Reconfigurable intelligent surface assisted index modulation (RIS-IM) scheme is a developed transmission technology in smart radio environment. However, the current relevant research only considers the direct transmission of M-ary modulation signal to a single user. It is necessary to use multiple access technology to make more users share time-frequency resources in the future scenario of wireless communication connecting massive users. Nonorthogonal multiple access (NOMA) technology uses power domain multiplexing of time-frequency blocks to connect more users and realizes efficient utilization of resources by actively introducing interference. Based on nonorthogonal multiple access, this paper proposed a reconfigurable intelligent surface assisted index modulation system (RIS-IM-NOMA) to realize multi-user access for RIS-IM. The system improves the quality of the received signal using the reconfigurable intelligent surface and at the same time selects the best transmitting antenna to transmit index information in this system. And time-frequency resources are allocated to more users through NOMA and the spectral efficiency is improved. The greedy detection method was used to detect the signal at the receiving end, and the upper bound of the bit error rate was derived and analyzed theoretically. Then an improvement scheme was proposed for the performance decline of bit error rate caused by interuser interference of NOMA. The spectral efficiency of the system was analyzed theoretically, and a power allocation method was proposed to solve the problem of fairness of spectral efficiency among users. The simulation results show that increasing the number of reflecting elements can effectively reduce the bit error rate of the system, and the proposed power allocation method can effectively ensure the fairness of the system. Thus, the effectiveness of the proposed schemes is verified.

The development of large-scale communication systems puts higher requirements on traditional filter design. Sparse finite impulse response (FIR) filters have the characteristics of low computational complexity and low implementation cost, but conventional convex relaxation approximation design methods produce additional approximation errors, exhibit suboptimal sparsity, and involve complex solving processes. To address the issue of high implementation costs caused by the large number of multipliers in FIR filter design, this paper proposed a sparse FIR filter design method based on a weighted least squares criterion. Firstly, the norm of the initial sparse representation is replaced based on the properties of different norms, thereby improving the objective function. This modification maintains sparsity while addressing the challenge of directly solving non-convex functions. Next, the target problem was reformulated as the difference between two convex sub-problems. Simplified sub-problems were constructed according to iterative rules, and an alternating solution method was adopted to further enhance solving efficiency and reduce complexity. Finally, after determining the positions of zero coefficients, a weighted least squares problem was solved to further reduce approximation errors. The simulation results show that compared with the existing sparse filter solving methods, the proposed method can improve the coefficient sparsity performance of FIR filters, reduce the number of multipliers and obtain a compromise between root-mean-square error and maximum error in the case of sparsity enhancement. Meanwhile, the computational solving time is significantly reduced, and solving efficiency is notably improved.