| Summary: | This paper investigates the sum capacity of a single-cell multi-user system under the constraint that the transmitted signal is adopted from M-ary two-dimensional constellation with equal probability for both uplink, i.e., multiple access channel (MAC), and downlink, i.e., broadcast channel (BC) scenarios. Based on the successive interference cancellation (SIC) and the entropy power Gaussian approximation, it is shown that both the multi-user MAC and BC can be approximated to a bank of parallel channels with the channel gains being modified by an extra attenuate factor that equals to the negative exponential of the capacity of interfering users. With this result, the capacity of MAC and BC with arbitrary number of users and arbitrary constellations can be easily calculated which in sharp contrast with using traditional Monte Carlo simulation that the calculating amount increases exponentially with the increase of the number of users. Further, the sum capacity of multi-user under different power allocation strategies including equal power allocation, equal capacity power allocation and maximum capacity power allocation is also investigated. For the equal capacity power allocation, a recursive relation for the solution of power allocation is derived. For the maximum capacity power allocation, the necessary condition for optimal power allocation is obtained and an optimal algorithm for the power allocation optimization problem is proposed based on the necessary condition.
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