A novel multi-resolution based PSD estimation method based on expectation maximization algorithm

Abstract

Power spectral density (PSD) estimation is used in many applications such as spectrum sensing for cognitive radio (CR). For a fixed number of samples, one must trade-off estimation accuracy against frequency resolution. We propose a multi-resolution method based on the expectation-maximization (EM) algorithm that provides both high frequency resolution and low estimation error variance. First a high resolution PSD estimate with high estimation error variance is produced. Then, from the same set of samples, we produce a low frequency resolution PSD estimate with low estimation error variance. Using information from the first PSD estimate, the EM algorithm is used to estimate the missing frequency bins of the PSD with low frequency resolution. It is shown by analysis and simulation that the proposed method improves both the resolution and estimation error variance compared to conventional PSD estimation.