 Research Article
 Open Access
FrequencyDomain Adaptive Algorithm for Network Echo Cancellation in VoIP
 Xiang(Shawn) Lin^{1}Email author,
 Andy W.H. Khong^{1},
 Milŏs Doroslovăcki^{2} and
 Patrick A. Naylor^{1}
https://doi.org/10.1155/2008/156960
© Xiang (Shawn) Lin et al. 2008
 Received: 1 November 2007
 Accepted: 8 April 2008
 Published: 22 April 2008
Abstract
We propose a new low complexity, low delay, and fast converging frequencydomain adaptive algorithm for network echo cancellation in VoIP exploiting MMax and sparse partial (SP) tapselection criteria in the frequency domain. We incorporate these tapselection techniques into the multidelay filtering (MDF) algorithm in order to mitigate the delay inherent in frequencydomain algorithms. We illustrate two such approaches and discuss their tradeoff between convergence performance and computational complexity. Simulation results show an improvement in convergence rate for the proposed algorithm over MDF and significantly reduced complexity. The proposed algorithm achieves a convergence performance close to that of the recently proposed, but substantially more complex improved proportionate MDF (IPMDF) algorithm.
Keywords
 Impulse Response
 Adaptive Filter
 Filter Coefficient
 Voice Over Internet Protocol
 Convergence Performance
1. Introduction
The increase in VoIP traffic in recent years has resulted a high demand for high density NEC in which it is desirable to run several hundred echo cancellers in one processor core. Defining as the length of the impulse response, the PNLMS and IPNLMS algorithms require approximately and number of multiplications per sample iteration respectively compared to for the substantially slower converging NLMS algorithm. Hence, in order to reduce the computational complexity of PNLMS and IPNLMS, the sparse partial update NLMS (SPNLMS) algorithm was recently proposed [12], which combines two adaptation strategies: sparse adaptation for improving rate of convergence and partialupdating for complexity reduction. For the majority of adapting iterations, under the sparse partial (SP) adaptation, only those taps corresponding to tapinputs and filter coefficients both having large magnitudes are updated. However, from time to time the algorithm gives equal opportunity for the coefficients with smaller magnitude to be updated by employing MMax tapselection [13]. This only updates those filter taps corresponding to the largest magnitude tapinputs. It is noted that partial update strategies have also been applied to the filteredX LMS (FxLMS) algorithms as described in [14, 15]. Other ways to reduce the complexity of adaptive filtering algorithm include the use of a shorter adaptive filter to model only the active region of the sparse impulse responses as described in [16].
It is well known that frequencydomain adaptive filtering such as the fastLMS (FLMS) algorithm [17] offers an attractive means of achieving efficient implementation. In contrast to timedomain adaptive filtering algorithms, frequencydomain adaptive algorithms incorporate block updating strategies, whereby the fastFourier transform (FFT) algorithm [18] is used together with the overlapsave method [19, 20]. However, one of the main drawbacks of these frequencydomain approaches is the delay introduced between the input and output, which is generally equal to the length of the adaptive filter. Since reducing the algorithmic processing delay for VoIP applications is crucial, frequencydomain adaptive algorithms with low delay are desirable especially for the identification of long network impulse responses. The multidelay filtering (MDF) algorithm [21] has been proposed in the context of acoustic echo cancellation for mitigating the problem of delay. This algorithm partitions an adaptive filter of length into blocks each of length . As a result, the delay of MDF algorithm is reduced by a factor of compared to FLMS. The benefit of low delay for MDF over FLMS in the context of NEC has been shown in [22].
The aim of this work is to develop a low complexity, low delay, and fast converging adaptive algorithm for identifying sparse impulse responses presented in the problem of NEC for VoIP applications. We achieve this by incorporating the MMax and SP tapselection into the frequencydomain MDF structure. As will be shown in this work, applying the MMax and SP tapselection to frequencydomain adaptive filtering presents significant challenges since the timedomain sparse impulse response is not necessarily sparse in the frequency domain. We first review in Section 2 the SPNLMS and MDF algorithms. We then propose, in Section 3.1, to incorporate MMax tapselection into MDF structure for complexity reduction. We show how this can be achieved using two approaches and we compare their tradeoffs in terms of complexity and performance. We next illustrate, in Section 3.2, how the sparseness of the Fourier transformed impulse response varies with the number of blocks in the MDF structure. Utilizing these results, we show how the SP tapselection can be incorporated into the MDF structure for fast convergence and low delay. The computational complexity for the proposed algorithm is discussed in Section 3.3. In Section 4, we present the simulation results and discussions using both colored Gaussian noise (CGN) and speech inputs for NEC. Finally, conclusions are drawn in Section 5.
2. Review of the SPNLMS and MDF Algorithms
where is the additive noise.
2.1. The SPNLMS Algorithm
The sparse partial (SP) update NLMS (SPNLMS) algorithm [12] utilizes the sparse nature of network impulse response. This algorithm incorporates two updating strategies: MMax tapselection [13] for complexity reduction and SP adaptation for fast convergence. Although it is normal to expect that adapting filter coefficients using partialupdating strategies suffers from degradation in convergence performance, it was shown in [12] that such degradation can be offset by the SP tapselection.
The variables and define the number of selected taps for MMax and SP, respectively, and the MMax tapselection criteria given by (6) for the timedomain is achieved by sorting using, for example, the SORTLINE [23] and short sort [24] routines. It has been shown in [12] that, including the modest overhead for such sorting operations, the SPNLMS algorithm achieves lower complexity than NLMS. To summarize, SPNLMS incorporates MMax tapselection given by (6) and SP tapselection given by (7) for complexity reduction and fast convergence, respectively.
2.2. The MDF Algorithm
where denotes complex conjugate, is the forgetting factor and is the stepsize with [21]. Letting be the input signal variance, the initial regularization parameters [8] are and . For and , MDF is equivalent to FLMS [17].
3. The Sparse Partial Update Multidelay Filtering Algorithm
The difference between (20) and (21) is that the latter employs , and we will describe in the following how this diagonal matrix can be obtained for the cases of MMax and SP tapselection criterion.
3.1. The MMaxMDF Algorithm
Hence, it can be seen that elements in the vector are obtained from the block of the selected Fourier transformed tapinputs contained in with indices from to . The adaptation of MMaxMDF_{N} algorithm is described by (23)–(25) and (21).
for and . As opposed to MMaxMDF_{N}, we denote this scheme as the MMaxMDF algorithm since normalization by is removed. Accordingly, elements in for MMaxMDF are computed using (24) and (25), where is obtained from (26). Hence, the adaptation of MMaxMDF algorithm is described by (24)–(26) and (21).
As will be shown in Section 4, the degradation in convergence performance due to tapselection is less in MMaxMDF_{N} than in MMaxMDF. However, since reducing complexity is our main concern, we choose to use MMaxMDF as our basis for reducing the computational complexity of the proposed algorithm. As will be described in Section 3.2, the proposed algorithm incorporates the SP tapselection to achieve, in addition, a fast rate of convergence.
3.2. The SPMMaxMDF Algorithm
for . Employing (32), the diagonal matrix in (21) for the SP tapselection can be described by (24) and (25).
This enables to reduce with increasing hence allowing adaptation to be more concentrated on the "active" region. A good choice of has been found experimentally to be given by . The proposed SPMMaxMDF algorithm is described in Algorithm 1.
3.3. Computational Complexity
Complexity of algorithms.
Algorithm  Multiplication  Division 

