Chapter 5
`Cooperative Security in D2D Communications
`
`Device-to-Device (D2D) communication based storage offers a potential solution
`for traffic offloading from the cellular infrastructure, and mobile devices themselves
`can act as caching servers, i.e., content helpers [1]. The content requesters can ask
`for content items from the helpers among cellular peers without the help of eNodeB.
`However, the success of such content sharing via D2D links depends on physical
`conditions of the direct wireless links, which must be weighted against possibly
`additional security threats in D2D links. To realize the successful content sharing,
`the selected source node (i.e., content helper) must have the data for which the
`destination node (i.e., content requester) desires, and the physical link condition and
`user mobility also cannot be ignored. Thus, the social interaction between content
`helpers and content requesters is firstly investigated in this chapter. However, the
`direct transmission among mobile users also increases the risk of eavesdropping.
`Selecting D2D users (DUEs) to act as friendly jammers or relays can be regarded as
`an effective way to eliminate the risk of eavesdropping [2, 3]. However, it should
`be admitted that not all nodes are willing to serve as cooperative jammers or
`relays due to the different levels of altruistic cooperative behaviors of user nodes.
`Thus, social trust, which can be quantified by link stability or deduced by the
`trustiness of cooperative nodes, is also a critical factor for cooperative node selection
`[4, 5]. To improve link stability and system robustness, this chapter considers both
`physical links and social characteristics, which includes the social interaction and
`social trust. It focuses on the mechanism for selecting the best content helper and
`cooperative jamming partner to enhance the secrecy and transmission reliability of
`content sharing via D2D links against eavesdropping. Particularly, an optimization
`problem for joint source and cooperative jammer selection with power allocation
`is developed to maximize the secrecy rate of D2D links under individual and sum
`transmit power constraints. In addition to a common scenario in which the CSI of all
`the links can be accurately acquired, two more practical cases where only statistical
`CSI is available are also considered in this chapter.
`
`© Springer International Publishing AG 2018
`L. Wang, Physical Layer Security in Wireless Cooperative Networks, Wireless
`Networks, DOI 10.1007/978-3-319-61863-0_5
`
`137
`
`Netskope Exhibit 1015
`
`

`

`138
`
`5 Cooperative Security in D2D Communications
`
`Physical
`Domain
`
`Social
`Domain
`
`Physical Links
`
`d
`
`Communication link
`
`Wiretap channel
`
`X(km)
`b
`
`c
`
`b
`
`Social Interaction
`d
`
`c
`
`b
`bq
`
`c
`
`cq
`
`Social Trust
`d
`
`dq
`
`Strong social interaction
`
`Weak social interaction
`
`ijp
`Social interaction for user i and j
`i
`j
`,a b c d, ,
`
`,
`{
`
`
`}
`jq
`Social trust for user j
`,
`,
`,
`j
`a b c d
`{
`}
`
`a
`
`a
`
`a
`
`aq
`
`Fig. 5.1 Physical domain and social domain in D2D communications
`
`5.1 Background and Motivations
`
`D2D communications offer a potential solution for traffic offloading from the cel-
`lular infrastructure. By storing content items, individual mobile devices themselves
`can act as caching servers (i.e., content helpers) to help the content requesters to
`obtain the desired content without going through eNodeB. Thus, the success of such
`content delivery via D2D links of mobile users depends on physical condition of the
`direct wireless links. Besides, the social characteristics should also be considered
`for communication enhancement. So in this chapter, we are going to analyze the
`secrecy performance by jointly considering the physical link conditions and social
`relationships among content requesters and content helpers.
`Figure 5.1 shows a three-layer structure which describes both physical domain
`and social domain in D2D communications. The first layer in Fig. 5.1 presents
`the conventional physical consideration for D2D communications, which would be
`effected by the quality of wireless physical links. Both the second layer and the
`third layer describe the social domain of users, and social considerations are made
`in terms of social interaction and social trust. The social interaction between users
`presented in the second layer of Fig. 5.1 is effected by the user mobility, which
`is indicated by the success probabilities between users, e.g., pij. In the third layer,
`each user is characterized with a social trust, which indicates user trustworthiness
`for cooperative communications, e.g., qj. Though D2D communications improve
`communication efficiency, there exist some security threats during the signal
`transmission, such as eavesdropping, which is one of the most common security
`risk for wireless communications.
`
`Netskope Exhibit 1015
`
`

