Adaptive Echo Cancellation Algorithms Towards Real-time Communication System

Network and Acoustic Echo impact the voice quality in the real-time audio communication equipment. An effective solution is to use an linear filter to identify the impulse response of echo path with adaptive algorithm. The filter outtput, which provides an electronic replica of the echo, is subtracted from the microphone signal to control the echo.The Normalized Least Mean Square (NLMS) algorithm is the most popular adaptive algorithm in Echo Cancellation (EC) system for its robustness, simplicity and stability. Its main disadvantage is the slow convergence speed. With the improvement of processing power, the Affine Projection Algorithm (APA), which has higher computational complexity and convergences faster than the NLMS algorithm, begins to be deployed in EC system. However, the non-stationarity and auto-correlativity of speech signal significantly deteriorate the convergence speed of various adaptive algorithms. Decorrelation APA (DAPA) is proposed to eliminate the correlation of input matrices at different time instant with inner product defined in real linear space. It enhances the convergence speed of APA while its computational complexity is moderate.Nonparametric Variable Step Size NLMS (NPVSS-NLMS) algorithm achieves both fast convergence and low misalignment, which are conflicting requirements in traditional adaptive algorithm. NPVSS-NLMS requires the Background Noise Power (BNP) estimate for recovering the background noise from error signal. After analyzing the power rate between background noise and misalignment noise, an on-line precise BNP estimate is obtained for NPVSS-NLMS to improve the accuracy and reliability of BNP estimate. In order to settle the conflicting requirements in APA, NPVSS-APA is proposed by making the2-Euclidian norms of error signal vector and background noise vector equal. After analyzing the misalignment rate in APA, a precise BNP estimate for NPVSS-APA is eventually achieved.The bulk delay in the echo path varies significantly. Therefore, the adaptive filter used for EC system has to be equiped with at least thousands of coefficients to ensure exact modeling situation. The excessive length of the filter leads to slow convergnce and high computational complexity. On the other hand, the echo path is sparse in nature. Most of its coefficients are zero or unnoticeably smal value for bulk delay. Only a small portion of the coefficients, which are known as active coefficients, is significantly different from zero. They gather around in time domain to produce echo.Exploiting the sparseness to improve the efficiency of adaptive algorithm has attracted more and more attentions. Two algorithms for sparseness, Proportionate algorithm (P algorithm) and Delay Estimate-Selective Partial Update (D-SPU) algorithm, are discussed in this thesis.1) P algorithm assigns proportionate step-size to differenct coefficients based on the coefficient magnitude. The large coefficients obtaining large proportionate step-size convegence faster than the small coefficients, which leads to high overall convergence. However, P algorithm achieves fast convergence on the cost of computational complexity. Moreover, its proportionate step-size should be computed based on the coefficient magnitude of echo path. Due to the unavailable echo path, the current estimated magnitudes have to be used instead, which introduces error.After analyzing the adaptation process of P algorithm with the stochastic approximation paradigm, a statistical model is obtained to describe the convergence process of each coefficient. Motivated by this result, an improved P algorithm is proposed whose proportionate step-size is based on the precise magnitude estimate. It saves computational complexity significantly by recomputing proportionate step-size every some iterations.Proportionate APA (PAPA) is proposed by assigning proportionate step-sizes to each coefficients in APA. The convergence characteristic of PAPA is discussed. The range of the step-size which ensures the convergence of PAPA is derivated.2) The most straightforward method in exploiting the sparseness of echo path is to estimate the bulk delay with an adaptive filter. Another short adaptive filter is then centered around this estimate to identify the active coefficients. Since the echo path is identified with two individual adaptive filters, this algorithm introduces information redundancy.Selective Partial Update (SPU) algorithm identifies the whole system with an entire filter. However, it saves computational complexity by adapting a block of the filter coefficients rather than the entire filter at every iteration. However, the performance of tradional SPU is negative for it hasn’t exploit the sparsenessTaking advantage of the sparseness with SPU algorithm, Delay-SPU (D-SPU) algorithm is proposed. D-SPU traverses the entire filter with slipping-window integrator. The block with the maximum integral indicates the location of active coefficients. Beside the active coefficients, D-SPU updates a block of the adaptive filter periodically at every iteration. The echo path is identified precisely by updating the active coefficients. Additionally, the algorithm is equipped with sensitive tracking capability by updating a block of adaptive filter irrespective of the active coefficients. D-SPU algorithm has both low computational complexity and high convergence speed, and it reacts instantaneously when the echo path changes. Consequently, it is practicable in real application.The main contributions of this thesis lay in adaptive algorithm and the EC system implementation. It aims at improving the convergence speed and enhancing the stability of EC system. Beisdes, this reseach enriches adaptive theory and promotes the development of adaptive algorithm. Some of the examples in this thesis could offer object lessons for other adaptive applications.