  Compressive sampling has shown great potential for making wideband spectrum
sensing possible at sub-Nyquist sampling rates. As a result, there have
recently been research efforts that aimed to develop techniques that leverage
compressive sampling to enable compressed wideband spectrum sensing. These
techniques consider homogeneous wideband spectrum where all bands are assumed
to have similar PU traffic characteristics. In practice, however, wideband
spectrum is not homogeneous, in that different spectrum bands could have
different PU occupancy patterns. In fact, the nature of spectrum assignment, in
which applications of similar types are often assigned bands within the same
block, dictates that wideband spectrum is indeed heterogeneous, as different
application types exhibit different behaviors. In this paper, we consider
heterogeneous wideband spectrum, where we exploit this inherent, block-like
structure of wideband spectrum to design efficient compressive spectrum sensing
techniques that are well suited for heterogeneous wideband spectrum. We propose
a weighted $\ell_1$-minimization sensing information recovery algorithm that
achieves more stable recovery than that achieved by existing approaches while
accounting for the variations of spectrum occupancy across both the time and
frequency dimensions. Through intensive numerical simulations, we show that our
approach achieves better performance when compared to the state-of-the-art
approaches.
