Abstract
This paper aims to derive accurate outage probability expressions of a cognitive decode-and-forward (DF) relay system over the Nakagami-m fading channel. A secondary system and a primary system coexist in a spectrum sharing the environment. In order to protect the data transmission of the primary system, the transmission power of the secondary system cannot exceed the tolerable interference threshold of the primary system and its available peak power. In particular, we also consider the impact on the secondary system when the primary system turns on its transmitter. Simulation results align with our theoretical formulas very well.
1. Introduction
The concept of relaying has been widely applied in cognitive radio networks. For example, a cognitive radio testbed was implemented in [1] for feasibility verification of cooperative relay. Power and channel allocation was investigated in [2] for cognitive radio networks with cooperative relay. Multicarrier modulation techniques were studied in a multihop cognitive radio system [3]. A greedy algorithm for joint bandwidth and power allocation was developed in a cognitive radio hybrid relaying network [4].
On the contrary, the outage probability of cognitive relay networks has been studied extensively. The exact outage probability of the secondary user was derived in opportunistic relaying with partial channel state information of the primary user [5]. The outage probability of cognitive relay networks was investigated in [6, 7] when relay selection was applied. A lower bound on outage probability of cognitive amplify-and-forward relay networks was examined in [8] subject to Nakagami-m fading.
However, common to the works in [5–8] is that, in their assumption, the primary system is idle and turns off the transmitter. Obviously, the secondary system will not receive additional signals from the primary system, which is an interference from the point of view of the secondary system. But in a spectrum-sharing environment, the primary and secondary systems may use the same spectral band together simultaneously. Therefore, the influence on the secondary system cannot be overlooked when the primary system is busy. Although the busy state of the primary system is studied in [9], only the Rayleigh fading environment was involved. This may not be realistic in practical applications owing to complex fading scenarios.
Inspired by the above description, the purpose of this paper is to study the accurate outage probability expression of a cognitive decode-and-forward (DF) relay system subject to Nakagami-m fading channels with the Rayleigh model as its special case. In order to guarantee the quality of service of the primary system, the transmission power of the secondary system is limited by the interference level that the primary user can tolerate and its own peak power constraint. Importantly, the primary system is busy and turns on the transmitter, while the idleness of the primary system can be regarded as a special case where the transmission power is zero. Therefore, the primary system also has a negative impact on the secondary system’s communication, which is often overlooked. When the closed-form outage probability expression is derived, we can immediately evaluate the outage performance of the following three special cases: single interference level constraint, single peak power constraint, and fault tolerant case.
2. System Model
Consider a spectrum-sharing environment where an authorized primary system and an unauthorized secondary system share the same spectrum band. The secondary system is composed of one secondary source node SS, one secondary DF relay node SR, and one secondary destination node SD. The primary system consists of one primary source node PS and one primary destination node PD. Denote , , , , , and as channel coefficients of links SS ⟶ SR, SS ⟶ PD, PS ⟶ SR, SR ⟶ SD, SR ⟶ PD, and PS ⟶ SD, respectively, as shown in Figure 1. Because the interference on PD cannot exceed the maximum signal-to-noise ratio (SNR) level , the transmission powers at SS and SR are less than or equal to and , where and are peak power constraints at SS and SR, respectively. represents noise variance. The instantaneous signal-to-interference-plus-noise ratio (SINR) at SD is given bywhereand is the transmission power at PS. If PS is idle and closes its transmitter, . This case has been widely studied [5–8]. But PS will definitely work, and its transmission power will definitely be greater than zero. Therefore, we consider a more general situation , while the case with can be regarded as a special case.
For convenience, let . Because all channels experience Nakagami-m fading, the probability density function (PDF) and cumulative distribution function (CDF) of X, , are given bywhere and denote the gamma function ([10], equation (8.310.1)) and the upper incomplete gamma function ([10], equation (8.350.2)), respectively. m and or are fading and shape parameters, respectively, in which represents statistical expectation.
3. Outage Probability
The outage probability at SD is given by , where is a certain threshold. The CDF of is given by
The second term of is denoted as , which can be computed as
Applying power series expansion in (6) yieldswhere and denote binomial coefficient and the lower incomplete gamma function ([10], equation (8.350.1)).
The third term of is denoted as . Calculating , we encounter one kind of integral form:
Using the binomial expansion and equation (3.381.3) in reference [10] in (8) can solve . Plugging the value of and finishing some arrangement in , we get
Substituting (7) and (9) into (5), we can obtain . Then the CDF of , , can easily be derived from by substituting corresponding parameters. Finally, the outage probability can be written as
Furthermore, we take into account three special cases to detect the influence of different power constraints on the outage performance.
Case 1. Single interference level constraint.
If the powers at SS and SR are just governed by the interference level on PD, this situation is equivalent to infinite peak power at SS and SR. Different from calculating the outage probability in accordance with its definition once again in [8], can simply be written by limitation manipulation as
Case 2. Single peak power constraint.
If we only consider the peak power constraint at SS and SR, this situation corresponds to the case that PD happens to turn off its receiver and be idle. Then, the outage probability is given by
Case 3. Fault tolerant scheme.
Sometimes, it is difficult to capture accurate instantaneous channel state information, especially in rapid varying channels. In this case, a fault tolerant scheme was proposed in [11], which only knew the statistical knowledge of the varying channel instead of the instantaneous value. The basic idea is the probability that the interference on the primary system from the secondary system beyond the predetermined threshold value does not exceed an acceptable error level. So, the power constraint is readjusted to meet the following conditions:where is a tolerated error. In this scenario, outage probability can be expressed by replacing and with and in (12), respectively, where is the inverse function of .
4. Simulation Results
In this section, we provide some typical simulation experiments to confirm our theoretical analysis. Without loss of generality, channel gain is normalized to unity, i.e., . Assume , and .
Figure 2 shows the outage probability versus average SNR under different tolerance interference level constraints of the primary system dB, where the SNR is defined as . The PS’s transmission power is = 0 dBW. A perfect match is observed between theoretical analysis and simulation results, which indeed corroborates the correctness of our formula, given in (10). Interestingly, different from the traditional wireless network where the outage probability decreases with the increase of SNR, when the SNR exceeds a certain value, for example, 10 dB in our experiment, the outage probability remains unchanged and constant in the cognitive system. The reason is that SS’s power is governed by the interference level in high SNR regime. The larger the interference that the primary system can tolerate, the lower the outage probability of the secondary system.
Figure 3 evaluates the impact of PS’s transmission power on the outage probability, where dB. Figure 3 is somewhat similar to Figure 2 due to the interference level . It is observed that the outage probability is deteriorated when PS increases its power. This is just the price that the secondary system pays for using spectrum holes because the secondary system is often unlicensed.
Finally, Figure 4 illustrates the outage probability when the primary system happens to be idle. Although this model may be ideal, it can still provide an insight. In contrast to Figure 3, the curves in Figure 4 have been declining due to . Furthermore, all curves are parallel to each other, indicating the diversity order is .
5. Conclusion
The accurate closed form of outage probability is evaluated in a cognitive DF relay system over i.n.i.d. Nakagami-m fading. In particular, our model also incorporates the busy situation of the primary system, which is usually ignored in the existing works. The outage probability expression is very useful and can directly export to three special cases, i.e., single interference level constraint, single power constraint, and fault tolerant scheme.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 61761030) and by the China Postdoctoral Science Foundation (Grant No. 2017M622103).