Energy Efficiency and Spectral Efficiency Tradeoff in PMA-Based Sparse RIS Aided Cell-Free System

Reconfigurable intelligent surface (RIS) is regarded as a promising candidate for green communication because of its passive characteristic. However, the employment of large-scale RIS or multiple RISs for enhancing the system rate may lead to extra overhead or power consumption. In addition, cell-free (CF) network is preferred in the Internet-of-Things (IoT) due to its ability to against the inter-cell interference. Hence, a phase modulation array (PMA)-based sparse RIS-aided CF multipleinput multiple-output (MIMO) system is proposed for IoT in this paper to save energy consumption. Firstly, a closed-form expression for SE is derived, under the consideration of RIS phase errors. Subsequently, the energy efficiency (EE)-spectral efficiency (SE) tradeoff optimization problem is proposed and modeled as a three-variable joint optimization problem. Since the problem is a non-convex fractional optimization problem and difficult to solve directly, it is decomposed into three subproblems. Next, an alternating optimization approach is introduced, leveraging the lagrangian dual reformulation (LDR) and multidimensional complex quadratic transform (MCQT). Furthermore, in order to reduce the complexity of the algorithm, a two-stage convolutional neural network (CNN) is proposed to deal with this complicated problem. Finally, simulation results verify the potential of PMA-based sparse RIS in enhancing EE of the system and the effectiveness of the proposed algorithms.