# Non-Coherent Direction-of-Arrival Estimation Using Partly Calibrated Arrays

## TL;DR

This paper explores non-coherent DOA estimation with partly calibrated arrays, demonstrating the potential to identify more sources than individual subarrays and deriving estimators and bounds to evaluate performance.

## Contribution

It introduces a novel non-coherent processing scheme for partly calibrated arrays, proving source identifiability beyond individual subarrays and deriving the MLE and CRB for this setup.

## Key findings

- Non-coherent processing can identify more sources than individual subarrays.
- The derived CRB approaches zero at high SNR only if a subarray can identify sources.
- A sufficient condition for source identifiability in non-coherent systems is established.

## Abstract

In this paper, direction-of-arrival (DOA) estimation using non-coherent processing for partly calibrated arrays composed of multiple subarrays is considered. The subarrays are assumed to compute locally the sample covariance matrices of their measurements and communicate them to the processing center. A sufficient condition for the unique identifiability of the sources in the aforementioned non-coherent processing scheme is presented. We prove that, under mild conditions, with the non-coherent system of subarrays, it is possible to identify more sources than identifiable by each individual subarray. This property of non-coherent processing has not been investigated before. We derive the Maximum Likelihood estimator (MLE) for DOA estimation at the processing center using the sample covariance matrices received from the subarrays. Moreover, the Cramer-Rao Bound (CRB) for our measurement model is derived and is used to assess the presented DOA estimators. The behaviour of the CRB at high signal-to-noise ratio (SNR) is analyzed. In contrast to coherent processing, we prove that the CRB approaches zero at high SNR only if at least one subarray can identify the sources individually.