L OS ACTORES SOCIALES Y LAS CIFRAS

Future wireless networks will present a highly complex and dynamic en- vironment characterized by a large number of heterogeneous information sources, and a variety of distributed network nodes. This is mainly due to the recent emergence of large-scale, distributed, and heterogeneous com- munication systems which are continuously increasing in size, traffic, ap- plications, services, etc. For maintaining a satisfactory operation of such networks, there is a constant need for dynamically optimizing their perfor- mance, monitoring their operation and reconfiguring their topology. For doing so, different autonomous nodes, that can be thought of as “agents”, will be deployed in future wireless networks in order to service these net- works at different levels such as data collection, monitoring, optimization, management, maintenance, among others [14, 19, 88–93]. These nodes belong to the authority maintaining the network, and must be able to sur- vey large scale networks, and perform very specific tasks at different points in time, in a distributed and autonomous manner, with very little reliance on any centralized authority [14, 19, 88, 91–93].

Although most approaches pertaining to multi-agent systems and multi- agent task allocation are oriented to robotics, control, software, or even military applications as seen in the previous subsection, it is, thus, im- portant to leverage these problems to applications in wireless and com- munication networks. Some existing work has already studied the role of agents in wireless networks, although the concept was rather implicit. One prominent application of agents in wireless networks is the deployment of unmanned aerial vehicles (UAVs). For instance, in [94], the authors study how a number of UAVs, acting as agents, can self-deploy to improve the connectivity of a wireless ad hoc network. In this work, the main focus is on the optimal locations of the UAVs. In [95], a 2-level hierarchical net- work structure is proposed, using UAVs as an embedded mobile backbone, for improving the routing performance in ad hoc wireless networks such as military networks. This idea of hierarchical routing using UAVs is fur- ther investigated in [96]. Further, in [97], a novel MAC protocol suited for communication between ground nodes and UAVs is proposed.

In addition to using UAVs as agents in wireless networks, there has been also a recent emergence of self-deploying mobile nodes such as mo- bile relay stations or mobile base stations. For instance, in [91], the con- cept of autonomous mobile base stations is studied for improving the con- nectivity of vehicular ad hoc networks, in roads where the traffic flow and

vehicles’ speed hinders this connectivity. Further, in [93], the concept of mobile base stations is used for improving the network lifetime of wireless sensor networks. The idea of agents can also be mapped to the concept of message ferrying, whereby a special node, called a message ferry, fa- cilitates the connectivity in a mobile ad hoc network where the nodes are sparsely deployed. The message ferry can be easily seen as an agent as it has autonomy and intelligence to self-deploy and interact with the nodes to improve connectivity. Different performance analysis of message ferrying in ad hoc networks is studied in [92, 98] and the references therein.

In a nutshell, the deployment of agents in next generation wireless net- works is imminent, as many of the current research has directly or indi- rectly investigated the use of such nodes such as UAVs mobile base sta- tions, or message ferries among others. One fundamental problem in this regards that remains relatively unexplored is to study the task allocation among agents in the context of wireless networks. While this problem has been studied in other disciplines as mentioned in the previous subsection, most of these existing models are unsuitable for task allocation problems in the context of wireless networks due to various reasons such as: (i)- The task allocation problems studied in the existing papers are mainly tailored for military operations, computer systems, or software engineer- ing and, thus, cannot be readily applied in models pertaining to wireless networks, (ii)- The tasks are generally considered as static abstract enti- ties with very simple characteristics and no intelligence (e.g. the tasks are just points in a plane) which is a major limitation, and (iii)- The existing models do not consider any aspects of wireless communication networks such as the characteristics of the wireless channel, the presence of data traffic, the need for wireless data transmission, or other wireless-specific specifications.

In this dissertation, we introduce a novel model and we provide an al- gorithm that allow a number of wireless agents to autonomously share a group of arbitrarily located tasks among each other. The main contribu- tions of this work are summarized in Section 8 and the details are found in Paper E.

