On the Performance of the DNPS-Based Relay Networks under Masquerading Attack

. Intherelaynetworks,twotypicalissuesofphysicallayersecurityareselfishnessandgarbling.Asamatteroffact,acertainnontypical butseverelyharmfulmisbehaviorcanalsoremovethecooperativediversitygain.Here,wecointhemasqueradingattacktoindicate thiskindofmisbehavior.Amasqueraderelaycanalwayspretendtobethebestonetoforwardsignalsand,inconsequence,deprive theothersoftheopportunitiestocooperate.Tothebestofourknowledge,theimpactofthemasqueradingattackhasnotyetbeen fullyinvestigated.Inthispaper,multiplemasqueraderelayswithrandommasqueradingbehavioraretakenintoaccount.Also,the completechanneleffects,includingtheeffectsoftheflatRayleighfading,log-normalshadowing,andpathloss,areconsideredsuch thatthegeographicaleffectsofthenetworktopologycanbecompletelycaptured.Atlast,theimpactofthemasqueraderelaysare evaluatedintermsoftheoutageprobabilityandend-to-endcapacity.


Introduction
Nowadays, the hyperdense heterogeneous network (HetNet) has been widely recognized as a necessity to boost data rate for future generation of wireless communication systems [1][2][3].With hyperdense deployment, the cooperative communication technologies can effectively extend system coverage and enhance quality of service (QoS).One important paradigm to accomplish these tasks is the cooperative relay networks [4][5][6][7].In the literature, many aspects of the relay networks have been investigated, including the relay selection scheme, network code design, and power allocation.However, one important issue about the physical layer security in the relay networks is still not being completely inspected, i.e., the masquerading attack.
In the relay networks, two typical issues of physical layer security are the selfishness and garbling [8,9].In the selfishness scenarios, the hypocritical relays may forward signals using minimum transmission power or, even worse, refuse to transmit any in-transit messages [10][11][12].On the other hand, the in-transit messages may also be garbled [10,13].To unmask the hypocritical relays, some specific tracing symbols can be added to the informative messages [10,13]; otherwise, the malicious detection can also be conducted blindly, based on the characteristics of hybrid automatic repeat request [11], the credit-based incentive transmission scheme [12], or the received signal's correlation [14].
In addition to the selfishness and garbling, we find that a certain nontypical but severely harmful misbehavior can also deprive the relay networks of cooperative diversity gain.It is well-known that a cooperative relay can be opportunistically selected to forward signals based on the distributed network path selection (DNPS) protocol [15].In DNPS, each candidate relay can set a timer according to channel gain; and the best cooperative relay can then be distributedly decided once its timer expires earlier than the others.However, in this scenario, it is highly possible that a hypocritical relay can maliciously set a timer which can always expire earliest, even though it owns the worst channel gain.Although the signals are forwarded, the degree of freedom (DoF) as well as the cooperative diversity gain can be seriously weakened [16].As a result, the advantage of deploying the hyperdense relay networks can be seriously diluted.To clearly indicate this problem, we pioneeringly coin masquerading attack to describe this kind of misbehavior.
To the best of our knowledge, the masquerading attack has not yet been fully investigated.Although its impact has been analyzed in [16], only single masquerade relay 2 Wireless Communications and Mobile Computing was considered.Likewise, it neglected the complete channel effects; i.e., only the Rayleigh fading with different variances was included.In consequence, the geographical effects of the network topologies can not be completely characterized by the analytical results.Here, to capture the complete effects of fading environment, including the effects of flat Rayleigh fading, log-normal shadowing, and path loss, the composite exponential log-normal (CELN) distributed channel gain is considered [17].Furthermore, multiple masquerade relays with random masquerading behavior are taken into account, i.e., the probability of a relay to become a masquerade relay and probability of a masquerade relay to become active.Then, the impact of the masquerading attack is evaluated in terms of the outage probability and end-to-end capacity.Note that part of this work has been presented in IEEE Wireless Communications and Networking Conference 2017 [18].However, herein, some important related works are surveyed, and all the details of the mathematical derivations are provided.Furthermore, additional topologies of relay networks (as shown in Figures 2(b) and 5) are considered to investigate the influence of the masquerading attack on the device-to-device (D2D) and cellular networks.
The rest of this paper is organized as follows.In Section 2, the system model of the DNPS-based relay network is introduced.Also, the problem description is expounded therein.Section 3 mathematically describes the masquerading behaviors.Then, the outage probability and end-to-end capacity are derived in Section 4. Simulation results and conclusion remarks, including some suggestions for future works, are given in Sections 5 and 6, respectively.

