  In this paper, we consider the problem of compressive sensing (CS) recovery
with a prior support and the prior support quality information available.
Different from classical works which exploit prior support blindly, we shall
propose novel CS recovery algorithms to exploit the prior support adaptively
based on the quality information. We analyze the distortion bound of the
recovered signal from the proposed algorithm and we show that a better quality
prior support can lead to better CS recovery performance. We also show that the
proposed algorithm would converge in $\mathcal{O}\left(\log\mbox{SNR}\right)$
steps. To tolerate possible model mismatch, we further propose some robustness
designs to combat incorrect prior support quality information. Finally, we
apply the proposed framework to sparse channel estimation in massive MIMO
systems with temporal correlation to further reduce the required pilot training
overhead.
