ADAPTIVE RECOVERY OF A CHIRPED SINUSOID IN NOISE, .2. PERFORMANCE OF THE LMS ALGORITHM

This paper studies the ability of the LMS adaptive algorithm to track a fixed amplitude complex chirped exponential buried in additive white Gaussian noise. The exponential is recovered using an M-tap predictor W. When W is controlled by the LMS algorithm with forgetting rate nu = mu-P(n) (mu is the algorithm step size an P(n) is the input noise power), the output misadjustment is dominated by a lag term of order nu-2 and a classical fluctuation term of order nu. Thus, a value nu-opt exists which yields a minimum misadjustment M(min). mu-opt and M(min) are evaluated as a function of the signal chirp rate PSI, the number of taps M, the noise power P(n), and the signal-to-noise ratio rho. For sufficiently small PSI [GRAPHICS] These results are new and important because they represent a precise analysis of a nonstationary deterministic inverse modeling system problem with the input being a colored signal. These results are in agreement with the form of the upper bounds for the misadjustment provided in a paper by Eweda and Macchi for the deterministic nonstationarity.