## 6 Conclusions  
In this paper, we have proposed a novel IRS-assisted MU photon-counting system and jointly optimized the precoder and the IRS configuration based on the MMSE principle. Under the assumption of extreme near-field conditions, we discussed the crosstalk-free properties of the NLOS channel achieved via optical IRS reflection and simulated the IRS configuration by aligning the IRS units with various LED/PD pairs. Subsequently, we decomposed the non-convex optimization problem into two convex subproblems through variable substitution and relaxation, and we developed an AO algorithm to solve  
Figure 10: Average BER performance of AO algorithm under imperfect CSI, where \(M=16\), \(N=40\), and \(K=4\).  
Figure 9: Average BER performance of AO algorithm under different background radiations, where \(M=16\), \(N=40\), and \(K=4\).  
it effectively. Additionally, we analyzed the convergence and complexity of the algorithm. Finally, the simulation results demonstrated the superiority of our AO algorithm compared to other benchmark schemes in terms of MSE and BER, highlighting that the optimization of the IRS configuration significantly enhances the performance of the communication system.  
It should be pointed out that the above simulation experiment did not consider the impact of dead time in the photon-counting system. Dead time refers to the minimum time delay required for the detector to detect two consecutive photons. In subsequent work, we can analyze the impact of dead time and optimization schemes on the system throughput. In addition, this system considers an MU system equipped with a single antenna, which can be expanded to an MU system equipped with multiple PDs in the future. In order to save transmission power, it is also a feasible option to optimize the DC bias as an optimization variable, which can be further explored in subsequent work.  
Methodology, J.W., Y.C., F.L. and X.Z.; software, J.W.; writing--original draft, J.W.; writing--review and editing, J.W., X.Z., C.C. and H.X. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Natural Science Foundation of Shanghai under Grant 24 ZR1407100 and in part by the National Natural Science Foundation of China under Grant 62231010, Grant 62071126, and Grant 61571135.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} IRS & Intelligent reflecting surfaces \\ MIMO & Multiple-input, multiple-output \\ NLOS & Non-line-of-sight \\ MSE & Mean square error \\ AO & Alternating optimization \\ IoT & Internet of Things \\ FSO & Free-space optical \\ PCP & Poisson counting process \\ AWGN & Additive white Gaussian noise \\ ZF & Zero forcing \\ BER & Bit error rate \\ CSI & Channel state information \\ OOK & On-off keying \\ PD & Photo-detector \\ LEDs & Light-emitting diodes \\ DC & Direct current \\ LEDs & Light-emitting diodes \\ PDF & Probability density function \\ \end{tabular}