Performance Analysis for Secure Cooperative Systems Under Unreliable Backhaul Over Nakagamim Channels
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Abstract
In this paper, the secrecy performance of cooperative heterogeneous networks with unreliable backhaul over Nakagamim fading channels is investigated. To secure the proposed system, a friendly jammer is considered to confuse eavesdroppers. To transmit the signals from the source to the destination, a twophase transmitter/relay selection scheme is proposed. The best transmitter is selected when the signaltonoise ratio at the relays is maximized. In the second phase, the best relay is chosen when the jamming signaltointerferenceplusnoise ratio of the eavesdroppers is minimized. To investigate the system performance, closed form expressions are derived for the secrecy outage probability, ergodic capacity and nonzero achievable secrecy rate. In order to gain an insight into the system, asymptotic analysis is also provided. The results show that the degree of cooperative transmission and backhaul reliability are key parameters in the system and these parameters determine the secrecy performance.
Keywords
Unreliable backhaul Heterogeneous networks Physical layer security Nakagamim fading channels1 Introduction
Due to the increasing wireless data traffic demand, future networks will become more dense and heterogeneous. In heterogeneous networks (HetNets), macro cells and small cells will be used to increase the capacity needed for this rise in traffic demand and to offload traffic. A backhaul link will connect these small cells with the core network. The traditional backhaul is wired and can ensure the connection. However, the cost of the deployment and maintenance is high, especially when a large number of small cells is needed to cover dense scenarios. Moreover, small cells may not need such a highly reliable backhaul as traditional macro cells do [27]. This is because small cells serve a lower traffic capacity than macro cells. In this way, wireless backhaul has emerged as an alternative and attractive approach due to its low cost and flexibility. However, wireless backhaul is not as reliable as its wired backhaul counterpart due to wireless channel impairments such as nonlineofsight (nLOS) propagation and channel fading [10].
The reliability of the backhaul is an important factor in HetNets and research has been undertaken to investigate how the backhaul reliability can affect the system performance [2, 10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 31]. In [2], the authors considered cochannel intercell interference (ICI) in HetNets with unreliable backhaul and coordinated multipoint (CoMP) transmission was considered to reduce the interference. In [12, 13, 14, 15, 22, 31], the impact of unreliable backhaul on cooperative relay systems was investigated. The outage probability of finitesized selective relaying systems with unreliable backhaul was studied in [15]. A cognitive network with unreliable backhaul was investigated in [21], and asymptotic analysis showed that performance was mainly decided by backhaul reliability. For all the research mentioned on unreliable backhaul connections, backhaul reliability is a key factor in the system performance. Therefore, in a HetNet context it is essential for us to investigate backhaul reliability.
Another aspect that cannot be ignored is security [5]. For a complete study in HetNets system, security needs to be considered. The traditional way to enhance security is deploying cryptographic techniques across upper layers. However, it consumes significant power to encrypt and decrypt data [25]. In addition, with the development of quantum computing, key schemes can be broken and the key infrastructure become insecure [30]. In recent years, physical layer security (PLS) has become increasingly popular to secure wireless communications [9, 26, 28]. The main idea of PLS is that the wireless channels are random and unpredictable, thus this can be exploited to keep the information confidential from eavesdroppers. Wyner proposed that when the main channel has better propagation conditions than the eavesdroppers’, the communication between legitimate users could be secure [29]. However, when the wiretap channel is better, the secrecy rate can even drop to zero [7]. Various PLS techniques have been investigated to tackle this problem and enhance the security of the main channel; one of the main techniques is using cooperative jamming to generate artificial noise to confuse eavesdroppers [1, 4, 6, 7, 16, 17, 23, 32]. In [6, 32], the authors considered PLS and energy harvesting with a friendly jammer, and the authors in [6] also proposed joint jammer and relay selection schemes. In related work [16], a jammer is assumed to be an energy constrained node with no power of its own and can harvest power from the source node, but cooperative relaying was not considered in this work. However, all of the research above ignored the reliability of the backhaul. As discussed an unreliable wireless backhaul results in poor performance. It is essential to consider backhaul reliability when studying PLS in a small cell HetNet contexts.
Research in [13, 14, 22, 31] has taken into account PLS in relay systems with unreliable backhaul. In [31], the authors studied PLS and energy harvesting. In [14], the authors studied PLS in fullduplex cooperative relay systems. In [13], multiple eavesdroppers that can wiretap information from relay and transmitters are considered in a finitesized cooperative system. In [22], a friendly jammer was used to confuse eavesdroppers in single carrier systems.

We investigate the secrecy performance of cooperative systems by exploiting cooperative relay and jamming signals in the presence of unreliable backhaul links between macrocells and smallcells over Nakagamim fading channels.

A twophase transmitter/relay selection scheme is proposed. The achievable SNR at the relays is maximized by applying the best small cell transmitter selection in the first phase. The relay selection scheme is deployed in the second phase to minimize the instantaneous signaltointerferenceplusnoise ratio (SINR) at the eavesdroppers.

