On the Spectral Efficiency of Noncoherent Doubly Selective Block-Fading Channels

In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels with discrete block-fading interval N . In our noncoherent setup, neither the transmitter nor the receiver know the channel fading coefficients, though both know the channel statistics. In particular, we consider discrete-time channels whose impulse-response trajectories obey a complex-exponential basis expansion model with uncorrelated coefficients, and we show that such a model holds in the limit N ¿ ¿ for pulse-shaped transmission/reception over certain wide-sense stationary uncorrelated scattering channels. First, we show that, when the inputs are chosen from continuous distributions, the channel´s multiplexing gain (i.e., capacity pre-log factor) equals max(0, 1 - N _delay N _Dopp/N) , for discrete delay spread N _delay and discrete Doppler spread N _Dopp. Next, for the case of strictly doubly selective fading (i.e., N _Dopp > 1 and N _delay > 1), we establish that, for cyclic-prefixed affine pilot-aided transmission (PAT) schemes designed to minimize the mean-squared error (MSE) attained by pilot-aided minimum-MSE channel estimation, the pre-log factor of the achievable rate is less than the channel´s multiplexing gain. We then provide guidelines for the design of PAT schemes whose achievable-rate pre-log factor equals the channel´s multiplexing gain and construct an example.