Machine-type communications is quite often of very low data rate and of sporadic nature. In a multi-user wireless sensor network, this sporadic transmission activity can favourably be exploited to facilitate a joint activity and data detection on the physical layer as it has been shown in previous works. This abolishes the need for shared channel access signaling on higher network layers and increases bandwidth efficiency. However, each data source transmits over a user-specific channel which makes channel estimation mandatory for phase-coherent reception and channel equalisation. Since a totally blind estimation of channels, transmit activities and user data simultaneously is practically infeasible, we propose a joint activity and channel estimation scheme based on pilots and matching pursuit algorithms. We show that Zadoff-Chu sequences lead to a better user separation and estimation performance than random Gaussian codes. And since we do not make any assumptions about the user's data payload, our results are generally valid for any frame structure.
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