On the spectral efficiency of noncoherent doubly selective block-fading channels

  • Authors:
  • Arun Pachai Kannu;Philip Schniter

  • Affiliations:
  • Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH;Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

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 - Ndelay NDopp/N), for discrete delay spread Ndelay and discrete Doppler spread NDopp. Next, for the case of strictly doubly selective fading (i.e., NDopp 1 and Ndelay 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.