This paper investigates the capacity region and detailed characterizations of capacity-achieving signaling schemes of a multiple access channel (MAC) with two users communicating to a base station (BS) equipped with 1-bit quantizers. We consider Rayleigh fading channels where channel state information (CSI) is known only at BS. Towards this end, we first study the weighted sum-rate maximization problem over the set of input distributions of one user for a fixed input signal at another user. By examining a necessary and sufficient Kuhn-Tucker condition (KTC) for an input to be optimal, it is first shown that the power constraint is active, i.e., the equality in the power constraint is achieved. By further exploiting novel bounds on the output distribution functions, the optimal distribution is shown to have a bounded amplitude. In the next step, we prove that if a fixed input with bounded amplitude is used at one user, the other user also needs to use a bounded amplitude signal to maximize the weighted sum-rate. To effectively analyze the KTC, our approach is to divide the domain of fading into two disjoint regions and examine the region with non-zero measure. It is then concluded that any boundary point in the capacity region is achieved by using bounded amplitude signals, and they are π/2 circularly symmetric. Building upon these results, we turn our focus to the sum-capacity segment, and demonstrate that any π/2 circularly symmetric input distribution having a constant amplitude is sum-capacity achieving. The sum-capacity can then be established.

This paper investigates the optimal signaling schemes and capacities of non-coherent correlated multiple-input single-output (MISO) channels in fast Rayleigh fading. We consider both channels under per-antenna power constraints as well as channels under joint per-antenna and sum power constraints. For per-antenna power constraint channels, we first establish the convex and compact properties of the feasible sets, and demonstrate the existence of optimal input distribution and the uniqueness of optimal effective magnitude input distribution. By exploiting the solutions of a quadratic optimization problem, we show that the Kuhn-Tucker condition on the optimal inputs can be simplified to a single dimension. As a result, we can apply the Identity Theorem to show the discrete and finite nature of the optimal effective magnitude distribution, with a mass point located at the origin. By using this distribution, we then construct a finite and discrete optimal input vector distribution. The use of this input allows us to determine the capacity gain of MISO over SISO via the phase solutions of a constrained quadratic optimization problem on a sphere, which can be obtained using a proposed penalized optimization algorithm. We also extend the results to MISO channels subject to the joint per-antenna and sum power constraints. Under this consideration, it is shown that not all per-antenna constraints are active. While the finiteness and discreteness of the optimal effective magnitude and the optimal input vector distributions still hold, the optimal phases and the optimal power allocation among the transmit antennas need to be determined simultaneously via a quadratic optimization problem under inequality constraints. These solutions can finally be used to obtain the MISO capacity gain.

This paper generalizes and proves the discrete and finite nature of the optimal signaling schemes for general classes of non-Gaussian aggregate interference point-to-point and multiple access channels (MACs) under peak power constraints. Specifically, we first investigate the detailed characteristics of optimal inputs for a single-user channel that is impaired by two types of noise: a Gaussian mixture (GM) noise consisting of Gaussian elements with arbitrary means, and the interference U with an arbitrary distribution. The only very mild condition imposed on U is that its second moment is finite. To this end, we establish the Kuhn-Tucker condition (KTC) on an optimal input and prove the analyticity of the KTC using Fubini-Tonelli's and Morera's theorems. It is then shown that an optimal input is continuous if only if the KTC is zero on the entire real line. However, by examining an upper bound on the output PDF, it is demonstrated that the KTC must be bounded away from zero. As such, any optimal input must be discrete with a finite number of mass points. Finally, we exploit U having an arbitrary distribution to show that the optimal input distributions that achieve the sumcapacity of an M-user MAC under GM noise are discrete and finite. Furthermore, there exist at least two distinct points that achieve the sum capacity on the rate region.

This paper presents simple methods to tightly estimate the information rate achieved by a Gaussian input and the constrained capacity of a finite-alphabet input of a Bernoulli-Gaussian (BG) impulsive noise channel in Rayleigh fading. Specifically, under the assumption of a Gaussian input, we propose a novel approach to calculate the achievable rate by examining the instantaneous output entropy in two regions of channel gains. In the high-gain region, the rate is evaluated via an upper bound obtained under the Gaussian output assumption. In the other region, we apply the piecewise-linear curve fitting (PWLCF) method to estimate the rate. It is then demonstrated that the information rate achieved by Gaussian inputs can be effectively calculated with a pre-determined accuracy. For a finite-alphabet input, we detail a PWLCF-based method to estimate the constrained capacity. In particular, we first propose a numerical technique to calculate the instantaneous output entropy using 2-dimensional Gauss-Hermite quadrature formulas. The average output entropy is then obtained using PWLCF. Combined with the closed-form expression the entropy of the BG impulse noise, an accurate estimation of the constrained capacity is finally established.

This paper presents a novel approach to tightly estimate the ergodic Shannon and constrained capacities of an additive Bernoulli-Gaussian (BG) impulsive noise channel in Rayleigh fading environments where channel gains are known at the receiver, but not at the transmitter. We first show that the differential entropy of the BG impulsive noise can be established in closed-form using Gaussian hypergeometric function2F1(1, 1; ·; ·). The Shannon capacity is then calculated via upper and lower bounds. Specifically, we derive in closed-form two upper bounds on the Shannon capacity using the assumption of a Gaussian output and using full knowledge of noise state, respectively. Under the assumption of a Gaussian input, we propose a novel approach to calculate a lower bound by examining the instantaneous output entropy in two regions of channel gains. In the high-gain region, the lower bound is evaluated via the upper bound obtained under the Gaussian output assumption. In the other region, we apply the piecewise-linear curve fitting (PWLCF) method to estimate the lower bound. It is then demonstrated that the lower bound can be calculated with a predetermined accuracy. By establishing the difference between the lower bound and the two upper bounds, we show that the lower bound can be used to effectively estimate the Shannon capacity. Finally, we detail a PWLCF-based method to estimate the constrained capacity for a finite-alphabet constellation. To this end, we first propose a numerical technique to calculate the instantaneous entropy of the output using 2-dimensional (2-D) Gauss-Hermite quadrature formulas. The average output entropy is then obtained using the PWLCF method. Combined with the closed-form expression of the entropy of the BG impulsive noise, the constrained capacity can be effectively estimated.

In this paper, we investigate the channel capacity of an additive Bernoulli-Gaussian (BG) impulsive noise channel in Rayleigh fading via lower and upper bounds. To this end, we first show that the differential entropy of the BG impulse noise can be established in closed-form using Gaussian hypergeometric function2F1(1, 1; .; .). This closed-form expression allows us to derive a lower bound on the capacity limit obtained by a Gaussian input using the Gauss-Hermite quadrature formula. We also derive in closed-form two upper bounds on the channel capacity. The first upper bound is obtained under the assumption of full knowledge of noise state, while the second upper bound is developed using a Gaussian distributed output. At high power regions, the lower bound achieved by Gaussian inputs and the upper bound generated by Gaussian inputs are indistinguishable. These two bounds can therefore be used as an accurate estimation for the channel capacity. When the channel input power is small compared to the power of the impulsive noise component, the lower bound obtained by using a Gaussian input and the upper bound under the perfect knowledge of impulse noise state are almost identical, which are useful to predict the capacity. The establishment of the lower bound and the two upper bounds in closed-form helps us to confirm the near-optimality of the Gaussian input in a wide range of input power levels over BG impulsive noise channels in Rayleigh fading.