Performance of cluster-based cognitive multihop networks under joint impact of hardware noises and non-identical primary co-channel interference

In this paper, we evaluate outage probability (OP) of a cluster-based multi-hop protocol operating on an underlay cognitive radio (CR) mode. The primary network consists of multiple independent transmit/receive pairs, and the primary transmitters seriously cause co-channel interference (CCI) to the secondary receivers. To improve the outage performance for the secondary network under the joint impact of the CCI and hardware imperfection, we employ the best relay selection at each hop. Moreover, the destination is equipped with multiple antennas and uses the selection combining (SC) technique to enhance the reliability of the data transmission at the last hop. For performance evaluation, we first derive an exact formula of OP for the primary network which is used to calculate the transmit power of the secondary transmitters. Next, an exact closed-form expression of the end-to-end OP for the secondary network is derived over Rayleigh fading channels. We then perform Monte-Carlo simulations to validate the derivations. The results present that the CCI caused by the primary operations significantly impacts on the outage performance of the secondary network.

from the previous node and forwards it to the next hop. Recently, the multi-hop relaying protocols were proposed to improve the end-to-end performance for the CR networks [13][14][15][16][17][18]. The authors of [13][14][15][16][17][18] investigated the trade-off between security and reliability for cluster-based multi-hop CR networks. In [14,15], the end-to-end throughput for the underlay multi-hop CR networks was measured, where transmit power of the secondary transmitters is constrained by the maximum interference threshold required by the primary and the energy harvested from a power beacon. However, the published works [13][14][15] did not study the impact of the primary interference on the performance of the secondary network. The authors of [16] investigated the impact of primary network interference on the performance of the cognitive multihop network using MIMO-based relaying approaches. Nevertheless, this published literature has assumed that all the channel links are subject to independent and identically distributed (i.i.d.) Rayleigh fading. However, in practice, the fading channels are often independent and non-identically distributed (i.n.i.d.) due to the different positions of the nodes [17,18].
Motivated by mentioned above, this paper studies the end-to-end outage probability (OP) of the multi-hop CR network in the presence of multiple primary transmitter/receiver pairs. Due to the mutual effect, we investigate the cross interferences between the two networks which are modeled by i.n.i.d. Rayleigh fading channels. The contribution of this paper can be summarized as follows: a) We consider a practical model where hardware transceiver of the terminals is not perfect [19][20][21][22]. In addition, we investigate the impact of the CCI caused by the primary operations on the outage performance of the secondary network. Moreover, we derive an expression of OP for the primary network, which is used to calculate the transmit power of the secondary transmitters including source and relays. b) We derive an exact closed-form expression of the end-to-end OP for the secondary network under the joint impact of multiple interference constraints and hardware noises. c) Monte Carlo simulations are performed to verify the theoretical results.
The rest of this paper is organized as follows. The research methodology, which includes the systemic model of the proposed protocols and key targets presents in section 2. The simulation results show in section 3, and section 4 concludes this paper.

Research Method 2.1. System Model
This paper studies the multi-hop CR network, operating on the decode-and-forward (DF) relaying fashion. As illustrated in Figure 1, there are L primary transmitter/receiver pairs in the primary network denoted by PT ,PR where 1/ K indicates that the secondary data transmission is split into K time slots. The P P is transmit power of the primary transmitters, S, -1 k P is transmit power of Gaussian noise which is assumed to be same at all of the receivers, 2 PP  is total hardware impairment level caused by the primary transmitter and the primary receiver, and 2 SP  is total hardware impairment level caused by the secondary transmitter and the primary receiver [13].
Moreover, in (2)  where 2 SS  is total hardware impairment level caused by the secondary transmitter and the secondary receiver, and 2 PS  is total hardware impairment level at the primary transmitter and the secondary receiver.
Using (3), we propose a relay selection method at in (4) implies that the relay is chosen to maximize the data rate at this hop. Let us consider the data transmission at the last hop; with the SC combiner, the channel capacity obtained at the destination can be formulated by

Outage probability (OP) of primary network
where P R is the target rate of the primary network, and Next, we can rewrite (6) under the following form: from (7), we have (8) can be expressed as: Finally, we define OP of the primary network as the probability that there exists at least one PT/PR pair in outage. Due to the independence between the pairs, we can calculate OP of the primary network when the node 1 S k  uses the licensed band as follows:      

Transmit Power of Secondary Transmitters
Firstly, to guarantee QoS for the primary network, the transmitter 1 S k  must adjust its transmit power so that g is a function given in (11). As we can observe,  

End-to-end OP of Secondary Network
At first, we can formulate the outage probability at the -th  (12), we obtain: (14) similarly, the outage probability at the last hop can be calculated by:  (15) then, the end-to-end OP is expressed by an exact closed-form formula as:   L) is high, the outage performance is severely degraded due to impact of more CCI generated from the primary transmitters. Finally, it is observed from Figure 2 that the simulation results (Sim) match very well with the theoretical results (Theory), which hence validates the correction of the derivation of (11). We also see that when P 0.1 R  , the secondary users can access the bands. In addition, the transmit power of the source 0 S , as we can see, is lowest. It can be explained that because the distance between the source and the primary receiver 1 PR is shortest, hence it must reduce the transmit power to avoid being harmful the primary QoS.   . In this figure, the number of nodes at each cluster is fixed by 4, and the number of antennas at the destination is set by 2. It is seen from Figure 4 that the value of OP increases with the increasing of 2 SS  . Moreover, the outage performance is also worse when the number of the primary pairs increases. Specially, when 4 L  , the value of OP equals 1 since the secondary network is not allowed to use the licensed bands. Figure 5 presents the end-to-end OP of the secondary network as a function of the number of hops. In this figure, we assume that k NN  for all k, and NM  . From Figure 5, we see that there exists an optimal value of K at which the value of the end-to-end OP is lowest. Moreover, the outage performance of the proposed protocol can be enhanced by increasing the number of relays at each cluster and the number of antennas at the destination. From Figures 4 and 5, it is worth noting that the simulation and theoretical results are in a good agreement which verifies our derivations.

Conclussion
In this paper, we investigated the outage performance of the cluster-based underlay cognitive radio network in the presence of multiple primary transmit/receive pairs, in terms of the end-to-end outage probability under the joint impact of hardware impairments and co-channel interference. The results showed that the performance of the secondary network is limited by the number of the primary pairs and the co-channel interference caused by the primary transmitters. The performance for the secondary network can be enhanced by increasing the number of nodes at each cluster, increasing the number of antennas at the destination, and designing the number of hops between the source and the destination appropriately.