6

Physical Layer Security

In this section, first we discuss the main concepts of physical layer secu- rity, then we present how cooperation can be used to improve the security of wireless transmission.

Physical Layer Security

6.1 Basics of Physical Layer Security

Due to the broadcast nature of the wireless channel, any unauthorized re- ceiver, i.e., eavesdropper, located within transmission range is capable of observing the signals being communicated between the legitimate trans- mitters. Moreover, the malicious node has the freedom to combine its own observations with those of neighboring eavesdroppers for example, thus improving its reception by means of cooperative inference. Although much has been achieved in terms of securing the higher layers of the classi- cal protocol stack, protecting the physical layer of wireless networks from one or multiple eavesdroppers remains a challenging task. In fact, with the emergence of large-scale heterogeneous wireless networks with little infrastructure, applying higher-layer techniques such as encryption can be quite complex and difficult. For this purpose, the implementation of information-theoretically secure communications means over the wireless channel has been receiving a recently increased attention. The main idea is to exploit the wireless channel physical layer characteristics such as fading or noise for improving the reliability of wireless transmission. This reliability is quantified by the rate of secret information sent from a wire- less node to its destination in the presence of eavesdroppers, i.e., the so called secrecy rate. The maximal achievable secrecy rate is referred to as the secrecy capacity.

The idea of implementing physical layer security over noisy channels, which builds on the notion of perfect secrecy established by Shannon in [99], has its foundation in the work done in [100]. For instance, in [100], Wyner introduced the wiretap channel to model the degraded broadcast channel where the eavesdropper observes a degraded version of the re- ceiver’s signal. In his model, the confidentiality is measured by the equiv- ocation rate, i.e., the mutual information between the confidential mes- sage and the eavesdropper’s observation. For the discrete memoryless degraded wiretap channel, Wyner characterized the capacity-equivocation region and showed that a non-zero secrecy rate can be achieved [100]. The most important operating point on the capacity-equivocation region is the secrecy capacity, i.e., the largest reliable communication rate such that the eavesdropper obtains no information about the confidential message (the equivocation rate is as large as the message rate). The secrecy capac- ity of the Gaussian wiretap channel was given in [101]. Csizar and Korner considered a more general wiretap channel in which a common message for both receivers is sent in addition to the confidential message [102].

Figure 1.6: Illustration of a basic wireless transmission model in the pres- ence of an eavesdropper.

Recently, there has been considerable efforts devoted to generalizing these results into the wireless channel and multi-user scenarios [103– 110]. In [103], the secrecy capacity of the ergodic slow fading with perfect channel state information at the transmitter (CSIT) was characterized and the power/rate allocation under partial CSIT (the knowledge on the chan- nel of the intended receiver only) was derived. The secrecy capacity of the parallel fading channels was given [104, 105] where [105] considered the model in [102] with a common message. The feasibility of traditional phys- ical layer security approaches based on single antenna systems is ham- pered by channel conditions: If the channel between the source and the destination is worse than the channel between the source and an eaves- dropper, the secrecy capacity is typical zero [100, 105]. For overcoming this limitation, in [106, 108, 109], the use of multiple antennas for im- proving the secrecy capacity was investigated. In summary, physical layer security presents an interesting and challenging field which is currently ongoing a significant growth, namely in the wireless community.

As previously mentioned, the main performance metric of interest in physical layer security problems is the concept of secrecy capacity (as well as the secrecy rate). The most basic model of transmission in the presence of an eavesdropper is shown in Figure 1.6. In this figure, Cd denotes the Shannon rate from the transmitter to its receiver while Ce _{represents the}

Physical Layer Security

Shannon rate at the eavesdropper. Given this basic model, the secrecy capacity Cs _{of the transmitter can be given by}

Cs= (

Cd− Ce

)+

. (1.12)

The fact that (1.12) represents the secrecy capacity and is achievable has been shown in [108, 109]. In the presence of multiple eavesdroppers, char- acterizing the secrecy capacity can be challenging [106–110]. However, it has been shown that, by the use of Gaussian inputs, an achievable secrecy rate Rs_{, in the presence of K > 1 eavesdroppers, can be given by [111]}

Rs= ( Cd− max 1≤k≤KC e k )+ , (1.13)

where Cd represents the Shannon rate of the transmitter and C_ke is the Shannon rate at eavesdropper k.

