Improved analysis and design of efficient adaptive transversal filtering algorithms with particular emphasis on noise, input and channel modeling

Adaptive filters are frequently employed in many applications in which the statistics of the underlying signals are either unknown a priori or slowly time-varying. Adaptive filtering algorithms are usually expected to have fast convergence speed, low computational complexity and high robustness to numerical problems and outlier interference. Many researchers have invested enormous efforts in deriving new algorithms with the above properties and analyzing their convergence behaviors. The latter is even more complicated due to the mathematical manipulations involved. Following the same guideline, in this dissertation we study a set of efficient adaptive transversal filtering algorithms and their convergence performance analysis. The development of the new algorithms and the establishment of the effective analytical framework are based on three important modeling approaches. (1) Noise modeling approach. By modeling the outliner impulsive noise as contaminated Gaussian distributed, we study the normalized least mean M-estimate (NLMM), transform domain NLMM (TD-NLMM) and partial update NLMM (PU-NLMM) algorithms which are more robust to impulsive noise than their conventional normalized least mean square (NLMS)-based counterparts. Complete convergence analyses of these algorithms are provided to interpret the underlying principles behind their performances. (2) Input modeling approach. By modeling the input signal as a low-order autoregressive process, the fast LMS/Newton algorithm can reduce the computational complexity of the traditional Newton-type algorithm while retaining its improved convergence speed. We propose two improved fast LMS/Newton algorithms. One is the block exact fast LMS/Newton algorithm which is mathematically equivalent to the original algorithm but has a significantly reduced complexity. The other is the robust fast LMM/Newton algorithm which is derived through the noise modeling approach used in (1). Moreover, we also develop a Newton-type algorithm with a uniform structure. It can realize flexible performance-complexity tradeoff and has the potential to be incorporated with the certain input modeling approach to achieve fast convergence performance with low complexity. (3) Channel modeling approach. By exploiting the sparse feature of the system channel encountered in vast applications, the generalized proportionate NLMS (GP-NLMS) algorithm possesses a faster initial convergence and tracking speed. Our proposed generalized proportionate stepsize (GPS)-fast LMS/Newton algorithm combines the advantages of the GP-NLMS and the fast LMS/Newton algorithms and exhibits a superior overall convergence and tracking performance. In addition, based on the GP-NLMS algorithm, another variable forgetting factor QR decomposition-based recursive least M-estimate (RLM) (VFF QR-RLM) algorithm is proposed. It has both an improved numerical stability and faster overall convergence and tracking speed than the conventional RLM algorithm using constant forgetting factor. All the proposed algorithms and the corresponding convergence analysis were tested through extensive computer simulations and good agreements between the theoretical predictions and the experimental results were observed. In general, the algorithms proposed in this dissertation have addressed some of the key problems in adaptive filtering algorithm design with the aid of three modeling approaches. They should form an algorithm set whose constituting components are intrinsically connected together and can potentially be utilized for various applications either individually or in a combination.