Fractional Game Theory for Dynamic Resource Allocation in Heterogeneous Integrated Sensing and Communication Systems

In this paper, we investigate a dynamic network service selection problem in heterogeneous Integrated Sensing and Communication (H-ISAC) systems. Therein, small base stations (SBSs) equipped with ISAC units request resource blocks (RBs) owned by a macro base station (MBS) to serve their heterogeneous users with different Quality of Services (QoSs). We design comprehensive utility functions for the ISAC-SBSs that incorporate the heterogeneous QoSs of the users and network service cost. A heterogeneous resource allocation approach is proposed to address <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> the dynamic network service selection problem between ISAC-SBSs and MBS and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> the resource allocation problems among ISAC-SBSs and their heterogeneous users. To solve this problem, a low-complexity fractional game theory is used to capture the memory effect in the dynamic behavior of ISAC-SBSs. The resource allocation problems are typically non-convex, so we employ a block coordinate descent method to efficiently find solutions in high-dimensional spaces by optimizing one block of coordinates at a time. Simulation results demonstrate the existence and stability of the game equilibrium, which implies the stable network selection behaviors of the ISAC-SBSs. While the fractional game boosts system utility more than traditional games, it also incurs a greater adaptive cost.