Communicating over nonstationary nonflat wireless channels

We develop the concept of joint time-frequency estimation of wireless channels. The motivation is to optimize channel usage by increasing the signal-to-noise ratio (SNR) after demodulation while keeping training overhead at a moderate level. This issue is important for single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems but particularly so for the latter. Linear operators offer a general mathematical framework for symbol modulation in channels that vary both temporally and spectrally within the duration and bandwidth of one symbol. In particular, we present a channel model that assumes first-order temporal and spectral fluctuations within one symbol or symbol block. Discrete prolate spheroidal sequences (Slepian sequences) are used as pulse-shaping functions. The channel operator in the Slepian basis is almost tridiagonal, and the simple intersymbol interference pattern can be exploited for efficient and fast decoding using Viterbi's algorithm. To prove the concept, we use the acoustic channel as a meaningful physical analogy to the radio channel. In acoustic 2 x 2 MIMO experiments, our method produced estimation results that are superior to first-order time-only, frequency-only, and zeroth-order models by 7.0,9.4, and 11.6 db. In computer simulations of cellular wireless channels with realistic temporal and spectral fluctuations, time-frequency estimation gains us 12 to 18 db over constant-only estimation in terms of received SNR when signal-to-receiver-noise is 10 to 20 db. The bit error rate (BER) decreases by a factor of two for a binary constellation.