Study On Set-membership Affine Projection Algorithms

Adaptive filter has been widely used in speech processing, echo cancellation, channel equalization, system identification, line enhancement, adaptive array processing and biomedical signal processing and many other fields. In colored input sceneratio, affine projection algorithm (APA) is more favoriable because it has a faster convergence than the least mean square (LMS) algorithm and lower complexity than the recursive least square (RLS) algorithm. But in some cases, the computational complexity of APA is still too high. With time sparse data-selective update, the set membership filter (SMF) reduces the computational complexity in adaptive filtering, without significant reduction in convergence rate and increase in steady-state misadjustment. In this thesis we intend to reduce the complexity of affine projection algorithm under the framework of SMF, a series of affine projection algorithm based on set-membership step-size have been proposed, and we verified their effectiveness by experiments of system identification, echo cancellation, interference suppression, etc.Set membership affine projection algorithm is the generalization of set-membership adaptive filtering problem to data-reuse adaptive algorithms, including the set membership normalized least mean square error (SM-NLMS) algorithm and the early set-membership binormalized data-reusing LMS (SM-BNDRLMS) algorithm as special cases.Using scalar error, the simplified SM-AP algorithm does not take full advantage of the error message. In this paper, a new error bound criteria was specified, and an improved SM-AP algorithm with vector error and uniform step-size (SM-APA-U) was proposed.It has faster convergence and smaller steady-state misadjustment than the simple SM-AP algorithm, at the cost of increasing a few calculations slightly. Performance of the improved algorithms is verified by experiments of system identification and interference cancellation in chaos-based communication.Partial update adaptive algorithm can efficiently reduce the computational complexity of high-order adaptive filters, which is also an important method in reducing the complexity of conventional AP algorithm. After reviewing partial update algorithms, we focus on the sparse partial update AP algorithm (SPU-AP). By introducing the set-membership step-size, to the SPU-AP algorithm, we proposed the set-membership SPU-AP algorithm (SM-SPU-APA), and analyzed the computational complexity and the mean square performance of the algorithm; finally the performance was verified by the experiments of system identification and acoustic echo cancellation.Identification of sparse and/or long discrete-time systems has always been a challenging research problem. In many applications, including acoustic/network echo cancellation and channel equalization, the system to be identified can be characterized as sparse and/or long. Proportionate adaptive filtering algorithm can speed up the adaptive filter convergence rate in the sparse system. Combined with the vector error based SM-APA-U algorithm, we improved the set-membership proportionate AP algorithm (SM-PAPA), and proposed the SM-PAPA-U algorithm with vector error, meanwhile we proposed the improved SM-PAPA-U with variable data-reuse number. Nonlinear system identification and channel equalization verified the algorithm.Another effective way to reduce the complexity of AP algorithm is the introduction of variable data-reuse factor. Based on the existing AP algorithm with selective regressor (SR-APA) according to certain ratio, and the AP algorithm with dynamic selection of input vectors (DS-APA), The two above algorithms were combined with the set-membership step-size, and proposed the set-membership version counterparts, namely SM-SR-AP algorithm and SM-DS-AP algorithm, which further reduce the overall complexity of SR-APA algorithm and DS-APA algorithm, respectively.Performances of the proposed algorithms were verified in several applications such as system identification in colored input signal, acoustic echo cancellation, interference suppression in chaotic communication, etc. In addition, we extend the improved affine projection algorithms to nonlinear volterra polynomial systems. Simulation results show that the proposed algorithms have similar convergence and misadjustment to the original algorithms, as well as considerable reduction of overall computational complexity.