An Analysis of Capacity-Distortion Trade-Offs in Memoryless ISAC Systems
CoRR(2024)
摘要
This manuscript investigates the information-theoretic limits of integrated
sensing and communications (ISAC), aiming for simultaneous reliable
communication and precise channel state estimation. We model such a system with
a state-dependent discrete memoryless channel (SD-DMC) with present or absent
channel feedback and generalized side information at the transmitter and the
receiver, where the joint task of message decoding and state estimation is
performed at the receiver. The relationship between the achievable
communication rate and estimation error, the capacity-distortion (C-D)
trade-off, is characterized across different causality levels of the side
information. This framework is shown to be capable of modeling various
practical scenarios by assigning the side information with different meanings,
including monostatic and bistatic radar systems. The analysis is then extended
to the two-user degraded broadcast channel, and we derive an achievable C-D
region that is tight under certain conditions. To solve the optimization
problem arising in the computation of C-D functions/regions, we propose a
proximal block coordinate descent (BCD) method, prove its convergence to a
stationary point, and derive a stopping criterion. Finally, several
representative examples are studied to demonstrate the versatility of our
framework and the effectiveness of the proposed algorithm.
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