Tensor-Based Target Sensing for Resource-Irregular ISAC Systems

Most existing target sensing approaches in integrated sensing and communication (ISAC) systems assume a regular time-frequency resource allocation. However, in practical ISAC systems, resources are often allocated irregularly because of the randomness of user scheduling. This paper addresses such resource-irregular scenarios by integrating the CANDECOMP/PARAFAC decomposition (CPD) framework with tensor completion. The proposed structured tensor completion and decomposition (STCD) method enhances target sensing by not only processing echo signals from irregularly allocated resource regions but also interpolating those from unallocated ones. Moreover, tensor completion reconstructs the Vandermonde structure of steering matrices. By enforcing a tensor rank-1 constraint, the STCD method leverages the Vandermonde structure to establish more relaxed uniqueness conditions for CPD compared with existing approaches. Additionally, we present the Cramér-Rao bound results for STCD in angle-range-velocity estimation, extending prior analyses from resource-regular to resource-irregular scenarios. Simulation results validate the effectiveness of the proposed STCD method for resource-irregular target sensing, demonstrating improved performance over traditional methods and its unstructured counterpart.