Delay-optimal power control and performance analysis in SDMA system with limited buffer size via stochastic decomposition

In previous study on multi-user delay optimal problem, the exponentially increasing state space become one of the main obstacle. Moreover, packet drop due to finite buffer size is not taken into account. In this paper, we exploit the birth-death dynamics of the buffered SDMA systems and proposed a new approach, namely stochastic decomposition, to derive the delay optimal power adaptation scheme in a SDMA system. Unlike the conventional CSI-only power control solution, the delay-optimal power control has the multi-level water-filling structure in which the QSI determines the water-level and the CSI determines the power allocation across the SDMA users. This new approach overcomes the complexity issue mentioned above and allow us to obtain closed-form performance expressions so as to obtain the following first-order insights: 1) The water-filling levels {1/alpha_{k, q} Nmacr_k} under different QSIs q isin {1, 2, ...L} is an increasing geometric series. 2) The optimal average delay Umacr_k* achieved by the multilevel water filling algorithm is tau/O(log Pmacr_k + O(log log Pmacr_k) - lambda_k while that achieved by traditional CSI-only scheme is tau/O(log Pmacr_k) - lambda_k. 3) Minimum average power required to satisfy a packet drop rate constraint isin_d (due to finite buffer) is given by: log log(Pmacr_{k, min}) prop - log isin_d/L + log (lambda_k) + log (Nmacr_k).