International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637
Acoustic Echo Cancellation of from the Signal Using NLMS Algorithm Ashu Sharma1, Yogesh Juneja2 Electronics and communication1, 2, PDM college of Engg1, 2 Email: kaushik.ashu12@gmail.com1 , yogeshjunejaer@gmail.com2
Abstract- The primary step while cancelling an echo is to identify the transmitted signal which reappears with some delay. Once the echo is identified it is cancelled by subtracting from transmitted signal. Echo cancellation can be done using either echo suppressors or echo cancellers, or in some case both. But suppressors support only half duplex communication leading to the invention of echo cancellers which allows both the speakers to talk at the same time. This paper is concerned with Adaptive Acoustic Echo Cancellation Based on Normalized Least Mean Square (NLMS) Algorithm. Here, we evaluate the performance of telecommunication systems like handsfree and teleconferencing systems which is affected by white noise. The term Acoustic Echo Cancellation (AEC) refers to a process of removing echo from the received signal that contains one or more delayed signals (copies of the original signal). Index Terms- LMS, NLMS, AEC 1. INTRODUCTION Adaptive filters are a type of digital filters that have self optimizing characteristics. Such filters have a finite number of parameters that are adjusted by adaptive algorithms to optimize some performance criteria. From last few decades adaptive filtering is gaining momentum in many Digital signal processing (DSP) applications. Digital signal processing (DSP) has been a major player in the current technical advancements such as noise filtering, system identification, and voice prediction. Standard DSP techniques, however, are not enough to solve these problems quickly and give acceptable results. Adaptive filtering techniques must be implemented for accurate solutions. An adaptive filter is a computational device that attempts to model the relationship between two signals in real time in an iterative manner. Adaptive filters are often realized either as a set of program instructions running on an arithmetical processing device such as a microprocessor or DSP chips[1]. An adaptive filter is defined by four aspects: 1. Signals being processed by the filters. 2. The structure that defines how the output signal of the filter is computed from its input signal. 3. The parameters within this structure that can be iteratively changed to alter the filter’s input-output relationship. 4. The adaptive algorithm that describes how the parameters are adjusted from one time instant to the next. Adaptive Filter The block diagram of an adaptive filter is as shown in fig. 1 [2]. It is the adaptive algorithm that utilizes the
coefficient updation according to the coefficient update equation of the form
…(1) Where ∆Wn is a correction that is applied toWn at time n to form a new Wn+1 at time (n+1). The keycomponent of adaptive algorithm is, how the correction ∆Wn to be formed [3].
Fig 1 Adaptive Filter
2. SYSTEM REQUIREMENT One of the primary disadvantages of the LMS algorithm is having a fixed step size parameter for every iteration. This requires an understanding of the statistics of the input signal prior to commencing the adaptive filtering operation. In practice this is rarely achievable. Even if the only speech signal is assumed to be input to the adaptive echo cancellation system, there are still many factors such as signal input power and amplitude which affect its performance. The normalised least mean square algorithm (NLMS) [4] is an extension of the LMS algorithm which bypasses this issue by selecting a different step size
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 value, µ(n), for each iteration of the algorithm. This step size is proportional to the inverse of the total expected energy of the instantaneous values of the coefficients of the input vector x(n). This sum of the expected energies of the input samplesis also equivalent to the dot product of the input vector with itself, and the trace of inputvectors auto-correlation matrix, R. tr[R]= =E …(2) The recursion formula for the NLMS algorithm is stated in equation (4.16). w(n+1)=w(n)+
e(n)x(n) …(3)
Derivation of the NLMS algorithm
w(n+1) = w(n)+2µ(n)e(n)x(n) e+(n) = d(n)-wT(n+1)x(n) = (1-2µ(n)xT(n)x(n)) e(n) …(4) Next minimise (e(n))2, with respect to µ(n). Using this, then find a value forµ(n) which forces e+(n) to zero. =
The NLMS algorithm can be implemented in Matlab. As the step size parameteris chosen based on the current input values, the NLMS algorithm shows far greater stability with unknown signals. This combined with good convergence speed and relative computational simplicity makes the NLMS algorithm ideal for the real time adaptive echo cancellation system. As the NLMS is an extension of the standard LMS algorithm, the NLMS algorithm spractical implementation is very similar to that of the LMS algorithm. Each iteration of the NLMS algorithm requires these steps in the following order. 1. The output of the adaptive filter can be calculated. = wT(n)x(n) …(8) 2.
An error signal can be calculated as the difference between the desired signal and the filter output. e(n) = d(n) − y(n)
3.
…(9) The step size value for the input vector can be calculated. µ(n)=
4.
…(10) The filter tap weights are updated in preparation for the next iteration. w(n +1) = w(n) +µ(n)e(n)x(n)
…(5) This µ(n) is then substituted into the standard LMS recursion replacing µ, resulting in the following. w(n+1) = w(n)+2µ(n)e(n)x(n) w(n+1) = w(n)+
…(7) Implementation of the NLMS Algorithm
y(n)=
To derive the NLMS algorithm, consider the standard LMS recursion, for which select a variable step size parameter, µ(n). This parameter is selected so that the error value, e(n), will be minimised using the updated filter tap weights, w(n+1), and the current input vector, x(n).
