Performance Analysis for Secure Cooperative Systems Under Unreliable Backhaul Over Nakagami-m Channels

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 non-line-of-sight (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, 10‐15, 19‐22, 31]. In [2], the authors considered co-channel inter-cell interference (ICI) in HetNets with unreliable backhaul and coordinated multi-point (CoMP) transmission was considered to reduce the interference. In [12‐15, 22, 31], the impact of unreliable backhaul on cooperative relay systems was investigated. The outage probability of finite-sized 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 full-duplex cooperative relay systems. In [13], multiple eavesdroppers that can wiretap information from relay and transmitters are considered in a finite-sized cooperative system. In [22], a friendly jammer was used to confuse eavesdroppers in single carrier systems.

Cooperative jamming in the presence of wireless backhaul over Nakagami-m fading channels has not been studied yet. In this research, we investigate the cooperative jamming in a small cells HetNet context with unreliable backhaul over Nakagami-m fading channel. In our system model, an outage occurs when the system is either not reliable or not secure, hence we assess the secrecy outage probability as a performance parameter. Our main contributions are summarized as below:

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 closed-form 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.

We consider a HetNet system with a macro base station, S, K small cells, T_{{1,⋯ ,K}}, M relays, R_{{1,⋯ ,M}}, a jammer, J, N eavesdroppers, E_{{1,⋯ ,N}} and a destination, D, as shown in Fig. 1. S is connected to T_k via wireless backhaul. We assume that there is no direct link between T_k and D because of the poor channel condition. T_k sends information to D with the help of R_m. A single J transmits jamming signals in the system, and we assume that the jamming signals can be nulled out at D [6]. E_n wiretaps the information transmitted from R_m. All of the nodes are equipped with single antenna and operate in half-duplex. We assume that all the channels are Nakagami-m fading, and the channel power gains are gamma distributed. The cumulative distribution function (CDF) and probability density function (PDF) of the random variable X can be written as

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 \(\mathbb {P}(\mathbb {I}_{k^{*}}= 0)= 1-s_{k}\). 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].

In the first hop, the received signals at R_m are of the form where \(\mathcal {P}_{t}\) is the transmit power at T_k and \(h_{T_k R_m}\) is the channel coefficient of the link T_k − R_m, x is the unit power transmitted symbol and z is the complex additive white Gaussian noise (AWGN) with zero mean and variance σ, i.e., z ∼ CN(0,σ). The path loss component corresponding to \(h_{T_{k} R_{m}}\) is denoted as \(\alpha _T^{k,m}\), respectively.

In the second hop, the received signals at D are of the form where \(\mathcal {P}_{r}\) is the transmit power at relays and \(h_{R_m D}\) is the channel coefficient of the link R_m − D. The path loss component corresponding to \(h_{R_m D} \) is represented by \(\alpha _D^{m}\), respectively.

Similarly, the received signals at E are of the form where \(\mathcal {P}_{j}\) is the transmit power at the jammer, \(h_{R_m E_n}\) is the channel coefficient of the link R_m − E_n and \(h_{J E_n}\) is the channel coefficient of the link J − E_n. The path loss component corresponding to \(h_{R_m E_n}\) and \(h_{J E_n}\) are denoted as \(\alpha _E^{m,n}\) and \(\alpha _J^{n}\), respectively.

We assume that the unreliable backhaul links are independent from the indices of the K transmitters, i.e., s_k = s,∀k.

In this section, SNR distributions are derived firstly which are necessary for system secrecy performance analysis in the next section.

From Eq. 3, the SNR from T_k and R_m can be given as where \(\widetilde {\alpha }_R = \frac {\mathcal {P}_{t} \alpha _T^{k,m}} {\sigma _n^2}\). λ^k,m ∼Ga(m_R,𝜃_R).

Similarly, according to Eqs. 4 and 5, the SNR between R_m and D and the SINR between R_m and E_n can be obtained as where \(\widetilde {\alpha }_D=\frac {\mathcal {P}_{r} \alpha _D^{m}} {\sigma _n^2}\), \(\widetilde {\alpha }_E = \frac {\mathcal {P}_{r} \alpha _E^{m,n}}{\sigma _n^2}\) and \(\widetilde {\alpha }_J = \frac {\mathcal {P}_{j} \alpha _J^{n}}{\sigma _n^2}\). \({\lambda _{D}^{m}} \sim \text {Ga}(m_{D},\theta _{D})\), λ^m,n ∼Ga(m_E,𝜃_E) and \({\lambda _{J}^{n}} \sim \text {Ga}(m_{J},\theta _{J})\).

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.

This section derives the performances of secrecy outage probability, non-zero achievable secrecy rate and ergodic capacity utilizing the SNR distributions obtained in the previous section. Towards deriving these performances, secrecy rate is required to be defined first. Secrecy capacity is equal to the difference between main channel and the wiretap channel, which is given by [31] where [x]⁺ = max(x,0). In addition, log2(1 + SNR_DF) is the instantaneous capacity obtained at D from selected relay and \(\log _{2} (1+ SNR_{R_{m^{*}} E_{n^{*}}})\) is the instantaneous capacity of the channel from selected relay to the selected eavesdropper.

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 phase-shift 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.

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. Closed-form expressions are derived and asymptotic expressions are also provided. Results show that when the number of small-cell 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.