An Innovative Cooperative Spectrum Sensing Algorithm with Non-ideal Feedback Channels and Delay...

Wireless Pers CommunDOI 10.1007/s11277-014-1755-6

An Innovative Cooperative Spectrum SensingAlgorithm with Non-ideal Feedback Channelsand Delay Considerations

Muhammed Fahim · Mahmoud H. Ismail ·Hazim Tawfik

© Springer Science+Business Media New York 2014

Abstract Cognitive radio (CR) is used to overcome the spectrum scarcity problem, whichresults from fixed allocation of wireless bands. CR allows the unlicensed secondary usersto exploit the idle spectrum, which is not occupied by any licensed primary user (PU), thusincreasing the overall spectrum utilization. In this paper, we first propose a simple cooperativesensing algorithm, which combines the local decision at each CR along with a group decisionreceived from a fusion center to produce a collective decision on the existence of the PU.The performance of the algorithm is investigated over ideal and non-ideal reporting channels,from the fusion center to the CR devices, both analytically and via simulations. Furthermore,the effect of cooperation delay, which causes the decisions received by the CR device fromthe fusion center to be outdated, is extensively studied, both analytically and via simulations.To overcome the significant performance degradation due to the effect of delay, an extralocal sensing cycle is performed at the CR side upon reception of the group decision. Resultsshow that the proposed algorithm outperforms the conventional hard decisions technique andexhibits a comparable performance to the soft decisions approach at a considerably lowercomplexity. Moreover, the algorithm is shown to enjoy more robustness against reportingchannel errors than the conventional hard decisions-based algorithm. Finally, the extra sensingcycle is shown to dramatically improve the performance for different delay scenarios.

Keywords Cognitive radios · Energy detection · Cooperative spectrum sensing ·Delay · Non-ideal feedback channels · Rayleigh fading

M. FahimNokia Siemens Networks, Giza 12577, Egypte-mail: [email protected]

M. H. Ismail (B) · H. TawfikDepartment of Electronics and Communications Engineering, Faculty of Engineering,Cairo University, Giza 12613, Egypte-mail: [email protected]

H. Tawfike-mail: [email protected]

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1 Introduction

1.1 Background

The exponential growth in wireless communications applications resulted in a scarcity in theavailable spectrum resources. Moreover, the static allocation techniques, set by the regula-tors, led to an under-utilization of most of the frequency bands [1]. Cognitive radios (CRs)technology was proposed to mitigate this problem. In CR technology, spectrum is sensedto detect the white (unused) portions in order to be used for new services by unlicensedSecondary Users (SUs) in a way that will not affect the operation of the licensed PrimaryUsers (PUs) [2].

Among the most popular techniques of spectrum sensing (SS) are matched filtering,wavelet-based sensing [3], fast fourier transform (FFT)-based sensing [4], waveform-basedsensing [5], cyclostationarity-based sensing [6,7], radio identification based sensing [8], andenergy detection (ED) [9–11]. The latter is the most popular technique because it does notneed prior information about the transmitted signal, except maybe for the signal-to-noise-ratio (SNR), which is required for calculating the threshold value, to which the received signalenergy will be compared. In spite of being relatively easy to implement, the ED spectrumsensing technique suffers from performance degradation under harsh channel conditions suchas fading and interference. These parameters will affect the received signal power, which isthe main decision metric in this technique [2]. Many methodologies have thus been devel-oped to improve the performance of ED in such channel conditions. These include the useof adaptive and double thresholds [12,13] or the use of hybrid techniques that merge EDwith another more accurate sensing technique [1]. Cooperative Sensing (CS) is one of themost effective techniques to overcome the impact of fading and interference [14,15]. In thistechnique, a number of CRs feedback their decisions either in soft [16] or hard forms [17,18]to a fusion center, which collectively indicates whether a PU is present or not based on aspecific optimal combining rule. The gain achieved through this technique is simply a resultof spatial diversity. Suboptimal results can also be obtained through combining the CRs softdecisions using suboptimal fusion techniques [16,19,20]. Soft decisions based CS requiresa high processing load on each CR as well as a high-rate feedback channel from the CRsto the data fusion center. CS based on sharing a one-bit decision between CRs, on the otherhand, is of lower complexity compared to the former scheme, yet, its performance is poorwhen compared to the soft decisions based algorithm [16]. Another approach focuses onalgorithms, which enhance the performance through different combining rules at the fusioncenter [17–19]. It is important to note here that most of the reviewed literature considererror-free links between the fusion center and the CRs [14,18–24].

