As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.

This letter proposes a signal processing method of passive bistatic radar (PBR) exploiting an uncooperative radar as an illuminator. Compared with other opportunity illuminators, the transmitting signal of a radar usually has a better ambiguity function, which leads to a higher range resolution. Two channels are needed in PBR system. The reference channel is used to estimate radar signal parameters and reconstruct directly propagated signal. The surveillance channel is used to receive scattered wave. An array antenna and a simultaneous multibeam algorithm are necessary in the surveillance channel due to the flexible beam scanning of the uncooperative radar. The procedure of the proposed method is explained in detail, which is then followed by a field experiment. Preliminary results from the field experiment show that the proposed method can be applied to target angle and bistatic range measurement successfully.