1
Spectrum Monitoring in Heterogeneous Cognitive Radio Network: How to Cooperate? 2
Prabhat Thakur1, Alok Kumar1, S Pandit1, G Singh1 and S N Satashia 1 Department of Electronics and Communication Engineering, Jaypee University of Information Technology, Waknaghat-173215, India 2 Space Application Centre, Indian Space Research Organization, Ahmedabad -380015, India
[email protected], (alok.kumar, shweta.pandit, ghanshyam.singh)@juit.ac.in,
[email protected] Abstract—The spectrum monitoring (SM) is a prominent technique to detect the emergence of primary user (PU) during the cognitive users’ (CUs’) data transmission. However, the imperfect SM causes delay in the detection of PU which results data-loss as-well-as introduces the interference at PU. The cooperation in CUs for SM is an effective solution to diminish these impairments of imperfection. Therefore, in this paper, a scenario is presented, where the CUs cooperate with each other for SM and have analyzed the effect of cooperation on various performance metrics namely, the data-loss, interference efficiency, and energy efficiency of the heterogeneous cognitive radio network (HCRN). An algorithm is illustrated for the computation of data-loss under various conditions of the traffic intensity of PU and different probability of SM error in the proposed HCRN. Moreover, the closed-form expressions of these metrics are derived for the cooperative and non-cooperative SM. Further, the simulation results are presented for various scenarios of probability of SM error (SME) and traffic intensity. Index Terms— Cognitive Radio, Data Loss, Energy Efficiency, Interference Efficiency, Throughput, Spectrum Monitoring.
I. INTRODUCTION The cognitive radio has emerged as a key technology to overcome the spectrum scarcity where the cognitive user (CU) senses the channel and starts data-transmission if the channel is sensed as idle otherwise move for another channel [1, 2]. During the CUs’ data transmission, the emergence of PU is a prospective event which needs to detect immediately in order to stop the CU transmission that results the data-loss improvement and avoid the interference with PU [3-6]. The detection of emergence of PU during the CUs’ transmission is achieved via spectrum monitoring (SM). The SM is a potential technique in which the CU exploits the received signal characteristics such as receiver error count (REC) and ratio of the energy for current window to the previous window (energy ratio) to detect the emergence of PU [7]. The SM on the bases of REC is proposed by Boyd et. al. [8], and further explored by various researchers [9-10]. It is worth to mention that the CU receiver receives the data (in the form of packets) with tolerable number of error in a packet which is known as REC. The emergence of PU creates interference at the CU receiver which increases the number of errors and that change in REC is employed to detect the emergence of PU. Similarly, the energy level increases on the emergence of PU which is also used to detect the same.
In [8], the authors have examined the SM over the Rayleigh fading channels and have exploited the multiple antennas on the CU to improve the effect of multipath fading via diversity combining techniques. Ali and Hamouda [9] have introduced an energy ratio SM algorithm for the orthogonal frequency division multiplexing (OFDM) based CRN and reported that the proposed approach outperforms the receiver statistics method in terms of detection delay however, the complexity is twofold as compared to that of the energy detector. Thakur et. al. [10] have proposed a decision statistic for SM using REC and have evaluated the detection and false-alarm probabilities. Moreover, an optimization problem is explored to maximize the channel utilization using constraint on the detection delay. Recently, the authors in [11] have analyzed the effect of SM on the “energy-and data-loss of CU” as well as on the “interference at the PU due to CU transmission”. It is observed that the introduction of SM in the high-traffic CRN (HTCRN) improves “energy- and data-loss of CU” as well as the “interference at PU due to CU transmission” as compared to that of the conventional (without SM system) HTCRNs. The SM is function of received signal which is affected by the random nature of channel and due to this reason, considering the SM as a perfect phenomenon is impractical scenario. Therefore, we have introduced the concept of imperfect SM and studied the effects on data-loss, power wastage, interference efficiency and energy efficiency in cognitive radio networks (CRNs) [12]. We have analyzed that the imperfection in SM degrades the performance of CRN, and a potential way to manage the imperfections is to establish the cooperation among CUs. Recently, the authors have analyzed the effect of cooperation in the CRN for a homogeneous1 environment which means all the CUs have equal probability of SM error [13, 14]. In practical, every CU has different value of spectrum monitoring error due to different channel conditions and hardware impairments. Therefore, it is worth to analyze the performance of cooperative CRN for heterogeneous CUs with different value of probability of SM error. The potential contribution in this paper is summarized as follows. 1
A CRN is defined as a homogeneous/heterogeneous CRN if all the CUs have same/different operating characteristics such as probability of error, channel conditions, hardware impairments, delay profiles etc.[14]. In the proposed CRN, the homogeneous/heterogeneous nature is considered in terms of probability of spectrum monitoring error which is due to different channel conditions and hardware impairments.
