## 5 Simulation and Results
On the other hand, the 'alternating optimisation' technique continues optimising the variables iteratively until a reasonable accuracy is obtained. Let us assume that the computational complexity of problem (P1) is in the order of \(\mathcal{O}(Q_{1}(n))\) and that of problem (P2) is \(\mathcal{O}(Q_{2}(n))\), where \(n\) is the number of optimisation variables. Then the complexity order of the 'SDR' method is \(\mathcal{O}(Q_{1}(n))+\mathcal{O}(Q_{2}(n))\), whereas the complexity of the 'alternating optimisation' technique is in the order of \(t(\mathcal{O}(Q_{1}(n))+\mathcal{O}(Q_{2}(n)))\), where \(t\) is the number of iterations. The 'random phase shift' method does not optimise the IRS phase-shift variable \(\mathbf{\Theta}\) and hence requires significantly lower computational tasks. The MRT and the 'without IRS' schemes are much simpler schemes and have even lower computational complexities. However, with the emergence of modern computational power combined with machine learning, computational resources are no longer a major bottleneck for many applications. For scenarios where system efficiency is a priority, the proposed 'alternating optimisation' is the preferred method at affordable costs. _(2) Transmit Power at AP versus AP-IRS Distance:_ In Figure 3, the asymptotic performances of IRS passive beamforming with respect to the movement of IRS's position horizontally has been analysed. In Figure 3 the distance between AP and user (e.g., d = 70) is constant. Then the IRS's position is moved form (e.g., \(d_{0}\) = 30 to 70). It can be seen that  
Figure 3: Transmit power at AP vs. AP-IRS distance (\(d_{0}\)) when user distance (\(d=70\)). the transmit power of AP is maximum at the starting point which have gradually decreased through the starting point to the position near the user. The more the IRS is moved nearer to the user's position, the lower the required transmit power. The alternating optimisation algorithm demonstrates a constant power consumption to a certain point and then it starts gradually decreasing at low power transmission at AP with respect to the distance between AP and IRS. In Figure 4, the distance between AP and user (e.g., \(d=50\)) is constant; then, the IRS's position has moved form (e.g., \(d_{0}=30\) to 70). It can be seen that the transmit power of AP is maximum at the starting point and at the ending point. When the IRS's position moved to the user's position, then the power consumption became gradually low. It can also be seen that the mirror reflection in the next movement. The transmit power became 14 dBm when the distance between IRS and user was the lowest. The more the IRS approaches the user's position, the lower the transmit power. The alternating optimisation technique has shown a constant power consumption initially to a certain point and then it started gradually decreasing near the user's position and then it started increasing like a mirror reflection when it started moving far from the user's position. Finally, it again shows a constant transmission-power at AP with respect to the distance of AP-IRS. In Figure 5, the distance between AP and user (e.g., \(d=30\)) is constant. Then the IRS's position changed form (e.g., \(d_{0}=30\) to 70). It can be seen that the transmit power of AP is at the minimum at the starting point. When the IRS's position moved far from the user's position, then the power consumption became gradually higher. Here, the transmit power became nearly 29 dBm when the distance between IRS and user was the highest. The farther the IRS is from the user's position, the higher the transmit power. Here, alternating optimisation technique has shown initially a little increment in power consumption to a certain point and then it has shown a constant power transmission at AP with respect to the distance of AP-IRS. Figure 4: Transmit power at AP vs. AP-IRS distance (\(d_{0}\)) when user distance (\(d=50\)).