As demonstrated in [106, 108, 109], the use of multiple antennas can significantly improve the secrecy rate both in the single eavesdropper case of (1.12) as well as the multiple eavesdroppers case in (1.13). However, as thoroughly discussed in Section 3, due to cost and size limitations, multi- ple antennas may not be available at the wireless nodes and, under such scenarios, cooperation is an effective way to enable single-antenna nodes to enjoy the benefits of multiple-antenna systems. In the next subsection, we discuss how different cooperation techniques can be used for improving the physical layer security of wireless transmission.

6.2 Cooperation for Improving Physical Layer Security

As mentioned in the previous subsection, in many scenarios, the wireless channel conditions can lead to a zero secrecy capacity for some users. In this case, the users need to perform advanced communications techniques to improve their secrecy capacity. It has been shown that the use of multi- ple antennas can improve the secrecy capacity and overcome some of the challenges of the wireless channel [106, 108, 109].

However, due to hardware limitation as well as costs, physically im- plementing multiple antennas on wireless devices might not always be feasible. As an alternative, a number of single antenna can cooperate in order to improve their secrecy capacity. For instance, consider a source node equipped with a single antenna seeking to cooperate a number of single antenna relay nodes in its vicinity in order to transmit its data to

Figure 1.7: Illustration of a cooperation for wireless transmission in the presence of eavesdroppers.

a far away destination in the presence of one or more eavesdroppers. An illustration of the model is given in Figure 1.7.

Different other cooperative schemes for improving the transmission in the presence of eavesdroppers have been proposed in [107, 110, 112–117]. These approaches consider different roles for the relay such as helping the source, or the eavesdropper, or both. Techniques such as jamming the eavesdropper or nulling the signal at the eavesdropper are used to improve the secrecy rate of the users in different scenarios. Most of this work is mainly focused on performance assessment, analysis of the secrecy rate, as well as the rate-achieving relaying strategy.

In order to illustrate how cooperation can improve the secrecy rate of a source node such as in in Figure 1.7, one approach, as described in [107, 110], is to allow the source and the relays to adopt a cooperative protocol composed of two stages

• In the first stage, the source transmits its signal locally to the trusted

relays in its vicinity.

• In the second stage, the source and the relays transmit, coopera-

tively, the signal to the destination using a well suited cooperation protocol.

Thus, the two-stage algorithm consists of an information exchange stage and a transmission stage. In the transmission stage, various well

Physical Layer Security

known techniques for relaying can be used such as decode-and-forward or amplify-and-forward. Using decode-and-forward and assuming that the signal is transmitted in the first stage with enough power to allow the relays to correctly decode it, the source as well as each relay (after decoding the message) transmit a weighed signal of the original decoded message. In contrast, using amplify-and-forward, in the second stage, the source transmits a weighed version of its signal while the relays transmit a weighed version of the noisy signal received during the first stage.

The weights used in the second stage can be optimized so that the se- crecy rate of the source node is improved. Hereafter, it is assumed, as is often the case in current physical layer security literature [107], that the source and the relays have complete knowledge of the channels to the destination and the eavesdroppers. The assumption that the users have knowledge of the eavesdroppers channel is commonly used in most physical layer security related literature (see [107, 110, 118] and refer- ences therein), and as explained in [118] this channel information can be obtained by the users through a constant monitoring of the behavior of the eavesdroppers. Alternatively, the eavesdroppers can be considered as location in space where the source suspects the presence of a malicious node.

