Low-Complexity Estimation Algorithm and Decoupling Scheme for FRaC System

With the leaping advances in autonomous vehicles and transportation infrastructure, dual function radar-communication (DFRC) systems have become attractive due to the size, cost and resource efficiency. A frequency modulated continuous waveform (FMCW)-based radar-communication system (FRaC) utilizing both sparse multiple-input and multiple-output (MIMO) arrays and index modulation (IM) has been proposed to form a DFRC system specifically designed for vehicular applications. In this paper, the three-dimensional (3D) parameter estimation problem in the FRaC is considered. Since the 3D-parameters including range, direction of arrival (DOA) and velocity are coupled in the estimating matrix of the FRaC system, the existing estimation algorithms cannot estimate the 3D-parameters accurately. Hence, a novel decomposed decoupled atomic norm minimization (DANM) method is proposed by splitting the 3D-parameter estimating matrix into multiple 2D matrices with sparsity constraints. Then, the 3D-parameters are estimated and efficiently and separately with the optimized decoupled estimating matrix. Moreover, the Cram\'{e}r-Rao lower bound (CRLB) of the 3D-parameter estimation are derived, and the computational complexity of the proposed algorithm is analyzed. Simulation results show that the proposed decomposed DANM method exploits the advantage of the virtual aperture in the existence of coupling caused by IM and sparse MIMO array and outperforms the co-estimation algorithm with lower computation complexity.