Current transport infrastructures are regarded as a significant source of the carbon dioxide () gases emitted into the atmosphere which consequently increase the global temperature. For instance, it was noticed that the transport-based emission comprises of the entire greenhouse impact in the United States . Therefore, a smooth transition from a carbon-greedy society to a carbon-free one can sufficiently improve this situation. Known for being highly efficient with low emission and better performance, electrical vehicles (EVs) have recently received significant public attention as an effective way to reduce the overall level of greenhouse gases. On the other hand, mass exploitation of EVs imposes several requirements on the current power grid (PG) systems such as being able to generate, aggregate and distribute large amounts of low-carbon energy in a real-time manner.
Such an integration of the EVs and PG is enabled by means of a reliable and secure bi-directional communication networks. Therefore, several communication technologies (i.e., Zigbee, WiFi, WiMAX, power-line communication (PLC) and cognitive radio (CR) networks) have been applied to support an interaction between the PG and individual EVs [2, 3]. For instance, Zigbee is a low-cost solution that can provide a satisfactory rate of 250 kbit/s and mostly suitable for intra-vehicle communications. At the same time, this technology has some drawbacks such as low delay tolerance and vulnerability to the engine noise and radio-frequency (RF) interference . Moreover, the authors in [5, 6] derived closed-form bit-error rate expressions and investigated the diversity of the proposed hybrid PLC/RF technique for the PG and vehicle-to-grid communications.
Integrating the PG with different communication technologies not only improves the efficiency and flexibility of the PG but also makes the latter vulnerable to cyber security risks typical to these communication systems [3, 7]. In general, these cyber security threats are usually divided into four categories: authenticity, integrity, confidentiality, and availability . The latter is the most important one to maintain communication services. For example, the loss of availability does not allow the PG to dynamically respond to the real-time power requests. On the other hand, the EVs which are disconnected from the PG will experience poor charging services. With the public information in the commercial wireless systems, illegal nodes can jam or distort the RF signal at the destination by transmitting an interfering signal over the air. As a result, the jammed or distorted received signal becomes unrecognizable. Such jamming attacks performed against the critical PG node can disable the operation of a large area since a central service controller does not obtain accurate load information. Consequently, local load unbalancing can affect a broader area .
The exponentially growing number of wireless devices and massive EV exploitation naturally result in RF spectrum scarcity which can be handled by using the CR paradigm [9, 10, 11, 12]. CR is an emerging wireless technology allowing an unlicensed user, known as a secondary user (SU), to use a licensed spectrum band such that a primary user (PU) does not experience harmful interference caused by the SUs . Such communication can be organized using three known approaches, i.e., interweave, underlay and overlay, which have different operational modes . For instance, the underlay CR grants permission to the SUs to operate in the licensed spectrum given that this communication does not result in excessive interference power at the PUs, which is referred to as an interference temperature constraint (ITC) . Moreover, it is worth mentioning that the CR features perfectly match the mass EV exploitation. In general, the EVs are highly dynamic and therefore can connect to the PG at any site irrespective of the type of a certain local communication network. Regarding the jamming attacks, the conventional anti-jamming techniques, e.g., frequency-hopping spread spectrum, direct-sequence spread spectrum, etc., can not be applied to the CR network since they do not take into account the unavoidable impact of the presence of primary network entities [3, 15].
Recently, visible light communications (VLC) has emerged as an attractive candidate to resolve the RF spectrum scarcity and avoid the CR restrictions simultaneously [16, 17, 18, 19]. The main advantages of VLC technology are its electromagnetic immunity to the RF interference and the availability of a wide unregulated visible light spectrum range (from 430 THz to 790 THz) used for concurrent illumination and communication purposes. This technology can be applied to the indoor and outdoor environments. For example, the authors in  investigated the outage performance of the indoor non-orthogonal multiple access based VLC network scenario. In , it was experimentally demonstrated that the outdoor VLC channels follow the Rician statistical distribution.
In this paper, we considered the downlink outdoor electric vehicular network when one EV is used as a relay to communicate with another EV whose direct link to the aggregator is jammed. We also specify several EV network scenarios to fully investigate the outage performance. Hence, our contributions are as follows. First, new closed-form analytical expressions were derived for the outage probability (OP) in outdoor cognitive relaying networks over mixed RF-RF/VLC channels. Second, we quantify the outage reduction enabled by deploying such a hybrid VLC/RF communication link. Third, we asymptotically analyze the OP and the corresponding outage reduction using the high signal-to-noise ratio (SNR) approximation and perfect CSI scenario. Forth, the provided analysis is validated by a good agreement with Monte Carlo simulations.
