Joint blind calibration for multichannel compressed sampling systems

With the rapid advancement of radar and communication systems, multichannel compressed sampling architectures have emerged as a pivotal solution for high-frequency and wideband signal acquisition. However, practical implementations are inevitably plagued by non-ideal factors, particularly unknown gain-phase errors and inter-channel mutual coupling, which severely degrade signal reconstruction accuracy. Existing calibration methods primarily focus on array manifolds or depend on prior knowledge, often proving inadequate for addressing the distinct measurement matrix structures in compressed sampling systems. To address this limitation, we propose a joint blind calibration framework that enables simultaneous sparse signal recovery and system error correction in multichannel compressed sampling systems, eliminating the need for dedicated test signals or auxiliary calibration equipment. We reformulated the joint calibration problem as a multilinear inverse problem, which is further transformed into an eigenvector/eigenvalue optimization task solvable via a dual-projection gradient descent algorithm. The main work of this paper lies in providing a theoretical analysis of eigenvalue distribution ranges and perturbation bounds for proposed eigenvector-solving problem. These analyses reveal that the eigenvalue gap is governed by mutual coupling attenuation coefficients, ensuring algorithmic convergence under practical noise conditions. Extensive numerical experiments validate the method's superiority. Notably, the theoretical bounds on mutual coupling effects align closely with empirical results, demonstrating the framework's reliability.