`

`5.1 Background and Motivations
`
`139
`
`Traditionally, security enhancement is considered by assuming static trans-
`mission links between the source nodes and the destination nodes. However,
`this assumption is not always practical due to users’ mobility and other specific
`demands. Moreover, in the multiple-source scenarios, i.e., there are many candidate
`caching nodes can be chosen as content helpers, which is vital for content requesters
`to make suitable decisions. Meanwhile, social factors such as contact frequency
`and duration should also be considered except for the physical factors for content
`transmission, as shown in Fig. 5.1. Besides, friendly neighbor nodes can be recruited
`to serve as cooperative relays or jammers to protect the communication links
`and overcome security vulnerabilities. However, in a mobile environment, one
`cannot simply rely on arranged jammers for each communication link. Instead, it is
`important to dynamically select friendly and efficient cooperative jamming partners
`by considering their physical link conditions, and their willingness for serving as
`cooperative jammers in the mobile environment.
`Based on Fig. 5.1, the social interaction impacted by user mobility and social
`trust based on the interactive relationship among network nodes can be exploited
`for efficient and effective cooperative networking. There are a number of existing
`studies on cooperative jamming for improving secrecy. However, most of them
`assume a full channel state information (CSI) knowledge between all user nodes,
`which is not very practical. For the links involving passive and mobile eavesdropper
`nodes, it is difficult and costly to acquire accurate and real-time CSI. Consequently,
`the basic system model for content sharing between source nodes and destination
`nodes via D2D links with the help of jammer nodes in the presentence of
`eavesdroppers is described and discussed under the consideration of either full CSI
`case or statistical CSI case. Both the physical domain and the social domain are
`discussed to improve the communication stability and system robustness.
`
`5.1.1 System Model and Assumptions
`
`The system model considers the problem of reliability and secrecy enhancement
`for wireless content sharing between content source nodes and content requesters.
`Scenario used in this chapter comprises of several source nodes (i.e., content
`helpers) in possession of content required by the destination nodes (i.e., content
`requesters), and potential social eavesdroppers who may attempt to eavesdrop on
`the legitimate data transmission. Several intermediate nodes serve as jammers to
`thwart eavesdropping and to improve security performance.
`Figure 5.2 shows a practical D2D wireless system model in D2D overlay,
`avoiding cross-tier interference between CUEs and D2D links. In other words,
`neighboring D2D links share the same spectrum is not considered here to avoid
`the complication of mutual interference. Let S D f1; : : : ; Sg, K D f1; : : : ; Mg,
`and J D f1; : : : ; Ng be the index sets of source nodes, eavesdroppers, and
`jammers, respectively. One source node is chosen for data transmission to the
`destination node, and a neighboring node is recruited as a cooperative jamming node
`
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`
`

`

`140
`
`5 Cooperative Security in D2D Communications
`
`Fig. 5.2 System model
`
`to disrupt passive eavesdropping and improve security. It is assumed that a simple
`control protocol is used at the destination node to measure the CSI associated with
`the source-to-destination and jammer-to-destination links. The wireless channels
`between any pair of mobile nodes are characterized as independent flat Rayleigh
`fading. The channel power gain between source node s and destination node d
`is denoted as gsd. Similarly, hjd and hjk denote the channel power gains from the
`jammer j to destination d and eavesdropper k, respectively. gsk is the channel gain
`between source node s and eavesdropper k.
`
`5.1.2 Channel State Information
`
`Considering whether the instantaneous information of the channels is available or
`not, there are three general CSI cases[6] used in research, and we first list them in
`the following to distinguish.
`
`• Full CSI case: as in the typical scenario, the channels between any pair of mobile
`nodes are assumed to be independent and identically distributed (i.i.d.) with flat
`fading. In addition, DUEs tend to be with low mobility or even stationary to keep
`the D2D links stable. In this case, it is usually assumed that the CSI of all the links
`can be accurately acquired at the BS by means of (blind) channel estimation.
`• Partial CSI case: practically, it is costly, difficult, and perhaps impossible to
`acquire accurate and real-time CSI, especially for situations involving passive
`and mobile eavesdropper nodes [7, 8]. Thus, the model can be expanded
`to a more general one to accommodate less powerful BS and less accurate
`
`Netskope Exhibit 1015
`
`

