For many practical applications in wireless communications, we need to
recover a structured sparse signal from a linear observation model with dynamic
grid parameters in the sensing matrix. Conventional expectation maximization
(EM)-based compressed sensing (CS) methods, such as turbo compressed sensing
(Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have
double-loop iterations, where the inner loop (E-step) obtains a Bayesian
estimation of sparse signals and the outer loop (M-step) obtains a point
estimation of dynamic grid parameters. This leads to a slow convergence rate.
Furthermore, each iteration of the E-step involves a complicated matrix inverse
in general. To overcome these drawbacks, we first propose a successive linear
approximation VBI (SLA-VBI) algorithm that can provide Bayesian estimation of
both sparse signals and dynamic grid parameters. Besides, we simplify the
matrix inverse operation based on the majorization-minimization (MM)
algorithmic framework. In addition, we extend our proposed algorithm from an
independent sparse prior to more complicated structured sparse priors, which
can exploit structured sparsity in specific applications to further enhance the
performance. Finally, we apply our proposed algorithm to solve two practical
application problems in wireless communications and verify that the proposed
algorithm can achieve faster convergence, lower complexity, and better
performance compared to the state-of-the-art EM-based methods.Comment: 13 pages, 17 figures, submitted to IEEE Transactions on Wireless
Communication