Sparsity based off-grid blind sensor calibration

Compressive Sensing (CS) based techniques generally discretize the signal space and assume that the signal has a sparse support restricted on the discretized grid points. This restriction of representing the signal on a discretized grid results in the off-grid problem which causes performance degradation in the reconstruction of signals. Sensor calibration is another issue which can cause performance degradation if not properly addressed. Calibration aims to reduce the disruptive effects of the phase and the gain biases. In this paper, a CS based blind calibration technique is proposed for the reconstruction of multiple off-grid signals. The proposed technique is capable of estimating the off-grid signals and correcting the gain and the phase biases due to insufficient calibration simultaneously. It is applied to off-grid frequency estimation and direction finding applications using blind calibration. Extensive simulation analyses are performed for both applications. Results show that the proposed technique has superior reconstruction performance.