`

`5.2 Social Characteristics for Cooperative Communications
`
`141
`
`channel information in D2D overlay. In this case, gsd and hjd can be always
`known at the BS since DUEs and cooperative jammers can feedback the CSI
`regularly. However, the BS only has statistical information for the CSI of links
`involving eavesdroppers. Without loss of generality, this chapter focuses on the
`popular Rayleigh fading channel model, assuming that the channel power gain
`follows exponential distribution due to fast fading. On the other hand, large-
`scale shadowing effect is absorbed into the mean of exponential distribution.
`Therefore, we can acquire the information of gsk  Exp .g/, hjk  Exp .h/,
`where g and h are the expected channel power gains of gsk and hjk, and Exp./
`denotes the exponential distribution with mean .
`• Statistical CSI case: compared with the partial CSI case, the statistical CSI case
`is more practical by assuming that the accurate CSI of channels gsd and hjd is
`not known either. In other words, only the statistical CSI of all links, i.e., gsk, hjk,
`gsd, and hjd, is provided, and the expected channel power gains of gsd and hjd are
`denoted as sd and jd, respectively.
`
`5.2 Social Characteristics for Cooperative Communications
`
`the
`impact
`links and social factors will
`As mentioned above, both physical
`successful content sharing between content requesters and content helpers with
`the assistance of jamming partners. Thus, selecting the source node and the
`friendly cooperative jamming partner is important to guarantee the communication
`reliability. In this chapter, social interaction based selection of source node and
`social trust based selection of jammer are discussed, respectively.
`
`5.2.1 Social Interaction for Content Sharing
`
`When there exist multiple source nodes in the network, it is critical to choose the
`optimal source node to help the destination node to obtain the desired content. To
`realize the successful communications, potential D2D links between the content
`helpers and the content requesters may have good physical channel conditions, and
`their contact time must be long enough for the desired content transmission. In this
`part, the social interaction will be exploited to describe the successful transmission
`of direct content sharing between content requesters and content helpers. Generally,
`the social interaction is mainly evaluated by two factors: social contact rate and
`social contact duration. Social contact rate is the number of encounters between two
`users during a time interval, while social contact duration can be calculated by how
`long two users remain effective communications within a short distance. Practically,
`data blocks can be considered successfully delivered if they can be transmitted
`within a single encountering time or through several encounters [9]. For simplicity,
`this part focuses on time-sensitive services that require one-time delivery.
`
`Netskope Exhibit 1015
`
`

`

`142
`
`5 Cooperative Security in D2D Communications
`
`As shown in the second layer in Fig. 5.1, psd is an indicator to demonstrate
`the social interaction between source node (i.e., content helper) and destination
`node (i.e., content requester), which is defined as a success probability for the d-th
`destination node receiving the data block transmitted by the s-th source node. Notice
`that the success probability of D2D data transmission in a cellular D2D underlay has
`been studied in [9], by considering spectrum resource sharing between cellular users
`and D2D users. The scenario in this case focuses on a D2D overlay without spectrum
`sharing between cellular users and D2D links, which is different from [9], and the
`D2D links are assigned with dedicated spectrum resources. However, cooperative
`jamming spans the same spectrum as the desired data transmission.
`Referring to the derivation in [9], the success probability psd can be expressed as
`
`Z
`
`Rsd
`
`psd D Pr Tsd 
`DZ 1
`Pssd CPjjd2
`
`Pssd
`
`0
`
`(5.1)
`
`exp
`
`2
`
`Z=tsd
`t 1
`Pssd
`
`t!dt;
`
`Z=tsd
`
`t 1
`
`where Z is the size of data blocks. Tsd indicates the social contact duration between
`the s-th source node and the destination node d, which is exponentially distributed
`with mean tsd [9].
`Obviously, narrowing the candidate set of source nodes with the minimum
`threshold of success probability min will result in lower complexity without
`noticeable performance loss. This yields a narrowed candidate source set for d, ST ,
`
`ST D fs 2 S W psd > ming :
`
`(5.2)
`
`5.2.2 Social Trust for Cooperative Jamming
`
`In addition to the requirements of the qualified content sharing for selecting the
`source nodes (i.e., content helpers), selection of potential cooperative jammers
`should also be considered with their trustworthiness. Recall that in the third
`layer in Fig. 5.1, each user is characterized with an indicator to demonstrate the
`trustworthiness for cooperative communications, thus to clarify the trustworthiness
`degree of jammers, qj is defined in this subsection to indicate the social trust index
`of the j-th jammer, and qj 2 Œ0; 1. It is noted that qj D 1 indicates a fully trusted
`and dependable node while qj D 0 indicates a node that is totally untrustworthy.
`Functionally, jammer j will cooperate by sending the requisite jamming signal with
`probability qj. Note that .1 qj/ can also be used to model the selfishness of jammer
`j to conserve its own energy.
`
`Netskope Exhibit 1015
`
`

