Performance of the BLMS algorithm for adjusting a DFE

Bounds of stability, filter misadjustment, convergence rate, and optimum algorithm step size ensuring the fastest convergence are analyzed for the BLMS (block least mean square) algorithm for adjusting a decision feedback equalizer (DFE) at the end of a transmission channel, where the assumption of Gaussian data is incorrect. In addition to exact calculations a close approximation, requiring fourth statistics, and a less accurate approximation, where second statistics are sufficient, are given to reduce the computational effort. The results are compared with those for Gaussian data. A close approximation decreases the computational effort, but requires fourth statistics, just as the exact calculation. A less accurate approximation does not require fourth statistics and always yields misadjustment and convergence rate larger than the exact calculation. Hence, the exact maximum step size and the step size ensuring the fastest convergence are always larger than those calculated by the less accurate approximation, and stability is ensured