In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels with discrete block-fading interval <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> . 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ¿ ¿ 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max(0, 1 - N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay</sub> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dopp</sub> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) , for discrete delay spread <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay</sub> and discrete Doppler spread <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dopp</sub> . Next, for the case of strictly doubly selective fading (i.e., <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dopp</sub> > 1 and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">delay</sub> > 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.