Error Bounds for 3D Localization and Maximum Likelihood Estimation of mm-Wave MISO OFDM Systems in the Presence of Hardware Impairments

Millimeter-wave (
$mm$
-wave) multiple-input single-output (MISO) systems are expected to be extremely advantageous for the fifth generation (5G) cellular systems. In fact, these systems are considered key enablers of centimeter-level localization accuracy, even in the case of a single base station (BS). However, there are still fundamental issues that need to be addressed when applying
$mm$
-wave MISO systems to practical scenarios, namely the effects of hardware impairments (HWIs). In this study, the 3D localization accuracy of
$mm$
-wave MISO OFDM systems is investigated when there are HWIs at both the BS and the mobile station (MS). The localization is performed by estimating the downlink channel parameters of the line-of-sight (LOS) path using only a maximum likelihood (ML) estimator at the MS. We then transform these channel parameters into ones for localization. The Fisher information matrix (FIM) is employed to assess the accuracy of the estimation processes, considering also any non-LOS (NLOS) paths. The limit of localization is calculated in terms of the position error bound (PEB). Computer simulations demonstrate the destructive impacts of HWIs on the localization process. Moreover, it was proven that the effect of NLOS paths from unknown scatters on the localization process is related to the ratio between LOS and NLOS path gains.