Robust receive beamforming and reflection coefficients optimization in an IRS-aided decode-and-forward relay system

Consider a decode-and-forward wireless relay system assisted by an intelligent reflection surface (IRS), where a robust design on receive beamforming at the relay and reflection coefficients at the IRS is studied. The worst-case signal-to-noise ratio maximization problem is formulated, subject to the reflection coefficients (with either continuous or discrete phases) constraints, under the assumption of imperfect channel state information for all channels. To cope with the hard problem, an equivalent nonconvex quadratic optimization problem with a simpler form is derived, and then the Cauchy-Schwarz inequality is applied to update the beamforming and a cyclic process is proposed to update the reflection coefficients, where a closed-form optimal solution is computed in each step. It turns out that the proposed algorithm achieves a locally optimal solution for the robust design problem. Simulation results show that the proposed robust design outperforms an existing non-robust design and two robust designs via semidefinite relaxation technique. In a DF IRS-aided wireless relay system, we design robust receive beamforming at the relay station and reflection coefficients at the IRS under the assumption of imperfect channel state information for all channels. We formulate an SNR (at the relay) maximization problem subject to unit-modulus constraints on the reflection coefficients, and the problem is reformulated into a hard quadratic maximization problem and solved iteratively by the Cauchy-Schwarz inequality to update the beamforming and by a cyclic process to search the optimal reflection coefficients, where a closed-form optimal solution is computed in each step.image