Effects of ill-conditioned data on least squares adaptive filters

Sensitivity results are presented for the LS weight vector of an all-zero adaptive equalizer in an ill-conditioned signal environment. The ill-conditioned data results from severe amplitude distortion introduced by the data channel. Specifically, a theoretical upper bound for the relative change in the magnitude of the weight vector due to additive noise is derived as a function of the channel characteristics and equalizer order, and simulation results are presented which indicate the derived bound to be applicable over a wide range of equalizer orders