System Model
Assume that  relays are deployed to assist the data transmissions between the source  and destination .The decode-and-forward protocol is applied for relay-assisted transmissions.That is, during Phase I's transmission period, the -th node   can be included into the decodable set D() when its normalized capacity    is larger than the predefined threshold  ℎ as where   =   / 0 is the transmitting signal-to-noise ratio (SNR) at the source;   is the source's transmission power;  0 is the power spectrum density of the additive white Gaussian noise; |ℎ   | is the channel gain of the link between  and   .To capture the complete effects of fading environment, including the effects of flat Rayleigh fading, log-normal shadowing and path loss, the CELN distributed channel gain are considered [17].Thus, the probability density function () of | ℎ   | 2 can be modeled by where μ  =    − ; σ = √  + 5.57 , where ℎ    stands for the channel gain of the link between   and .Since only one hop is required for the transmissions via the direct link, no superscription is needed for   and μ (which are associated with |ℎ  | 2 ).Similarly, there is no superscription to distinguish σ and  during Phase I from those during Phase II because the same environment is assumed for both Phases I and II.Moreover, the cumulative distribution function () of the CELN distribution can be obtained by integrating (2) as follows: During Phase II's transmission period, one of the candidate nodes in D() is selected to forward data packets to the destination  using the DNPS protocol [15] (will be briefly introduced in the latter).Finally, at the destination, the signal directly from  and that from the selected relay are combined according to the maximal ratio combining (MRC) rule, which gives the effective end-to-end capacity as where   =   / 0 is the transmitting SNR at the relay;   is relay's transmission power; ℎ  represents the channel gain of the direct link.Note that when D() is empty, only the signal received via the direct link, i.e., from  to , is used for the demodulation process.In this case, the end-to-end capacity   can be expressed as More details about the DNPS protocol can be found in [15].

Problem Description.
To begin with, the "masquerader" and "nonmasquerader" are defined as the "masquerade" and "ordinary" relays, respectively.Now, it is assumed that the masqueraders attack the relay-assisted networks by mimicking virus' behavior so that it can be violent and untraceable.Specifically, it can be contagious; and the infected relays can be asymptomatic carrier or explicitly symptomatic.average end-to-end capacity with respect to   for the infected relay-assisted cellular network under the exponential and CELN channel environments, where   = 0.5.Also,  = 9 relays are fixed at middles of the sector as illustrated in Figure 5(a).Therein, the radius of the cell is   = 1000 m, and the location of the mobile station (MS) is uniformly distributed over the sector's coverage area, while the minimum distance between the MS and base-station (BS) is 50 m.The transmission power of the source (i.e., the MS)   is set so that the thermal noise outage (  ) at the destination (i.e., the BS) can be 0.2 as the MS is at the cell edge [19].Similarly, the transmission power of each relay   is set so that   = 0.2 can be achieved at the BS.The required SNR corresponding to   = 0.2 is defined as 0 dB, whereas, for the purpose of evaluating the outage probability, the SNR threshold is set at 8 dB.The results are obtained by averaging over 200,000 simulation rounds.
defined as the probability for an ordinary relay to become a masquerader.Moreover, a masquerader can be active (i.e., explicitly symptomatic in other words) and attack with probability   .Note that this kind of masquerading attack was ignored in the conventional counterpart [16].Moreover, solely the Rayleigh fading with different variances (i.e., the exponential channel model) was considered therein.Figure 1 demonstrates the performance degradation for the infected relay-assisted cellular network under the exponential and CELN channel environments.Apparently, the masquerading attack can cause serious performance degradation.Moreover, the performance differences between the cases under the exponential and CELN channel environments are significant.Thus, one can tell that it is necessary and important to investigate the impact of the random masquerading attack by taking the CELN environment into account.Note that the larger dynamic range of the channel gain incurred by log-normal shadowing results in the higher diversity gain, which explains the better performance for the CELN environment.

Analytical Characteristics of Masquerader
The impact of masquerading attack will be evaluated in terms of the outage probability and end-to-end capacity in Section 4. To this end, two scenarios of the decodable set D() are firstly analyzed in this section, i.e., at least one masquerader in D() and no masqueraders in the nonempty D().

