Nonlinear distortion stemming from low-cost power amplifiers may severely affect wireless communication performance through out-of-band (OOB) radiation and in-band distortion. The distortion is correlated between different transmit antennas in an antenna array, which results in a beamforming gain at the receiver side that grows with the number of antennas. In this paper, we investigate how the strength of the distortion is affected by the frequency selectivity of the channel. A closed-form expression for the received distortion power is derived as a function of the number of multipath components (MPCs) and the delay spread, which highlight their impact. The performed analysis, which is verified via numerical simulations, reveals that as the number of MPCs increases, distortion exhibits distinct characteristics for in-band and OOB frequencies. It is shown that the received in-band and OOB distortion power is inversely proportional to the number of MPCs, and it is reported that as the delay spread gets narrower, the in-band distortion power is beamformed towards the intended user, which yields higher received in-band distortion compared to the OOB distortion.

翻译：由低成本功率放大器引起的非线性失真可能通过带外辐射和带内失真严重影响无线通信性能。在天线阵列中，不同发射天线之间的失真具有相关性，这导致接收端产生随天线数量增长而增强的波束赋形增益。本文研究了信道频率选择性对失真强度的影响规律。我们推导出接收失真功率的闭式表达式，将其表示为多径分量数量和时延扩展的函数，揭示了这两个参数的关键作用。通过数值仿真验证的分析结果表明：随着多径分量数量的增加，带内和带外频率的失真呈现出不同特性。研究显示，接收端带内和带外失真功率与多径分量数量成反比，并且当时延扩展变窄时，带内失真功率会向目标用户方向形成波束赋形，导致接收端带内失真功率高于带外失真功率。