`

`5.2 Social Characteristics for Cooperative Communications
`
`143
`
`5.2.3 Objective Problem Formulation
`
`As described above, the objective is to select the optimal source node and coop-
`erative jamming partner, with the consideration of social characteristics and power
`allocation, to hamper reception by the worst-case eavesdropper for secrecy guar-
`anteed transmission. Meanwhile, the source node and the friendly jammer can be
`selected considering the social interaction and social trust, respectively.
`Let Ps and Pj be the transmit powers of source node s and that of jammer
`j, respectively, which are normalized by the power of noise. Thus, the power of
`AWGN on each channel will be  2 D 1. Furthermore, given the limited energy
`of mobile nodes, it is necessary to control interference between jamming nodes
`and legitimate transceivers when they share the same spectrum. Thus, in our
`formulation, we consider both individual power constraints for source and jammer,
`max and Pj
`i.e., Ps
`max, and joint power constraint, i.e., Pmax. For convenience, the
`feasible set of the power parameters can be defined as,
`
`.Ps; Pj/ W
`
`0  Ps  Ps
`max
`0  Pj  Pj
`max
`0  Ps C Pj  Pmax
`
`X D8<
`:
`
`:
`
`(5.3)
`
`9=
`;
`
`Considering the social trust of jammer j, the security rate of the data transmission
`from the s-th source node to the d-th destination node against the k-th eavesdropper
`can be expressed as
`
`Cs;j;k.Ps; Pj/ D qjlog21C
`
`Psgsd
`
`Pjhjd C 1log21C
`
`Psgsk
`
`Pjhjk C 1C
`
`C.1qj/ Œlog2.1 C Psgsd/log2.1 C Psgsk/C ;
`
`(5.4)
`
`where ŒxC D max.0; x/, and qj is the social trust for jammer j as aforementioned.
`The most damaging eavesdropper is the one that causes the lowest secrecy rate.
`The worst-case eavesdropper depends only on the physical channel conditions. Here
`stable and reliable wiretap links are considered to demonstrate worst-case eaves-
`dropping. With the objective to maximize the achievable secrecy rate Cs;j;k.Ps; Pj/,
`against the worst-case k-th non-colluding eavesdropper, the controller selects the
`single best s-th source node and j-th cooperative jammer and optimizes Ps and Pj in
`the problem formulation of
`
`max
`s2S ;j2J
`
`max
`.Ps;Pj/2X
`
`min
`k2K
`
`Cs;j;k.Ps; Pj/ :
`
`(5.5)
`
`As discussed above, the social interaction between the source nodes and the
`destination nodes plays a role in improving the communication reliability. By
`considering the social
`interaction,
`the previous problem in Eq. (5.5) can be
`reduced to
`
`max
`s2ST ;j2J
`
`max
`.Ps;Pj/2X
`
`min
`k2K
`
`Cs;j;k.Ps; Pj/ :
`
`(5.6)
`
`Netskope Exhibit 1015
`
`

`

`144
`
`5 Cooperative Security in D2D Communications
`
`Then the set of candidate source nodes can be identified by excluding nodes
`with poor link stability, in order to improve the stability and robustness of content
`sharing. Meanwhile, the smaller number of candidate source nodes leads to a lower
`computational complexity.
`Notice that once the solution to Eq. (5.7) is found, the cooperative source and
`jamming partner selection process in Eq. (5.6) can be addressed more easily.
`
`max
`.Ps;Pj/2X
`
`min
`k2K
`
`Cs;j;k.Ps; Pj/ :
`
`(5.7)
`
`5.3 Optimization for Secrecy Rate Maximization
`
`Recall that the secrecy rate optimization problem of Eq. (5.7) is non-convex and NP-
`hard. Consequently, both heuristic simulated annealing and approximate solutions
`will be considered, and bounds on the achievable secrecy rate will be used to
`simplify the above optimization problem and yield a suboptimal solution with little
`performance loss.
`
`5.3.1 Secrecy Rate Maximization with Full CSI
`
`In this subsection, the secrecy rate maximization problem is considered in the full
`CSI case. In other words, the instantaneous information of all the links is known
`at the controller. Firstly, a direct solution with the simulated annealing algorithm
`is presented, and then upper and lower bounds on the achievable secrecy rate are
`discussed to obtain the suboptimal solution with low complexity.
`
`5.3.1.1 Heuristic Simulated Annealing Based Direct Evaluation
`
`In this subsection, a heuristic simulated annealing (SA) approach is presented to
`solve the optimization problem in full CSI case. SA is a probabilistic method for
`finding the global minimum of a function that may possess several local minima
`[10]. It works by emulating the physical process whereby a solid is slowly cooled
`so that eventually its structure is “frozen” in a minimum energy configuration.
`Given a set of source nodes, eavesdroppers, and cooperative jammers, the
`accurate values of qj, gsd, gsk, hjk, and hjd are determined when assuming full CSI
`for all the links. Therefore, the variables of the optimization problem in Eq. (5.4)
`are Ps and Pj. Below is a brief overview of the steps:
`
`Step 1: Randomly generate an initial solution .Ps; Pj/ to be valued by the cost
`function of Eq. (5.4);
`
`Netskope Exhibit 1015
`
`

