On the Fundamental Limits of Bistatic ISAC Over Vector Channels
This paper studies the fundamental limits of bistatic integrated sensing and communications (ISAC) systems over vector channels. We first consider a class of parallel channels in which, on each component channel, the channel from the transmitter (Tx) to the communication receiver (Rx) is degraded with respect to the channel from the Tx to the sensing Rx, or vice versa, where the direction of degradation may vary across component channels. For this class of channels, we establish matching achievability and converse results, which yield a single-letter characterization of the capacity-distortion function $C(D)$. For parallel Gaussian channels with additive Gaussian states, the evaluation of the capacity-distortion-power function $C(D,P)$ under the squared error distortion measure reduces to a joint power and distortion allocation problem across the component channels. We then extend the analysis to general vector channels and derive single-letter lower and upper bounds on $C(D)$. In particular, for vector Gaussian channels with additive Gaussian states, we prove the optimality of Gaussian superposition coding without requiring a global degradation order between the communication and sensing channels, by combining the channel enhancement technique with a matrix extremal inequality based on Fisher information. This leads to an exact characterization of $C(D,P)$.