**8. Summary**

use all spatial resources at the transmitter for the high SNR regime. The utility and metric based selection techniques achieve the same performance over all range of *K*. The NSP approximation metric in [26] achieves more than 95% of the optimum capacity and the performance gap reduces as the number of users increases. Notice that the approach in Section 6.3 optimally solves problem (24) and its performance is an upper bound for the user selection in [26]. The performance of all approaches presented in Section 6 is suboptimal, yet they represent different and acceptable trade-offs between sum rate perform‐ ance, computational complexity, and multiplexing gain for different values of *K* and the

In Fig. 5 the average sum rate is a function of the SNR for ZFBF and *K* =10. The results show that for *P* <*P*<sup>0</sup> ≈10(dB) the utility-based selection is more efficient than the metricbased selection in the low SNR regime. In the high SNR regime the performance gap between the optimum selection and the approaches in Section 6 is less than 10%. Observe that even the NSP approximation metric in [26] can efficiently exploit multiuser diversity and the approaches based exclusively on channel magnitudes (MCG) and random selec‐ tion incur in a large performance degradation. Comparing the performance of the utilitybased versus the metric-based user selection is in general not fair since the former will optimize directly its utility function while the latter attempts to reduce computational complexity by optimizing a simpler utility function. The performance gap between the two approaches is large for low SRN and *K* regimes. The reason is that the former directly optimizes the set of selected users while the latter indirectly estimates if a given set can maximize the sum rate. In the high SNR regime, the gap between both approaches diminishes and results in [18] show that the achievable sum rate in both approaches is

proportional to the number spatial resources *Nt* at the transmitter.

**Figure 4.** Average sum rate versus the number of users (*K*) with SNR =18 (*dB*) and *Nt* =4 for (a) ZFBF and (b) ZFDP.

SNR regime.

46 Contemporary Issues in Wireless Communications

In this chapter, we have presented several metrics and techniques for user selection in multiuser MISO scenarios. This topic has been object of extensive research over the last years for different wireless scenarios. Several metrics that evaluate spatial compatibility, matrix invertibility, pairwise orthogonality, and eigenvalue dispersion were presented and compared for the sum rate maximization with user selection problem. Results show that the null space projection and its approximations are the metrics that most efficiently identify the set of users that maximizes the sum rate for both precoders ZFBF and ZFDP. Since the optimal user selection for sum rate maximization is a complex combinatorial problem different sub-optimal selection strategies were presented. The metric-based and utility-based techniques compute the user selection in a greedy fashion finding close-to-optimal solution. The metric-based selection was reformulated as an integer program selection which provides an upper bound of the performance of a metric based on the null space projection. Numerical results show that depending on the multiuser diversity and SNR regime one strategy of user selection can be preferred over the others reaching a fair trade-off between performance and complexity.