1.2 Summary of Contributions

In this paper, a novel multi-stage simple ED-CSS algorithm is proposed that will use bothlocal and group decisions to collectively declare the status of the sensed channel. The algo-rithm combines the group decision delivered from the fusion center and the local decisiontaken by a specific CR in such a way that improves the final local decision taken at the CR. Itis not as complex as soft combining, and will be shown to achieve better results than the con-ventional hard decisions-based cooperative sensing. Our results will also show a considerableimprovement in the probability of detection (Pd ) when compared to hard decisions-basedscheme at the same average. Furthermore, the effect of non-ideal feedback channels will alsobe considered, which, to the best of authors’ knowledge, has not been extensively studied in

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An Innovative Cooperative Spectrum Sensing Algorithm

most of literature. In particular, it will be shown that the new proposed scheme can achievea high degree of robustness against channel errors compared to the conventional cooperativetechniques. On a related front, the performance of the proposed CS algorithm will be studiedwhen cooperation delay is taken into consideration. This delay causes the decisions broad-casted from the fusion center to the local CRs to be outdated [25], thus causing a noticeabledegradation in performance. Cooperation delay can be a result of the local sensing delay,the round-trip propagation delay and/or the processing time at the fusion center. A simplemodification to our proposed algorithm is suggested in order to reduce the effect of the coop-eration delay. The modification simply entails performing another sensing cycle at the localCR after receiving the fusion center decision, then applying a certain multiplexing criterionto take into account both the local CR decision and the group decision. This modificationis shown to dramatically improve the performance of the proposed algorithm in terms ofPd . To the best of the authors’ knowledge, our work is one of a kind, which considers suchimpairments in their analysis.

The rest of the paper is organized as follows: in Sect. 2, the system model under con-sideration is presented. In Sect. 3, the proposed CS algorithm is presented with and withoutreporting channels errors. In Sect. 4, the effect of cooperative delay on the performance of theproposed algorithm will be studied and a simple second sensing cycle is proposed to compen-sate the performance degradation resulting from the outdated decisions. Section 5 presentsthe analytical and simulation results. Finally, in Sect. 5, concluding remarks are discussed.

2 System Model and Assumptions

Figure 1 shows an illustration of the cooperative spectrum sensing system under considerationwhich consists of M+1 CRs, where M is an arbitrary even integer. When the i th CR wishes toaccess the unlicensed spectrum, it sends a query to the fusion center, which in turn asks all thecooperative CRs ( j = 1, . . . , M+1) to report back their decisions. The fusion center will thenmake the required processing on the data collected from each individual CR and generates afinal decision that will be relayed back to the local CR. Three main aspects should be takeninto consideration while analyzing a cooperative scheme; namely the nature of collected data,the combining rule at the fusion center and the channel conditions between the fusion centerand the local CRs. Usually, the sensing technique is named after the type of the collecteddata, e.g., N -bits hard decision, soft decision or softened-hard decision [16,17,26]. The datacombining rule describes how the collected data will be combined in the fusion center tomake a final decision as in [14,17,18,24]. In this work, we assume a one-bit hard decision

Fig. 1 Illustration of the proposed cooperative SS scheme

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Fig. 2 Energy detector block diagram

with majority rule combining at the fusion center. Since each CR should report its data to thefusion center, and receive a final decision accordingly, then the channel conditions should betaken into account [17] during the analysis of cooperative algorithms. From the performancepoint of view, the main key performance indicators of any spectrum sensing system are theprobabilities of false alarm Pf and detection Pd . The probabilities of detection and falsealarm are derived for one-bit hard decision with majority rule combining at the fusion centerin terms of the local CR corresponding probabilities and assuming error-free channels. Theseare given by:

Pd,group =M+1∑

i= M2 +1

(M + 1

i

)Pi

d,local

(1 − Pd,local

)M+1−i, (1)