The remainder of the paper is organized as follows. In Section II, we describe the system model while, in Section III, we derive the closed-form expressions for the OP and outage reduction of the considered system model. In Section IV, we present analytical and simulation results and their discussion. Next, we summarize the paper with main concluding remarks in Section V. Finally, the analytical OP expressions over the RF/RF channels and of the asymptotic outage reduction are presented in Appendices A and B, respectively.
Ii System model
The adopted system model represents a downlink outdoor underlay cognitive radio network scenario represented by a mixture of the primary and secondary networks consisting of an aggregator (i.e., a source node denoted by ), two electrical vehicles (EV 1 and EV 2), a jamming node () and a primary user (). The network scenario can be described as follows. The primary network (PN) utilizes a given set of frequencies (i.e., a pool of the frequencies) for communication purposes. As being part of the PN, the aggregator attempts to send information to the destination node (i.e., EV 1 denoted by ) using one vacant frequency from the pool while the other EV (i.e., EV 2) is idle (e.g.
, parked and getting charged). At this moment,suppresses the communication link between and . To overcome this, selects another frequency (e.g., it can be vacant or occupied) from the pool to reach the jammed EV via the idle EV 2 that will act as a relay node (in the detect-and-forward mode and denoted by ). For the sake of practicality of the system setup, we consider four (4) cases given below:
Case 1: the newly selected frequencies are already being used in the PN such that the establishment of an end-to-end -to- relay-assisted communication session causes interference to the primary nodes exploiting these frequencies. Thus, underlay CR mode is needed.
Case 2: one of the selected frequencies is vacant in the PN such that can be assigned with it to establish the communication link between and with no interference at . On the other hand, the other frequency utilized for the -to- communication session is occupied and, thus, may lead to the intolerable level of interference at . Then, the power constraint at is required.
Case 3: this case is similar to Case 2 with only difference, i.e., the interference at is caused by only that needs to be power-restricted.
Case 4: the frequencies selected from the pool for an end-to-end -to- relay-assisted communication session are vacant and can be exploited for interference-free communication in the PN.
The end-to-end communication is realized over two identical time slots, with duration of each, where
stands for the time period over which the channel estimates are assumed to remain constant. To avoid intolerable interference in the PN, the aggregator and EV 2,i.e., and , have to restrict their transmit power levels, if needed, as
where , with standing for the interference temperature constraint (ITC) defined at 111Without loss of generality, we assume that orthogonal resources are assigned to all primary users. Hence, the SN communication session creates interference to only one primary receiver, i.e., ., and is the maximum allowed transmit power at node222This implies that the aggregator is also involved into the secondary network (SN) during the communication session operating on the chosen frequency channel. In other words, the aggregator can be treated as a gateway node between the primary and secondary networks. . , and indicate the channel coefficient between and node , the corresponding distance and the path-loss exponent, respectively. The communication sessions in the PN and between the aggregator and relay are organized in the RF spectrum due to its wide coverage and non-line-of-sight (NLOS) nature while the EVs communicate with each other through the RF or VLC channels.
The RF links are modeled by considering imperfect channel state information (CSI) as follows 
where and denote the channel estimate and the estimation error, with , respectively.
The received signal at (i.e., EV 2) can be expressed as
where , , and denote the channel coefficient between and , the corresponding distance, the message dedicated to and the additive white Gaussian noise (AWGN) term at
, with variance, respectively. The corresponding signal-to-interference-plus-noise ratio (SINR) can be given by
It is reasonable to assume that (i.e., EV 1) can acquire the RF and VLC CSI estimates333In different network scenarios, it is common for the nodes to exploit pilot signals in a cyclic manner for the channel estimation and synchronization purposes [21, §12.3.1]. Thus, secondary nodes are also able to acquire their own channel estimates between the primary/secondary transmitters and themselves through participating in this training process . and then send the feedback to the relay which detects the received message using Eq. (4) and transmits the data over the best channel444Since EVs are deployed with RF and VLC transceivers, selecting the best channel is identical to the best relay selection scheme .. Hence, the received RF signal at can be written as
where , and denote the channel coefficient between and , the corresponding distance, and the AWGN term, with variance , respectively. The corresponding SINR in the RF domain can be expressed as
Regarding the VLC communication link, we consider outdoor vehicular visible light communications (V2LC), where a point-to-point communication link is established between a headlight of EV 2 and the tail of EV 1. The headlight uses light-emitting diode (LED) as the transmitter and a positive-intrinsic-negative photodetector (PIN PD) is installed on the tail as the receiver. Such a link experiences Rician fading as experimentally verified in . Therefore, the received signal can be expressed as
where is the path-loss following Lambertian emission, denotes the effective photo-current conversion ratio, is the atmospheric turbulence, and the is a Gaussian variable with variance . Therefore, the corresponding SNR is given by
where denotes the power of message . The path-loss is modeled as 
where is the PD detection area, is the angle of irradiance, is the angle of incidence, is the optical filter gain, is the concentrator gain, and is the field-of-view (FOV).