µ(n)
where µ(n) =
e(n)x(n)
…(11) Each iteration of the NLMS algorithm requires 3N+1 multiplications, this is only N more than the standard LMS algorithm and this is an acceptable increase considering the gains in stability and echo attenuation achieved.
…(6) Often the NLMS algorithm is expressed as equation (6), this is a slight modification of the standard NLMS algorithm detailed above. Here the value of ψ is a small positive constant in order to avoid division by zero when the values of the input vector are zero. The parameter µ is a constant step size value used to alter the convergence rate of the NLMS algorithm, it is within the range of 0<µ<2, usually being equal to 1. w(n+1) = w(n)+µ(n)x(n)
3. SET UP AND RESULTS Acoustic Echo Cancellation using NLMS adaptive algorithm The Near-end and Far-end speech are prerecorded speech. That are loaded and then linked with the model via “To wave device” blocks. Far-echo is generated using “Echo Generator” subsystem. White noise having zero mean and variance unity, Near-end
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 and Far-echo are added and fed into the NLMS filter i.e. “Desired Signal”. Following values of the parameters are used in the model simulation Audio Speech • Length of audio Speech: 10 s • Sampling rate of Audio Speech: 8000 Hz • Sample width of Audio Speech: 16 bits • Speech Data type: Double • Samples per frame of Audio Speech: 80 • Frame size: 20ms Echo Generator Subsystem • Delay of Echo Generator Subsystem: Z-400, Z-800and Z-1200 • Delay type: Samples White Noise • Mean: 0 • Variance: 1 • Source type: Gaussian • Method: Ziggurat • Inherit attributes: Output port Buffer • Convert to: Frame • Buffer size: 80 NLMS Filter • LMS Filter Length: 60 • Convergence step size of LMS filter: 0.002 • LMS filter Rounding mode: ceiling • LMS Over flow mode: saturate
Fig. 3 shows the white noise for NLMS algorithm. Fig. 4 shows the Far echo for NLMS algorithm. Fig.5 shows the error for NLMS algorithm. Fig. 6 shows the desired for NLMS algorithm. Fig. 7 shows the far signal for NLMS algorithm. Fig. 8 shows the near signal for NLMS algorithm. Fig.9 shows the output for LMS algorithm.
Fig.3 White noise for NLMS algorithm
Fig.4 Far echo for NLMS algorithm
Fig. 2 Acoustic Echo Cancellation using NLMS adaptive algorithm
Fig. 2 shows the simulink diagram for the Acoustic Echo Cancellation using NLMS adaptive algorithm.
Fig.5 Error for NLMS algorithm
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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 4. CONCLUSION
Fig.6 Desired for NLMS algorithm
Fig.7 Far signal for NLMS algorithm
In modern telecommunication systems like hands-free and teleconferencing systems, the problem arise during conversation is the creation of an acoustic echo. This problem degrades the quality of the information signal. All speech processing equipments like noise cancelling headphones and hearing aids should be able to filter different kinds of interfering signals and produce a clear sound to the listener. Currently, echo cancellation is a most interesting and challenging task in any communication system. Echo is the delayed and degraded version of original signal which travels back to its source after several reflections. It occurs when an audio source and sink operate in full duplex mode, an example of this is a hands-free loudspeaker telephone. In this situation the received signal is output through the telephone loudspeaker (audio source), this audio signal is then reverberated through the physical environment and picked up by the systems microphone (audio sink). The effect is the return to the distant user of time delayed and attenuated images of their original speech signal. The performance of telecommunication system for efficient echo cancellation such that it does not affect the system performance. We are using two adaptive filter for the acoustic echo cancellation. This observation depicts that in NLMS outperform LMS in terms of performance.
REFERENCE
Fig.8 near signal for NLMS algorithm
[1]. Marcel Dekker. Advances in Speech Signal Processing, 1992. [2]. Thomas Drumright; Adaptive filtering, Academic Publisher, USA, spring 1998. [3]. J. G. Proakis, "Digital Communications", 3rd edition, McGraw-Hill, 1995. [4]. S. Haykin, "Adaptive Filter Theory", PrenticeHall, 3rd Ed., 1996. [5]. ] S. Park, D. Youn and S. Park, "Acoustic interference cancellation for hands-free terminals," Digital Signal Processing, 2002. DSP 2002. 2002 14th International Conference on , vol.2, pp. 1277- 1280, 2002. [6]. S. K. M. VeeraTejaGarre, "An Acoustic Echo Cancellation System based on Adaptive Algorithms," M.S. Thesis, Dept. of Signal Processing, Blekinge Tekniska Hogskola, BTH, Sweden, October 2012. [7]. I. T. M. K. B. Homana, "Echo Cancellation using Adaptive Algorithms," Design and Technology of Electronics Packages, (SIITME) 15th International Symposium., pp. 317-321, Sept 2009.
Fig. 9 Output for LMS algorithm
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