A Comprehensive Analysis of Energy Efficiency Using Cooperative Spectrum Sensing Network

The proposed cooperative spectrum sensing network presented in this paper has potential properties that could improve the detection probability. The proposed network consists of multiple cognitive radio (CR) nodes. Each CR node is equipped with several antennas, and selection combining is used to identify the highest value of sensing data associated with each antenna. Further, this sensing data is passed to fusion center and primary user activity is identified at the fusion centre using the fusion rules. This study mainly focuses on identifying unknown signals in a Rayleigh fading environment using an improved energy detector. Initially, the novel analytical closed-form of expressions for false alarm and missing detection probabilities was provided under Rayleigh fading with multiple antennas at each CR. Further, the performance of the total error rate is studied under single and multiple antenna scenarios, and a quantitative evaluation is offered to determine average throughput and energy efficiency performance. Later, to simulate the performance with a solid foundation of mathematical analysis, a simulation test-bed is created in MATLAB. Finally, the performance is improved with the proposed scheme compared to conventional scheme.


Introduction
Recent developments in wireless applications have resulted in the continued advancement of wireless technology, and demand has grown at a geometric rate, resulting in a substantial increase in spectrum usage [1]. According to fixed spectrum access (FSA), the heavy utilization causes a shortage of the radio spectrum because of spectrum usage depends on the permitted end users [2][3][4]. The spectrum active and idle status depends on the licensed user or primary users (PUs) that reflects the inefficiency of the FSA policy. An alternative spectrum policy needs to be developed to meet the rising demand for spectrum usage more efficiently, thus giving rise to dynamic spectrum access (DSA) [5]. According to DSA, the radio spectrum can be accessed by licensed as well as unlicensed users called secondary users (SUs) [6,7]. The raise in demands to access the unused spectrum is overcomes with the introduction of SUs or cognitive radio (CR) users in the network. The CR's unique technology is that it will access the unoccupied bands of radio spectrum dynamically [8]. The real-time decision can be made regarding PU is using spectrum sensing (SS) technique [9]. In practice, SS is frequently impeded by two fundamental phenomena, namely multipath fading, and interference. Due to these effects, detection performance value reduces in SS technique. Sometimes, SS technique becomes unreliable and face hidden node issues also. These drawbacks can be overcome using cooperative spectrum sensing (CSS) technique, this technique is used to combat multipath fading and to improve overall detection performance with the help introducing large number of CR users in the network [10][11][12][13]. Various fusion rules are employed at fusion center (FC)in the CSS network to determine whether PU exists or not. As the number of SU grows, so does the amount of energy need for spectrum detection and reporting to FC increases, this influences the energy efficiency (EE) performance, as the energy efficiency value rises, throughput value also increases [14][15][16]. Reduction of energy utilization is an important task to address in this paper. The CSS scheme is addressed in [17,18] which describes about reduction of energy consumption by reducing the number of SUs. The EE scheme was proposed in [19] to reduce the energy consumption. It was suggested in [20] that the distributed SS algorithm reduces the average energy usage for SS by taking the optimal sensing rate and censoring threshold into account. The CSS network is addressed in [21] to enhance EE value and it reduces sensing time. In [22,23], it is suggested that detection threshold value is optimized to improve EE value, when CSS network is influenced by various fading effects. The EE performance is analysed using CSS network in AWGN environment using various fusion rules at FC. The detailed analysis of EE and throughput analysis under various fading and non-fading environments are provided in [24][25][26][27][28]. All the publications listed above utilizes the conventional energy detection (CED) technique to address EE performance. The CED-based CSS network is more suited at low-noise situations, but its performance is restricted. As a result, to improve the performance, improved energy detector (IED) is utilized in further research. In [29], it is shown that how an IED-based CSS network with several antennas at each SU in the network improves performance. This motivates us to evaluate the EE performance using an IED scheme and multiple antennas at each CR in CSS network when it influenced by Rayleigh fading environment (Fig. 1).
The remaining paper is organized as follows: Section 2 briefly discusses the suggested CSS network paradigm. Section 3, addresses a study of the energy efficiency and throughput of the proposed network. Section 4 represents the simulated results, Lastly Section V deals with the conclusion of the article.

