# Hybrid MU-MIMO Precoding Based on K-Means User Clustering
## 6 Simulations  
This section evaluates the performance in terms of the average sum rate and computational complexity of the presented precoding schemes. Spatio-temporally-correlated channels and perfect channel estimation were assumed. Monte Carlo simulations were performed in a single-cell MU-MIMO system with \(N_{T}=16\) and \(K=16\) single-antenna users. A 16 QAM modulation was used throughout the simulations. We assumed the channel changed non-coherently from one block to another. Figure 8 evaluates the sum rate performance of the RZF and THP precoding schemes as a function of \(E_{b}/N_{0}\) and the inter-user angular separation, when the users were equally spaced with an angle \(\theta=\theta_{\text{min}}\). The performance of both schemes decreased as the users became closer to each other; however, THP always outperformed RZF since it employs a more sophisticated successive interference cancellation technique. For example, to reach the 50 b/s/Hz, RZF requires 17 dB more \(E_{b}/N_{0}\) when \(\theta_{\text{min}}=1^{\circ}\) than when \(\theta_{\text{min}}=5^{\circ}\). In the same scenario, THP requires just 8 dB more \(E_{b}/N_{0}\). Although these results reflect the performance under equal angle separation, this is the lower bound in a worst case scenario, and similar trends are expected when certain users are separated at different angles. To plot the sum rate performance of a hybrid BD-THP precoding scheme in Figure 9, it was assumed that the users could be grouped into four groups located at \(\theta_{g}=[-45^{\circ},-15^{\circ},15^{\circ},45^{\circ}]\). The users within each group were uniformly spread around \(\theta_{g}\) and were equally spaced with an angle of \(1^{\circ}\). As the minimum angle between any two groups was \(30^{\circ}\) and between any two users of the same group was \(1^{\circ}\), we could apply a linear precoding scheme between groups and non-precoding within the groups. The performance of hybrid BD-THP precoding was better than the RZF precoding, except for low values of \(E_{b}/N_{0}\), as BD did not account for the noise enhancement. In the following, the user groping algorithm and the performance of precoders are evaluated, accounting for a realistic user spatial distribution. In Figures 10 and 11, Sector B2 serves users spread using two different traffic distributions, in a 120\({}^{\circ}\) azimuth. The first distribution captured the working day traffic from the morning and the evening hours (busy hours) and the second, in between (working hours). Due the mobility of users, the busy hour traffic was spread more than during the working hours, when it was concentrated in hotspots (around office buildings). To limit the performance degradation of linear precoding schemes, the required angular separation between clusters was set to 30\({}^{\circ}\). This resulted in users being grouped into four clusters for the working hour user distribution and in three clusters during busy hours. Figure 10: Working hour user distribution and clustering for Sector B2 and \(\Delta\theta=30^{\circ}\). In practice, the AoA is not always perfectly estimated. For that, in Figures 12 and 13, we evaluated the impact of the AoA estimation error on the clustering algorithm's performance. The AoA estimation error was modeled as a normal random variable, with zero mean and a variable standard deviation. Because the angles between users were computed by the K-means clustering algorithm, the error was added to the actual coordinates of the users. In Figure 12, the probability of grouping users into the same clusters (as in the ideal case of perfect AoA estimation) was investigated for different values of the standard deviation error and number of clusters. As expected, as the AoA error increased, the probability of assigning users in the same clusters decreased. The impact was even higher when the number of clusters increased. Figure 11: Busy hour user distribution and clustering for Sector B2 and \(\Delta\theta=30^{\circ}\).