Blind fractionally-spaced equalization, perfect-reconstruction filter banks and multichannel linear prediction

Equalization for digital communications constitutes a very particular blind deconvolution problem in that the received signal is cyclostationary. Oversampling (OS) (w.r.t. the symbol rate) of the cyclostationary received signal leads to a stationary vector-valued signal (polyphase representation (PR)). OS also leads to a fractionally-spaced channel model and equalizer. In the PR, channel and equalizer can be considered as an analysis and synthesis filter bank. Zero-forcing (ZF) equalization corresponds to a perfect-reconstruction filter bank. We show that in the OS case FIR ZF equalizers exist for a FIR channel. In the PR, the multichannel linear prediction of the noiseless received signal becomes singular eventually, reminiscent of the single-channel prediction of a sum of sinusoids. As a result, the channel can be identified from the received signal second-order statistics by linear prediction in the noise-free case, and by using the Pisarenko method when there is additive noise. In the given data case, MUSIC (subspace) or ML techniques can be applied