  Compressive sensing (CS) has recently emerged as an extremely efficient
technology of the wideband spectrum sensing. In compressive spectrum sensing
(CSS), it is necessary to know the sparsity or the noise information in advance
for reliable reconstruction. However, such information is usually absent in
practical applications. In this paper, we propose a blind-block orthogonal
least squares-based compressive spectrum sensing (B-BOLS-CSS) algorithm, which
utilizes a novel blind stopping rule to cut the cords to these prior
information. Specifically, we first present both the noiseless and noisy
recovery guarantees for the BOLS algorithm based on the mutual incoherence
property (MIP). Motivated by them, we then formulate the blind stopping rule,
which exploits an $\ell_{2,\infty}$ sufficient statistic to blindly test the
support atoms in the remaining measurement matrix. We further evaluate the
theoretical performance analysis of the holistic B-BOLS-CSS algorithm by
developing a lower bound of the signal-to-noise ratio (SNR) to ensure that the
probability of exact recovery is no lower than a given threshold. Simulations
not only demonstrate the improvement of our derived theoretical results, but
also illustrate that B-BOLS-CSS works well in both low and high SNR
environments.