MDF 


IPMDF 


MMaxMDF 


MMaxMDF_{N} 


SPMMaxMDF 


Complexity for the case of , and
Algorithm  Multiplication  Division 

MDF 


IPMDF 


MMaxMDF 


MMaxMDF_{N} 


SPMMaxMDF 


4. Results and Discussions
We used a sampling frequency of 8 kHz and white Gaussian noise (WGN) was added to achieve a signaltonoise ratio (SNR) of 20 dB. The following parameters for the algorithms are chosen for all simulations [22]: . Stepsize control variable has been adjusted for each algorithm so as to achieve the same steadystate performance.
5. Conclusions
We have proposed SPMMaxMDF for network echo cancellation in VoIP. This algorithm achieves a faster rate of convergence, low complexity, and low delay by novelly exploiting both the MMax and SP tapselection in the frequency domain using MDF implementation. We discussed two approaches of incorporating MMax tapselection into MDF and showed their tradeoff between rate of convergence and complexity. Simulation results using both colored Gaussian noise and speech inputs show that the proposed SPMMaxMDF achieves up to dB improvement in convergence performance with significantly lower complexity compared to MDF. In addition, the performance of our low cost SPMMaxMDF algorithm approaches that of IPMDF. Since the MDF structure has been applied for acoustic echo cancellation (AEC) [21] and blind acoustic channel identification [29], where the impulse responses are nonsparse, the proposed SPMMaxMDF algorithm can also be potentially applied to these applications for reducing computational complexity and algorithmic delay.
Algorithm 1: The SPMMaxMDF algorithm.
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Authors’ Affiliations
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