Abstract—Rapid temporal variations in wireless channels pose a significant challenge for space–time modulation and coding algorithms. This letter examines the performance degradation that results when time-varying flat fading is encountered when using trained and unitary space–time modulation. Performance is characterized for a channel having a constant specular component plus a time-varying diffuse component. A first-order autoregres-sive (AR) model is used to characterize diffuse channel coefficients that vary from symbol to symbol, and is shown to lead to an effective signal-to-noise ratio (SNR) that decreases with time. Differential modulation is shown to have an advantage in effective SNR over trained unitary modulation at high power. Simulation results are provided to support our analysis. Index Terms—Differential modulation, fading channels, mul-tiple antennas, space–time modulation, time-varying channels, trained modulation, wireless communications. I.

We consider a MIMO Ricean fading channel with perfect side information at the receiver. We derive an analytic upper bound on the difference between the capacity of this channel and the mutual information that is induced by an isotropic circularlysymmetric Gaussian input. This bound is based on a dual expression for mutual information. If the number of receiver antennas m is at least equal to the number of transmitter antennas n, i.e., m ≥ n, this bound tends to zero as the signal-tonoise ratio tends to infinity. This shows that for this case a uniform power allocation is asymptotically optimal. If m<nsuch a uniform power allocation need not be asymptotically optimal. 1

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