On Secure Communication in Large Cooperative Wireless Networks

Naturally, given the shared and open medium in wireless networks, confidentiality is a crucial security requirement. Conventional cryptographic techniques have drawbacks especially in large-scale networks, e.g., the increasing with the network size key management complexity, the assumption of limited attacker computational power and the traffic analysis of encrypted data. This motivated efforts to complement these techniques and fueled interest in information-theoretic physical layer security [1]. Securing the information at the physical layer, based on information-theoretic tools, leverages the channel statistics to overcome attackers; depending on the channel conditions, a secure positive rate can be attainable if suitable coding schemes are employed [2, Section 22.1]. Finding out how overhead due to the secrecy constraints affects the fundamental limits of performance measures (notably the secure rate legitimate nodes can achieve) has attracted considerable research interests, notably in multi-user wiretap channels. However, even in simple threeor four-node networks, the problem is open [2]; the complex nature of large wireless networks with stochastic node distribution makes the derivation of exact results intractable. This motivated the investigation of scaling laws or the asymptotic behavior of the network to gain useful insights. Gupta and Kumar in [3] pioneered the problem of finding scaling laws for large wireless networks and showed that multihopping schemes can achieve at most an aggregate rate that scales like √ n under an individual (per node) power constraint in a network of n randomly located nodes. The main characteristic of this line of works is a point-to-point communication assumption, where each receiver (not necessarily the final destination) is interested only in decoding the signal of a particular transmitter; all other signals, roughly termed interference, are treated as noise. Therefore, these are mostly referred to as interference-limited channel models. Although the broadcasting nature of wireless networks decreases the security level, it also makes cooperation easier. Contrary to the interference-limited model, it has been shown that cooperative schemes increase the aggregate rate to a near-linear scaling under individual power constraints and achieve unbounded capacity for fixed total power (in [4] and follow-up works). Recently, there is a growing interest in considering how secrecy constraints affect scaling laws of large wireless networks [5]. To best of our knowledge, all existing works considered point-to-point interference-limited communications (multi-hopping) to analyze the secrecy capacity scaling; no active cooperative or relaying schemes were considered. Only under the assumption of an interference-limited channel, scaling laws for the secure aggregate rate were derived for large wireless networks. Koyluoglu et al. [5] recently achieved a secure aggregate rate of scaling √ n for dense networks of n legitimate nodes, as long as the ratio of the densities of eavesdroppers and legitimate nodes scales as (log n)−2. In multiuser wiretap channels, cooperation among legitimate users is possible in two different ways. First, the active cooperation: legitimate nodes act as relays and cooperate with the source of the message in transmitting its message to the destination [6]. Second, the passive one, known as deaf cooperation, in which the helper nodes transmit the independent signals to confuse the eavesdroppers and increase the secure rate [7]. In both cooperation modes, one can try to apply beamforming at the helper nodes to improve the secrecy, by constructing the virtual multi-antenna and possibly perform Zero-Forcing (ZF) at eavesdroppers [7]. In this paper, we concentrate on active cooperation schemes based on information-theoretic secrecy coding. Although there is considerable effort in these works on small networks, consisting of few nodes with deterministic locations, the problem of secure communication in large networks received less attention.