Novel Direction Findings for Cyclostationary Signals in Impulsive Noise Environments

We consider the problem of direction-of-arrival (DOA) estimation for cyclostationary signals in impulsive noise modeled as a complex symmetric α-stable (SαS) process. Since the DOA estimation based on second-order cyclic statistics degrades seriously in an α-stable distribution noise environment, we define a novel pth-order cyclic correlation by fusing the fractional lower order statistics and second-order cyclic correlation. After briefly introducing the statistical characteristics of pth-order cyclic correlation and building the extended data model, we first propose a novel extended pth-order cyclic MUSIC algorithm (EX-POC-MUSIC) by exploiting both pth-order cyclic correlation and pth-order cyclic conjugate correlation. The algorithm allows us to select desired signals and to ignore interference in the communication system. Second, in order to increase the resolution capabilities and the noise robustness significantly, an improved EX-POC-MUSIC algorithm called the extended pth-order cyclic Root-MUSIC (EX-POC-RMUSIC) algorithm is also presented. This algorithm has all the merits of the EX-POC-MUSIC algorithm, and it is also a fast DOA estimation algorithm because it avoids spatial spectrum searching. Under some conditions, both proposed algorithms are able to handle more sources than the number of sensors. Simulation results strongly verify the effectiveness of the two algorithms.