Proposed CSS Network Model
An efficient IED based CSS model is proposed in this paper. The CSS network consists of one PU, one FC, multiple SUs, and each SU equipped with multiple antennas. The FC unit controls the three-step process in CSS network as follows. In the first step each CR senses the radio spectrum and store the sensing information with it. In the second step, sensed data is reported to FC via reporting channel. Finally, FC decides the existence of PU using the fusion rules in it. The detailed explanation about CED and IED are provided in [11]- [26].
Based on the signal received at j-th CR, activity of PU ( H 0 : absence of PU and H 1 : presence of PU) can be decided using [30]; In Eq. (1), j-th CR noise value is n j (t) , fading coefficient is represented by h j , and input signal to IED is s(t) . The proposed CSS network consists of multiple antennas (M) at each CR. The sensing data associated with each CR about PU at i-th antenna can be expressed as in [31]; From Eq. (2), the largest value of w i (represented as Z) is selected using selection combining (SC) technique. This value is reported to FC. According to the ED technique, comparison between pre-defined threshold (λ) value and Z is performed to identify the PU activity and it is given as follows [32]; The Rayleigh fading channel PDF is given in [33] as; The expression for probability of missed detection (P m ) is given in as [33]; n is S-channel SNR. The P m expression when the multiple antennas (M) are equipped at each CR is quantified as [33]; The expression for probability of false alarm (P f ) is computed using the following PDF given in [34] as; The P f expression is computed as [33]; The P f expression using the multiple antennas at each CR is given in [33] as; The overall false alarm (Q f ) and missed detection probability (Q m ) expressions are quantified using OR-Rule are given in [35] as; Similarly, for AND-Rule, Q f and Q m expressions are given in [35] as; The flow chart shown in Fig. 2 provides a detailed overview of how we achieved the simulation findings. Initially, we created the necessary BPSK signal as received signal, AWGN signal as noise and fading coefficients. Later, we decided to compute PU by comparing the received signal value to a pre-defined threshold value. Furthermore, in the suggested system architecture, several CRs are employed, and each CR have numerous antennas. The PU decision has been received by all CRs antennas using the SC scheme and we have implemented SC scheme. Finally, all CR decisions have transmitted to FC, and fusion rules (OR-Rule and AND-Rule) implemented to identify the activity of PU. Further, through and energy efficiency performances are evaluated.

Energy Efficiency and Throughput Framework
This section deals with the network parameters called EE and throughput performances using the expressions given in [35]. The average channel throughput (C avg ) expression for k-out-of-N fusion rule is given in [26] as; In the above expression, t p , t s , t p and t s are the throughput values of PU and SU in the presence and absence of them.
This paper concentrates on improvement of energy value when CR network is affected by fading environment. In the process of maximization of EE value, number of CRs and threshold values are considered as the key factors. Hence, in this context, each CR node uses energy to perform sensing (e 1 ) , to transmit information to FC, and CR itself requires energy (e 2 ) . Similarly, e p and e s are energies utilized by PU and SUs. Finally, total energy (E) consumed by the CR network is calculated as follows [30]; Energy efficiency can be computed as [35]; where can be OR-Rule or AND-Rule.

Computation of Optimal Number of SUs Using OR-Rule
The expression for EE using OR-Rule is given in [35] as;

Fig. 2 Flow chart for Simulation
An optimal number of SUs are required to maximize EE value using OR-Rule can be computed as [35]; where OR is a positive value, it ranges from 0 ≤ ≤ 1 and it can be computed as;

Computation of Optimal Number of SUs Using AND-Rule
The expression for EE using AND-Rule is given in [35] as; An optimal number of SUs are required to maximize EE value using AND-Rule can be computed as [35]; where AND is a positive value, it ranges from 0 ≤ ≤ 1 and it can be computed as;