The probability density function (PDF) of the Rician atmospheric turbulenceis expressed as
where denotes the modified first kind Bessel function of order zero while and stand for the characteristic parameters of the Rician distribution. Moreover, we define another parameter, known as shape parameter , which represents the ratio of the power arrived from the line-of-sight (LOS) path to the power corresponding to the remaining NLOS component. Then, substituting , the PDF of the overall channel coefficient can be written as
The noise variance of the PIN PD is the summation of the variances of the shot and thermal noises given as
where is the electronic charge constant, is the background current, and are the noise bandwidth factors, is the data rate, is the Boltzmann’s constant, is the absolute temperature, is the fixed capacitance, is the field effect transistor (FET) channel noise factor, is the gain of open-loop voltage, and is the FET transconductance.
Iii Performance analysis
In this section, we derive analytical expression of the outage probability of Case 1 since it involves both CR-based power constraints deployed at and . The outage expressions for Cases 2-4 can be derived by following the same approach.
Since the best channel is selected for transmission, the effective SNR can be expressed as
The outage probability is given as
where and denote the data rate threshold and its corresponding SNR-based value.
The term can be expressed as
where the term is calculated as
and the term is given by
where . Note that
follows an exponential probability distribution, and
is the rate parameter of the random variable (RV).
where, due to the independence of the RVs in , it can be simply expressed as
On the other hand, after some algebraic manipulations, the term can be computed as
Finally, the CDF of can be expressed as
The CDF of the RV can be calculated as
where is the Marcum Q-function of order 1 .
Then, substituting the terms , and into Eq. (III), the outage probability for Case 1 can be expressed in closed form as in Eq. (III), shown at the top of the next page. The outage expressions for Cases 2-4 are presented in Eqs. (27)-(29), shown at the top of the next page.
Now, using Eq. (III), the average throughput can be evaluated as
where denotes the achievable data rate given by
where the factor implies that the end-to-end transmission requires two time slots.
Iii-a Asymptotic Analysis
To obtain meaningful insights on the impact of the involved fading parameters on the network performance, we investigate the system performance in the high SNR regime. By setting , the high SNR approximation of the end-to-end OP for all Cases can be expressed as the expressions given by Eqs. (III-A), (III-A), (III-A) and (41), where the terms in the OP expressions represent the impact of CR communication555Note that Case 4 presumes that the secondary -to- communication does not cause any interference in the PN.. Moreover, further approximation given by the expressions in Eqs. (33), (36) and (39) represent the scenario when the transmit power levels and are not constrained by Eq. (1), i.e., the secondary communication does not harm the primary receiver (). Another useful insight is that the expressions related to all Cases coincide with each other, and this implies that they imitate Case 4, as expected. As it can be seen from the general expressions of the approximated OP, it depends on the quality of CSI estimates and the maximum level of interference that can tolerate. Moreover, the outage expressions can be further simplified by applying for small as in Eqs. (34), (37), (40) and (42), shown at the top of the next page, where . Finally, in the case of perfect CSI, network failure will not occur, i.e., since for any due to .
|-to- distance,||15 m|
|-to- distance,||20 m|
|-to- distance,||5 m|
|Shape index of the Rician distribution,||dB|
|Optical concentrator gain,||1|
|Optical filter gain,||1|
|Effective photo-current conversion ratio,||0.53 A/W|
|PIN PD detection area,||m|
|PIN PD FOV,||60|
|Noise bandwidth factor,|
|Noise bandwidth factor,|
|Absolute temperature,||300 K|
|FET channel noise factor,|
|Gain of open-loop voltage,|
Iii-B Reduction of Outage
It is interesting to quantify the performance advantage of exploiting such a dual-hop CR network comprising two complementary wireless technologies. This advantage can be effectively evaluated in terms of communication reliability, i.e., reduction of outage. With this in mind, we define the OP achievable by the dual-hop RF-based CR network as in Eqs. (A)-(A) (see Appendix A). Therefore, the outage reduction can be defined as
which is written in detail in Eqs. (43)-(46), shown at the top of the next pages. Moreover, their high SNR approximation can be further expressed as in Eqs. (B)-(B) (for more detail, please refer to Appendix B). From them, we can observe that the outage performance of the considered system model improves as both and tend to 1. Finally, it is worth noting that, unlike the other involved terms, the ITC term is the most critical one since the outage benefit severely decreases as increases and consequently results in performance saturation.