With the rapid development of wireless sensor networks (WSNs) technology, a growing number of applications and services need to acquire the states of channels or sensors, especially in order to use these states for monitoring, object tracking, motion detection, etc. A critical issue in WSNs is the ability to estimate the source parameters from the readings of a distributed sensor network. Although there are several studies on channel estimation (CE) algorithms, existing algorithms are all flawed with their high complexity, inability to scale, inability to ensure the convergence to a local optimum, low speed of convergence, etc. In this work, we turn to variational inference (VI) with tempering to solve the channel estimation problem due to its ability to reduce complexity, ability to generalize and scale, and guarantee of local optimum. To the best of our knowledge we are the first to use VI with tempering for advanced channel estimation. The parameters that we consider in the channel estimation problem include pilot signal and channel coefficients, assuming there is orthogonal access between different sensors (or users) and the data fusion center (or receiving center). By formulating the channel estimation problem into a probabilistic graphical model, the proposed Channel Estimation Variational Tempering Inference (CEVTI) approach can estimate the channel coefficient and the transmitted signal in a low-complexity manner while guaranteeing convergence. CEVTI can find out the optimal hyper-parameters of channels with fast convergence rate, and can be applied to the case of code division multiple access (CDMA) and uplink massive multi-input-multi-output (MIMO) easily. Simulations show that CEVTI has higher accuracy than state-of-the-art algorithms under different noise variance and signal-to-noise ratio. Furthermore, the results show that the more parameters are considered in each iteration, the faster the convergence rate and the lower the non-degenerate bit error rate with CEVTI. Analysis shows that CEVTI has satisfying computational complexity, and guarantees a better local optimum. Therefore, the main contribution of the paper is the development of a new efficient, simple and reliable algorithm for channel estimation in WSNs.
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