1. Introduction

The cognitive radio (CR) [1] concept has emerged as a candidate for mitigating the problem of spectrum scarcity faced by the wireless communication systems under the present policy of fixed allocation of the radiofrequency spectrum. This is done by allowing that unlicensed devices access a specific licensed band in periods of time or geographic areas in which it is unoccupied by the primary users (PU), which owns the right of using this band. These unlicensed devices are called cognitive users or secondary users (SU), and such an access method is usually referred to as an opportunistic spectrum access.

Before using a licensed band opportunistically, a CR must be capable of examining a portion of the spectrum, looking for the so-called white spaces (portions of unused spectrum). This spectrum sensing [2] capability is one of the main tasks of a CR. It will permit a CR to transmit its data without harm to the PU operation.

Due to the receiver noise, multipath fading and shadowing, the performance of the spectrum sensing when made by a single SU may be seriously degraded, hindering an accurate SU decision about the channel occupancy. The cooperative spectrum sensing (CSS) is capable of mitigating this problem [3]. In centralized CSS, a set of SUs sense the spectrum and send their sensing measurements or local decisions about channel occupancy to a fusion center (FC), where the global decision about the channel occupancy is made by combining the SU’s measurements or decisions [4]. The transmission of the sensing information is normally made via dedicated report channels.

Bandwidth and energy efficiency are aspects of paramount importance in present wireless communication systems, but even more for the development of the future fifth-generation (5G), in which the cognitive radio concept plays an important role [5]. Within this context, a common concern regarding CSS schemes is the bandwidth and energy consumption during the transmissions of sensing information to the FC. This concern is intensified if the number of cooperating SUs is large, since more bandwidth and energy resources will be needed.

A number of attempts have been made for saving energy and bandwidth resources during the report of secondary user's decisions; see for example [6-12]. Besides the bandwidth efficiency, the energy efficiency is also an important aspect of the spectrum sensing, being considered for example in [13-22].

Recently, a novel bandwidth-efficient fusion scheme for CSS was proposed in [23], along with extended results and discussions in [24]. In this scheme, the cooperating secondary users transmit their local decision at the same time and in the same bandwidth to the fusion center. Consequently, it provides a significant reduction in the required bandwidth of the report channel when compared with systems that use some orthogonal transmission approach, like time or frequency division multiple access. Shortly, in the idea proposed in [23] each SU transmits its local decision on the channel occupancy to the FC using a binary phase shift keying (BPSK) signaling. Since all SUs send their BPSK symbols simultaneously and occupying the same frequency band, the received symbols at the FC add non-coherently. Under the K-out-of-M rule, two sets of symbols are formed at the FC due to this non-coherency, one set being associated to K or more SUs deciding in favor of the presence of the PU signal, and the other set being associated to less than K SUs deciding for the presence of the PU signal. In [23] it is also proposed a computationally costly decision rule for discriminating these two sets. However, in [23] no attention has been directed to the energy consumption related to the decision reporting task. In other words, the new scheme of [23] increases the spectrum efficiency, but does not provide any means for improving the energy efficiency.

In this paper we adopt the spectrum-efficient fusion scheme of [23] and propose a new transmission strategy for saving energy in the report channel transmissions, without compromising the global decision performance. In our scheme, the simultaneous transmission technique proposed in [23] is combined with censoring [25] in the reporting phase, as follows: after local spectrum sensing, only the SUs that detect the presence of the PU signal are allowed to transmit the sensing information to the FC. The SUs that find no active PU signal do not send any information to the FC, decreasing the total energy consumption in the cognitive network. To reach the global decision the FC only needs to know how many SUs have reported their local decisions, which transforms the complex original decision rule of [23] into a simple threshold-based decision scheme. We derive expressions for computing the key performance metrics of the spectrum sensing (the probabilities of detection and false alarm), and these expressions are validated through computer simulations. An extensive analysis about the total energy consumption is also made for our fusion scheme, as well as for the one proposed in [23], allowing for a fair comparison between them in terms of energy efficiency. We also present a comparison between our fusion scheme and the censoring scheme proposed in [22], due to the similarity between them in one specific configuration of the scheme of [22].

