Thomas Wen-Wei Yang

Simple Interleaving Technique that Significantly Improves the Frequency Estimates of the Subspace-Based Methods for Closely Spaced Frequencies

MS Thesis
Date: January 1998

Abstract:

The high resolution subspace-based method, such as ESPRIT, is widely used to estimate the frequencies of noise corrupted sinusoids. However, during analysis of this algorithm, the results show that the performance of this method degrades drastically for closely spaced frequencies. In other words, with the reduced frequency spacing the error variance of the estimates increases with this suboptimal methods faster than corresponding Cramer-Rao bound (CRB).

In fact, for closely spaced frequencies, the variance of the estimates increases with oversampling due to the decrease in the frequency spacing despite the increase in the number of samples. This also implies that with over sampled signals we can achieve better estimates from the subspace-based methods using downsampling. However, over sampling is inherient to samples of any cluster of a few closely spaced sinusoidal frequencies. This motivates us to explore the possibility of obtaining improved estimates for closely spaced frequencies using down sampling. Besides estimation accuracy and enhancing the resolution of the ESPRIT algorithm, the detection efficiency, that is the probability of correct detection, of the minimum description length (MDL) methos is also improved using the interleaving technique.

Committee:

Prof. Ram S. Raghavan (advisor)