Joint activity and channel estimation for asynchronous grant-Free NOMA with chaos sequence

This paper considers an asynchronous grant-free non-orthogonal multiple access (NOMA) systems which can be applied in massive machine-type communications (mMTCs) and underwater IoT acoustic communication scenarios due to its high spectral efficiency and low power consumption characteristics. In particular, the system's asynchronous reception of user signals can effectively reduce the additional overhead caused by synchronous reception. We investigate the joint activity and channel estimation in the asynchronous case, where an asynchronous frame structure is considered, and a pilot sequence designed by chaotic sequence is used to reduce the pilot storage space. The joint estimations are formulated as single measurement vector (SMV) and multiple measurement vector (MMV) problems for single-antenna and multiple-antenna systems. Different from the existing estimation algorithms, where prior information is considered for estimation, an adaptive alternating direction method of multiplier (ADMM)is proposed for the SMV problem and a two-stage ADMM is proposed for the MMV problem. In particular, an index set is first estimated in each iteration of our proposed adaptive ADMM, and a linear ADMM is performed based on the index set. The first stage of our proposed two-stage ADMM is to estimate the delay and the activity, and then the channel state information is estimated. Further, we analyze the complexity of the two algorithms and their sensitivity to the initial values of chaotic sequences. Finally, simulation results reflecting the detection performance of the algorithms are given. Based on the simulation results, the proposed two algorithms are computationally efficient, providing superior signal recovery accuracy and user activity detection performance. More importantly, the signal delay has a relatively small impact on the proposed algorithm.