`

`5.3 Optimization for Secrecy Rate Maximization
`
`145
`
`Step 2: Generate a random neighboring solution and compute the new solution’s
`function value;
`Step 3: Pick the new solution if its function value is larger. Otherwise, accept the
`new solution with a certain probability;
`Step 4: Repeat Steps 2–3 until an acceptable solution is found or upon reaching a
`number of iterations.
`
`As proved in [11], after a number of iterations, the SA algorithm will converge
`s ; P
`to a solution, .P
`j /, which, with high likelihood, represents the optimal or
`acceptably good suboptimal solution to the optimization problem. However, one
`limitation of the SA heuristic algorithm is the lack of worst-case performance
`guarantee. Furthermore, its potential for computational time reduction is limited.
`Considering the weaknesses of the SA, a potentially more effective alternative
`is to design approximation algorithms with higher reliability and lower complexity.
`Here, upper and lower bounds are firstly derived on the secrecy rate. Notice that
`many existing relaxation methods optimize either the upper bound or the lower
`bound of the original problem before taking the optimized parameters as the
`final result [12, 13]. Thus, in addition to present algorithms based on the exact
`optimization, both upper and lower bounds are considered in this subsection to
`simplify the original optimization of transmit powers.
`
`5.3.1.2 Low-Complexity Optimization Leveraging Upper Bound
`
`Applying the well-known inequality ln.x/  x 1 to Eq. (5.4) gives
`
`: (
`
`5.8)
`
`ln 2 Cs;j;k.Ps; Pj/  qj" 1 C Psgsd
`
`Pjhjd C1
`1 C Psgsk
`PjhjkC1
`
` 1#
`
`C
`
`C .1 qj/ 1 C Psgsd
`
`1 C Psgsk
`
` 1C
`
`Reorganizing the formula above, the achievable secrecy rate can be upper
`bounded as
`
`Cs;j;k.Ps; Pj/ 
`
`qj
`
`ln 2h Psgsd
`
`Pjhjd C1 Psgsk
`1 C Psgsk
`PjhjkC1
`
`PjhjkC1iC
`
`C
`
`.1qj/
`ln 2
`
`Ps Œgsd gskC
`1 C Psgsk
`
`:
`
`(5.9)
`
`For simplicity, further define the following:
`
`f .Ps; Pj/ D Psgsd
`
`Pjhjd C 1
`
`
`
`Psgsk
`
`Pjhjk C 1C
`
`;
`
`g.Ps; Pj/ D 1 C
`
`Psgsk
`Pjhjk C 1
`
`;
`
`(5.10a)
`
`(5.10b)
`
`Netskope Exhibit 1015
`
`

`

`146
`
`5 Cooperative Security in D2D Communications
`
`h.Ps/ D Ps Œgsd gskC ;
`
`w.Ps/ D 1 C Psgsk;
`
`uk.Ps; Pj/ D g.Ps; Pj/w.Ps/;
`
`vk.Ps; Pj/ D
`
`qj
`ln 2
`
`f .Ps; Pj/w.Ps/C
`
`.1qj/
`ln 2
`
`g.Ps; Pj/h.Ps/:
`
`(5.10c)
`
`(5.10d)
`
`(5.10e)
`
`(5.10f)
`
`It follows that the objective function in Eq. (5.7) can use the secrecy rate upper
`bound in Eq. (5.9) giving
`
`max
`.Ps;Pj/2X
`
`min
`
`k n qj
`
`ln 2
`
`f .Ps; Pj/
`g.Ps; Pj/
`
`C
`
`.1 qj/
`ln 2
`
`h.Ps/
`
`w.Ps/o D max
`
`.Ps;Pj/2X
`
`min
`
`k n vk.Ps; Pj/
`uk.Ps; Pj/o:
`
`(5.11)
`
`By referring to mathematically equivalent problems in [14], the formula above can
`be reformulated as follows:
`
`min
`.Ps;Pj/2X
`
`max
`k
`
`uk.Ps; Pj/
`vk.Ps; Pj/
`
`:
`
`(5.12)
`
`value f D
`
`s ; P
`Therefore, if the optimal solution .P
`j / and the corresponding optimal objective
`s ;P
`uk.P
`j /
`s ; P
`is found for the problem of Eq. (5.12), then .P
`j / is also the
`s ;P
`vk.P
`j /
`optimal solution to Eq. (5.11).
`Notice that uk.Ps; Pj/ and vk.Ps; Pj/ are nonlinear functions of Ps and Pj.
`Although this optimization problem is still non-convex, fortunately, such a non-
`convex optimization problem has been studied before by adopting the generalized
`fractional programming (GFP) algorithms, e.g. in [15]. Particularly, we utilize the
`Dinkelbach-type algorithm, one of the most popular GFP algorithms [16, 17] to
`solve our optimization problem.
`It should be noted that both uk.Ps; Pj/ and vk.Ps; Pj/ are bounded. Furthermore,
`max/ and Pj 2 .0; Pj
`vk.Ps; Pj/ > 0 for Ps 2 .0; Ps
`max/. Hence the optimization
`problem in Eq. (5.12) has an optimal solution. Firstly, Eq. (5.12) can be rewritten as
`follows for simplicity,
`
`.P/
`
`min
`.Ps;Pj/2X
`
`max
`k
`
`uk.Ps; Pj/
`vk.Ps; Pj/
`
`:
`
`To solve problem .P/, one considers the following parametric problem:
`
`.P/ Fk./ D min
`.Ps;Pj/2X
`
`max
`k
`
`fuk.Ps; Pj/  vk.Ps; Pj/g:
`
`Apparently, the optimal objective value  of problem .P/ satisfies Fk. / D 0.
`In other words, Fk./ D 0 implies  D  . Therefore, solution of problem .P/
`
`Netskope Exhibit 1015
`
`

