On the Robustness of Distributed Orthogonalization in Dense Wireless Networks

This paper examines capacity scaling in dense wireless fading networks, where L single-antenna source-destination terminal pairs communicate concurrently through a common set of K single-antenna relay terminals using two-hop half-duplex relaying. In the perfectly synchronized case, assuming perfect channel state information (CSI) at the relays (coherent network), the network capacity is known to scale (asymptotically in K for fixed L) as C = L 2 log(K)+O(1) [1]. Moreover, relay partitioning as described in [1] and matched-filtering at the relay terminals achieves network capacity with independent (coherent) decoding at the destination terminals. On a conceptual level this result implies that coherent relaying orthogonalizes the effective multiple-input multiple-output (MIMO) channel between the source and the destination terminals in a distributed fashion, hence the name “distributed orthogonalization”. In the absence of CSI at the relay terminals (noncoherent network), it was shown in [1] that a simple amplify-and-forward protocol, asymptotically in K for fixed L, turns the network into a point-to-point MIMO link with high-SNR capacity C = L 2 log(SNR) + O(1). The results in [1] were derived under the idealistic assumptions of perfect synchronization, perfect CSI at the relays and frequency-flat fading. The purpose of this paper is to relax these assumptions and study the resulting impact on the scaling laws in [1] assuming single-antenna terminals. Our contributions can be summarized as follows: • 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 coherent and March 15, 2005 DRAFT