The modified Pisarenko´s algorithm for adaptive spectrum estimation

The authors present a computationally efficient gradient-type algorithm for adaptively implementing Pisarenko´s method. Using the property that the Z-transform of the error filter equation has linear phase, they adaptively implement Pisarenko´s method with the weight vector p(n) whose dimension is (L+1), instead of the weight vector W(n) whose dimension is (2L+1), where L is the number of sinusoids buried in noise. The required computational complexity per iteration is about half that of previous implementations of Pisarenko´s method. Simulation results are presented. The authors derive the convergence properties of the modified Pisarenko´s algorithm in the vicinity of a stationary point. Additionally, they derive an expression for the range of the feedback coefficient for stable convergence