Analytical expressions to evaluate the secrecy outage probability, nonzero achievable secrecy rate, and ergodic capacity are derived in closedform. The asymptotic secrecy expressions are also attained to gain full insights into the impact of backhaul reliability on the network secrecy performance in the high SNR regime.

The effect of the number of smallcell transmitters, relays, eavesdroppers and backhaul reliability on the system performance is investigated.
The remainder of the paper is organized as follows. System and channel models are described in Section 2. Derivation of the SNR distributions in the proposed system is obtained in Section 3. The closedform expressions for outage probability, ergodic capacity and symbol error rate as well as the asymptotic analysis are carried out in Section 4, while numerical results are presented in Section 5. Finally, the paper is concluded in Section 6.
Notation:P[⋅] is the probability of occurrence of an event. For a random variable X, F_{X}(⋅) denotes its cumulative distribution function (CDF) and f_{X}(⋅) denotes the corresponding probability density function (PDF). max(⋅) and min(⋅) denote the maximum and minimum of their arguments, respectively.
2 System model
Where Γ(⋅,⋅) is the incomplete gamma function [8, Eq. (8.352.6)].
Backhaul reliability is modeled as a Bernoulli process \(\mathbb {I}_k\) with success probability s_{k} where \(\mathbb {P}(\mathbb {I}_{k^{*}}= 1)=s_{k}\) and \(\mathbb {P}(\mathbb {I}_{k^{*}}= 0)= 1s_{k}\). This indicates that T_{k} is participating in the transmission if the message is successfully delivered over its dedicated backhaul with probability s_{k} whereas it defers its transmission with probability 1 − s_{k}.
We assume the global channel state information (CSI) is available, which is a common assumption in PLS [22]. The CSI of the eavesdroppers can be known when eavesdroppers are active in the network and their status can be monitored [3].
We assume that the unreliable backhaul links are independent from the indices of the K transmitters, i.e., s_{k} = s,∀k.
3 SNR distributions
In this section, SNR distributions are derived firstly which are necessary for system secrecy performance analysis in the next section.
In order to achieve a high performance of the considered system, our selection scheme is to maximize the performance at the relays and destination and minimize the performance at the eavesdroppers.
3.1 Distribution of the link \(T_{k^{*}}R_{m}\)
3.2 Distribution of the link \(R_{m} E_{n^{*}}\)
Corresponding CDF of \(SINR_{R_{m} E_{n^{*}}}\) can be derived according to Appendix B.
3.3 Distribution of the link \(R_{m^{*}}E_{n^{*}}\)
3.4 Distribution of the endtoend SNR
4 Secrecy performance analysis
4.1 Secrecy outage probability
and \(\tilde {\beta } = {\sum }_{t = 0}^{m_{R}1}t \omega _{t + 1}\), \(\tilde {\Phi } = \frac {k}{\theta _R}\), \( \widetilde {\sum \limits _{D^{\infty }}} ={\sum }_{k = 1}^{K} {\sum }_{\omega _{1},...,\omega _{m_{R}}}^{k}\)\(\binom {K}{k} \left (\frac {k!}{\omega _{1}!...\omega _{m_{R}}!} \right ) \frac { (1)^{k1} s^{k}} {{\prod }_{t = 0}^{m_{R}1} \left (t!(\theta _R)^{t} \right )^{\omega _{t + 1}}}\)
4.2 Probability of nonzero secrecy rate
4.3 Ergodic capacity
The ergodic capacity is defined as the average secrecy rate averaged over all the SNR distributions.
where \(H_{p q}^{m n} \left [ . \right ]\) denotes the Fox Hfunction [18, Eq. (1.1.1)].
5 Numerical results
In this section, numerical results along with simulations are shown for the analysis carried out on the proposed system. The threshold of secrecy outage probability is fixed at 𝜃 = 1 bits/s/Hz. The binary phaseshift keying (BPSK) modulation is adopted in the simulations with transmission block size S = 64 symbols. In figures, “Sim” represents the simulation results, “Ana” represents the analytical results and “Asy” represents the asymptotic analysis results. We investigate the network performance with various parameters to examine the effects of the degrees of cooperative transmission and backhaul reliability.
5.1 Secrecy outage probability
In addition, when s = 0.95 and the number of smallcell transmitters increases from K = 1 to K = 3, the secrecy outage probability decreases due to the increased received signal power at D.
5.2 Ergodic capacity
5.3 Nonzero achievable secrecy rate
In the figure, simulation results match well with the numerical results, thus, validating the analysis presented in the paper.
6 Conclusions
This paper investigates the secrecy performance of cooperative heterogeneous networks with unreliable backhaul links. A two phase transmitter/relay selection scheme was proposed to maximize the SNR at the relays and minimize the SINR at the eavesdroppers. Closedform expressions are derived and asymptotic expressions are also provided. Results show that when the number of smallcell transmitters and relays increases, the system can achieve a better performance. However, the increase of eavesdroppers can significantly degrade the system performance. Moreover, backhaul reliability is a key parameter for the improvement of secrecy performance.
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