Studies On Proportional Sparse Adaptive Filtering Algorithms

With its excellent performance and strong adaptability,adaptive filters are widely used in system identification,echo cancellation,channel equalization,linear prediction,spectral line enhancement and other fields.As the core element of the filtering system,the adaptive filtering algorithm determines the filtering performance.Therefore,the research on the adaptive filtering algorithm has been a hot spot in the signal processing field.The traditional adaptive filtering algorithm is generalized and universal without developing some special performance in communication system.However,in practical applications,such as wireless multipath channel,echo path,underwater acoustic channel,responses have typical sparseness.The sparse channel means that most of the channel impulse response coefficients are zero or close to zero,and only a few non-zero large amplitude coefficients.Therefore,studying sparse adaptive filtering algorithm can better utilize the sparse characteristics of the system and can improve the filtering performance.The existing sparse adaptive filtering algorithms can be divided into two types:zero-attraction and proportional.Among them,zero-attraction algorithm is sensitive to input signals.Therefore,this paper takes the proportional sparse adaptive filtering algorithm as the research object,and conducts in-depth research according to different application backgrounds and requirements.The specific content includes the following three aspects:Firstly,the proportional sparse adaptive filtering algorithm with set-membership criterion is studied aiming at the convergence speed sharply dropping and large computation of the PNLMS algorithm.By adding zero attractor to the cost function of the PNLMS,the small value coefficients are forced to return to zero quickly,so as to speed up the convergence of the proposed algorithm.The zero attractors include three types:symbol function,re weighted symbol function and CIM.In addition,in order to reduce the computational complexity,set-membership criterion is adopted.By setting error threshold,the number of iterations is effectively controned within a certain range,which not only increases the stability of the algorithm,but also reduces the computational cost.In order to verify the performance of the proposed algorithms,simulation experiments are carried out in the wireless multipath channel environment.The results show that the proposed algorithms are superior to the original algorithm in terms of convergence speed,steady-state error and computational complexity.Secondly,the proportional sparse adaptive filtering algorithm is studied under block sparse characteristics aiming at the existing algorithms not exploit the sparsity.By introducing mixed norm constraint into the cost function of the PNLMS algorithm,the channel impulse response coefficients are divided into several blocks,and each block is assigned a unified step size,which replaces the scheme of the original algorithm to assign the step size separately for each coefficient.So as to better develop the block sparse characteristics of the system and speed up the convergence of the proposed algorithm.The set-membership criterion is also adopted to improve the steady-state error and reduce the computation cost.Because the network echo has typical one-block sparse characteristics while the satellite communication echo has typical multi-block sparse characteristics,the proposed algorithms are simulated in the framework of echo cancellation.The results show that the proposed algorithms can effectively deal with the block sparse response of single and multiple blocks,and they have faster convergence speed and lower computation cost.Finally,the proportional sparse adaptive filtering algorithm is studied under unbiased criterion aiming at the existing algorithms usually only consider the output noise and ignore the input error.By adding the deviation compensation term into the cost function of the PNLMS algorithm and deducing the concrete expression of it on the basis of unbiased criterion,the estimation deviation caused by input noise of the adaptive filter can be effectively eliminated and the accuracy of the filter can be increased.Moreover,the convergence speed of the proposed algorithms are improved by adding three different zero attractors into the cost function of the PNLMS algorithm.In order to verify the effectiveness of the proposed algorithms,simulation experiments are carried out under the models of wireless multipath channel,echo path and underwater acoustic channel,respectively.The results show that the proposed algorithms are superior to the algorithms without bias compensation in terms of estimation accuracy and convergence speed.