Max-and-Min Fractional Programming for Communications and Sensing

There is considerable interest in the use of fractional programming (FP) for the communication system design because many problems in this area are fractionally structured. Notably, max-FP and min-FP are not interchangeable in general if there are multiple ratios, so the two types of FP are often dealt with separately in the existing literature. As a result, an FP method for maximizing the signal-to-interference-plus-noise ratios (SINRs) typically cannot be used for minimizing the Cramér-Rao bounds (CRBs). In contrast, this work proposes a unified approach that bridges the gap between max-FP and min-FP. Particularly, we examine the theoretical basis of this unified approach from a minorization-maximization (MM) perspective, and in return obtain a matrix extension of this new FP technique. Moreover, this work presents two application cases: (i) joint radar sensing and (ii) multi-cell secure transmission, neither of which can be efficiently addressed by the existing FP tools.