# Optimization of Intelligent-Reflecting-Surface-Enabled Covert Communication in Multi-Sensor Systems
## 8 Discussion and Conclusions  
In this work, we investigated covert communication in multi-sensor systems employing intelligent reflecting surfaces. Diverging from prior works, we examined the optimization of transmission amplitudes and optimal phase angles for a 2-BPSK codebook under the condition of asymmetric noise over complex Gaussian channels. We employed KL divergence as a metric for the covertness constraint and mutual information as a metric for the transmission rate. We approximated KL divergence and mutual information with Taylor series expansion. Leveraging the approximated KL divergence and mutual information, we solved for the optimal phase angles. Specifically, we proposed a gradient descent algorithm to obtain all optimal phase angles. Based on the optimal phase angles, we could achieve the optimal transmission amplitude gain. With numerical simulations, we verified the effectiveness and precision of our adopted Taylor approximation method. Validating our algorithm across two distinct scenarios, we demonstrated its robust convergence and capability to derive all optimal phase angles. Comparing the initial phase angles from existing works to the optimal phase angles obtained via the gradient descent algorithm, we observed a higher covert transmission rate.  
In previous covert communication studies, along with the optimization of transmission power, phase angles change. However, phase angles are rarely considered as an independent optimization parameter. In this work, we employ a 2-BPSK codebook and optimize the phase angles. Simulation results demonstrate that by solely optimizing the phase angles, a significant enhancement in covert transmission rates can be achieved. In scenarios 2 and 3, the improvement in covert transmission rates is 30% and 50%, respectively. Unlike traditional IRS covert communication, the 2-BPSK codebook we utilize offers greater feasibility, requiring no intricate flipping operations to achieve substantial enhancements in IRS covert communication rates. In future work, we plan to extend the codebook to an N-BPSK codebook and optimize all initial phase angles.  
Conceptualization, H.F. and X.J.; methodology, H.F. and R.Z.; software, H.F. and R.Z.; validation, H.F. and X.J.; writing--original draft preparation, H.F. and R.Z.; writing--review and editing, X.H. and S.Q.; visualization, X.H. and S.Q.; supervision, S.Q. and X.J.; funding acquisition, X.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant numbers U1836104, 61801073, 61931004, 62072250; the National Key Research and Development Program of China, grant number 2021 QY0700; and the Startup Foundation for Introducing Talent of NUIST, grant number 2021r039.  
**Institutional Review Board Statement:** Not applicable  
Figure 7: Covert communication performance in scenario 3. **(a)** Main view of covert transmission rate versus phase angles. **(b)** Top view of covert transmission rate versus phase angles.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.