The remaining of the paper is organized as follows: the system model proposed in [23] is discussed in Section 2. Section 3 is devoted to the proposed censored decision and energy efficient fusion system. The analysis of the energy efficiency is provided in Section 4. Our system is compared with a similar one in Section 5. Section 6 concludes the paper.

2. Reference System

In this section we first present the system model proposed in [23], which we hereafter refer to as the reference system, and give the expressions for its performance analysis. Then we discuss the accuracy of such expressions when compared with simulations. Subsequently, we discuss the energy efficiency of the reference system.

2.1 Reference system model

Basically, the whole process in the CSS scheme proposed in [23] can be divided into three phases: i) local spectrum sensing, ii) local decision transmission and iii) global decision at the FC. In the first phase, the activity of the PU is observed by each SU. The hypotheses H1 and H0 denote the PU signal presence and absence, respectively. The kth SU forms its local decision as mk = 1 if T > ξ, and mk = 1 if T < ξ, where T is the test statistic for the detection technique1 adopted by the SUs, and ξ is a local decision threshold, which is determined according to the desired probabilities of detection and false alarm. In the second phase, the SUs simultaneously transmit their local decisions by converting mk into BPSK symbols that can be represented in baseband as where Es is the average energy per transmitted symbol, which is equal to average energy per bit Eb. Therefore, the received signal sample at the fusion center is given by

where M is the number of cooperating SUs in the cognitive network, hk is the gain of the report channel between the kth SU and the FC, and w is the additive white Gaussian noise (AWGN) at the FC receiver input, having zero mean, variance and unilateral power spectral density per hertz.

It is assumed in [23] that hk is known at the FC, which allows for the classification of the local decision vector s = [s0,s1,⋯,sM-1]T as belonging to one of two sets, D0 or D1, respectively associated with the hypotheses H0 and H1, under the K-out-of-M decision fusion rule. In this rule, the FC chooses H1 when at least K among M secondary users declare an active primary user in the band of interest. According to the decision rule given in [23], the FC will choose H1 if

and will choose H0 otherwise.

If AWGN report channels are considered, the noiseless received signal samples follow a Binomial distribution with M + 1 values that can be represented geometrically as points in a one-dimensional space. The points belong to the set D1, and the points belong to the set D0.

Applying the max-log approximation ln it can be shown that the global probability of detection and false alarm at the FC can be calculated as [23-24]

where Q(⋅) is the Gaussian tail probability function, PD,SU and PFA,SU are the probabilities of detection and false alarm at the SUs and γFC = Es / N0 is the average SNR per bit at the FC.

As pointed out in [24], when the reporting channel gains are complex-valued and possibly time-varying, the decision regions become two-dimensional, with irregular and random shape, rendering the derivation of the probabilities of false alarm and detection a much more challenging task when compared to the case of real-valued gains. However, one must recall that the fusion scheme proposed in [23] assumes that the channel gains are known at the FC, which means that the signal levels can be differentiated for the proper operation of the K-out-of-M rule. In terms of performance, it can happen, for instance, that two closely-nearby signal points will belong to different hypotheses, no matter how large the SNR is. In this case, the instantaneous performance is expected to be severely degraded, as also happens, for instance, in a deep fading condition caused by destructive interference.

2.2 On the adherence between theoretical and actual results for the reference system

The main conclusion in [23] is that its resource-efficient scheme is capable of achieving the target values of PD,FC = 0.9 and PFA,FC = 0.1, as does a scheme that applies orthogonal transmissions over the report channels. However, this is accomplished only when the SNR in the report channel (γFC) is relatively high, for example above around 6 dB for AWGN report channels [24]. Moreover, the max-log approximation used to derive (3) and (4) from (2) is accurate only in specific cases: i) when K = ⎾ M / 2 ⏋ in the K-out-of-M rule, or ii) when the values of γFC is high, normally above 6 dB. As a consequence, theoretical and actual performances of the scheme proposed in [23] only match in special cases, as reported in [24].

