A Pipelined Reduced Complexity Two-Stages Parallel LMS Structure for Adaptive Beamforming

Abstract

In this paper, we propose a reduced complexity parallel least mean square structure (RC-pLMS) for adaptive beamforming and its pipelined hardware implementation. RC-pLMS is formed by two least mean square (LMS) stages operating in parallel (pLMS), where the overall error signal is derived as a combination of individual stage errors. The pLMS is further simplified to remove the second independent set of weights resulting in a reduced complexity pLMS (RC-pLMS) design. In order to obtain a pipelined hardware architecture of our proposed RC-pLMS algorithm, we applied the delay and sum relaxation technique (DRC-pLMS). Convergence, stability and quantization effect analysis are performed to determine the upper bound of the step size and assess the behavior of the system. Computer simulations demonstrate the outstanding performance of the proposed RC-pLMS in providing accelerated convergence and reduced error floor while preserving a LMS identical $O(N)$ complexity, for an antenna array of $N$ elements. Synthesis and implementation results show that the proposed design achieves a significant increase in the maximum operating frequency over other variants with minimal resource usage. Additionally, the resulting beam radiation pattern show that the finite precision DRC-pLMS implementation presents similar behavior of the infinite precision theoretical results.