Achieving the Scaling Law of SNR-Monitoring in Dynamic Wireless Networks

The characteristics of wireless communication channels may vary with time due to fading, environmental changes and movement of mobile wireless devices. Tracking and estimating channel gains of wireless channels is therefore a fundamentally important element of many wireless communication systems. In particular, the receivers in many wireless networks need to estimate the channel gains by means of a training sequence. This paper studies the scaling law (on the network size) of the overhead for channel gain monitoring in wireless network. We first investigate the scenario in which a receiver needs to track the channel gains with respect to multiple transmitters. To be concrete, suppose that there are n transmitters, and that in the current round of channel-gain estimation, no more than k channels suffer significant variations since the last round. We proves that "\Theta(k\log((n+1)/k)) time slots" is the minimum number of time slots needed to catch up with the k varied channels. At the same time, we propose a novel channel-gain monitoring scheme named ADMOT to achieve the overhead lower-bound. ADMOT leverages recent advances in compressive sensing in signal processing and interference processing in wireless communication, to enable the receiver to estimate all n channels in a reliable and computationally efficient manner within O(k\log((n+1)/k)) time slots. To our best knowledge, all previous channel-tracking schemes require \Theta(n) time slots regardless of k. Note that based on above results for single receiver scenario, the scaling law of general setting is achieved in which there are multiple transmitters, relay nodes and receivers.