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.

翻译：在本系列论文的第二部分中，我们证明了第一部分所提出的简化信息几何方法（SIGA）的收敛性。针对一般的贝叶斯推断问题，我们首先证明了公共二阶自然参数（SONP）的迭代与公共一阶自然参数（FONP）的迭代是分离的。因此，公共SONP的收敛性可以独立检验。我们证明，在满足一个特定但范围较大的初始化条件下，无论阻尼因子的取值如何，公共SONP都是收敛的。对于公共FONP，我们建立了其收敛的一个充分条件，并证明了公共FONP的收敛性依赖于一个与阻尼因子相关的特定矩阵的谱半径。我们给出了在最坏情况下保证收敛的阻尼因子范围。进一步地，我们利用测量矩阵的特定性质，确定了大规模MIMO-OFDM信道估计中阻尼因子的取值范围。仿真结果验证了理论分析的正确性。