On The Capacity of IRS-Assisted Gaussian SIMO Channels

Intelligent reflective surface (IRS) has recently emerged as a valuable addition to other key technologies for 5/6G to improve their energy efficiency and achievable rate at low cost. An IRS-assisted single-input multiple-output (SIMO) channel is studied here from an information-theoretic perspective. Its channel capacity includes an optimization over IRS phase shifts, which is not a convex problem and for which no closed-form solutions are known either. A number of closed-form bounds are obtained for the general case, which are tight in some special cases and thus provide a globally-optimal solution to the original problem. Based on a closed-form globally-optimal solution for the single reflector case, a computationally-efficient iterative algorithm is proposed for the general case. Its convergence to a local optimum is rigorously proved and a number of cases are identified where its convergence point is also globally optimal. Numerical experiments show that the algorithm converges fast in practice and its convergence point is close to a global optimum.