Convergence Issues in Sequential Partial-Update LMS for Cyclostationary White Gaussian Input Signals

The computational complexity of adaptive filtering algorithms increases with the number of filter coefficients. In applications where a long adaptive filter is required, the complexity can become prohibitively large due to scarce digital signal processing (DSP) resources such as the available DSP slices on a field programmable gate array (FPGA). Several partial-update least mean square (PU-LMS) algorithms have been proposed to address this problem. Among these algorithms, the sequential PU-LMS alleviates the computational complexity by updating a small subset of adaptive filter coefficients in a round-robin fashion at each iteration. Being data independent, it has no complexity overheads associated with coefficient selection. However, a major problem with the sequential PU-LMS is its vulnerability to poor convergence for cyclostationary input signals encountered in many practical applications. This letter presents a detailed analysis of the convergence issues with the sequential PU-LMS algorithm for cyclostationary white Gaussian input signals. The convergence analysis predicts when poor convergence is likely to occur based on a relationship between partial update and cyclostationary input signal parameters. The insights gained through this analysis can be used to adjust the sequential partial update parameters in order to avoid convergence difficulties. Simulation examples are presented to confirm the validity of the convergence analysis conducted.