Pf,group =M+1∑

i= M2 +1

(M + 1

i

)Pi

f,local

(1 − Pf,local

)M+1−i, (2)

where Pd,group, Pf,group, Pd,local and Pf,local are the probabilities of detection and false alarmfor both the cooperating group and local cases, respectively. The results above can be deduceddirectly if we note that the detection and false alarm events follow a binomial distributiongiven the majority rule combining. Similar expressions can be derived for other fusion rules[17], if needed. At each CR, an SS module is implemented. As the name indicates, ED SS isbased on measuring the energy in the received signal, and then comparing it to a pre-definedthreshold to decide whether the band of interest is occupied or not. This threshold is chosenbased on prior knowledge of the average SNR [2]. Figure 2 shows the block diagram of anED system employed at each CR. In particular, the received signal is first filtered to sense acertain band and the received signal samples are then squared and added up to measure theamount of energy in the captured samples. Finally, this energy is compared with a predefinedthreshold to decide whether a secondary user can use the band or not. The received signal,r(n), at any cognitive radio can be modeled as:

r(n) ={

w (n) , under hypothesis H0

h (n) ∗ s (n) + w (n) , under hypothesis H1,(3)

where w(n) is the Additive White Gaussian Noise (AWGN) component, s(n) is the PUsignal, h(n) is the channel impulse response and the hypotheses H0 and H1 represent thecase whether a PU is absent or present, respectively. The decision variable, representing themeasured energy, is thus given by:

M =N∑

n=1

r2(n), (4)

where N is the number of samples used for the sensing process. The conditional ProbabilityDensity Function (PDF) of this decision variable under both hypotheses can be derived for

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the AWGN case as [20,24]:

P (M |H0) =(

Mσ 2

) N2 −1

e−

(M

2σ2

)

σ 22N2 Γ

( N2

) , (5)

P (M |H1) = 1

2σ 2 e−

(M

2σ2 + Nγ2

)(M

σ 2 Nγ

) N4 − 1

2

I N2 −1

(√Nγ

M

σ 2

), (6)

where γ is the average SNR, σ 2 is the noise power, Γ (·) is the Gamma function and Im(·)is the mth order modified Bessel function. For the AWGN channel, the expressions for theprobabilities of detection and false alarm are given, respectively, by [24]:

Pd,local = prob (M > λ|H1) = Q N2

(√

Nγ ,

√λ

σ 2

), (7)

Pf,local = prob (M > λ|H0) = Γ

(λ

2σ 2 ,N

2

). (8)

where Γ (a, x), Q(a, x) are the incomplete Gamma and Marcum Q functions, respectively,and λ is the ED threshold. It is worth mentioning that for any fading model, Pf,local will bethe same as that of the AWGN channel since it is not a function of the instantaneous SNR,while Pd,local will need to be averaged over the fading distribution under consideration. Inthis work, we assume that the channel is Rayleigh faded.

The choice of the threshold in ED spectrum sensing plays a critical role as it directly affectsthe system performance. In this work, we define an overall probability of error as the weighedsum of the detection and false alarm probabilities in (7) and (8), respectively, and will choosethe value of λ, which minimizes this weighed sum. Despite the fact that this threshold willnot be optimum for Rayleigh fading, yet, it will act as a reference value in schemes wherethe threshold cannot vary in correspondence with the received power [20]. Differentiatingthe overall probability of error with respect to the threshold, one gets an expression of theoptimum threshold in terms of the SNR and the number of samples used during the sensingprocess as follows:

Pe = αPf,local + β(1 − Pd,local

)

∂ Pe

∂λ= 0 ⇒ β

I N2 −1

(√Nγ λopt

)

λoptN4 − 1

2

= α

(√Nγ

) N2 −1

e−

(Nγ2

)

Γ( N

2

) , (9)

where α and β represent the weighting factors for Pf,local and Pd,local, respectively. Thesefactors will be used for changing the operating point on the Receiver Operating Characteristics(ROC) curve for the same SNR according to the constraints of the system under consideration.In particular, for environments where the throughput of the secondary user is of prime concern,we should choose α � β while for environments with strict constraints on the amount ofinterference affecting primary users, we should choose β � α. Equation (9) could be solvednumerically to obtain an estimate for the optimum threshold for different values of the SNR.It is worth mentioning here that, in this work and without loss of generality, we assume thatα = β.

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3 Proposed Cooperative ED SS Algorithm

We propose an algorithm that combines the group decision delivered from the fusion centerand the local decision taken by the i th CR. The combination of the local and group decisionswill be according to the following simple rule:

– If the group decision dgroup = 1, then the final decision at the i th CR is di = 1.– If the group decision dgroup = 0, then the final decision at the i th CR is di = dlocal, where

dlocal is the local decision of the CR that was previously sent to the fusion center.