The mismatch between the theoretical and the actual performances of the scheme proposed in [23] can be justified firstly by the use of the max-log approximation in the derivation of the expressions for computing the probabilities of false alarm and detection in [23], that is, the logarithm of the sum of exponentials in (2) was replaced by the max function. However, the max function close approximates the log of the sum of exponentials only when the exponents are quite different, meaning that the sum will be governed mainly by the largest one. When γFC is high, the differences among the exponents in (2) are large, meaning that the max-log approximation is accurate. When γFC is low, the differences among the exponents in (2) tend to become small, penalizing the accuracy of the approximation. In the specific case of K = ⎾ M / 2 ⏋ in the K-out-of-M rule, no matter the value of γFC, any inaccuracy of the max-log approximation penalizes equally both sides of (2), since the number of terms in both summations is the same.

The above considerations can be more clearly addressed by means of receiver operating characteristic (ROC) curves, which show the probability of detection versus the probability of false alarm as a decision threshold ξ at the SU is varied. No specific detection technique at the SUs was called in [23], since it does not influence the operation of the decision fusion strategy. Furthermore, it was indeed not necessary to define any detection technique in [23], because the performance results report the global probabilities of detection and false alarm as a function of γFC. Nevertheless, hereafter we consider that the M cooperating SUs perform energy detection (ED). In this case, a local test statistic is where σ is the noise variance at the input of each SU receiver, N is number of samples collected by each SU, and x[n] is the received signal sample collected by an SU in the nth discrete-time instant. Notice that, by defining the above test statistic independent of the specific SU, we are implicitly assuming that the noise variance and the sensing performances of all SUs are the same. Then, the detection and false alarm probabilities at the SUs can be respectively computed as [26]

where is the variance of the PU signal. The average signal-to-noise ratio for the links between the PU and the SUs is simply γSU = σx / σ.

From Fig. 1 it can be seen that theoretical and simulated performance results for the reference system of [23] match for higher values of γFC, being considerably different in lower values of γFC. To plot these results, we have arbitrarily assumed N = 100, M = 5, K = 1 (left) and K = M = 5 (right), γSU = -5 dB and γFC = 0 dB and 8 dB. The results for K = ⎾ M / 2 ⏋ = 3 were omitted since, in this specific case, the theoretical and simulation results always agree. Notice that these values of K configure the well-known decision fusion rules OR, AND, and majority-voting, respectively. Each value on the simulated ROC curves was obtained from 500,000 Monte Carlo events. Each event corresponds to computing PD,SU and PFA,SU from (5) and (6), respectively, for a given decision threshold ξ and signal-to-noise ratio γSU. The probability PD,SU is set as the probability of success in the Binomial distribution for generating a set of SUs decisions when the PU signal is on. Similarly, PFA,SU governs the Binomial distribution of the SUs decisions when the PU signal is off. The SUs decisions are then sent to the FC through the report channel using BPSK signaling. The final decision at the FC are used for computing false alarm (if the PU is off) and detection (if the PU is on) rates, which are the estimates of the associated probabilities. Repeating the above procedure, by varying the decision threshold at the SUs, the ROC curves are traced out.

Fig. 1.Differences among theoretical and simulated ROC results for the reference system proposed in [23]. K = 1 left, K = 5 right.

2.3 On the energy consumption of the reference system

In this section we make an analysis about the energy consumption in the CSS network under the scheme proposed in [23].

As described in Section 2.1, the CSS of [23] is based on the simultaneous transmissions of all secondary users’ decisions to the FC. So, the total energy consumption in the cognitive network per sensing round can be formulated as [20]

where ELS, ER and ET are the energy consumed by a single SU due to local sensing, reporting of the local decisions to the FC and opportunistic data transmission, respectively. The first term in (7) is constant and exists in all sensing rounds. Using lower values for M we can reduce the contribution of this term, but this will penalize the performance of the CSS. The second term in (7) also increases with M, and represents a significant contribution in the total energy consumption. Since the SUs transmit their local decisions in all reporting phases via BPSK symbols, the energy consumption MER is always equal to MEb. The last term depends on the probability that the FC decides in favor of a free channel, which is given by Pfree = PH1 ( 1 - PD,FC) + PH0 ( 1 - PFA,FC), where PH1 and PH0 = (1 - PH1) are, respectively, the probabilities that the PU transmitter is on and off, and PD,FC and PFA,FC are computed from (3) and (4), respectively.

The energy efficient fusion system described in the next section aims at reducing the total energy consumption based on a censored local decision reporting strategy, which acts by reducing the second term in (7).

