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 lter bank. Zero-forcing (ZF) equalization corresponds to a perfect-reconstruction lter 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 noiseless 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 secondorder statistics by linear prediction in the noisefree case, and by using a Pisarenko-style modi cation when there is additive noise. In the given data case, Music (subspace) or ML techniques can be applied. We also present some CramerRao bounds and compare them to the case of channel identi cation using a training sequence. I. Previous Work Consider linear digital modulation over a linear channel with additive Gaussian noise so that the received signal can be written as