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.