`

`5.3 Optimization for Secrecy Rate Maximization
`
`147
`
`Algorithm 1: Dinkelbach-type Algorithm
`
`.i/
`.i/
`j /: the i-th iteration of the transmit power for source node s and jammer node j.
`s ; P
`.P
`X : the feasible set of power parameters.
`l: positive integer.
`begin
`Referring to Eq. (5.10) to Eq. (5.12),
`.0/
`.0/
`j / 2 X , compute 1 D max
`s
`and let l D 1.
`.l/
`s ; P
`
`Step 1: Take .P
`
`; P
`
`Step 2: Determine .P
`
`.l/
`j / D arg min
`
`k
`
`Fk.l/ D min
`.Ps;Pj/2X
`
`max
`
`Step 3:
`if Fk.l/ D 0 then
`s ; P
`The optimal solution is .P
`j / D .P
`Stop.
`
`.l/
`s ; P
`
`.l/
`j / with optimal value  D l and
`
`Let lC1 D max
`
`and go to Step 2.
`
`k nuk.P
`
`.l/
`s ; P
`
`.l/
`j /=vk.P
`
`.l/
`s ; P
`
`.l/
`
`j /o, l D l C 1,
`
`else
`
`end
`
`end
`
`can be achieved by finding a solution to Fk./ D 0. Based on this observation,
`Dinkelbach-type algorithm solves a subproblem .P/ in each step, generating a
`sequence l which converges to the optimal objective value  of problem .P/.
`The detailed process is described in Algorithm 1.
`
`5.3.1.3 Low-Complexity Optimization Leveraging Lower Bound
`
`Similarly, the lower bound of the optimization problem in full CSI case is further
`discussed in this subsection.
`Firstly, Eq. (5.4) is rewritten as
`
`Psgsd Psgsk
`
`1 C Psgsk C
`
`:
`
`C
`
`35
`1A
`
`Psgsd
`
`Pjhjd C1 Psgsk
`PjhjkC1
`1 C Psgsk
`PjhjkC1
`
`
`
`, gives
`
`4log20Cs;j;k.Ps; Pj/ Dqj2 @1 C
`
`C .1 qj/log21 C
`2Cx C
`Applying inequality Œln.1 C x/C  2x
`
`ln 2 Cs;j;k.Ps; Pj/ 
`
`2qj
`1C Ps gsk
`Pj hjk C1
` Ps gsd
`Pj hjd C1 Ps gsk
`
`2
`
`Pj hjk C1C C1
`
`C
`
`2.1 qj/
`
`Ps.gsd gsk/iC
`2h 1CPsgsk
`
`:
`
`C1
`
`.0/
`s
`
`; P
`
`.0/
`j /=vk.P
`
`.0/
`s
`
`; P
`
`.0/
`
`j /o,
`k nuk.P
`fuk.Ps; Pj/ lvk.Ps; Pj/g .
`.Ps;Pj/2X  max
`k ˚uk.Ps; Pj/ lvk.Ps; Pj/(cid:9).
`
`Netskope Exhibit 1015
`
`

`

`148
`
`5 Cooperative Security in D2D Communications
`
`Thus, the achievable secrecy rate from the s-th source node to d-th destination
`node against the k-th eavesdropper using the j-th cooperative jammer as shown in
`Eq. (5.4) can be lower bounded as:
`
`Cs;j;k.Ps; Pj/ 
`
`2qj= ln 2
`1C Ps gsk
`Pj hjk C1
` Ps gsd
`Pj hjd C1 Ps gsk
`
`Pj hjk C1C C1
`
`2
`
`C
`
`2.1 qj/= ln 2
`
`Ps.gsd gsk/iC
`2h 1CPsgsk
`
`C1
`
`:
`
`(5.13)
`
`Given the lower bound, our optimization problem in Eq. (5.7) can be relaxed as,
`
`max
`.Ps;Pj/2X
`
`min
`k2K
`
`2qj= ln 2
`1C Ps gsk
`Pj hjk C1
` Ps gsd
`Pj hjd C1 Ps gsk
`
`Pj hjk C1C C1
`
`2
`
`C
`
`2.1 qj/= ln 2
`
`Ps.gsd gsk/iC
`2h 1CPsgsk
`
`C1
`
`;
`
`(5.14)
`
`which can also be solved with GFP in terms of the Dinkelbach-type algorithm.
`
`5.3.2 Secrecy Rate Maximization with Statistical CSI
`
`This subsection focuses on the joint power optimization and cooperative nodes
`selection problem when only statistical CSI of all the links is available. Firstly, a
`direct solution to the optimization problem will be presented. Then, to reduce opti-
`mization complexity, an approximate solution will be determined by maximizing
`the lower bound on the expected secrecy rate.
`
`5.3.2.1 Heuristic Simulated Annealing Based Direct Evaluation
`
`The ergodic sum rate of the system is now maximized under the circumstances that
`only statistical CSI of gsd, hjd, gsk, and hjk can be acquired. Mathematically, the
`optimization problem in Eq. (5.7) can be reformulated as,
`
`max
`.Ps;Pj/2X
`
`min
`k2K
`
`E˚Cs;j;k.Ps; Pj/(cid:9) ;
`
`(5.15)
`
`where
`
`Pjhjk C 1C
`E˚Cs;j;k.Ps; Pj/(cid:9) D qjE log21 C
`Pjhjd C 1 E log21 C
`C.1 qj/hE flog2 .1 C Psgsd/gE flog2 .1 C Psgsk/giC
`
`:
`
`(5.16)
`
`Psgsd
`
`Psgsk
`
`Netskope Exhibit 1015
`
`

