Determining the Number of Coherent/Correlated Sources Using FBSS-based Methods

Shahriar Shirvani Moghaddam,Somaye Jalaei

doi:10.5923/j.fs.20120206.12

Abstract

Determining the number of sources from observed data, is a fundamental problem in array signal processing. In this paper, first we focus on two popular estimators based on information theoretic criteria, AIC and MDL. Then another algorith m based on eigenvalue grads, namely EGM is presented. The co mputer simu lation results prove the effective performance of the EGM for non-coherent signals but in the small differences between the incident angles of non-coherent sources, MDL and AIC have a much better detection performance than EGM . These methods can detect only non-coherent signals, and the performance of them will be sharply declined even signals are coherent and/or correlated. So, first forward/backward spatial s moothing (FBSS) method is used as a pre-processing step to solve the coherency/correlation, and then MDL, AIC and EGM algorithms are run to estimate the number of signals. Nu merical results show that FBSS-based EGM offers higher detection probability rather than FBSS-based MDL and AIC in the case of coherent sources as well as correlated ones. Also, the higher detection probability can be achieved for correlated case compared to coherent one.

Highlights

Wireless direction finding is the p rocedure for determining signal sources by observing signal direction of arrivals (DOAs)
We focused on the performance evaluation of three popular methods, Akaike’s informat ion criterion (AIC), m description length (MDL) as well as eigenvalue gradient methods (EGMs)
As shown in simulat ion results, these algorithms are appropriate for determin ing the number of non-coherent signals and the performance of them will be decreased when signals are coherent and/or correlated

Summary

Introduction

Wireless direction finding is the p rocedure for determining signal sources by observing signal direction of arrivals (DOAs). They proposed an approach to this problem, based on the Akaike’s informat ion criterion (AIC) and minimu m description length (MDL) According to these two algorith ms, the number of signal sources is determined. Luo Jing Qing[8] proposed a set of eigenvalue gradient methods (EGMs), wh ich like AIC and MDL methods, it determines the number of non-coherent sources according to the eigenvalues of auto-correlation matrix Another algorith m that considers a bound or threshold for eigenvalues is investigated in[9]. The MDL descriptor is computed for signal and noise co mponents separately, and the results are added to obtain the total MDL cost Another way is to use spatial smoothing (SS) method to solve the coherency/correlation, and estimate the number of signals.

Signal Model

Esti mating the Number of Signals with Information Theoretic Criteria

Esti mating the Number of Signals Using EGM

Simulation of Non-Coherent Signals

Conclusions