The logic behind the above decision rule is quite simple. As Pf,local drops rapidly to reachalmost 0 at very low SNRs, then whenever the group decides “1”, a primary user is mostprobably present on the sensed band. Therefore, the final decision at the local CR should beinclined towards a “1”. On the other hand, when the group decides “0”, this can result eitherfrom a miss detection or a real opportunity to use the channel. In this case, the benefit of usingthe proposed scheme becomes evident, as the CR will not experience miss detection unlessboth the group and the local decisions are in agreement. This will decrease the overall missdetection probability, or equivalently increase Pd of the whole scheme. The improvement ofPd will be dependent on the conditional probability (Pd,local| group decision = “0”), whichis expected to be relatively small at low SNRs. This is due to the fact that the local and groupdecisions are highly correlated as the amount of information in the received signal poweris very poor. Hence, both Pd,group and Pd,local will be almost 0.5. As the SNR increases,this correlation will decrease causing the conditional probability to increase. Figure 3 showsthe behavior of this conditional probability versus SNR for a Rayleigh fading channel withM = 10 and assuming BPSK modulation. For this case, at very low SNR values ∼ −10 dB,local sensing carries almost no information about the status of the PU, hence, the conditionalprobability approaches 0. As the SNR increases, it starts to rise gradually. At relatively highSNR values ∼0–5 dB, the conditional probability starts to degrade. This is due to the fact that

Fig. 3 Conditional Pd at local CR given a group decision of “0” for BPSK, 11 CRs and Rayleigh fading

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as the correlation between the local and group decisions increases, it is unlikely to detect thepresence of the PU at the local CR if the group misses it.

For this case, at SNRs of around −5 dB, the correlation will start to increase againas the cooperation will lose its advantage due to the high margin of received energycompared to the predefined threshold even in deep fades. It is worth mentioning thatwhen the group decides “0”, the local decision will be considered, which will in turn,increase the overall Pf , but with an insignificant amount as will be shown later in ourresults.

3.1 Performance Analysis in Ideal Channels

In this subsection, expressions for Pd and Pf for the proposed scheme are derived in terms ofthe probability of detection and false alarm given by (7) and (8) as well as the local conditionalprobabilities. We assume that all the communication channels used in the procedure areerror free. Equivalently, the one-bit collective decision arrives correctly from the fusioncenter to the interested CR. Figure 4 is used to clarify where the gain of the proposedscheme comes from and to derive the overall Pd and Pf . Generally, detection will takeplace when the final decision is “1” and the primary user is indeed occupying the band. Inthe proposed algorithm, the final decision will be “1” if either the group decision is “1” orthe local conditional decision (local decision given that the group decision is “0”) is “1”,which occurs with a probability Pd,local. On the other hand, a false alarm will be declaredwhen the final decision is “1” which indicates that the band is not occupied by any PUs.According to the proposed scheme, this will occur if the group takes a decision of “1” orthe local conditional decision is “1”, which take place with a probability Pf,local. Thus,we can formulate the detection and false alarm probabilities of the proposed algorithm asthe sum of the conventional cooperative probabilities and the local conditional probabilitiesyielding:

Pd = Pd,group + (1 − Pd,group

) (Pd,local|group decision = “0”

), (10)

Pf = Pf,group + (1 − Pf,group)(Pf,local|group decision = “0”). (11)

Fig. 4 State diagram of the proposed spectrum sensing in error-free channels

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Fig. 5 State diagram of theproposed spectrum sensingscheme with a non-idealfeedback channel from the fusioncenter to the local CR

3.2 Performance Analysis in Non-ideal Channels

Realistically, the feedback channel between the fusion center and the local CR will not beerror free and will sometimes flip bits with a certain probability. This will indeed affect theoverall detection and false alarm probabilities [17]. For ease of analysis, we will model thisfeedback channel as a Binary Symmetric Channel (BSC) with a probability of error Pe. Toderive Pd and Pf of the proposed scheme under this new assumption, we summarize thedifferent possibilities that the system might encounter in Fig. 5, which is a modified versionof Fig. 4. In order to derive Pd,e and Pf,e of the proposed scheme for non-ideal channels interms of the conventional Pd,group,e and Pf,group,e, we first derive those of the conventionalcooperative scheme for non-ideal channels in terms of those in (1) and (2) as:

Pf,group,e = Pf,group (1 − Pe) + (1 − Pf,group

)Pe, (12)