At Least One Masquerader in D(𝑆).
In this scenario, the impact of the ordinary relays belonging to D() can be ignored.This is because once an active masquerader exists in the decodable set D(), the ordinary relays can never be selected to forward packets during Phase II.To facilitate the presentation, some terminologies are defined as follows.
Wireless Communications and Mobile Computing Apparently, we can have Also, the conditional probability [M  (, ) | M(, )] can be expressed as where A/B is the set-operator to remove set B from set A; where we can have Moreover, it is intuitional to obtain At last, multiplying (7), (8), and ( 12) gives (6).It should be noticed that, with ℓ ≥ 2, the following performance metric (i.e., the outage probability and capacity in Section 4) should be averaged over the ℓ cases.This is because each of the ℓ masquerade relays individually sets a timer such that it can expire earliest.Then, the relay selection in Phase II becomes a random selection approach, which means each of them can be selected with probability 1/ℓ.Denote   () and   () as the outage probability for the cases of  belonging to a subset of M  (ℓ) or O  (), respectively, while   (0) denotes that with an empty decodable set D().Also, let   (),   (), and   (0) represent the corresponding average end-to-end capacity.Since   (),   (), and   (0) are mutually exclusive, the overall outage probability can be expressed as

Performance Analysis
Similarly, we can have In the following, we derive the mathematical expressions of   (),   (), and   (0).The closed form expressions of   (),   (), and   (0) will be derived as well.
Let  u ( | ) and   ( | ) represent the conditional outage probability and end-to-end capacity.Given ℓ, , and , it follows that and respectively.Finally, the overall outage probability and endto-end capacity for the case with at least one masquerader in D() can be expressed as and ( | ) and   ( | ) are derived as follows.
Let  = ( ln − μ )/( √ 2σ) and V = ( ln − μ )/( √ 2σ) which leads to It is known that the Hermite polynomial approach can be applied to calculate the following integration: where   and   are the abscissas and the weight factor of the Hermite polynomials with order   , respectively [20].Applying (32) into (31) renders and (1) Case A: No Relays Become the Masqueraders.Denote  A  ( | ) and  A  ( | ) the outage probability and endto-end capacity when the -th relay is selected from O  (, ) under the condition of O().Similar to the procedures of deriving ( 21) and ( 22), the average outage probability and end-to-end capacity can be expressed as and respectively.(a) .Regardless of which relay is selected from O  (, ) in Phase II, an outage event can occur when the end-to-end capacity of all the relays belonging to O  (, ) is below the target value, i.e.,    <  ℎ ∀ ∈ O  (, ).Let F () denote the  of this case.Referring to (3), the outage probability with a given  can be written as Wireless Communications and Mobile Computing 7 Then, similar to (24), the outage probability in this case can be expressed as Applying the same procedures of deriving (28) gives where   is the same as that in (27).(b) .In this case, the end-to-end capacity can be written as where f () represents the corresponding  of (38).Taking derivation of (38) gives where    associated with the   -th relay in O  (, ) is similar to   associated with the -th relay in O  (, ).Then, the average end-to-end capacity can be expressed as Letting  = ( ln  − μ )/( √ 2σ) and V = ( ln  − μ )/( √ 2σ) gives Applying the Hermite polynomial approach into (44) renders (2) Case B: No Masqueraders Are Decodable.Denote by  B  ( | ) and  B  ( | ) the conditional outage probability and end-to-end capacity when the -th relay is selected from O  (, ) under the conditions of M  (, ) and M(, ).Then, the outage probability and end-to-end capacity can be expressed as ( 46) and (47), respectively.represent the conditional outage probability and endto-end capacity when the -th relay is selected from O  (ℓ, ) under the conditions of M  (, ), M  (, ), and M(, ).Moreover, the outage probability and end-to-end capacity can be expressed as ( 48) and (49), respectively.
(2) .The capacity can be expressed as where [log 2 (1 +   ) | D() = 0] can be expressed as Following the procedure of deriving (33), we can have the numerical expression of (54) as

Numerical Results
In this section, the relay-assisted D2D and cellular networks are considered to evaluate the exactness of the analytical model and investigate the performance degradation caused by the masquerading attack.In either scenario, the unitvariance Rayleigh fading is assumed.Also, the path loss exponent is 3.5 and the standard deviation of the Log-Normal shadowing is 6 in the dB domain.All the simulation results are obtained by averaging over 200,000 rounds.

