Capacity Scaling Laws in Asynchronous Relay Networks

This paper examines capacity scaling in asynchronous relay networks, where L single-antenna source-destination terminal pairs communicate concurrently through a common set of K single-antenna relay terminals using one-hop relaying. In the perfectly synchronized case, assuming perfect channel state information (CSI) at the relays, the network capacity is known [1] to scale (asymptotically in K for fixed L) as C = L2 log(K) + O(1). In the absence of CSI at the relay terminals, it was shown in [1] that a simple amplify-and-forward architecture, asymptotically in K for fixed L, turns the network into a point-to-point multiple-input multipleoutput (MIMO) link with high-SNR capacity C = L2 log(SNR) + O(1). In this paper, we demonstrate that lack of synchronization in the network, under quite general conditions on the synchronization error characteristics, leaves the capacity scaling laws for both scenarios fundamentally unchanged. However, synchronization errors do result in a reduction of the spatial multiplexing gain (pre-log in the capacity expression) and the effective signal-to-noise ratio at the destination terminals. Quantitative results for these losses, as a function of the synchronization error characteristics, are provided.