Fundamental Limit of Angular Resolution in Partly Calibrated Arrays with Position Errors

We consider high angular resolution detection using distributed mobile platforms implemented with so-called partly calibrated arrays, where position errors between subarrays exist and the counterparts within each subarray are ideally calibrated. Since position errors between antenna arrays affect the coherent processing of measurements from these arrays, it is commonly believed that its angular resolution is influenced. A key question is whether and how much the angular resolution of partly calibrated arrays is affected by the position errors, in comparison with ideally calibrated arrays. To address this fundamental problem, we theoretically illustrate that partly calibrated arrays approximately achieve high angular resolution. Our analysis uses a special characteristic of Cramer-Rao lower bound (CRB) w.r.t. the source separation: When the source separation increases, the CRB first declines rapidly, then plateaus out, and the turning point is close to the angular resolution limit. This means that the turning point of CRB can be used to indicate angular resolution. We then theoretically analyze the declining and plateau phases of CRB, and explain that the turning point of CRB in partly calibrated arrays is close to the angular resolution limit of distributed arrays without errors, demonstrating high resolution ability. This work thus provides a theoretical guarantee for the high-resolution performance of distributed antenna arrays in mobile platforms.

Direction Finding in Partly Calibrated Arrays Exploiting the Whole Array Aperture

We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve this goal, existing algorithms, such as subspace separation and sparse recovery, have to rely on multiple snapshots, which increases the burden of data transmission and the processing delay. Therefore, we aim to enhance angular resolution using only a single snapshot. To this end, we exploit the orthogonality of the signals of partly calibrated arrays. Particularly, we transform the signal model into a special multiple-measurement model, show that there is approximate orthogonality between the source signals in this model, and then use blind source separation to exploit the orthogonality. Simulation and experiment results both verify that our proposed algorithm achieves high angular resolution as distributed arrays without position errors, inversely proportional to the whole array aperture.