Pd,group,e = Pd,group (1 − Pe) + (1 − Pd,group

)Pe. (13)

Then, we can derive the detection and false alarm probabilities of the proposed schemefor non-ideal channels in terms of the results in (12) and (13) as follows:

Pf,e = Pf,group,e + (1 − Pf,group,e

) (Pf,local|group decision = “0”

), (14)

Pd,e = Pd,group,e + (1 − Pd,group,e

) (Pd,local|group decision = “0”

). (15)

From the previous set of equations, it is clear that the conventional cooperative technique isnot robust against the channel errors (as Pd is directly proportional to Pe), while the proposedtechnique will be more robust against the channel errors because of the gain term (Pd,local|group decision = “0”)(1− Pd,group,e). This will be further clarified in Section 4. One thing tobe noted here is that the false alarm probability in case of non-ideal channels will be biasedup by the value of Pe at high SNRs as given by (14).

3.3 Performance Analysis Under Cooperation Delay

In this subsection, the effect of cooperation delay τ on the performance of the proposedED SS algorithm, is studied. By the time the group decision reaches the local CR, a PUmight have already occupied a previously empty band or left a previously occupied one, thusrendering the group decision outdated and, in fact, misleading as well. Figure 6 depicts atiming diagram of the complete cooperative sensing cycle. First of all, sensing takes placelocally at the CR, consuming a time Ts . Local sensing results are then forwarded to the fusioncenter, taking a propagation delay Tpr . The time needed for the fusion center to combine and

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Fig. 6 Timing diagram of the proposed cooperative SS algorithm

process all the received data will be denoted Tp before the final decision is sent back to thelocal CR causing another propagation delay Tpr . All these quantities add up to represent theoverall delay, which is experienced by the cooperative spectrum sensing cycle as follows:

τ = Ts + 2Tpr + Tp. (16)

As the CRs are randomly distributed in terms of the geographical location, it is reasonableto assume that the propagation delay Tpr and consequently the overall link delay τ is arandom variable. Specifically, we assume that τ follows a Gaussian distribution with meanμ and variance σ 2. The arrival rate of the PUs sessions will be assumed to follow a Poissonarrival process with rate λarr , while the session duration of a PU will be assumed to followan exponential distribution with a departure rate of λdep .

To analyze the performance with cooperation delay, the state of the PU at the edges (t0and t0 + τ ) of a complete sensing cycle is shown in Fig. 7 along with the correspondingprobabilities. The states represent the cases where the PU exists (1)/does not exist (0) at timet0, the start of the cooperative sensing process and at time t0 + τ , the end of the process.To determine the possible transition probabilities between any two states, we define P(x,y),where x and y represent the state of PU at the start and the end of the sensing process,respectively. In order to calculate these transition probabilities, we proceed as follows. First,assuming that τ is fixed for the time being, we note that the Poisson arrival process is definedas:

P (k, τ ) = e−τλarr (τλarr )k

k! , (17)

where P(k, τ ) is the probability of k arrivals within a period τ . Consequently, we can calculatethe probability of no PU arrival P(0,0) within τ as:

P(0,0) = P (k = 0, τ ) = e−τλarr . (18)

We also note that the exponential departure process is defined as:

Λ(t) = λdepe−tλdep . (19)

Hence, one can calculate the probability P(1,1) that the PU will have a session longer thanτ as:

P(1,1) = P (t ≥ τ) =∞∫

τ

λdepe−tλdep dt = e−τλdep . (20)

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Fig. 7 State diagram of a PU within time τ of the start of the cooperative sensing cycle

Finally, the probabilities P(0,1) and P(1,0) are the complements of P(0,0) and P(1,1), respec-tively. Based on the above, it is now possible to calculate the modified probabilities of detec-tion and false alarm, which takes into account the cooperation delay, as follows:

Pτd = P (decision = “1”|PU present at T = t0 + τ)

= P (decision = “1”|PU present at T = t0) P(1,1)

+ P (decision = “1”|PU not present at T = t0) P(0,1), (21)

Pτf = P (decision = “1”|PU not present at T = t0 + τ)

= P (decision = “1”|PU not present at T = t0) P(0,0)

+ P (decision = “1”|PU present at T = t0) P(1,0). (22)

