## 4 Numerical Simulation Analysis
In terms of sub-connected structure, according to Formula (23), both Nsw and Nps have nothing to do with N\({}_{\text{rf}}^{\text{t}}\), while they both increase linearly with N\({}_{\text{rf}}^{\text{t}}\) in the fully connected structure. Therefore, as N\({}_{\text{rf}}^{\text{t}}\) increases, the energy consumption of the fully-connected structure increases much faster than that of the sub-connected structure, which means the denominator in Formula (22) increases faster, and because the spectral efficiency(SE) of OMP algorithm is already close to the full-digital precoding, according to Figure 3, the increase in the RF chains only brings about a little increase in spectral efficiency, which is the numerator in Formula (22), thus leading to a continuous drop in its energy efficiency(EE). While the spectral efficiency of the proposed IAAM algorithm increases rapidly with N\({}_{\text{rf}}^{\text{t}}\) at first, but the increase slows down after the number of RF chains exceeds 8, thus its energy efficiency experiences a slight increase at first. Later, it also decreases with the increase in N\({}_{\text{rf}}^{\text{t}}\), but because its overall energy consumption increases slower than the fully-connected structure, its overall energy efficiency declines slower than the fully-connected based OMP algorithm. It can be seen from Figure 4 that the energy efficiency of the proposed sub-connection-based IAAM algorithm is much higher than that of the fully-connected OMP algorithm, and the performance gap gradually expands with the increase in N\({}_{\text{rf}}^{\text{t}}\). Figure 4: The average Energy Efficiency versus N\({}_{\text{rf}}^{\text{t}}\) with SNR = 10 (dB). Since the proposed IAAM algorithm needs to be processed in two steps: Algorithms 1 and 2, and Algorithm 1 involves alternating minimization, the convergence speed is also worthy of attention. Figure 5 shows the simulation result of the spectral efficiency of the IAAM algorithm under three different \(\mathrm{N}_{\mathrm{rf}}^{t}\) and three different SNR with iteration times. When \(\mathrm{N}_{\mathrm{rf}}^{t}\) increases, the result of Formula (20) will be closer to the optimal [15], which makes the performance of the initial value calculated by Algorithm 2 more effective. An excellent initial value can naturally ucethe iteration times requi for convergence. It can be seen from Figure 5 that that, regardless of SNR = 5, 10, 15 dB, when \(\mathrm{N}_{\mathrm{rf}}^{t}\) = 4, 8, and 12, the numbers of iterations requi for convergence are about 8, 4, and 2, respectively, indicating that the larger \(\mathrm{N}_{\mathrm{rf}}^{t}\), the lower the algorithm's time complexity, and the better the spectral efficiency performance. Additionally, combined with the conclusion of the energy efficiency simulation result in Figure 4, it can be concluded that this scheme is very practical when the number of RF chains is large, and the energy efficiency is higher than that of the fully-connected hybrid precoding and the algorithm complexity is also low. After discussing the number of iterations requi for algorithm convergence, the technological complexity of each iteration also needs to be analyzed. For Algorithm 1, the complexity is dominated by getting the pseudo-inverse of the analog precoding matrix when calculating digital precoder, which brings about \(\mathrm{O}\big{(}\mathrm{N}_{\mathrm{rf}}^{2}\mathrm{N}_{\mathrm{rf}}^{t} \big{)}\) computations. For Algorithm 2, the computational complexity can be divided into three parts--initially grouping, checking for empty subset and phase modulation--with a total complexity of \(\mathrm{O}\big{(}N_{\mathrm{rf}}N_{\mathrm{rf}}^{t}+2 LN_{\mathrm{rf}}N_{\mathrm{ rf}}^{t}+N_{\mathrm{f}}\big{)}\), in which L denotes the number of empty subsets after the first round antenna grouping, and we found that the value of L is always 0 after intensive simulation.