Extended Arimoto–Blahut Algorithms for Bistatic Integrated Sensing and Communications Systems

Integrated Sensing and Communication (ISAC) has emerged as a cornerstone technology for next-generation wireless networks, where accurate performance evaluation is essential. In such systems, the capacity-distortion function provides a fundamental measure of the trade-off between communication and sensing performance, making its computation a problem of significant interest. However, the associated optimization problem is often constrained by non-convexity, which poses considerable challenges for deriving effective solutions. In this paper, we propose extended Arimoto-Blahut (AB) algorithms to solve the non-convex optimization problem associated with the capacity-distortion trade-off in bistatic ISAC systems. Specifically, we introduce auxiliary variables to transform non-convex distortion constraints in the optimization problem into linear constraints, prove that the reformulated linearly constrained optimization problem maintains the same optimal solution as the original problem, and develop extended AB algorithms for both squared error distortion and logarithmic loss distortion. The numerical results validate the effectiveness of the proposed algorithms.