Average minimum transmit power to achieve SINR targets: performance comparison of various user selection algorithms

In multi-user communication from one base station (BS) to multiple users, the problem of minimizing the transmit power to achieve some target-guaranteed performance (rates) at users has been well investigated in the literature. Similarly, various user selection algorithms have been proposed and analyzed when the BS has to transmit to a subset of the users in the system, mostly for the objective of sum rate maximization.We study the joint problem of minimizing the transmit power at the BS to achieve specific signal-to-interference-and-noise ratio (SINR) targets at users in conjunction with user scheduling. The general analytical results for the average transmit power required to meet guaranteed performance at the users' side are difficult to obtain even without user selection due to joint optimization required over beamforming vectors and power allocation scalars. We study the transmit power minimization problem employing non-linear dirty paper coding (DPC) technique and with various user selection algorithms, namely semi-orthogonal user selection (SUS), norm-based user selection (NUS), and angle-based user selection (AUS). Starting from the derivation of a transmit power upper bound (that becomes tight for large SINR targets), the average minimum transmit power is derived for NUS and SUS, for any number of users. For the special case when only two users are selected, we further derive a similar expression for AUS and a power lower bound, which may serve to benchmark the performance of any selection scheme. Simulation results performed under various settings indicate that SUS is by far the better user selection criterion.