Neural Network Approach to Pisarenko's Harmonic Retrieval Method

Pisarenko's Harmonic Retrieval (PHR) Method Is Perhaps The First Eigenstructure Based Spectral Estimation Technique. The Basic Step In This Method Is The Computation Of The Eigenvector Corresponding To The Minimum Eigenvalue Of The Autocorrelation Matrix Of The Underlying Data. This Eigenvector Is Obtained As The Solution Of A Constrained-minimization Formulation. In This Paper, We Recast This Constrained Minimization Problem Into The Neural Network (NN) Framework By Choosing An Appropriate Cost Function (or Energy Function) For The NN. We Also Present The Theoretical Analysis Of The Proposed Approach For The Asymptotic Case. It Is Shown That The Minimizers Of The Energy Function Are The Eigenvectors (with A Given Norm) Of The Autocorrelation Matrix Corresponding To The Minimum Eigenvalue, And Vice Versa. Further, All The Minimizers Of This Energy Function Are Also Global Minimizers. Results Of Computer Sirntilations Are Presented To Support Our Analysis.