Blind Calibration of Sparse Arrays for DOA Estimation with Analog and One-bit Measurements

Abstract

In this paper, the focus is on the gain and phase calibration of sparse sensor arrays to localize more sources than the number of physical sensors. The proposed technique is a blind calibration method as it does not require any calibrator sources. Joint estimation of the gain errors, phase errors, and source directions is a complicated non-convex optimization problem, which is transformed into a convex optimization problem by exploiting the underlying algebraic structure. It is shown that the developed solver is suitable for analog as well as one-bit measurements. Numerical experiments based on sparse rulers are provided to illustrate the developed theory.

Blind calibration for arrays with an aberration layer in ultrasound imaging

“…See e.g. [16] for tackling this problem structure, or [17]- [19] for solving this problem from covariance data.…”

One-Bit DoA Estimation via Sparse Linear Arrays

“…The aforementioned research works considered using ULAs for onebit DoA estimation. Exploitation of SLAs for one-bit DoA estimation has been studied in [53][54][55][56]. The authors in [53] deployed the arcsine law [52] to reconstruct the ASCM from one-bit SLA data.…”

“…Cross-dipoles sparse arrays were deployed in [55] to develop a method for one-bit DoA estimation which is robust against polarization states. In [54], the authors proposed an approach to jointly estimate DoAs and array calibration errors from one-bit data.…”

Joint Blind Calibration and Time-Delay Estimation for Multiband Ranging

“…To evaluate the performance of the calibration, we use the average RMSE of the gain estimates over all the subcarriers and bands. The RMSE are computed using 10 3 independent Monte-Carlo trials and compared with RMSEs of the algorithms proposed in [18,22] which are shortly denoted with ALMIN and BLC, respectively. The original formulation of the BLC algorithm does not require knowledge of the noise covariance Σw, as the authors in [22] assume that the nonideal response of the sensor array is affecting both signal and noise.…”

“…Therefore, we propose to re-cast the biconvex optimization problem as a rank-1 constrained linear system using the lifting technique [19][20][21], which can be solved efficiently as a group Lasso problem. The proposed algorithm is benchmarked through simulations by comparing its performance with algorithms proposed in [18,22]. The results show that the proposed algorithm provides better calibration performance and a higher resolution for TD estimation.…”