2 We have proposed a potential and feasible framework of cooperative SM (CM) for the heterogeneous CRN which is analyzed for different scenarios of the traffic intensity and probability of spectrum monitoring error. A closed-form expression of the Poisson-Binomial distribution (PBD) is derived which is exploited to formulate probability of x number of CUs confirmation among N CUs for the emergence of PU. The closed-form expressions of the achieved throughput, data-loss, interference efficiency and energy efficiency are derived and numerically simulated results are presented. This paper is structured as follows. The Section II comprises the background regarding the cooperative communication and the Poisson-Binomial distribution. In the section III, the system model of the proposed framework is described. The section IV comprises the performance analysis of the proposed system model and simulation results with their analysis are presented in section V. Finally, section VI concludes the work with future perspectives. II. BACKGROUND In the cooperative CRN, all the CUs make a decision (yes/no) on the bases of received information from the electromagnetic environment and send this decision to the central node/ fusion center (FC) in order to yield the final decision by combining all individual decisions. The type of cooperation where the individual CU sends the decision rather than the received information is known as hard-combining rules [15-17]. The hard-combining rule comprises OR, AND, and M-out-of-N-rules (MOON-rule). In MOON rule, the final decision(yes/no) is confirmed if M out of N CUs support the same [18, 19].The mathematical modelling of the distribution function of the M number of CUs’ confirmation (yes/no) is achieved by the Binomial distribution if all the CUs decide the decision with same probability [20]. The Binomial distribution is a potential approach in order to yield the discrete probability distribution, 𝑃 (𝑥/𝑁), to achieve exactly 𝑥 successes out of 𝑁 Bernoulli trials (where the result of each Bernoulli trial is true with probability 𝑝 and false with probability (1 − 𝑝)) which is well explored in the mathematics as well as implemented in various engineering applications such as communication engineering, computer engineering, signal and image processing etc. One popular application of the Binomial distribution is in cooperative communication in order to know the probability of error after cooperation when MOON rule is used to combine the results from various observation points (nodes/CUs). The key limitation of Binomial distribution is that it supports the homogeneous environment i.e. when every Bernoulli trial is true with same probability p and false with (1-p). However, in most of the feasible scenarios, every node has different probability of error either due to hardware or channel conditions. Therefore, it is
worth to analyze the considered network for such feasible scenario and for this, we need to explore the Poisson-Binomial distribution [21]. The Poison-Binomial distribution is defined to yield the discrete probability distribution 𝑃 (𝑥/𝑁), to achieve exactly 𝑥 successes out of 𝑋 Bernoulli trials (where the result of ith Bernoulli trial is true with probability 𝑝 and false with probability (1 − 𝑝 ). Various researchers have presented their investigation to compute the closed-form expression of the Poisson-Binomial distribution [22, 23]. Wang [21] have derived the probability of having x successful trials out of total N trials which is defined as [11]: 𝑃
𝑥 = 𝑁
𝑃 ∈
∈
(1 − 𝑃 )
(1)
∈
where, 𝐹 is the set of all subsets of x integers that can be selected from the set {1,2,3,4…N}. For instance, if N=4 and x = 2, then 𝐹 = {{1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}}and 𝐴 denotes the complement of A. The number of elements in the !
set 𝐹 are:
(
)! !
. The large value of N results the large
values of elements which is very difficult and complex to yield and results the increase in computational complexity. Thus, the computational complexity is very large for this approach and by keeping this in mind the Fernandez and Williams [23] have exploited the discrete Fourier transform (DFT) to achieve the closed-form expression for the PoissonBinomial distribution. 𝑥 1 = 𝑁 𝑁+1
𝑃
where 𝐶 = 𝑒
𝐶
1 −𝑃 + 𝐶 𝑃
and 𝑖 = √−1. In this paper, 𝑃
(2) yields
the complex number of probability which is against the norms/axioms of probability theory. Therefore, in order to overcome this issue, we have followed the fundamental steps of formation of the x successes out of N number of events [23] and have exploited the MATLAB 2010a [24]. We conclude that the expression in Equation (2) has a deficiency which is avoided by taking the absolute value of the computed probability. Therefore, the improved form of equation (2) is: 𝑃
=
∑
𝐶
∏
1 −𝑃 + 𝐶 𝑃
(3)
Further, in the MOON rule, the decision yes/no is confirmed when M number of nodes says yes/no. Therefore, the probability of decision yes/no is confirmed when M or greater than M number of users will say yes/no. Thus, the probability of this event is defined as: 𝑃 (𝑦𝑒𝑠/𝑛𝑜) =
𝑃
𝑥 𝑁
(4)
3
Fig. 1 The scenario of the proposed cooperative SM in cognitive radio networks.
