  Compressive subspace learning (CSL) with the exploitation of space diversity
has found a potential performance improvement for wideband spectrum sensing
(WBSS). However, previous works mainly focus on either exploiting antenna
auto-correlations or adopting a multiple-input multiple-output (MIMO) channel
without considering the spatial correlations, which will degrade their
performances. In this paper, we consider a spatially correlated MIMO channel
and propose two CSL algorithms (i.e., mCSLSACC and vCSLACC) which exploit
antenna cross-correlations, where the mCSLSACC utilizes an antenna averaging
temporal decomposition, and the vCSLACC uses a spatial-temporal joint
decomposition. For both algorithms, the conditions of statistical covariance
matrices (SCMs) without noise corruption are derived. Through establishing the
singular value relation of SCMs in statistical sense between the proposed and
traditional CSL algorithms, we show the superiority of the proposed CSL
algorithms. By further depicting the receiving correlation matrix of MIMO
channel with the exponential correlation model, we give important closed-form
expressions for the proposed CSL algorithms in terms of the amplification of
singular values over traditional CSL algorithms. Such expressions provide a
possibility to determine optimal algorithm parameters for high system
performances in an analytical way. Simulations validate the correctness of this
work and its performance improvement over existing works in terms of WBSS
performance.
