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In this paper, we propose a comprehensive framework to jointly analyze theangle estimation error and design the three-dimensional (3D) positioningalgorithm for a millimeter wave (mmWave) positioning system. First, we estimatethe angles of arrival (AoAs) at the anchors by applying the two-dimensionaldiscrete Fourier transform (2D-DFT) algorithm. Based on the property of the2D-DFT algorithm, the angle estimation error is analyzed in terms ofprobability density functions (PDF). The analysis shows that the derived angleestimation error is non-Gaussian, which is different from the existing work.Second, the intricate expression of the PDF of the AoA estimation error issimplified by employing the first-order linear approximation of trianglefunctions. Then, we derive a complex expression for the variance based on thederived PDF. Specifically, for the azimuth estimation error, the variance isseparately integrated according to the different non-zero intervals of the PDF.Finally, we apply the weighted least square (WLS) algorithm to estimate the 3Dposition of the MU by using the estimated AoAs and the obtained non-Gaussianvariance. Extensive simulation results confirm that the derived angleestimation error is non-Gaussian, and also demonstrate the superiority of theproposed framework.

Joint Angle Estimation Error Analysis and 3D Positioning Algorithm Design for mmWave Positioning System