For the case of a single eavesdropper, the optimal weights can be found as follows. By considering the decode-and-forward case, given a total of N − 1 relays and a single eavesdropper, we let h = [h1, . . . , hN]†, gk =

[g1,k, . . . , gN,k]†, and w = [w1, . . . , wN]† be the the N× 1 vectors representing,

respectively, the channels between the nodes (source and relays) and the destination, the channels between the nodes (source and relays) and the eavesdropper k channels, and the signal weights (note that, the first ele- ment of each vector corresponds to the source). In this case, the secrecy capacity of the source, as defined in (1.12), can be written as [107, Eq. (6)]

Cs= 1 2log2 ( σ2_{+ w}†_R hw σ2_{+ w}†_Rk gw ) , (1.14)

where the scalar factor 1₂ is due to the fact that the algorithm requires two stage for cooperation, σ2 is the variance of the Gaussian noise, Rh = hh†,

and Rk_g = g_kg†_k.

For the case of one eavesdropper, assuming that the total power that the source and it relays can use to transmit is ˜P, and considering that the power used in the first stage of cooperative transmission is negligible, the

problem of maximizing the secrecy capacity can be written as max w σ2+ w†Rhw σ2_{+ w}†_Rk gw , (1.15) s.t. w†w = ˜P .

The solution of this optimization problem, as found in [107, 108, 119], is the scaled eigenvector corresponding to the largest eigenvalue of the symmetric matrix ( ˜Rk_g)−1R˜h where ˜R

k g , σ 2 ˜ P IN+ R k g and ˜Rh , σ 2 ˜ PIN + Rh.

Unlike the single eavesdropper case, whenever there are K > 1 eaves- droppers in the network, finding an optimal weight can be quite difficult to find [107]. Alternatively, one approach is to weigh the signal in a way to completely null out the signal at all the eavesdroppers. By doing so, the secrecy rate of the source is certainly improved (although not maximized). In this case, it is shown that, cooperatively and while nulling the signal at the eavesdroppers’, the source’s secrecy rate, as per (1.13) would be- come [107, Eq. (14)]

Rs = 1

2log2(1 +

(w∗)†Rhw∗

σ2 ), (1.16)

where w∗ is the weight vector that maximizes the secrecy rate while nulling the signal at the eavesdropper and is given in [107, Eq.(20)] by

w∗ = βG†(GG†_S)−1e (1.17) with G = [h, g₁, . . . , g_K]† a (K + 1)× N matrix, β = √ ˜ P e†(GG†)−1e a scalar and e = [1, 01×K]† a (K + 1)× 1 vector.

It is shown in [107] that, for a source node having a number of relays in its vicinity, the secrecy rate as per (1.16) is improved significantly with respect to the non-cooperative case, in the presence of multiple eaves- droppers. Similar analysis can also be found in [110], for the amplify-and- forward case. It is also shown [107, 110] that, for a given cluster of nearby relays and a single source the decode-and-forward case performs better than the amplify-and-forward case but at the expense of more complexity. In brief, existing work has established that, by cooperation, gains in terms of secrecy rate can be achieved when wireless transmission occurs in the presence of eavesdroppers. However, as previously mentioned, most of the existing work in [107, 110, 112–117] focuses on information theo-

Multi-hop Architectures in Next Generation Networks

retic analysis of the secrecy rate, at a link level, with no cost for coopera- tion.

Although the main concepts behind physical layer security are still largely theoretical, it is of interest to study how the gains, in terms of secrecy rate, stemming from cooperation can be achieved in a practical network. In particular, it is important to study: (i)- What kind of tradeoff exists between the cooperation gains and the information exchange costs, (ii)- What kind of cooperative strategies the users can adopt to improve their secrecy rate, and (iii)- The impact of physical layer security coopera- tion on the network structure. In this dissertation, we attempt to answer these questions by studying and analyzing the use of cooperation for phys- ical layer security improvement using the analytical framework of coalition formation games. The main contributions of this work are summarized in Section 8 of this introduction and the details are found in Paper F.

7

Multi-hop Architectures in Next Generation Net-

works

In this section, first, we briefly introduce the main ideas behind multi- hop communication, and, then, we discuss how the deployment of relay stations in next generation wireless networks impacts the network archi- tecture.