Applying bussgang's theorem to fixed-gain OFDM-based relay networks: A profile decay analysis
Nidhi Simmons, Hachem Yassine, Justin P. Coon · 2017
In recent years, Bussgang's theorem has proven useful when studying and optimizing peak-power constrained OFDM-based amplify-and-forward (AF) networks. For the variable-gain (VG) scenario, Bussgang's theorem can be applied at the relay without taking into consideration the instantaneous behavior of the channel. This significantly improves the mathematical tractability of performance evaluation. For fixed-gain (FG) relaying, this is not necessarily the case, and we must also ensure that a sufficient number of significant channel taps are present in the channel response if we wish to ignore the channel's instantaneous behavior. In this paper, we determine conditions that the power-decay profile of the channel's l tap response must satisfy so that, in the limit of large l the FG Bussgang parameters become independent of the channel's instantaneous behavior. We conclude our analysis by considering some examples (exponential and power-law decay profiles). For exponential profiles we find that exact calculation of the Bussgang parameters always requires instantaneous channel knowledge, regardless of the number of channel taps present; while for power-law profiles this is not necessarily the case, provided the decay is not too steep.