The effect of constellation size on energy efficiency of Multi carrier Direct Sequence code-division multiple-access (MC DS/ CDMA) system for M-QAM modulation is studied using a game theoretic approach. A non cooperative game is proposed in which each user seeks to choose its transmit power, transmit symbol rate as well as the constellation size in order to maximize its own utility while satisfying its delay quality of service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed and it is particularly suitable for energy-constrained networks. It is shown that in order to maximize the user's utility, a user must choose the lowest constellation size that can accommodate the user's delay constraint. This strategy is different from one that could maximize spectral efficiency. Using this approach, the trade offs among energy efficiency, delay, throughput and constellation size are also studied and quantified.
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