# IRS-Enabled Ultra-Low-Power Wireless Sensor Networks: Scheduling and Transmission Schemes
## 6 Results
However, this is not the case for the benchmark; it can be seen that when \(L\) is larger the average throughput is improved, which is because we are maximizing over a larger sample from the same channel distribution, and have a higher chance of finding a stronger channel. For \(L=100\), OS with random phases at the IRSs surpasses RR scheduling with optimal phases, which is due to opportunistic beamforming and multi-sensor diversity gains being exploited [18]. Under this setup, we can conclude that the choice of scheduling is more significant than the choice of phases at the IRSs. On the other hand, for \(L=10\), OS gains are smaller, as there is less multi-sensor diversity; hence, OS performs worse than RR with optimal phases. Figure 10 shows the effect of the number of IRS elements \(N\) in the system on the performance of OS. A larger number of IRS elements \(N\) places a higher importance on the choice of the optimal phases. The search space of phases grows exponentially with \(N\), and  
Figure 8: Minimum ISN throughput versus transmitting power for different scheduling protocols. the probability of randomly choosing a configuration close to its optimal configuration decays exponentially; thus, multi-sensor diversity does not occur, and as a result RR with optimal phases outperforms OS in this case. We can conclude that OS gains are highlighted for smaller \(N\), and that OS is virtually ineffective for larger \(N\). In practice, the phase shifts at the IRSs are from a discrete set. In this work, we assume that we are working with continuous phases, yet show the advantage of our work in the case of practical IRSs with discrete phases. For instance, Figure 11 shows the close performance between the BER of the continuous-phase IRS compared to a one-bit IRS that can only choose phases from a set \(\mathcal{S}_{1}=\{0,\pi\}\) or a two-bit IRS that can only choose phases from a set \(\mathcal{S}_{2}=\{0,\pi/2,\pi,\frac{3\pi}{2}\}\). The way to choose quantized phases is to consider the desired phase shift vector \(\mathbf{v}_{l}^{*}\) for ISN \(l\) and choose from the set of feasible phases; for instance, for a one-bit IRS, each element can be chosen such that  
Figure 10: Average system throughput vs. transmitting power for OS with random phases and RR scheduling with optimal IRS configuration \(\mathbf{\Theta}_{l}^{*}\), where \(L=100\). Figure 9: Average system throughput vs. transmitting power for optimal IRS configuration \(\mathbf{\Theta}_{l}^{*}\) with greedy scheduling, OS with random phases, and optimal IRS configuration \(\mathbf{\Theta}_{l}^{*}\) with RR scheduling, where \(N=8\). \[\theta_{n}^{\theta_{n}^{\star}}=\underset{\theta_{n}^{\theta_{n}^{\star}}\in\mathcal{ S}_{1}}{\text{arg min}}\|\theta_{n}^{\star}-\theta_{n}^{\theta_{n}^{\star}}\|_{2} \tag{46}\]  
In addition, it can be seen that quantization effects are noticeable when the IRS is configured optimally. On the other hand, quantization minutely affects the BER with random phases chosen at the IRS. Because random phases are deployed when using OS, it is apparent that assuming practical quantization in the system has no adverse effect on the resulting BER, which is an advantage. In the next section, we compare a transmitter-equipped sensor and an ISN in terms of power consumption and range.