Capacity analysis and optimisation of OFDM with distortionless PAPR reduction

We analyse the impact of distortionless peak-to-average power ratio (PAPR) reduction methods on the ergodic capacity of orthogonal frequency division multiplexing (OFDM) systems in AWGN and frequency selective channels. We consider the following tradeoff: decreasing PAPR increases the efficiency of the linear power amplifier (PA), yielding an increase in the average power emitted and consequentially an increase in capacity, However, implementing distortionless PAPR reduction methods requires the allocation of power and/or bandwidth, which causes a decrease in capacity. We evaluate this tradeoff by deriving a lower bound on the required increase in PA efficiency to achieve capacity gain, and an expression for the achievable increase in PA. efficiency. We resolve this tradeoff by optimising key method parameters to achieve maximal ergodic capacity. We apply the analysis to three representative methods: selected mapping (SLM), tone reservation (TR) and tone injection (TI). Their corresponding optimal number of candidates, number of reserved tones and constellation sizes are derived as a function of channel conditions. We demonstrate how capacity could be lost in common practical scenarios, and suggest practical means for achieving capacity gains which are very close to optimal for each representative method. The analysis may be applied to other PAPR reduction methods as well.