## 3 Conventional Data Detection Algorithm Based on Manifold Optimization
### Problem Formulation and Solving
Therefore, in practical applications, using Algorithm 3 with \(B=1\) can achieve both superior performance and lower computational complexity. We also investigate the BER performance of the algorithms under different signal modulation schemes. Keeping the antennas, carriers, and data frame length the same as the previous settings, we focused on the case where the number of symbols is 1 and examined the performance when the signal modulation scheme is changed. Figure 3 shows the BER of the proposed Algorithm 2, Algorithm 3 with a different number of symbols \(B\), and the direct ZF detection algorithm under BPSK modulation. From Figure 3, it is easy to observe that Algorithm 3 is superior to that of the direct ZF detection algorithm, with an SNR gain of approximately 6 dB when the BER is \(10^{-2}\). This shows that Algorithm 3 performs well in the case of various modulation schemes. The results also indicate that the performance of Algorithm 3 with different subframe lengths is basically similar, except that with \(B=7\) it improves slightly under high SNR. However, the higher the value of \(B\), the higher the computational complexity of Algorithm 3. Comparing the BER performance of Algorithms 2 and 3, the performance of Algorithm 2 is similar to that of Algorithm 3 with \(B=1\). Similarly to the case of QPSK modulation, the complexity of Algorithm 3 is lower than Algorithm 2. These simulations show that Algorithm 3 is effective in different modulation scenarios, and the utilization of subframe and pilots for signal estimation in Algorithm 3 contributes to BER performance and computational complexity improvement. Figure 2: BER vs. SNR under QPSK modulation. ## 6 Conclusions

In this paper, we propose a time-varying channel manifold optimization algorithm for MIMO-OFDM systems, which enables efficient signal detection with low complexity. The proposed algorithm utilizes manifold optimization techniques to optimize the signals for MIMO-OFDM systems and involves the following steps. First, the estimated channel obtained from a GAN-based method is used for ZF detection to obtain the initial estimated signals. Subsequently, the optimization problem is solved by dividing the signals into subframes and the pilot part of the signals is used as a criterion to determine the completion of the optimization process. The simulation results show that Algorithm 3 has superior performance compared to direct ZF detection. When the BER is \(10^{-2}\), Algorithm 3 with \(B=1\) has an approximately 5 dB SNR gain compared to the direct ZF detection algorithm under QPSK modulation. Furthermore, the algorithm achieves a reduced bit error rate while maintaining low computational complexity. Conceptualization, Y.L. and D.H.; methodology, Y.L. and D.H.; investigation, Y.L. ; resources, Y.L. ; writing--original draft preparation, Y.L. ; writing--review and editing, D.H. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China under Grant 62271155. The data presented in this study are available on request from the corresponding author. The authors declare no conflicts of interest. Figure 3: BER vs. SNR under BPSK modulation. ## References

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