Capacity Scaling of Hybrid Erasure Networks Based on Polynomial Power-Law

A capacity scaling law is studied for a hybrid erasure network where a number of wireless nodes and infrastructure nodes, or equivalently base stations, exist. A polynomial decay model is used to suitably characterize an erasure probability for transmission between nodes. Based on the model, upper and lower bounds on the total capacity scaling are derived. Our result indicates that the two bounds are of exactly the same order under a certain condition on the decay parameter for the hybrid erasure network.

I. Introduction

In ad hoc networks where a number of wireless nodes communicate with each other with no infrastructure support, the capacity scaling law for Gaussian channels was first studied in [1]. It was shown that the aggregate throughput scales as in a large wireless network where nodes are randomly located in a unit area.¹

We use the following notation: i) means that there exist constants and such that for all . ii) if . iii) if and .

This throughput scaling is achieved in such a way that data is delivered from a node to another node in a multihop fashion. The almost linear scaling law for an arbitrarily small was then derived using a hierarchical cooperation scheme [2] in the Gaussian network model. As an alternative approach to improving the total throughput up to a linear scaling, infrastructure nodes, or equivalently base stations (BSs), can be added to the wireless ad hoc network [3], [4]. In [5], a more general hybrid network where multiple antennas are deployed at each BS was studied. It was shown in [5] that using one of BS-supported single-hop routing, BS-supported multihop routing, pure multihop routing [1], and hierarchical cooperation [2] is needed to achieve the optimal capacity scaling law in the general hybrid network based on Gaussian channel models.