  In Part II of this two-part paper, we prove the convergence of the simplified
information geometry approach (SIGA) proposed in Part I. For a general Bayesian
inference problem, we first show that the iteration of the common second-order
natural parameter (SONP) is separated from that of the common first-order
natural parameter (FONP). Hence, the convergence of the common SONP can be
checked independently. We show that with the initialization satisfying a
specific but large range, the common SONP is convergent regardless of the value
of the damping factor. For the common FONP, we establish a sufficient condition
of its convergence and prove that the convergence of the common FONP relies on
the spectral radius of a particular matrix related to the damping factor. We
give the range of the damping factor that guarantees the convergence in the
worst case. Further, we determine the range of the damping factor for massive
MIMO-OFDM channel estimation by using the specific properties of the
measurement matrices. Simulation results are provided to confirm the
theoretical results.
