New algorithms for blind equalization and blind source separation/phase recovery

Blind source separation (BSS) and blind equalization (BE) are two important blind signal processing tasks. Blind source separation (BSS) is a method of recovering unobserved source signals from observed mixtures, exploiting only the assumption of mutual independence between source signal. Blind equalization (BE) refers to the problem of determining the system impulse response or the input signal when the system is unknown and the input is inaccessible. As an interesting application of BSS, we consider the use of BSS techniques in blind carrier phase estimation problem of M-ary signaling. By exploiting the independence of the in-phase and quadrature components of the signal constellation, BSS techniques can be applied to blindly estimate the carrier phase of single M-ary signal. In multiple mixed M-ary sources, by considering the complex mixtures of independent complex sources as real mixtures of mutually independent in-phase and quadrature components of sources, we propose a constrained BSS techniques for simultaneously separation and phase recovery with proper I/Q association. Stochastic-gradient iterative blind equalization algorithms are relatively simple to implement and are generally capable of delivering a good performance, as is evidenced by their actual use in digital communication systems. We investigate connections between the well-known blind equalization algorithms, such as Reduced Constellation Algorithm (RCA) and Constant Modulus Algorithm (CMA) and the recently proposed Multimodulus Algorithm (MMA). Based on the idea of combining the benefits of CMA and RCA, we propose a new Square Contour Algorithm (SCA) for blind equalization in QAM communication system. The new algorithm is better in its ability to converge to correct solutions.