Communications over Noncoherent Doubly Selective Channels

Wireless communication systems transferring broadband data in high mobility situations encounter fading channels which are both time and frequency selective. In the noncoherent scenario, the time varying impulse response of the doubly selective channel (DSC) is not available at both the transmitter and the receiver. In this dissertation, we consider the problem of communications over such noncoherent doubly selective channels. Our work has two main themes: to find the fundamental limits on the information rates for reliable communication across noncoherent DSC and to develop simple and efficient encoding/decoding techniques to achieve the promised information rates. Towards this end, we consider block transmissions over DSC and utilize complex-exponential (CE) basis expansion model (BEM) to characterize the channel variation within a block. For noncoherent CE-BEM DSC, we characterize the pre-log factor of the constrained ergodic channel capacity in the high SNR regime, when the channel inputs are continuously distributed. Next, we consider the design of pilot aided transmissions (PAT) for CE-BEM DSC, which embeds known pilot (i.e., training) signals that the receiver uses to estimate the channel. For a given fixed pilot energy, we derive the necessary and sufficient conditions on the pilot/data pattern to attain minimum mean squared error (MMSE), uncover time-frequency duality of MMSE-PAT structures and obtain novel MMSE-PAT patterns. We obtain bounds on the ergodic achievable ii rates of MMSE-PAT schemes and perform high signal to noise ratio (SNR) asymptotic analysis which suggests that, a multi-carrier MMSE-PAT achieves higher rates than a single-carrier MMSE-PAT when the channel’s delay spread dominates its Doppler spread, and vice versa. We also establish that the pre-log factor of the ergodic rates of all the MMSE-PAT patterns are strictly less than that of the constrained channel capacity, for strictly doubly selective channels. We also design spectrally efficient PAT schemes whose asymptotic achievable rates have the same pre-log factor as that of the constrained channel capacity. Our results show that there are fundamental differences between singly selective and doubly selective channels and provide insights on how the DSC’s delay spread and Doppler spread influence the constrained channel capacity and the PAT design. We extend the MMSE-PAT design to multi-input multi-output (MIMO) CE-BEM DSC. We establish that the spectral efficiency of MIMO-MMSE-PAT does not necessarily increase even if the number of transmit and receive antennas are increased simultaneously. We also present the optimal number of active antennas which maximizes the spectral efficiency.