Channel Model Mismatch Analysis for XL-MIMO Systems from a Localization Perspective

Abstract

Radio localization is applied in high-frequency (e.g., mmWave and THz) systems to support communication and to provide location-based services without extra infrastructure. For solving localization problems, a simplified, stationary, narrowband far-field channel model is widely used due to its compact formulation. However, with increased array size in extra-large multiple-input-multiple-output (XL-MIMO) systems and increased bandwidth at upper mmWave bands, the effect of channel spatial non-stationarity (SNS), spherical wave model (SWM), and beam squint effect (BSE) cannot be ignored. In this case, localization performance will be affected when an inaccurate channel model deviating from the true model is adopted. In this work, we employ the misspecified Cramér-Rao lower bound to lower bound the localization error using a simplified mismatched model while the observed data is governed by a more complex true model. The simulation results show that among all the model impairments, the SNS has the least contribution, the SWM dominates when the distance is small compared to the array size, and the BSE has a more significant effect when the distance is much larger than the array size.

Toward 6G Holographic Localization: Enabling Technologies and Perspectives

“…Such models that capture the coupling between the distance and angles in the near-field can be found in [10] and [6], [11] for ELAA and RIS, respectively. Novel positioning algorithms that exploit holographic localization are required, as current far-field-based algorithms encounter an additional positioning error due to the model mismatch when the user is in the near-field [12]. To this aim, in the following, we illustrate (i) the latest contributions for establishing the localization performance limits in RIS-aided scenarios; (ii) some of the localization algorithms and their complexity.…”

“…Moreover, this put in evidence the need of having a proper RIS phase design, which is still challenging when RISassisted localization is performed. Further numerical results for holographic localization can be found in [6], [9]- [12].…”

Misspecified Cramér-Rao Bound of RIS-Aided Localization Under Geometry Mismatch

“…Note that we omit the constant term and the parameter p b as they do not affect the estimation. Now, the lower bound matrix of the estimation mean squared error (MSE) based on f M can be obtained as [12] LBM(r, r)…”

“…When using MCRB, the assumed channel model is different from the true model, and a misspecified performance bound can be derived with the model mismatch considered. The MCRB analysis for radio localization under hardware impairment [11] and channel model mismatch [12] have been reported in previous works. In the MCRB derivation, one of the most essential steps is determining the pseudo-true parameters [10], which is to find a solution that minimizes the Kullback-Leibler divergence (KLD) between the true and mismatched statistical models and is usually accomplished using numerical methods [11,12].…”

“…The MCRB analysis for radio localization under hardware impairment [11] and channel model mismatch [12] have been reported in previous works. In the MCRB derivation, one of the most essential steps is determining the pseudo-true parameters [10], which is to find a solution that minimizes the Kullback-Leibler divergence (KLD) between the true and mismatched statistical models and is usually accomplished using numerical methods [11,12]. In this work, we aim to derive the MCRB to evaluate the impact of RIS geometry mismatch on RIS-assisted localization.…”