On the Capacity of Reconfigurable Intelligent Surface Assisted MIMO Symbiotic Communications

Reconfigurable intelligent surfaces (RISs) appear as one of the most promising paradigms for future wireless communications, because of their high adjustability for diverse communication demands and the additional information-carrying capability by reflecting patterns. This paper investigates the capacity of RIS-assisted multiple-input multiple-output (MIMO) symbiotic communications utilizing multiple reflecting patterns, where each reflecting pattern is non-uniformly activated to carry additional information. To enhance transmission performance, the reflecting patterns, reflecting activation probability, and the transmit covariance matrix are jointly designed. Since the exact expression of the system capacity is intractable, the lower and upper bounds on the capacity are derived and used for optimization in this paper. Based on the lower bound on the capacity, a gradient ascent algorithm is developed to find the optimal reflecting patterns, reflecting activation probability, and the transmit covariance matrix. By taking advantage of the concise-form upper bound on the capacity, closed-form solutions of the reflecting activation probability and transmit covariance matrix can be derived after optimizing the reflecting patterns. The superiority of the proposed design is investigated and verified by computer simulations. Some selected numerical results demonstrate that the proposed design can achieve a higher capacity than the benchmark adopting only one reflecting pattern.