Equations (21) and (22) can be rewritten in terms of the legacy cooperative detection Pd

and false alarm Pf probabilities, given by (10) and (11), respectively, to yield

Pτd = Pd P(1,1) + Pf P(0,1) = Pde−τλdep + Pf

(1 − e−τλarr

),

Pτf = Pf P(0,0) + Pd P(1,0) = Pf e−τλarr + Pd

(1 − e−τλdep

). (23)

The above expressions are valid conditioned on the cooperation delay τ . To get an averagevalue for Pd and Pf , we use the well-known fact that if x is a random variable and y = g(x),then E(y) = g(E(x)) [27]. Hence, the average Pd and Pf can be finally written as:

Pτd = Pde−μλdep + Pf

(1 − e−μλarr

),

Pτf = Pf e−μλarr + Pd

(1 − e−μλdep

), (24)

where μ, as indicated earlier, represents the mean value of the delay.Assuming that λarr = λdep = λ, from the above equations, it is clear that the factor λμ

is an important metric that has a great impact on the performance of the CR SS system. Inparticular, as λμ increases, the probability that the PU stays in its current state decreasesas given by the decaying exponential terms in (18) and (20). Hence, there will be a higherprobability of transition to other states and the decision received from the fusion center couldbe outdated. On the other hand, if λμ decreases, the transition probability of a PU withinτ will decrease, and the performance should converge to that of the legacy cooperationscheme. Using simulations, the ratio of outdated decisions versus λμ is depicted in Fig. 8,which confirms the previous observation. It is clear from the figure that as λμ increases

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Fig. 8 Ratio of outdated decisions versus λμ assuming λarr = λdep

gradually, the ratio of outdated decisions increases progressively reaching about 85 % of thetotal decisions sent at λμ = 1.9.

3.4 Performance Enhancement Through a Second Local Sensing Cycle

Performance degradation, in case of cooperation delay, results from the fact that the finaldecision received at the local CR is unaware of the current PU state. As a proposed solutionfor this problem, the local CR will be requested to perform another sensing cycle afterreceiving the group decision dg , where the final decision is to be obtained according to thefollowing rule:

– If the new local decision dlocal,new = 1, then the final decision di = 1.– If the new local decision dlocal,new = 0, then the final decision di = dgroup.

The above rule is based on the fact that starting from SNR values around −3 dB, theprobability of false alarm at the local CR becomes almost zero [1,2,19,28], thus, wheneverthe local CR decides “1”, then most probably a PU is currently occupying the band underinvestigation. This will remedy the case when the PU state changes from “1” to “0” during thecycle. On the other hand, if the local decision is “0”, then the group decision will be consideredinstead . The resulting probability of detection and false alarm of this new proposed schemecan be formulated as follows:

Pd,new = Pd,local,new + (Pd,group|Local CR misses a PU

), (25)

Pf,new = Pf,local,new + (Pf,group|Local CR misses a PU

). (26)

It is worth mentioning here that a new delay will have elapsed by the time the final decisionbecomes available. In particular, the delay will be increased by Ts .

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Table 1 Simulation relatedparameters

Parameter Value

Bit rate 10 kbps

Number of decision samples (N ) 200

Noise PSD −140 dB

Sampling rate 107 samples/s

Number of cognitive radios (M + 1) 11

λarr = λdep λ

λμ 0.01–0.5

Pe 0.1–0.3

Fading model Flat/slow Rayleigh

Fusion technique Majority rule

Modulation BPSK

4 Numerical and Simulation Results

In this section, we will illustrate the performance of the proposed ED SS using numerical andcomputer simulations. We will focus on the behavior of the probabilities of detection and falsealarm versus the SNR. The simulation parameters are summarized in Table 1. Although wechoose to present results for 11 CRs in cooperation, it is important to note that our proposedscheme showed performance gain for different number of CRs, thus this choice is not, byany means, restrictive. We will also focus on the behavior of the detection and false alarmprobabilities versus the SNR for different session duration/PU arrival rates combinations.The system performance will also be investigated for the case of the proposed second localsensing cycle.

