9.1 Introduction

There is considerable literature about second-order statistics-based algorithms for estimating DOAs of narrowband sources impinging on an array of sensors. These algorithms, however, have been examined only under the complex circular Gaussian assumption. The interest in these algorithms stems from a large number of applications, including mobile communications systems [1]. In this application, after frequency downshifting the sensor signals to baseband, the in-phase and quadrature components are paired to obtain complex signals. Complex noncircular signals [2], such as binary phase shift keying (BPSK) and offset quadrature phase shift keying (OQPSK) modulated signals, are often used. Naturally, the second-order algorithms devoted to complex circular signals relying on the positive definite Hermitian covariance matrix can be used in this context. Because the second-order statistical characteristics are also contained in the complex symmetric unconjugated spatial covariance matrix for noncircular signals, a potential performance improvement ought to be obtained if these two covariance matrices are used. However, only a few contributions [3 5] have been devoted to noncircular signals in DOA estimation in the last decade.

The aim of this chapter is to present an overview of algorithms and performance bounds of DOA estimates of noncircular signals. This chapter is organized as follows. The array signal model with some notations and the statement of the problem are given in Section 9.2. The potential benefit due to the noncircularity property is underscored by the help of subspace-based algorithms built only from the unconjugated spatial covariance matrix. Three attractive MUSIC-like algorithms...