A novel self-learning adaptive recursive equalizer with unique optimum for QAM

Most self-adaptive equalizers are FIR filters controlled by a nonlinear function of the output. But they can present local minima which do not equalize the channel. For a QAM system, this paper brings two novel ideas which jointly suppress this drawback (i) the complex equalizer is the cascade of a backward innovator, a forward innovator and a complex gain realizing both the power control and the carrier phase tracking; (ii) a novel minimization criterion combines the two criteria of prediction and equalization. This criterion is unimodal and is minimized by the optimum equalizer. It can be minimized adaptively at the same low computational cost as any other Bussgang technique. By implementing the forward innovator second, the latter can be made recursive and if output decisions are fed back in its loop, the structure resumes to a classical feedback equalizer. This method is successful with very severe channels, such as that of Porat and Friedlander (see IEEE Trans. on Signal Processing, vol.39, p.522-526, 1991), where other methods fail