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Analog beamforming technology is being used to overcome various technical drawbacks of mm-wave wireless communications systems. However, the errors caused by circuit implementations, quantized control, and imperfect isolation between antenna elements result in radiation pattern (RP) distortion and performance deterioration. In particular, the quantization error and mutual coupling cause the active reflection coefficient (ARC) of each antenna element to vary with respect to the main beam direction, resulting in statistical behavior changes depending on steering angles. In this article, we derive the statistical behavior of RPs with all those dominant errors taken into account. The analysis reveals that Beckmann distribution offers the exact solution for the cumulative distribution of the sidelobe level (SLL), which is very consistent with a Monte Carlo simulation including the ARC. In addition, the Rician distribution reflecting the three errors exhibits overall good accuracy, with inherent deviation from the Monte Carlo simulation results at certain steering angles due to the approximation of uncorrelated RPs and identical variances that are not valid in real antenna arrays. Our analysis also indicates that, to define the maximum probability of exceeding a certain SLL, the variance and correlation should be considered along with the mean of the RPs.

Accurate Statistical Model of Radiation Patterns in Analog Beamforming Including Random Error, Quantization Error, and Mutual Coupling