D2D Network.
Here, the vertical deployment of the relay network (as shown in Figure 2(a)) is firstly applied for investigating the impact of the masquerading attack.Then, the horizontal deployment of Figure 2(b) is used to quantitatively investigate the effect of the location of a single designated masquerader.As shown in the figures, the distance between  and  is   = 1000 m; and that between two neighboring relays is   = 50 m.The transmission power of the source   is set so that the thermal noise outage (  ) at the destination can be 0.2 [19].Similarly, the transmission power of each relay   is set so that   = 0.2 can be achieved by the central relay (e.g.,  2 with  = 3 or  3 with  = 5).Note that the required SNR corresponding to   = 0.2 is defined as 0 dB, whereas, for the purpose of evaluating the outage probability, the SNR threshold is 8 dB.Also, the capacity threshold  ℎ in Sections 2, 3, and 4 can be obtained by substituting the SNR threshold into the wellknown equation of Shannon capacity. Figure 6 shows the (a) outage probability and (b) average end-to-end capacity with respect to   for the relay-assisted D2D network under the CELN channel environment, where   = 0.5;  = 3,  = 5, and  = 9 relays are placed according to the vertical deployment as illustrated in Figure 2(a).Apparently, the analytic and simulation results match with each other quite well.Most importantly, as demonstrated in the figures, the masquerading attack can cause significant performance degradation.For example, as the   increases from 0 to 0.4, the outage probability for the case with  = 5 can increase from 0.03 to 0.16.In addition, it can lead to 16% capacity loss (from 2.95 to 2.49 bps/Hz).Moreover, as   keeps growing, its impact becomes marginal.It should be noticed that the equivalent activity of the masquerading behavior for each relay is   ×   , whereas the overall masquerading behavior across the whole network is  ×   ×   .Thus, with  = 5,   = 0.5, and   = 0.2, solely   ×   = 0.5 × 0.2 = 10% (or overall 5 × 0.5 × 0.2 = 50%) equivalent activity of the masqueraders can cause 9.2% capacity loss (from 2.95 to 2.68), while the outage probability can increase from 0.03 to 0.1.When the equivalent activity becomes   ×   = 0.5 × 1 = 50% (or overall ×  ×   = 5× 0.5×1 = 250%), it ends in 25% capacity loss and unacceptably high outage probability of 0.23 (667% rise).
This phenomenon can become deteriorated when the number of relays increases.For example, comparing the curve of  = 5 at   = 0.4, using  = 9 relays can result in additional 6% capacity loss (from 2.49 to 2.34 bps/Hz), and higher outage probability (increasing from 0.16 to 0.21).Moreover, as   grows to one, 34% capacity loss can be resulted; and the outage probability can be extremely risen by 6310%.It should be noticed that, in general, using more relays can contribute to a better system performance.However, the masqueraders seriously dilute the diversity gain.Thus, how to tackle the issue of masqueraders could be an important issue for the future generation of hyperdense relay networks.Figure 3 shows the (a) outage probability and (b) average end-to-end capacity with respect to   for the relay-assisted D2D network under the CELN channel environment, where   = 0.5;  = 3,  = 5, and  = 9 relays are placed according to the vertical deployment as illustrated in Figure 2(a).
Figure 4 shows the (a) outage probability and (b) average end-to-end capacity for the relay-assisted D2D network under the CELN environment with a single designated masquerader according to the horizontal deployment as illustrated in Figure 2(b), where  = 7 and   = 1.Note that the cases without masquerader mean that all the  = 7 relays are ordinary ones, whereas the cases with masquerader mean that there is only one masquerader indicated by the horizontal axis.In addition to the similar phenomenon observed from Figure 6 (i.e., the significant performance degradation caused by the masquerader), one can also find that the masquerader located farther from the destination can cause severer performance degradation.This explains the lowest capacity and highest outage probability for the case of the first relay (i.e.,  1 ) being the designated masquerader.Therefore, it can be expected that a masquerader can possibly incur a serious bottleneck effect on the multihop transmissions in the future generation of wireless communication systems.

Cellular Network.
In the cellular scenario, one cell with three 120 ∘ sectors is considered.As per the parameter setting in Figure 1, the simulation is conducted for the network topologies illustrated in Figures 5(a) and 5(b).Therein,  = 3 and 9 relays are fixed at the middles or uniformly distributed over its coverage area, respectively.In the latter case, the minimum distance between a relay and BS is 100 m.Also, in both cases, the location of MS is uniformly spread over the sector.Since the analytical results are obtained by averaging over 100 randomly generated network topologies, the time required to calculate all the cases discussed in Sections 3 and 4 can be prohibitively prolonged when  ≥ 7. Thus, only  = 3 is considered for generating the analytical results.Firstly, the exactness of the analytical results can still be verified.Secondly, as observed in the D2D network, more stringent performance degradation can be incurred by the larger amount of relays.Thirdly, the masquerading attack can cause more significant performance degradation for the cases with uniformly distributed relays.For the example with  = 9 uniformly distributed relays, serious masquerading attack can cause 30% capacity loss (from 4.93 to 3.46 bps/Hz).However, the loss becomes 18% (from 3.71 to 3.05 bps/Hz) when the relays are fixed at the middles of the sector.Note that the larger diversity gain can be obtained when the relays are "not fixed" at the middles of the sector (which explains the better performance for the cases with uniformly distributed relays as well).However, the masquerading attack dilutes the achievable diversity gain and causes larger performance degradation for the cases with larger diversity gain (as aforementioned).

