Distance-Azimuth Joint Cramér-Rao Lower Bound for Spherical-wavefront-based Scatterer Localization

In our previous work a scatterer-localization algorithm based on maximum-likelihood estimation was derived using spherical wavefront assumption. Individual Cramér-Rao Lower Bounds (CRLBs) for distance and azimuth estimation were presented. As a continuation, we now derive a joint CRLB for both distance and azimuth. The novelty lying in the joint CRLB is that the underlying Fisher Information Matrix (FIM) is a non-diagonal partition matrix, yielding the fact that the CRLB obtained is tighter than the CRLBs derived individually. A closed-form representation of the approximate of the joint CRLB is presented which is expressed as a function of the FIM elements. Monte-Carlo simulations are performed to assess the validity and the accuracy of the derived bounds. Finally, the applicability of the derived CRLB is illustrated for vehicle or obstacle localization when a vehicle-mounted millimeter-wave environment-sensing system is considered.

I. Introduction

Multiple techniques are applied in the fifth generation (5G) communication systems [1], [2], some of which are based on large-scale antenna arrays, such as massive multiple-input multiple-output (MIMO) [3], hybrid-beamforming [4], scatterer localization [5], and so on. In large-scale antenna arrays, millimeter waves are commonly used, as they lead to a desirable physical size for the antenna arrays. A typical technique based on large-scale antenna arrays is the massive MIMO scenario, which is also a benchmark of 5G communication systems. To begin with, our work is based on a single-input multiple-output (SIMO) scenario, which can be the first step of massive MIMO researching. In our previous work presented in [5], we introduced the spherical wavefront assumption and a multidimensional parameter estimation algorithm derived based on the assumption. The parameters to estimate contain necessary information for localization of nearby scatterers in the premises of the communication end with large-scale antenna arrays mounted.