500

3000

3500

4000

Iteration no. FIG 25. The return p a t h signal

x(n),

with a single tone near-end signal.

w (n) 1.8

i

!

i

,

I

i

i

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

0

I

i

i

500

1000

1500

i

2000

i

2500

i

3000

i

3500

4000

Iteration no. FIG 26. The trajectory o f

w(n), using

the conventional configuration with a dc near-end signal.

704

M . A. Khasawneh and T. F. Haddad x (n)

2

0 -I -2 -3

0

500

1000

1500

2000

2500

3000

3500

4000

Iteration no. FIG 27. The return path signal x(n), with a dc near-end signal.

self-optimize its parameters to match the dynamics of the forward path in a telephone network. Experimental results, which were based on simulating the near-end for a telephone network showed that our new adaptive configuration perfectly achieved echo cancellation without bursting under conditions which would normally invoke bursting. Despite the fact that bursting is less likely to occur in real networks of double adaptive hybrids for relatively short periods of time (1), our new adaptive hybrid, which can be installed at both ends of a telephone network, is more convenient to be adopted, since it naturally provides crosstalk immunity, thereby averting the need for double-talk detectors to eventually yield uninterrupted echo cancelation.

References

(1) William A. Sethares, C. Richard Johnson Jr and Charles E. Rohrs, "Bursting in adaptive hybrids", IEEE Trans on Communications, Vol. 37, No. 8, Aug. 1989. (2) Gonzalo J. Rey, et al., "The dynamics of bursting in simple adaptive feed-back systems with leakage", IEEE Trans. on Circuits and Systems, May 1991. (3) L. Wang and T. Aboulnasr, "Practical adaptive hybrids with no bursting", IEEE ICASSP, Minneapolis, MN, 1993. (4) Z. Ding and C. R. Johnson Jr, "Frequency dependent bursting in adaptive echo cancellation and its prevention using double-talk detectors", Int. J. Adaptive Control and Signal Processing, 1990. (5) R. L. Zinser Jr et al., "Some experimental and theoretical results using a new adaptive filter

An Algorithm-independent Burst-free Adaptive Hybrid

705

structure for noise cancellation in the presence of crosstalk", Proc. IEEE ICASSP, pp. 1253-1256, Tampa, FL, Mar. 1985. (6) B. D. Anderson, "Adaptive systems, lack of persistency of excitation and bursting phenomena", Automatica, Vol. 21, pp. 247-258, May 1985. (7) W. A. Sethares, D. A. Lawrence, C. R. Johnson Jr and R. R. Bithmead, "Parameter drift in LMS adaptive filter", IEEE Trans. on Acoustics, Signal Processing, Vol. ASP-34, pp. 868 879, No. 4, Aug. 1986.