Conclusions
In this paper, we have defined the masquerading attack for the relay-assisted networks.For the purpose of numerically characterizing the masquerading attack, the mathematical expressions for the end-to-end capacity and outage probability have been derived.To make the discussions more complete, the CELN channel model was taken into account such that the geographic effects of the network topology can be captured.Moreover, the random masquerading behavior was considered as well, including the probability of a relay to become a masquerader and probability of a masquerader to become active.Via the analytical and simulation results, it was found that the masquerading attack can cause 34% and 30% capacity loss for considered D2D and cellular networks.Also, the corresponding outage probability can be extremely risen.
Nowadays, the necessity of relay-assisted transmission scheme for the next generation of wireless communication networks has been widely recognized.With the aid of relay, the performance of secondary users in the cognitive network can be improved [21]; the physical layer security in the largescale fifth-generation network can be strengthened [22]; the energy efficiency and link reliability for the vehicular ad hoc networks can be enhanced [23]; the cellular coverage area can be extended via multihop D2D communications [6,7,24], especially for the millimeter-wave-based systems [25][26][27] and Internet-of-Things [28]; the high quality transmissions for the sensor network can be achieved [29] as well.However, based on the finding of this paper, the achievable diversity gain via relay transmissions will be seriously diluted under the masquerading attack.De facto, in addition to the DNPS protocol, any arbitrary relay networks (especially for the ones operating in the distributed mode) can encounter this Wireless Communications and Mobile Computing kind of threat, which hypocritically forwards packets and removes the diversity gain in silence.Thus, how to evaluate and alleviate the impact of the masqueraders could be a critical issue to fully utilize the advantages of relay-assisted transmissions.This paper can be recognized as a first step to inspire the investigation of the masquerading attack for the relay networks.

Figure 1 :
Figure1: (a) Outage probability and (b) average end-to-end capacity with respect to   for the infected relay-assisted cellular network under the exponential and CELN channel environments, where   = 0.5.Also,  = 9 relays are fixed at middles of the sector as illustrated in Figure5(a).Therein, the radius of the cell is   = 1000 m, and the location of the mobile station (MS) is uniformly distributed over the sector's coverage area, while the minimum distance between the MS and base-station (BS) is 50 m.The transmission power of the source (i.e., the MS)   is set so that the thermal noise outage (  ) at the destination (i.e., the BS) can be 0.2 as the MS is at the cell edge[19].Similarly, the transmission power of each relay   is set so that   = 0.2 can be achieved at the BS.The required SNR corresponding to   = 0.2 is defined as 0 dB, whereas, for the purpose of evaluating the outage probability, the SNR threshold is set at 8 dB.The results are obtained by averaging over 200,000 simulation rounds.

Figure 3 :
Figure 3: (a) Outage probability and (b) average end-to-end capacity with respect to   for the relay-assisted D2D network under the CELN channel environment, where   = 0.5;  = 3,  = 5, and  = 9 relays are placed according to the vertical deployment as illustrated in Figure 2(a).

Figure 4 :
Figure 4: (a) Outage probability and (b) average end-to-end capacity for the relay-assisted D2D network under the CELN environment with a single designated masquerader according to the horizontal deployment as illustrated in Figure 2(b), where  = 7 and   = 1.
(a) A sector with fixed relays (b) A sector with uniformly distributed relays
Note that the mean of |ℎ   | 2 is distance-dependent.Thus, a superscription is needed to distinguish    and μ  during Phase I from those during Phase II, i.e.,    and μ  .Specifically, the    and μ  are associated with |ℎ    | 2 2; and  ≈ 0.577 is Euler's constant;    and  are the mean and standard deviation (std.) of the log-normal shadowing in the dB domain during Phase I's transmission period;  = 10/ ln 10.
(), e.g., the aforementioned M  (ℓ, ), O  (, ), O  (, ), or O  (ℓ, ) in Section 3. To ease the presentation, let  = |ℎ    | 2 ; and then   stands for the mean of  in the dB domain, which leads to μ =   − .Moreover,   () and   () represent the  and  of , respectively.Similarly, let  = |ℎ  | 2 ; and, in consequence, we can have   to represent the mean of  in the dB domain, which leads to μ =   − .Likewise,   () and   () stand for the  and  of .
Let the -th relay be selected to forward packets during Phase II.Therefore,  must belong to a particular subset of M  (ℓ) or O