Analysis of the RLMS adaptive beamforming algorithm implemented with finite precision

This paper studies the influence of the use of finite wordlength on the operation of the RLMS adaptive beamforming algorithm. The convergence behavior of RLMS, based on the minimum mean square error (MSE), is analyzed for operation with finite precision. Computer simulation results verify that a wordlength of nine bits is sufficient for the RLMS algorithm to achieve performance close to that provided by full precision. The performance measures used include residual MSE, rate of convergence, error vector magnitude (EVM), and beam pattern. Based on all these measures, it is shown that the RLMS algorithm outperforms other earlier algorithms, such as least mean square (LMS), recursive least square (RLS), modified robust variable step size (MRVSS) and constrained stability LMS (CSLMS).