A Quadratic Programming Approach to Blind Equalization and Signal Separation

Blind equalization and signal separation are two well-established signal processing problems. In this paper, we present a quadratic programming algorithm for fast blind equalization and signal separation. By introducing a special non-mean-square error (MSE) objective function, we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem. Based on a clear geometric interpretation and a formal proof, we show that a perfect equalization solution is obtained at every local optimum of the quadratic program. Because blind source separation is, by nature and mathematically, a closely related problem, we also generalize the algorithm for blind signal separation. We show that by enforcing source orthogonalization through successive processing, the quadratic programming approach can be applied effectively. Moreover, the quadratic program is easily extendible to incorporate additional practical conditions, such as jamming suppression constraints. We also provide evidence of good performance through computer simulations.