Results and Discussions
This section deals about the simulation results and their detailed explanation. Using the simulations, we have computed the EE value and total error rate using an IED-based CSS network and multiple antennas at each SU over Rayleigh fading and analysis is carried out for various fusion rules. Finally, an optimal number of SUs are also calculated to maximize the EE value. The comparison tables are also provided to prove that the proposed CSS network gives better results compared to conventional schemes. The simulations results are in this section are evaluated with the strong support of mathematical analysis (Table 1).  Figures 3 and 4 are drawn between EE and threshold value and the analysis carried out for different numbers of SUs using OR-Rule at FC using single (M = 1) and multiple antennas (M = 2) at each CR. It is observed from the simulation that raise in SUs value rises from L = 1 to L = 5, EE value increases by 29% at =10. Similarly, when M value at each CR grows from M = 1 to M = 2, EE value increases by 11.4% at =10. Tables 2  and 3 are clearly demonstrating these comparisons. Finally, it can be concluded that improve in number of antennas at each CR enhances the EE value. Figure 5 depicts the EE performance execution for various SNRs using OR-Rule at FC with multiple antennas (M = 2) at each CR. The simulation shows that when the SNR value grows, EE value rises. This is due to that as SNR value increases, noise value reduces and signal strength increases. As SNR value rises from SNR = 5 dB to  Table 4 gives the detailed analysis about the effect on EE for various number of CR users and fixed SNRs. Figures 6 and 7 are depicted to assess EE performance for various number of SUs using AND-Rule at FC for M = 1 and M = 2, respectively. The simulation shows that when L value grows from L = 1 to L = 5, EE value drops by 21.4% at =10 and M = 1. The simulations also show that when the number of antennas at each CR increases from M = 1 to M = 2, EE value increases by 11.4% at =10. Tables 5 and 6 clearly demonstrate these similarities. Finally, it is obvious that rise in SUs and antennas at each SUs, decreases the EE value utilising the AND-Rule at FC.   Figure 8 depicts the EE performance for numerous SNRs utilising AND-Rule at FC with M = 2 at each CR. The simulation shows that when the SNR value grows, so does the EE value. With the increase in SNR value, missed detection probability decreases which makes detection probability to increase its value and that leads to improve in EE value. As the SNR value rises from SNR = 5 dB to SNR = 10 dB, EE value improves by 29.1% with M = 2. Table 7 gives the detailed analysis about the effect on EE for various number of CR users and fixed SNRs.
Not only from our simulation results but also with the observation from the literature it was found that OR-Rule performance is better compared to AND-Rule. It is because of increased number of SUs in the network will report more precise information about the PU to FC. The basic rule behind OR-Rule is that in two user scenario, if any one user respond positively about PU, then final result at FC will be high. As the number of users increases, more sensing information about PU will be sent to FC which improves the detection probability value. In this way, with the cooperation of SUs in the network, detection probability value increases with OR-Rule.
Using the AND-Rule, EE performance falls as the number of CRs rises. As the number of CRs grows according to the AND-Rule, all the CRs must report to the FC that PU exists, then final judgement concerning PU is one, else it is zero. As the number of CR users increases in the network, cooperation among them will decreases, as a result, utilising the AND-Rule, the EE value falls.
In Fig. 9, EE performance w.r.t SNR is evaluated and performance comparison between two fusion rules (AND-Rule and OR-Rule) are also shown. It is observed from the simulation that SNR maximizes the energy efficiency for AND-rule and OR rule. But The performance of OR is better than the AND rule. It is observed that increase in SNR value improves EE value because EE value depends upon missed detection probability value. This missed detection probability value depends upon SNR value, as the SNR value increases, missed detection probability value decreases which leads to improve in EE value. For lower SNR values, EE value does not affect much but whereas for higher SNR values, missed detection probability value decreases and further energy efficiency value increases. The analysis discussed above is achieved from the mathematical approach using Eqs. (6), (14), (15), and (16). The total error probability Q m + Q f performance is assessed in Fig. 10 for various simulation settings such as λ, (L = 1, 2,3,4 & 5), (M = 2), ( p=3) and using OR-Rule at FC. Figure 10 shows that Q m + Q f value decreases up to minimum point for initial values of , and for larger values of , its value rises and there after it approaches to a constant value. For a particular case, p = 3, M = 2, =20 and =5 dB, Q m + Q f value falls by 78.3%, with the rise in L value from L = 1 to L = 5. The optimal threshold ( opt ) value also determined using Fig. 10. The value at which (Q m + Q f ) is the smallest that value can be treated as opt . As L value rises, opt value drops, tilts towards right, and moves away from the origin. Finally, it is clear from the graph that increase in -value, drives the total error curve to right side, implying that total error rate moves away from the origin.
Finally, it is clear from the graph that rise in λ -value drives the total error curves towards left, indicating that the average error rate moves towards the origin as increase in L value. The comparison values of ( Q m + Q f ) are for various fusion rules are presented in Tables 8 and 9 for fixed value of , respectively.
The error rate value is more with AND-Rule compared to OR-Rule. The detection probability value increases as well as probability of false alarm value decreases which leads to falls in total error value for OR-Rule because of the cooperation of among the CR users. Similarly, vice versa happened with AND-Rule so that total error rate increases with the increase in SUs value. Figures 12 and 13 show the optimal number of SUs calculation when multiple antennas are used at each CR for various threshold values and fusion rules. The simulations shows Fig. 10 Total error rate performance using OR-Rule at FC that when the SNR value grows from SNR = 5 dB to SNR = 15 dB, the number of SUs decreases from 5 to 1 at =10, decreases from 20 to 5 at =5 for OR-Rule & AND-Rule respectively. An optimal number of SUs is smaller for lower threshold values and grows with threshold value in Fig. 12. The optimal number of SUs is large for lower threshold values and it decreases with threshold value in Fig. 13. The optimal value reduces with the increase in SNR value. An optimal value of L is high at SNR = 5 dB and it reduces with increase in SNR this is due to that noise value is more at lower SNRs.  Similarly, as value increases, noise value decreases in S-channel and it improves the detection probability of PU. As value increases from 4 to 7 dB, P m value decreases by 66.3% at P f =0.1, M = 3, and p = 3.
In Fig. 15, P d performance is examined as a function of SNR values with simulation parameters M = 1,2 & 3, p = 3, and threshold values =10, 20 & 30. It can be observed from simulation that P d value increases with value, similar nature is observed with other simulation parameters, it is due to that increase in SNR value reduces the noise value. As M value at each CR increases, it improves the diversity order, hence, detection probability of PU is increases. If M value increases from M = 1 to M = 3, P d value decreases by 42.7%, at =5 dB, p = 3, and =30. When value increases from 10 to 30, P d value decreases by 13.9% at =5 dB, p = 3, and M = 3. Energy efficiency value rises with the number of antennas for both fusion rules such as OR-Rule & AND-Rule. We do not have fixed value for EE but we can maximize its value as much as possible with the different approaches. As per our paper concern, we have proposed a CSS network that gives higher EE value compared to existing networks and this comparison also shown using Tables. Finally, we can state that if EE value is high, it means that we are using radio spectrum and energy resources effectively.
Energy efficiency performance evaluation is also one of the sensing applications. In our paper, we have used CSS network, using this network, we are able to calculate missed detection probability value under Rayleigh fading environment. The missed detection probability value can be calculated by sensing the radio spectrum. This missed detection probability value is inter related to energy efficiency value and this mathematical approach also shown in this paper.

