Connectivity and Transmission Delay in Large-Scale Cognitive Radio Ad Hoc Networks With Unreliable Secondary Links

In this paper, we investigate connectivity and transmission delay of secondary users in large-scale wireless cognitive radio (CR) ad hoc networks from a percolation-based perspective. Using the random connection model, we study the unreliability of wireless secondary links in CR ad hoc networks, which has not been well studied in the existing literature. By introducing two auxiliary random graphs and using continuum percolation theory, we study the impacts of key system parameters on connectivity and transmission delay in a CR network. We first characterize three behavioral regions of connectivity for a secondary network, i.e., disconnectivity, long-term connectivity and instantaneous connectivity regions. We show that the unreliability of secondary links does not affect the disconnectivity region, but affects the long-term connectivity and instantaneous connectivity regions. Using the ergodic theorem, we then study the scaling behavior of transmission delay with respect to the distance between two randomly chosen secondary users in a connected secondary network for two cases. Specifically, when propagation delay is negligible, we show that transmission delay scales linearly and sub-linearly with distance in the long-term connectivity and instantaneous connectivity regions, respectively. When propagation delay is considered, we show that transmission delay scales linearly with respect to distance in both the long-term connectivity and instantaneous connectivity regions.

I. Introduction

Today, as wireless communication witnesses explosive growth in the number of customers, the efficiency of spectrum usage has become a major concern. Recent measurements show that in the conventional networks, where spectrum is allocated statically, a large percentage of licensed bands remain unused over 90% of time [1]. To address this spectrum under-utilization problem, the concept of Cognitive Radio (CR) network [2] is introduced. CR network provides higher spectrum efficiency via a heterogeneous wireless structure and dynamic spectrum access techniques. Specifically, in a CR network, a secondary network is overlaid with a primary network. Secondary users detect and reuse temporarily unused frequency bands of primary users without causing unacceptable interference to primary users.