`

`5.3 Optimization for Secrecy Rate Maximization
`
`149
`
`In order to reduce the computation complexity, Eq. (5.16) can be reduced
`by evaluating the expectations. Specific details can be seen from the following
`Lemma 5.1, based on some derivations from [18, 19].
`
`Lemma 5.1 For X1  Exp.˛1/, X2  Exp.˛2/, it holds that
`
`Eh ln.1 C P1X1/i D .P1˛1/;
`1 C P1X1 D
`Eln1 C
`where .x/ D e1=xE1.1=x/; E1.x/ DR 1
`E Œln .1 C P1X1/ DZ 1
`
`Proof First, we expand the expectation E Œln .1 C P1X1/,
`
` x
`˛1 ln .1 C P1x/ dx:
`e
`
`1 ˛
`
`1
`
`0
`
`P2X2
`
`Œ.P2˛2/ .P1˛1/
`1 P1˛1
`P2˛2
`
`;
`
`etdt; x  0.
`
`1 t
`
`x
`
`Using Eq. (9) on page 194 of [19], we have
`
` x
`˛1 ln .1 C P1x/ dx D e
`e
`
`1
`
`1 ˛
`
`1
`
`0
`
`Z 1
`P1 ˛1 E1 1P1˛1 D .P1˛1/:
`
`1CP2X2i can be expanded as,
`Similarly, Ehln1 C P1X1
`1 C P2X2
`Eln1 C
`DZ 1
`˛2 Z 1
`1 C P2x 1
`˛1 dy dx
`ln1 C
`˛2 dxZ 1
`DZ 1
`.1 C P2x/=.˛1P1/ eydy
`ln1 C
`DZ 1
`DZ 1
`
`
`P1X1
`
` x
`e
`
` x
`e
`
`0
`
`0
`
`P1y
`
` y
`e
`
`˛1
`
`y
`
` x
`˛2 e.1CP2x/=.˛1P1/E1 ..1 C P2x/=.˛1P1// dx
`e
`
`1 ˛
`
`2
`
`1 ˛
`
`2
`
`1 ˛
`
`2
`
`0
`
`0
`
`0
`
`P1 ˛1  P1˛1P2˛2 e
`
`1
`
`1
`
`P2 ˛2 exp1
`
`P1˛1
`
`P2˛2 z E1.z/dz:
`
`Defining  D P1˛1=.P2˛2/, and using Eq. (3) on Page 197 of [19], and Eq. (12)
`on page 308 of [20], we have,
`
`Z 1
`P1 ˛1  P1˛1
`P2˛2e
`
`1
`
`1
`
`P2 ˛2 exp1
`
`P1˛1
`
`P2˛2 z E1.z/dz
`
`Netskope Exhibit 1015
`
`

`

`P2 ˛2 Z 1
`P2 ˛2 Z 1
`P2 ˛2 1
` 1 e
` 1 e
`
`e.1/xE1.x/dx!
`e.1/xE1.x/dx Z
` 1e
`
`
`P1 ˛1 E1 1
`P2 ˛2 E1 
`P1˛1 e
`P1˛1
`
`P1 ˛1 E1 1P1˛1 e
`
`P2 ˛2 E1 1P2˛2
`
`.1/
`
`1
`
`1
`P2 ˛2 e
`
`1
`
`1
`
`1
`
`1
`
`1
`
`D e
`
`D e
`
`D e
`
`
`
`P1˛1
`P2˛2
`P1˛1
`P2˛2
`
`D
`
`D
`
`D
`
`150
`
`5 Cooperative Security in D2D Communications
`
`e.1/xE1.x/dx
`
`1
`P1 ˛1
`
`0
`
` 1
`
`1
`P1 ˛1
`
`0
`
`1
`
`ln 
`
`.1/
`
`P1˛1P1 ˛1 E1 1P1˛1Cln  CE1 
`
` .P1˛1/  .P2˛2/
`1 P2˛2
`P1˛1
`
`:
`
`Applying the Lemma 5.1, the optimization problem in Eq. (5.16) can be
`expressed as
`
`max
`.Ps;Pj/2X
`
`min
`
`
`
`1 Pjjd
`Pssd
`
`.1 qj/
`
`C
`
`k2K ( qjln 2" .Pssd/.Pjjd/
`ln 2 h.Pssd/ .Psh/iC) :
`
`
`
`.Psg/.Pjh/
`1 Pjh
`Psg
`
`#C
`
`(5.17)
`
`5.3.2.2 Ergodic Lower Bound for Complexity Reduction
`
`The achievable ergodic secrecy rate shown in Eq. (5.17) can be lower bounded as
`
` log21 C
`E˚Cs;j;k.Ps; Pj/(cid:9) qj .Pssd/ .Pjjd/
`Pssd
`ln 2 1 Pjjd
` log2.1 C Psg/C
`C .1 qj/ .Pssd/
`
`Pssk
`Pjh
`
`ln 2
`
`.Pjh/C
`
`;
`
`(5.18)
`
`which can also be proved from the Jensen’s inequality as similar with the Eq. (1.15),
`and the derivations are omitted in this part.
`Leveraging the conclusion in Eq. (5.18), a lower bound on the objective function
`can be maximized, i.e., the following lower bound on the ergodic sum rate can be
`maximized to achieve optimized transmit powers.
`
`Netskope Exhibit 1015
`
`

