Sparse Adaptive Filtering Technique And Its Application In Underwater Acoustic Channel Equalization

With the development of compressed sensing techniques,people realize the inherent sparsity of a system can be utilized to improve the performance of conventional adaptive filter algorithms.Based on two typical design ideas:norm regularization(NR)and proportionate updating(PU),the sparse adaptive filtering techniques have been studied extensively.The NR-based sparse adaptive filtering techniques achieve steady-state performance improvement over traditional adaptive filtering techniques by attracting inactive taps to zero,such as the l₁-least mean squares(l₁-LMS),l₀-LMS,l₁-recursive least square(l₁-RLS)and l₀-RLS;the PU-based adaptive filtering techniques achieve faster convergence over conventional algorithms by employing step sizes proportional to tap magnitudes,such as the improved proportionate normalized LMS(IPNLMS)and sparseness-controlled IPNLMS(SC-IPNLMS).The adaptive equalization technique had been widely researched as a key component of single carrier underwa-ter acoustic communication(UWA)receiver has been widely investigated.The most typical adaptive equalization scheme is the LMS or RLS based decision feedback equalizer(DFE)plus a digital phase-lock Loop(DPLL).With the recognition of the sparsity of an equalizer,sparse adaptive filtering techniques hava been gradually applied in the adaptive equalization of UWA channels.At present,many progresses have been made on the adaptive equalizer based on the sparse LMS adaptive filtering algorithm,while the sparse RLS adaptive filtering algorithm with faster convergence speed has received much less attention due to its high computational complexity.In this thesis,two types of sparse RLS algorithms based on the NR principle and PU principle were investigated and applied in multi-input multiple-output(MIMO)underwater acoustic communications.On one hand,NR-based sparse RLS algorithms have been proposed,but the high computational complexity hinders their practical application.Inspired by the fast implementation of a standard RLS,we propose fast implementations for NR-based sparse RLS algorithms.On the other hand,the PU-based sparse RLS algorithm has been rarely studied.Motivated by the IPNLMS,we propose a proportional RLS(PRLS)algorithm by introducing a proportionate matrix into a standard RLS and also analyze its transient and steady-state performance.Furthermore,we develop fast implementation named the proportionate stable fast transversal filter(PSFTF)for the PRLS and put it into the use of UWA channel equalization.Adaptive equalizers based on aforementioned two types of fast sparse RLS algorithms have been verified by experimental data collected in at-sea UW communication trials and showed the superiority over traditional adaptive equalizers.