Blind fractionally-spaced equalization based on cyclostationarity

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 noise-free multichannel power spectral density matrix has rank one and the channel can be found as the (minimum-phase) spectral factor. The multichannel linear prediction of the noise- less received signal becomes singular eventually, reminiscent of the single-channel prediction of a sum of sinusoids. As a result, a ZF equalizer can be determined from the received signal second- order statistics by linear prediction in the noise-free case, and by using a Pisarenko-style modification when there is additive noise. In the given data case, Music (subspace) or ML techniques can be applied. We also present some Cramer-Rao bounds and compare them to the case of channel identification using a training sequence.