Asymptotic Capacity Loss Under Spectral Leakage Constraints for Weakly Nonlinear Transmitters

We investigate and elaborate upon a folklore in wireless communication systems that, when the nonlinearity at a transmitter is sufficiently weak so that the resulting spectral leakage is at a sufficiently low level, the capacity of the channel (including the transmitter) should be sufficiently close to the ideal channel capacity without transmitter nonlinearity. The context for this study is that effective predistortion techniques have been widely applied to linearize the transmitter nonlinearity in modern wireless communication systems, so as to render the electromagnetic radiation pattern to satisfy stringent spectral regrowth requirements. Based on the quasi-memoryless/memory polynomial model for the transmitter nonlinearity, via an information-theoretic approach, our study affirmatively validates the folklore, and more importantly, characterizes a quantitative relationship between the spectral leakage level and the capacity loss. Specifically, we prove that as the adjacent channel power ratio (ACPR) asymptotically vanishes, the capacity loss is upper bounded by a term that is proportional to the ACPR. We also establish a converse result, and further extend our results to spatial beamforming.