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This paper considers a terahertz (THz) dual-function multi-input multi-output (MIMO) radar and communication system with the assistance of a reconfigurable intelligent surface (RIS) and jointly designs the constant modulus (CM) waveform and RIS phase shifts. A weighted optimization scheme is presented, to minimize the weighted sum of three objectives, including communication multi-user interference (MUI) energy, the negative of multi-target illumination power and the MIMO radar waveform similarity error under a CM constraint. For the formulated non-convex problem, a novel alternating coordinate descent (ACD) algorithm is introduced, to transform it into two subproblems for waveform and phase shift design. Unlike the existing optimization algorithms that solve each subproblem by iteratively approximating the optimal solution with iteration stepsize selection, the ACD algorithm can alternately solve each subproblem by dividing it into multiple simpler problems, to achieve closed-form solutions. Our numerical simulations demonstrate the superiorities of the ACD algorithm over the existing methods. In addition, the impacts of the weighting coefficients, RIS and channel conditions on the radar communication performance of the THz system are analyzed. [ABSTRACT FROM AUTHOR]

This paper considers a terahertz (THz) dual-function multi-input multi-output (MIMO) radar and communication system with the assistance of a reconfigurable intelligent surface (RIS) and jointly designs the constant modulus (CM) waveform and RIS phase shifts. A weighted optimization scheme is presented, to minimize the weighted sum of three objectives, including communication multi-user interference (MUI) energy, the negative of multi-target illumination power and the MIMO radar waveform similarity error under a CM constraint. For the formulated non-convex problem, a novel alternating coordinate descent (ACD) algorithm is introduced, to transform it into two subproblems for waveform and phase shift design. Unlike the existing optimization algorithms that solve each subproblem by iteratively approximating the optimal solution with iteration stepsize selection, the ACD algorithm can alternately solve each subproblem by dividing it into multiple simpler problems, to achieve closed-form solutions. Our numerical simulations demonstrate the superiorities of the ACD algorithm over the existing methods. In addition, the impacts of the weighting coefficients, RIS and channel conditions on the radar communication performance of the THz system are analyzed.