Adaptive Filtering Algorithms For Sparse Impulse Responses And Multi-agent Networks

This thesis studies stand-alone sparse adaptive algorithms and distributed strategies over adaptive networks independently.In terms of stand-alone sparse adaptive algorithms,firstly,in order to estimate general sparse parameter vectors,an L0-norm constraint least mean square(L0-LMS)algorithm with adaptive zero attractor is proposed,where the zero attractor is updated based on the criterion of maximizing the decrease of the transient mean square deviation(MSD).In the L0-LMS algorithm,the zero attractor is an important parameter which balances the trade-off between the convergence rate and steady-state error of the algorithm.However,there is no practically effective choice guideline of this parameter.In addition,the optimal value of this parameter should be time-varying when the measurement noise power varies with time,and a fixed value of the zero attractor is no longer suitable.The proposed algorithm is tested in the case when the measurement noise level keeps changing over time.Secondly,in order to estimate block-sparse parameter vectors,a novel effective tap-length normalized least-mean-square(NLMS)algorithm is proposed for the application of network echo cancellation.At each iteration,the effective tap-length is updated to locate the active taps of the unknown impulse response,by minimizing the mean-square-error(MSE)cost function.In case the active region of the unknown echo path shifts in a large scale,the start tap and end tap estimates are reset to the full length when the effective tap-length estimate is lower than a predetermined threshold value.Simulation results demonstrate that the proposed algorithm can efficiently locate and track the effective tap-length of the unknown echo path when the active coefficients change abruptly in locations and magnitudes.In terms of distributed strategies over adaptive networks,firstly,in order to estimate some parameter vector of interest with unknown or variable tap-length in a distributed manner,a new diffusion-based variable tap-length algorithm is proposed,where both the tap-weights and tap-length of the tap-weight vector are updated at each node and at each iteration by minimizing the sum of MSEs across the agents.Theoretical analyses are provided for both tap-weights and tap-length convergence processes,from which closed-form formulations for the steady-state MSD and tap-length are derived.Moreover,the sufficient condition that ensures that the tap-length converges in the mean is also formulated,based on which general criteria for parameter selections are provided.Simulation results verify the theoretical findings and the parameter choice guidelines.In addition,the proposed algorithm is tested in the case when the tap-length of the unknown parameter vector keeps changing over time.Secondly,a diffusion strategy over adaptive networks is proposed under a generalized coordinate-descent scheme.In this setting,the adaptation step by each agent is limited to a random subset of the coordinates of its tap-weight vector.The selection of coordinates varies randomly from iteration to iteration and from agent to agent across the network.Such scheme is useful in reducing real-time computational complexity at each iteration,and is suitable for the distributed estimation problem when the gradient vector suffers from missing at random.Stability of the proposed algorithm is firstly studied,then,closed-form formulations for the steady-state MSD,excess risk(ER),as well as convergence rate are derived.Moreover,the proposed scheme is compared to the existing diffusion strategy under a stochastic gradient-descent scheme,in terms of computational complexity,convergence rate,MSD and ER.Finally,these theoretical findings are verified in MSE and logistic networks.