Global convergence of fractionally spaced Godard (CMA) adaptive equalizers

The Godard (1980) or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSEss) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. We present a convergence analysis of Godard/CMA FSEs that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: (1) a finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and (2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE.