Fast-converging minimum frequency error RLS lattice filter for narrowband interference with discrete frequency steps

This paper discusses the fundamental convergence and frequency tracking properties of the recursive-least-squares (RLS) lattice filter in the presence of narrowband interference (NBI) whose frequency varies in discrete steps. It is shown for filters of this type, that the residual forward energy (RFE) after a frequency transition is a function of the input signal-to-noise ratio (SNR), separation of the sequential frequencies and the filter time constant and is exponentially decaying in nature. Reducing the RFE is important in removing unwanted transient artefacts from the desired signal. The convergence behaviour of the RLS algorithm based on a posteriori estimation errors is analysed under a number of conditions by varying the SNR and frequency step size. In order to limit the impact of the RFE while maintaining a minimum frequency tracking error in steady conditions, a fast-converging minimum frequency error (FCMFE) RLS lattice filter is suggested. For comparison, a least-mean-square (LMS) based gradient-adaptive lattice (GAL) filter is also analysed for this class of narrowband interference.