Conclusion
This paper introduces a CSS network that has potential to improve the detection probability value of PU. This study focuses on identifying unknown signals in a Rayleigh fading environment using the proposed CSS network with an IED scheme. Initially, the activity of the primary user (PU) is identified by utilising fusion rules (OR-Rule and AND-Rule) at FC in the proposed CSS network. In order to evaluate energy efficiency performance, mathematical assessment is offered and simulation analysis are also provided. From the analysis it has been observed that energy efficiency performance is improved by employing an IED technique and using numerous antennas at each CR in the network. Further, total error rate performance is also evaluated using various fusion rules. The total error rate performance comparison between single and multiple antennas situations are also presented using the simulations. Further, an optimal number of CR users are calculated to maximize the EE value. Finally, it is concluded that addressed network parameters performances are improved with the proposed network compared to conventional networks.
Funding The authors received no financial support for the research work.
Data and Material Availability Data sharing not applicable to this article as no datasets were generated during the current study.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Debasish Pal was born in the year 1975. He received his BTech degree from Bangalore University. He received his M.Tech degree from University of Burdwan. He received his PhD degree from Indian Institute of Technology Roorkee. He is currently working in Central Electronics Engineering Research Institute, Pilani, as a principal scientist. He has worked on high-power vacuum microwave devices particularly in pulsed and CW klystrons. His area of interest are klystron, antenna, microwave passive devices, and meta-material assistance devices and components.

Naveen Kumar
Ayan Kumar Bandyopadhyay is working as a principal scientist in the Central Electronics Engineering Research Institute, Pilani, India, since 2010. He has done M.Sc (Physics) and M Tech (Microwaves) degrees from Burdwan University, Burdwan, West Bengal, in 1998 and 2001, respectively. He has obtained his PhD degree from Otto-von-Guericke University, Germany, with distinction (Summa-cum-laude) and worked as a postdoctoral fellow in the European Synchrotron Radiation Facility (ESRF), France. During his postdoctoral research, he has contributed in designing the higher order mode-free radiofrequency accelerating cavities of the ESRF. Dr Bandyopadhyay was a visiting fellow at the Department of Electrical Engineering, Perugia, Italy, and at the Deutsche Electronen Synchrotron (DESY), Hamburg, Germany. His current research interests include design and development of microwave components, systems and high power microwave tubes.
Chaitali Koley was born in West Bengal, India, in 1985. She received her PhD degree in Microwave from the University of Burdwan. She is currently working as an Assistant Professor in the Department of Electronics and Communication Engineering, National Institute of Technology Mizoram. Her research interests are in Microwave communication and microwave oscillators. She has published more than 40 research papers in reputed journals and conferences.