Bayesian Receiver Design for Asynchronous Massive Connectivity

Abstract

In this paper, we consider asynchronous massive connectivity, where massive low-power and low-rate devices with sporadic activity patterns connect to a multi-antenna access point (AP) in an asynchronous manner. Asynchronous transmission minimizes the amount of coordination between the devices and the AP, and thereby simplifies the transmitter design, yet at the cost of a more challenging receiver design. Specifically, asynchronous transmission results in inter-symbol interference (ISI) since the sampling at AP generally cannot match with the symbol intervals of uncoordinated devices. To enable reliable reception, we develop a turbo approximate message passing (TAMP) algorithm that consists of a channel-signal decomposition (CSD) module and a delay learning (DL) module. The CSD carries out sparse matrix factorization to estimate the channels and the ISI corrupted signals of active devices, and the DL is designed to estimate the delay of each active user and resolve the corresponding ISI based on the Bayesian principle. To refine the delay estimation, we further divide the DL module into symbol-level delay learning (SDL) and sub-symbol-level delay learning (sub-SDL) submodules. In particular, the sub-SDL estimates the residue delays (obtained by taking modulo of the symbol interval) and then finely compensates the ISI. Due to the continuity and randomness of time delay, the receive signal constellation consists of lines and curves instead of discrete points, even if the transmit signal constellation is discrete. To reduce the complexity of soft demodulation, we introduce a truncation and projection based approximation method to simplify the related message calculation. Numerical results demonstrate the superior performance of the proposed TAMP algorithm. Particularly, the TAMP algorithm is able to approach the single-user bound with known user delay.