Analysis of minimum transmit sum power and scheduling power gain for multi-user MIMO-OFDM networks with rate constraints

Minimum transmit sum power (MTSP) is of high theoretical and practical value in multi-user rate-constrained systems; it is, however, quite difficult to be numerically characterized in complex channels for the prohibitively high computational power required. In this paper, we present a computationally efficient method to approximate the MTSP in multi-user multiple-input multiple-output orthogonal frequency division multiplexing (MU-MIMO-OFDM) wireless networks. Specifically, we propose both lower and upper bounds of the MTSP, which are asymptotically accurate in the limit of large K, the number of users. Then, we develop two iterative water-filling algorithms to numerically solve the proposed bounds. These algorithms are with low complexity, that is, linear in K, and therefore enable the analysis of MTSP in complex channels even if K is large. Numerical results demonstrate the effectiveness of the bounds in approximating the MTSP and the high computational efficiency of the proposed iterative water-filling algorithms. With the proposed bounds, we further numerically study scheduling power gain (SPG), which is defined as MTSP reduction achieved by scheduling resources over multiple channel blocks in time domain. We simulate the SPG in different wireless environments defined in Third Generation Partnership Project spatial channel extended model and find insignificant SPG in some cases, indicating that the benefit from scheduling over multiple channel blocks is limited and simply allocating resources within the present channel is sufficient. Our analysis on the MTSP and SPG provides guidelines on the design of resource schedulers in MU-MIMO-OFDM networks.