Blind Radio Channel Identification and Equalization Based on Oversampling And/or Antenna Arrays

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 l-ter 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 second-order statistics by linear prediction in the noise-free case, and by using a Pisarenko-style modiication 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 identiication using a training sequence. Consider linear digital modulation over a linear channel with additive Gaussian noise so that the received signal can be written as y(t) = X k a k h(t ? kT) + v(t) (1) where the a k are the transmitted symbols, T is the symbol period, h(t) is the (overall) channel impulse response. Assuming the fa k g and fv(t)g to be (wide-sense) stationary, the process fy(t)g is (wide-sense) cy-clostationary with period T. If fy(t)g is sampled with period T, the sampled process is (wide-sense) stationary and its second-order statistics contain no information about the phase of the channel. Tong, Xu and Kailath 1] have proposed to oversample the received signal with a period = T=m; m > 1. This leads to m symbols-spaced channels. The results presented here generalize the results in 2] where an oversampling factor m = 2 was considered. As an alternative to over-sampling, multiple channels could also arise from the use of multiple antennas. Corresponding to each antenna signal, there is a channel impulse response. Each antenna signal could furthermore be oversampled. The total number of symbol rate channels is then the product of the number of antennas and the oversampling factor. In what follows, we …