Simplified p-norm-like Constraint LMS Algorithm for Efficient Estimation of Underwater Acoustic Channels

Underwater acoustic channels are recognized for being one of the most difficult propagation media due to considerable difficulties such as: multipath, ambient noise, time-frequency selective fading. The exploitation of sparsity contained in underwater acoustic channels provides a potential solution to improve the performance of underwater acoustic channel estimation. Compared with the classic l0 and l1 norm constraint LMS algorithms, the p-norm-like (lp) constraint LMS algorithm proposed in our previous investigation exhibits better sparsity exploitation performance at the presence of channel variations, as it enables the adaptability to the sparseness by tuning of p parameter. However, the decimal exponential calculation associated with the p-norm-like constraint LMS algorithm poses considerable limitations in practical application. In this paper, a simplified variant of the p-norm-like constraint LMS was proposed with the employment of Newton iteration method to approximate the decimal exponential calculation. Numerical simulations and the experimental results obtained in physical shallow water channels demonstrate the effectiveness of the proposed method compared to traditional norm constraint LMS algorithms.