This paper is concerned with the computation of the capacity region of a continuous, Gaussian vector broadcast channel (BC) with covariance matrix constraints. Since the decision variables of the corresponding optimization problem are Gaussian distributed, they can be characterized by a finite number of parameters. Consequently, we develop new Blahut-Arimoto (BA)-type algorithms that can compute the capacity without discretizing the channel. First, by exploiting projection and an approximation of the Lagrange multiplier, which are introduced to handle certain positive semidefinite constraints in the optimization formulation, we develop the Gaussian BA algorithm with projection (GBA-P). Then, we demonstrate that one of the subproblems arising from the alternating updates admits a closed-form solution. Based on this result, we propose the Gaussian BA algorithm with alternating updates (GBA-A) and establish its convergence guarantee. Furthermore, we extend the GBA-P algorithm to compute the capacity region of the Gaussian vector BC with both private and common messages. All the proposed algorithms are parameter-free. Lastly, we present numerical results to demonstrate the effectiveness of the proposed algorithms.

Bistatic sensing refers to scenarios where the transmitter (illuminating the target) and the sensing receiver (estimating the target state) are physically separated, in contrast to monostatic sensing, where both functions are co-located. In practical settings, bistatic sensing may be required either due to inherent system constraints or as a means to mitigate the strong self-interference encountered in monostatic configurations. A key practical challenge in bistatic radio-frequency radar systems is the synchronization and calibration of the separate transmitter and sensing receiver. In this paper, we are not concerned with these signal processing aspects and take a complementary information-theoretic perspective on bistatic integrated sensing and communication (ISAC). Namely, we aim to characterize the capacity-distortion function—the fundamental tradeoff between communication capacity and sensing accuracy. We consider a general discrete channel model for a bistatic ISAC system and derive a multi-letter representation of its capacity-distortion function. Then, we establish single-letter upper and lower bounds and provide exact single-letter characterizations for degraded bistatic ISAC channels. Numerical examples illustrate the theoretical results, highlighting the benefits of ISAC over separate communication and sensing, as well as the role of leveraging communication to assist sensing in bistatic systems.

We design an algorithm from the perspective of information theory to calculate the capacity region of the Gaussian vector broadcast channel with private messages. For a continuous channel, a common method to approximately calculate its capacity is to apply the Blahut-Arimoto algorithm after discretization. In this work, we derive an equivalent form of the objective function and decouple the coupled variables in the original problem by exploiting the property that a Gaussian distribution is uniquely determined by its mean and variance. And thus develop a Gaussian Blahut-Arimoto algorithm without discretization.

Bistatic Integrated Sensing and Communication (ISAC) systems circumvent the issue of strong self-interference present in monostatic ISAC systems by employing a pair of physically separated sensing transceivers. They maintain the advantage of co-designing radar sensing and communications on shared spectrum and hardware. Motivated by the favorable attributes of bistatic radar, this paper investigates bistatic ISAC. In this setup, a transmitter sends messages to a communication receiver, while a sensing receiver at another location conducts a “decoding-and-estimation” (DnE) operation to obtain the state of the communication receiver. We propose three achievable DnE strategies based on the degree of information decoding at the sensing receiver: blind estimation, partial decoding-based estimation, and full decoding-based estimation. We explore the corresponding rate-distortion regions associated with each strategy. Furthermore, we provide a specific example to illustrate the comparison of the rate-distortion regions among the three DnE strategies and demonstrate the advantage of ISAC over independent communication and sensing.