A bilinear approach to constant modulus blind equalization

We consider the problem of blind equalization of a constant modulus signal that is received in the presence of Inter-Symbol-Interference (ISI) and additive noise. Awell-known class of adaptive algorithms for this problem is the so-called Godard family of blind equalizers[1], including among others the CMA[2] and SATO[3] algorithms. These algorithms are known for their ability in general to open the eye ofacommunications channel and for their low computational complexity. However, a common disadvantage of all algorithms of this class is that they might exhibit ill-convergence if not properly initialized, due to the non-convex form of their cost function. In this paper we present a different approach to the problem, namely, a bilinear approach in order to construct a convex cost function with a unique minimum point. After presenting the formulation for this approach, we show that in the case of an exactly invertible noiseless channel the optimal solution that completely opens the communication channel's eye may always be attained, regardless of the initial equalizer's setting. This implies that equalization may bealsoachieved for a noisy FIR channel, provided that the equalizer is long enough to approximate adequately the channel's inverse impulse response. Computer simulations are provided to show the validity of our theoretical arguments