Low resolution analog-to-digital converter (ADC) has been considered as an attractive solution to save power and cost in communication systems using high bandwidth and/or having multiple RF chains. Examples include emerging massive multi-antenna and UAV-based communications. During the last few years, there have been significant contributions to the information theoretical aspects of communication channels with low resolution ADC. However, the focus was only on either static additive white Gaussian noise (AWGN) channels where the channel quality does not change over time, or Rayleigh fading channels where there is no line-of-sight (LOS) component between the transmitter and receiver. In many wireless environments, the LOS path does exist, and it can dominate the wireless propagation. Unfortunately, there does not exist any information-theoretic results or guidelines for the design of practical codes/signals for wireless fading channels in the presence of LOS components. The scientific goal of this thesis is therefore to address the design of optimal signaling schemes and establish the capacity limit of LoS fading channels with 1-bit output quantization. The focus is on non-coherent Rician fading channels where neither the transmitter nor the receiver knows the CSI. Rician fading can be considered one of the most general models to represent LoS wireless fading channels, and it includes Rayleigh fading as a special case.

By first examining convexity and compactness of the feasible set of the input distributions, and the continuity of the input-output mutual information, it is demonstrated that the optimal input signal exists. Based on the formulated input-output mutual information, it is also shown that an optimal input signal is circularly symmetric. To further examine the structure of the optimal input, a necessary and sufficient condition for an input signal to be optimal, which is referred to as the Kuhn-Tucker condition (KTC), is established. By checking the KTC, it is shown that the optimal input distribution must be bounded. Then by exploiting the KTC and formulating a Lagrangian optimization problem, a unique characteristic of the phase of any mass point in the support set of the optimal distribution is revealed. Specifically, for a given mass point's amplitude, the corresponding complex mass points must be the four vertices of a rotated square in the complex plane. The proof is relied on novel log-quadratic bounds on the Gaussian Q-function. Using similar bounding techniques, the derivative of the KTC is further examined with respect to the amplitude and show that the amplitude of the mass points in the optimal distribution can take on only one value. As a result, the optimal input is a rotated QPSK constellation. Finally, by using this input, the channel capacity is established in closed-form. Numerical results are finally provided to confirm the theoretical analysis.