On the use of basis functions in blind equalization based on deterministic least squares

Abstract

A blind channel identification scheme for narrowband digital communications with linear modulation is proposed that relies solely on the respective outputs of at least two spatially separated antennas. The proposed method is based on a deterministic relationship between the respective outputs of two FIR filters fed by the same input signal observed by Xu, Liu, Tong, and Kailath (see IEEE Trans. on Signal Processing, p.2982-93, 1995). It also relies on the use of basis functions derived from the Nyquist symbol waveform to characterize each channel's respective impulse response as first proposed by Schell and Smith (see IEEE Milcom-94, p.128-32, 1994). For urban cellular scenarios where the delay spread is on the order of T/sub 0/, where 1/T/sub 0/ is the symbol rate, we show that the continuous-time channel for a given antenna may be well approximated by a linear combination of a small number of time-shifted versions of the Nyquist symbol waveform. The corresponding time shifts may be equi-spaced across the delay spread regardless of the number of actual multipaths and their respective times of arrival. This leads to a critical observation that for a given antenna the same basis coefficient values characterize both the "real" discrete-time channel realized by symbol-spaced sampling starting at t=0 and the virtual discrete-time channel realized by symbol-spaced sampling starting at t=(T/sub 0/)/2. This, in turn, leads to a channel identification scheme requiring two samples per symbol at each antenna that blindly identifies each channel with a relatively small number of symbols in a moderate SNR scenario. A further result is that a bank of small order FIR equalizing filters spanning roughly the delay spread may be computed directly from the basis function coefficient values for each antenna.