On the Fundamental Trade-Offs of Time-Frequency Resource Distribution in OFDMA ISAC

Integrated sensing and communications (ISAC) is widely recognized as a pivotal and emerging technology for the next-generation mobile communication systems. However, how to optimize the time-frequency domain radio resource distribution for both communications and sensing, especially in scenarios where conflicting priorities emerge, becomes a crucial and challenging issue. In response to this problem, we first formulate the theoretical relationship between frequency domain subcarrier distribution and the range Cram\'er-Rao bound (CRB), and time domain sensing symbol distribution and the velocity CRB, as well as between subcarrier distribution and achievable communication rates in narrowband systems. Based on the derived range and velocity CRB expressions, the subcarrier and sensing symbol distribution schemes with the optimal and the worst sensing performance are respectively identified under both single-user equipment (single-UE) and multi-UE orthogonal frequency-division multiple access (OFDMA) ISAC systems. Furthermore, it is demonstrated that the impact of subcarrier distribution on achievable communication rates in synchronous narrowband OFDMA ISAC systems is marginal. This insight reveals that the constraints associated with subcarrier distribution optimization for achievable rates can be released. To substantiate our analysis, we present simulation results that demonstrate the performance advantages of the proposed distribution schemes.