III. SYSTEM MODEL In the proposed system model of heterogeneous heterogeneo CRN (HCRN), a transceiver pair of PU network communicates using a channel having bandwidth B as shown s in Fig. 1. The CRN consist of N number of CU pairs which are allowed to exploit the spectrum of PU in such a way that all the CUs get equal bandwidth and thus the bandwidth allocated to each CU is B/N. The CU communication is established via time frame (T) where time τ is devoted for spectrum sensing and (T-τ) for the data transmission. The number of packets transmitted during the sensing period without the emergence of PU is 𝑁 . In the proposed model, a high-traffic traffic environment with traffic intensity of PU greater than 0.5 is considered. Therefore, the CUs perform spectrum prediction in the previous time frame during the data transmission to select the channel with highest idle probability for spectrum sensing in the current frame. Consequently, there is improvement in the sensing process since it saves the sensing time and energy spent on the th sensing of active channels [25]. ]. Since the spectrum prediction predicti is performed in the background therefore, the time devoted is null however, the certain power (𝑃 ) is required to execute this process. The spectrum prediction is well matured technique presented in the literature [25-27], ], therefore, this paper mainly emphasizes on the cooperative SM. In the current time frame, the CU performs spectrum sensing for time τ and starts data transmission for time (T-τ) with power 𝑃 on the idle sensed channel. In the data transmission period, the process of SM is performed,, simultaneous to the data transmission to know the emergence of PU. The role of SM seems significant only when the PU recommences its communication during the data transmission, therefore, for the consideration of this event, the probability of PUs’ emerg emergence in the data transmission period is provided by the traffic intensity of PU (ρ). ). The traffic intensity of PU is presumed to be a binary stochastic hypothesis, in which 0 and 1 represents r the idle and active states of channels, respectively [19]. Further, r, the average arrival and channel holding time of PU is
modeled as the Poisson distribution (parameter λ) and Binomial distribution (parameter μ), respectively [28]. [28 Thus, the probability of channel to be active/busy (𝑃(𝐻 )) is defined ( owever, the probability of channel being as: 𝑃(𝐻 ) = μ/λ however, idle (𝑃(𝐻 ))) is defined as: 𝑃(𝐻 ) = (𝜆 − μ)/λ. In the proposed system model, the probability of channel to be idle 𝑃(𝐻 ) is assumed as the traffic intensity of the PU channel (𝜌) ( μ/λ. The higher value of traffic which means 𝜌 = 𝑃(𝐻 ) = μ intensity signifies that the PU emerges in the starting phase of data transmission period however the lower value represents the emergence of PU in the later part. Moreover, every CU senses the state of channel (active or idle) during duri the sensing period exclusively and cooperates with each other to formulate the final decision i.e. either idle or active. If thefinal decision is idle,, all the CUs start data transmission in the form of packets. Due to prospect of the PUs’ emergence during the CUs’ data transmission, it is the responsibility of the CU to detect the emergence PU and stop its communication. The detection of emergence of PU is a potential phenomenon which is achieved by applying SM. In the proposed model, the ed as the feasible imperfect phenomenon and SM is assumed imperfections in this process are presented by the probability of SM error (𝑃 ). In the proposed network 𝑃 _ denotes the probability of SM error for the ith CU where i = 1,2,3,…N. The imperfection in SM means the emergence of PU is not detected immediately, however detected after certain detection delay. This imperfection causes due to channel uncertainties and/or the hardware system impairments. The higher value of in the detection of PU. 𝑃 indicates that there is more delay d The delay in detection of the emergence of PU results the continuation of CU communication and causes the data collision/loss as well as introduces the significant interference at PU. In addition to this, the interference power at PU depends on the channel gain between CU transmitter and PU receiver(ℎ ) which is also known as interference link. Therefore, to managethe effect of imperfections, the cooperation between CUs plays a key role. The CUs decide the state of emergence of PU either 0 or 1and reports to the FC