Figure 8 shows the ratio of outdated decisions in an environment where cooperation delayis considered, as the delay metric λμ increases, ratio of outdated decisions continuouslyincrease, reflecting increase in number of arrivals and departure to and from the band respec-tively, same performance of proposed scheme can be achieved by conventional techniqueat ∼0–5 dB higher SNRs value. Figures 9 and 10 depict Pd,group and Pf,group, respectively,for the conventional cooperative technique (hard decisions majority rule combining) andsoft decisions combining scheme compared to the proposed ED SS algorithm assuming anerror-free feedback channel. It is clear from Fig. 9 that the probability of detection of theproposed scheme outperforms that of the conventional cooperative one, and is very muchcomparable to Pd of the soft decisions combining algorithm, at a significantly lower com-plexity. At low SNRs, and due to the high correlation between the local and group decisions,the improvement of the proposed scheme over the conventional cooperative algorithm is notas significant as in the case of high SNRs > −5 dB. From Fig. 10, the probability of falsealarm is shown to be almost the same for the three algorithms. This is expected as the cor-relation between the local and group false alarm probabilities is so high that the conditionalprobability

(Pf,local|group decision = “0”

)will be almost 0 causing minimal effect on the

false alarm probability.Figures 11 and 12 depict a comparison between the different cooperation techniques in

terms of detection and false alarm probabilities, respectively, in channels with feedbackerrors. Clearly, the detection probability of the proposed scheme outperforms that of theconventional scheme at the same SNR value, which is expected, since as the group decision

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Fig. 9 Comparison between the probability of detection for the proposed, the conventional and the soft-decisions-based combining schemes in an error-free channel

Fig. 10 Comparison between the probability of false alarm for the proposed, the conventional and the soft-decisions-based combining schemes in an error-free channel. Note that the curves for the soft-decisionscombining scheme and the proposed algorithm coincide on one another

fails, the conventional algorithm will completely fail, while for the proposed scheme, theconditional probability will not be correlated to the faulty decision anymore causing theoverall detection probability to be improved. As for the false alarm probability, it is foundto be almost identical to that of the conventional technique. It is worth mentioning here thatboth curves will saturate at values near Pe due to the component

(1 − Pf,group

)Pe.

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Fig. 11 Comparison between the probability of detection for the proposed and conventional algorithmsassuming a non-ideal feedback channel with Pe = 0.1

Fig. 12 Comparison between the probability of false alarm for the proposed and conventional algorithmassuming a non-ideal feedback channel with Pe = 0.1. Note that the curves for the hard-decisions combiningscheme and the proposed algorithm coincide on one another

The robustness of the proposed scheme against different values of the channel probabilityof error is demonstrated in Figs. 13 and 14. It is clear that for different values of Pe, theperformance of the conventional scheme deteriorates rapidly. However, for the proposedscheme, the detection probability is only suffering minor losses for different Pe.

Now, we switch our attention to the case where the effect of cooperation delay is taken intoconsideration. Figures 15 and 16 depict the analytical and simulated Pf,group and Pd,group,

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Fig. 13 Detection probability of the conventional scheme for different values of Pe

Fig. 14 Detection probability of the proposed scheme for different values of Pe

respectively, against SNR for different values of λμ. First, we notice that there is a goodagreement between the simulated and analytical values, which confirms the validity of theresults. Also, it is clear from the figures that for any specific value of SNR, Pf and Pd arealmost identical to those of the cooperative system with zero delay for very low values of λμ

(approximately <0.01). For relatively high values of λμ (approximately >0.3), there will bea considerable percentage of outdated decisions, which causes a significant deterioration inthe overall system performance, especially at high SNR values.

In order to investigate the effect of the second local sensing cycle proposed earlier inSect. 3.4, the probabilities of detection and false alarm are plotted versus the SNR for the

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Fig. 15 Simulated and analytical probability of detection versus λμ for the proposed scheme

Fig. 16 Simulated and analytical probability of false alarm versus λμ for the proposed scheme

proposed scheme with/without the extra sensing cycle in Figs. 17 and 18. It is evident that theextra sensing cycle has dramatically improved the probability of detection with cooperationdelay. The reason behind this is that it involves the local decision in the final sensing decision.As for the false alarm probability, it is shown to be almost identical to the conventionalscheme due to the fact that at moderate to high values of SNR (>−3 dB), the local falsealarm probability will be almost zero, yielding Pf,group to dominate the overall probabilityof false alarm.

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Fig. 17 The probability of detection for the proposed algorithm under cooperation delay with/without theextra second sensing cycle

Fig. 18 The probability of false alarm for the proposed algorithm under cooperation delay with/without theextra second sensing cycle

5 Concluding Remarks

In this paper, an efficient yet simple ED-based spectrum sensing algorithm was proposed. Thenew algorithm was shown to outperform the conventional hard decisions-based cooperativescheme over both ideal and practical feedback channels in terms of probability of detection.It was noticed that the same probability of detection of the conventional algorithm can beachieved using the proposed scheme at much lower SNRs (specifically, ∼8–10 dB lower).

