Energy Minimization of a QAM System with Fading

In this paper, the problem of choosing constellation size and transmit power that minimizes the energy-per-goodbit in a frequency-flat, long-term static fading channel is considered. A goodbit is a bit that is received without error. A low-complexity, near-optimal algorithm to find constellation size and transmit power is presented. Although perfect Channel State Information (CSI) at the transmitter is assumed, fading can cause situations where the system cannot meet user constraints on acceptable performance. The implications of this type of system outage and the consequent trade-off between energy-efficiency and range are discussed. Assuming that the fading process is ergodic, the average energy-efficient spectral efficiency can be computed for various fading distributions of interest. As an application of the techniques developed, we evaluate, by simulation, the average minimum energy-per-goodbit for a Rayleigh fading channel and note that over a short range of distances (1m to 10m), it can cost at most 1 dB more than for the corresponding non-fading AWGN channel. We also show that the restriction of using only a square-QAM constellation does not incur a large penalty in cost.