A Complex Adaptive IIR notch Filter Algorithm with Optimal Convergence Factor

Adaptive notch filters (ANF) are widely used in many signal processing applications to extract, eliminate or trace narrow-band or sinusoidal signals embedded in broadband noise [1]. If such signal consists of in-phase and quadrature components, a complex coefficient ANF must be implemented. Most of such applications are in radar and communication systems. To yield sharp-cutoff bandpass characteristics, IIR filter formulation is more efficient than its FIR counterpart. An early contribution by Nehorai [2] imposed constraints on a notch transfer function, which leads to simple relations between poles and zeros, thus, it can be exploited advantageously in adaptive filter design. Numerous algorithms for ANF have been proposed (e.g., [2-5]), most of them belonging to the recursive prediction error type. An important issue to consider when implementing these ANF algorithms is the choice of the convergence factor associated with the algorithm for coefficient updating and the pole radius factor associated with the notch bandwidth. These two factors affect the stability and the convergence speed of the algorithm. The choice of these factors is a tradeoff between tracking ability and noise sensitivity [1]. In this paper we propose a variable convergence factor that optimizes a well-defined instantaneous error criterion not requiring assumptions about the signal and noise characteristics. The paper is organized as follows. Section 2 defines the system model for a Gauss-Newton algorithm based complex