`

`5.3 Optimization for Secrecy Rate Maximization
`
`151
`
`max
`.Ps;Pj/2X
`
`min
`
`ln 2
`
` log21 C
`k2K  qj .Pssd/ .Pjjd/
`Pssd
`ln 2 1 Pjjd
` log2.1 C Psg/C :
`C.1 qj/ .Pssd/
`
`Pssk
`Pjh
`
`.Pjh/C
`
`(5.19)
`
`Thus far, the sum secrecy rate has been considered under the assumptions of
`both full CSI and statistical CSI, respectively. The brute force search and SA
`were both used to solve the optimization problem in Eqs. (5.7) and (5.17). Also,
`low-complexity optimization problems based on bounds of the secrecy rate were
`developed. To further reduce the computation complexity, a one dimensional search
`with low complexity is proposed in the following to solve the optimization problems
`with little performance loss.
`
`5.3.3 One-Dimensional Search with Low Complexity
`
`Recall that the brute-force approach is an available algorithm to solve the opti-
`mization problem, which must search over a 2-dimensional (2-D) space of .Ps; Pj/
`for every k. To reduce the computation complexity, a lower complexity algorithm
`which is suggested by focusing on a one-dimensional (1-D) space is presented in
`this subsection with little performance loss.
`
`Proposition 5.1 The optimal solution .Ps; Pj/ to maximize the sum secrecy rate of
`Eq. (5.4), Eq. (5.11), Eq. (5.14) and the ergodic sum rate of Eq. (5.17) and Eq.
`(5.19) must satisfy Ps D Pmax
`or Ps C Pj D Pmax.
`s
`
`Proof Taking the optimization problem in Eq. (5.4) for example, the expression of
`achievable secrecy rate can be rewritten as
`
`Cs;j;k.Ps; Pj/
`
`(5.20)
`
`C
`
`Pjhjd C1
`1 C Psgsk
`
`D qj"log2 1 C Psgsd
`PjhjkC1!#
`D qj log20
`@1 C" Psgsd
`D qj log20
`@1 C" gsd
`
`1 P
`
`s
`
`C .1 qj/log2 1 C Psgsd1 C PsgskC
`
`C1
`Pjhjd C1 Psgsk
`C .1 qj/ log2 1 C
`#
`PjhjkC1
`A
`1 C Psgsk
`PjhjkC1
`PjhjkC1 #C1
`C .1 qj/ log2 1 C
`A
`
`1 C Psgsk !
`C gsk ! :
`
`1 P
`
`s
`
`Ps Œgsd gskC
`
`Œgsd gskC
`
`Pjhjd C1 gsk
`PjhjkC1
`C gsk
`
`Netskope Exhibit 1015
`
`

`

`152
`
`5 Cooperative Security in D2D Communications
`
`Table 5.1 Main abbreviations of simulation results
`
`Abbreviations
`
`Explanations
`
`BF
`
`DE-SA
`
`LB-SA
`
`UB-D
`
`LB-D
`
`1-D, DE
`
`1-D, UB
`
`1-D, LB
`
`Brute force search is used to optimize the objective function
`
`The optimization problem is solved by direct evaluation by utilizing SA
`
`The optimization problem is solved by leveraging the lower bound solved
`by SA
`
`The optimization problem is solved by leveraging the upper bound solved
`by Dinkelbach
`
`The optimization problem is solved by leveraging the lower bound solved
`by Dinkelbach
`
`The optimization problem is solved by direct evaluation leveraging the
`1-D search
`
`The optimization problem is solved by upper bound leveraging the 1-D
`search
`
`The optimization problem is solved by lower bound leveraging the 1-D
`s