A Deterministic Blind Equalization Method for Multi-Modulus Signals

We describe a new deterministic blind equalization method specifically for multi-modulus signals, the "algebraic multi-modulus algorithm" (AMMA). Deterministic methods of blind equalization provide an attractive and capable alternative to methods based on statistical frameworks because they are inherently more tolerant to source-signal temporal correlation, they typically require many fewer symbols to produce similar-performing solutions, and they can be much more computationally efficient. The proposed AMMA method emerges from the solution of a problem conceptually similar to that posed by van der Veen and Paulraj in developing the Algebraic (Analytical) Constant Modulus Algorithm (ACMA), which was originally developed for blind signal separation of IID constant-modulus signals and later extended to blind equalization of convolutive mixtures. The new method directly exploits the multiple moduli in a multi-level signal, thereby offering the possibility of better performance for non-constant-modulus signals. At the core of AMMA is a quadratic eigenvalue problem (QEP), the solution of which pushes up against the state-of-the-art in (rectangular) matrix pencil problems. We discuss several sub-optimal methods for solving the QEP, including a direct but limited approach, an efficient approach that solves an equivalent generalized eigenvalue problem, and other feasible methods. Finally, we present a brief simulation study in which we compare AMMA with ACMA and with an optimal equalizer