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Also, the proposed algorithm has a comparable performance to the soft decisions-based one ata much lower complexity. As for the probability of false alarm of the proposed scheme, it wasfound to be almost identical to that of the conventional scheme for error-free channels as wellas channels with feedback errors. For the latter, the probability of false alarm saturates at thelevel of the probability of transmission error at relatively high SNRs due to the domination ofthe error component over the group false alarm component. Moreover, the proposed schemewas found to be more robust against feedback channel errors than the conventional algorithm.Finally, the effect of the delay of the sensing process on the performance of the proposedalgorithm was studied. The degradation encountered in the performance was found to bedependent on the factor λμ, which gives an indication of how fast the PU changes its state.If λμ is small enough (<0.01), then the PU will rarely experience state transition during thesensing cycle, and the system will likely behave as the zero-delay system, while if λμ is high(>0.3), the performance will dramatically degrade due to the frequent change of the PU stateduring the sensing cycle, such that most of the decisions are outdated. A simple modificationto the proposed algorithm was found to effectively improve its performance based on an extralocal sensing cycle, yielding an SNR gain of about ∼4–5 dB, which makes it an attractivechoice for CSS.

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Muhammed Fahim received the B.Sc. degree (with highest honors)in Electronics and Electrical Communications Engineering from CairoUniversity, Giza, Egypt, in 2007. From 2007 to 2008, he worked asa Teaching Assistant in the German University in Cairo (GUC), NewCairo, Egypt. Since 2009, he has been with Nokia Solutions and Net-works (NSN) in Giza, Egypt, where he is currently an OSS engineer.He is also currently working towards his M. Sc. degree in Communi-cations Engineering, from Cairo University. His research interests arein the area of cognitive radios with emphasis on cooperative spectrumsensing.

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Mahmoud H. Ismail received the B.Sc. degree (with highest honors)in Electronics and Electrical Communications Engineering, the M.Sc.degree in Communications Engineering both from Cairo University,Giza, Egypt, in 2000 and 2002, respectively, and the Ph.D. degree inElectrical Engineering from The University of Mississippi, MS, USA,in 2006. From August 2000 to August 2002, he was a Research andTeaching Assistant in the Department of Electronics and ElectricalCommunications Engineering at Cairo University. From 2004 to 2006,he was a Research Assistant in the Center for Wireless Communica-tions (CWC) at the University of Mississippi. He is currently an Asso-ciate Professor at the Department of Electronics and Electrical Com-munications Engineering, Cairo University. He has also been a Sys-tems Engineering Consultant at Newport Media Inc. Egypt DesignCenter in Cairo from 2008 to date. His research is in the general areaof wireless communications with emphasis on performance evaluationof next-generation wireless systems, communications over generalized

and composite fading channels we well as cognitive radios. He is the recipient of the University of Missis-sippi Summer Assistantship Award in 2004 and 2005, The University of Mississippi Dissertation Fellow-ship Award in 2006, The University of Mississippi Graduate Achievement Award in Electrical Engineeringin 2006, the Best Paper Award presented at the 10th IEEE Symposium on Computers and Communications(ISCC 2005), La Manga del Mar Menor, Spain and the Best Paper Award presented at the 29th NationalRadio Science Conference (NRSC 2012), Cairo, Egypt. He has 21 publications in international journals aswell as 38 papers presented at international conferences. He has one US patent as well as co-authored a bookon wireless communications. He served as a reviewer for several refereed journals and conferences and heis a Member of Sigma Xi, Phi Kappa Phi, and a Member of the IEEE.

Hazim Tawfik received his Ph.D. degree from Southern MethodistUniversity (SMU), Dallas in 1987. From 1987 to 1994, he was withBell Northern Research (BNR), Richardson, TX, where he contributedin the design and testing of the first digital cellular radio in the U.S.He represented BNR in standard committees for DAMPS. He thenworked on VSAT technologies in Egypt building the first data networkvia satellite using NEC technology. He served for 9 years in VodafoneEgypt in different capacities including Director of Network Engineer-ing and Technology strategy building 2G/3G network. He is currently aProfessor at the Faculty of Engineering, Cairo University, Giza, Egypt.His research interests include spectrum sensing, cooperative commu-nication, location techniques, handover algorithms, and system perfor-mance.

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