4 where the final decision is achieved by combining all the reported state. If the final decision confirms the emergence of PU, all the CUs stop their communication otherwise continues. Further, the cooperation in the SM improves the probability of SM error. When the data are fused using MOON rule which is discussed in previous section, the probability of SM error (𝑄 ) is defined and presented by (4). 𝑄
1 𝑁+1
=
𝐶
1−𝑃
_
+𝐶 𝑃
_
(5)
Moreover, 𝑁 ,𝑁 , ℎ , and ℎ denote the noise power at PU receiver, noise power at CU receiver, channel gain from CU transmitter to CU receiver, channel gain from CU transmitter to PU receiver respectively. IV. PERFORMANCE ANALYSIS OF PROPOSED CRN In this section, the effect of imperfect SM on the data-loss of proposed HCRN is illustrated and derived the closed-form expressions of the achieved throughput, data-loss, interference efficiency and energy efficiency. The data-loss occurs in the CRN when the PU re-appears during the data transmission of CU and the probability of re-appearance is yielded by the traffic intensity of PU. The perfect SM is an impractical scenario in which the reappearance of PU is detected very quickly which means within a data packet time2 (loss of that single packet). On the other hand, the imperfect SM is a feasible scenario in which the data-loss is the function of the probability of SM error (𝑃 ). In the considered HCRN, the fix number of packets gets lost among the total number of packets (𝑁𝑜), which depends on the SM error. In the considered CRN, the computation of number of packets lost among total number of packets follows the Binomial distribution [20]. Therefore, in the proposed CRN, the discrete probability distribution 𝑃(𝑘/𝑁𝑜) of obtaining exactly 𝑘 number of packets lost out of 𝑁𝑜 (where the data-loss result is true for the ith CU with probability 𝑃 _ and false with probability (1 − 𝑃 _ ).Thus, the probability of data-loss due to probability of SM error for the ith CU in the non-cooperative SM3,4,5 (NCM) is defined as: 𝑃
_
𝑘 =( 𝑁𝑜
) 𝑃
1−𝑃
(6)
Similarly, the probability of data-loss due to probability of SM error in the cooperative monitoring (CM) for all the CUs is presented as: 𝑘 (7) 𝑃 = ( ) (𝑄 ) (1 − 𝑄 ) 𝑁𝑜 Further, the average number of data packets lost (𝑘 )2,3,4 for the ith CU in case of cooperative and non-cooperative monitoring are evaluated by computing the expectation of variables as follows: 2
Assumption: The perfect SM system is very quick and ideal, even though a particular packet is required to compute decision statistics. 3 The subscript NCM represents the non-cooperative spectrum monitoring. 4 The subscript CM represents the cooperative spectrum monitoring. 5 The subscript i represents the ith CU.
𝑘
_
_
𝑘
_
=
𝑘. 𝑃
=
_
𝑘. 𝑃
𝑘 𝑁𝑜
(8)
𝑘 𝑁𝑜
(9)
There is loss of one single packet even for 𝑃 = 0. Therefore, to compute the total number of packet lost in the CRN (𝑘 ) for both the cases, one packet need to add to 𝑘 which is presented as: 𝑘 _ _ = (1 + 𝑘 _ _ ) and 𝑘 _ = (1 + 𝑘 _ ). In the proposed CRN, the communication is established using frame structures which means after fix time interval i.e. the frame time (T), the CU periodically repeats the process of spectrum sensing and data transmission. Therefore, it is possible that the CU switches from data transmission mode to spectrum sensing mode of the next frame, immediately after the emergence of PU because of ending of the data transmission interval. In this case, the number of packets lost relies on the time of emergence of PU which is the function of traffic intensity (ρ) in the proposed CRN. Thus, the complete data loss in the proposed HCRN (𝑘 ) is not only the function of the SM error but also of the traffic intensity of PU. Therefore, to find the complete data-loss in the proposed HCRN, there is need to compute the total number of packets to be transmitted after the emergence of PU (𝑘 ) which relies on the traffic intensity and computed as: 𝑘 = (1 − 𝜌) × 𝑁𝑜. The complete data loss in the nonth cooperative(𝑘 CU and in _ _ ) CRN for the i cooperative (𝑘 ) for all CUsis: _ 𝑘
_
𝑘
_
_
= =
𝑘
_
_
𝑘 𝑘
_
𝑘
𝑖𝑓 𝑘 𝑖𝑓 𝑘
≥𝑘