3. Proposed Energy Efficient System

As in the case of the reference system, the whole process in the censored CSS scheme proposed here can be divided into three phases: i) local spectrum sensing, ii) reporting of local decisions and iii) global decision at the FC. The differences between our scheme and the reference reside in phases ii and iii.

3.1 Proposed system model

To achieve the same bandwidth efficiency of the reference system suggested in [23], the new energy efficient CSS scheme also adopts the simultaneous transmission of local decisions to the FC over the same frequency band. However, differently of [23], only the SUs that detect the presence of a PU signal are allowed to report their decisions to the FC. The remaining SUs must stay silent. Therefore, the received signal sample at the FC can be expressed as

where, M* ∈ [0, M] is an integer that represents the number of SUs that have reported their local decision or, in other words, it is the number of SUs with local decision mk = 1.

Notice that during the reporting phase, the transmission of information occurs only if a detection or a false alarm event occurs. The SUs’ transmitters remain turned-off otherwise. Therefore, the average energy per bit is computed conditioned on transmission events. So, as in the case of the reference system, Eb = Es and, for the same γFC in new and the reference schemes, a fair comparison in terms of the global decision performances among these two techniques can be made.

Again assuming AWGN report channels, the noiseless received signal sample in this new scheme also follows a Binomial distribution with M + 1 values, now represented as depicted in Fig. 2.

Fig. 2.Noiseless received symbols at the FC for the new fusion scheme.

Each point in Fig. 2 is associated to an event in which J SUs send the local decision, J = 0,1,⋯,M. Under the K-out-of-M rule, the points correspond to the choice of H0, and the points correspond to the choice of H1 Therefore, the FC will choose H1 if rnew ≥ λ and H0 otherwise. Notice that this threshold-based rule is by far less complex than (2), which is the decision rule adopted in the reference system. On the basis of Fig. 2, the global probabilities of detection and false alarm for the new energy efficient scheme can be derived in a manner similar to the one adopted in [24], leading to

Without loss of generality, we assume unitary average bit energy, i.e. Eb = Es. Then, from Fig. 2, the decision threshold λ ∈ [K - 1, K]. The correct choice of λ in this interval can lead to a better system performance in terms of ROC. In other words, we can find the value of λ, restricted to K - 1 ≤ λ ≤ K, that minimizes the probability of making a wrong decision at the FC, that is

where Pe,FC(λ) is the probability of occurrence of a false alarm or a missed detection as a function of λ. This probability is given by

where PD,FC(λ) and PFA,FC(λ) are computed from (9) and (10), respectively. However, it is not reasonable to assume that the values of PD,SU and PFA,SU required to compute PD,FC(λ) and PFA,FC(λ) are known at the FC. Then, to find λopt here we consider that the local spectrum sensing at the SUs are designed to achieve target values of false alarm and detection probabilities for an error-free report channel condition. We refer to these target values as respectively.

We have adopted two rules to determine In the first rule, the target performance metrics at the FC, are chosen to meet performance specifications, for example to comply with standard requirements. In this case, are computed as the solutions of the following equations [27]

In the second rule for determining we have used the fact that the minimum decision error probability at the FC happens when the decision error probability at the SUs also attains its minimum. Then, we assume that are computed from (5) and (6) for a given set of system parameters and for a target SU decision threshold ξ(T) that satisfies

where the functions PFA,SU(ξ) and PD,SU(ξ) are also defined from (5) and (6).

Even assuming target probabilities at the SUs, it is not trivial to find the value of λ ∈ [K - 1, K] that minimizes the error probability at the FC: to solve (11) analytically, one would have to operate with a summation of exponentials that are functions of λ and whose terms are weighted by binomial probabilities. These exponentials arise from the derivative of the Gaussian Q function present in (9) and (10). For this reason we have solved (11) numerically.

3.2 Performance results for the proposed system

The accuracy of our expressions is evidenced in Fig. 3 and Fig. 4, where the global probabilities of detection and false alarm for the new and the reference schemes are shown for K = 1 (left) and K = 3 (right). To plot Fig. 3, the target metrics chosen according to the first rule was yielding, from the solution of (13) and (14), for K = 1 with λopt = 0.9649 for γFC = 0 dB and λopt = 0.6112 for γFC = 8 dB; and for K = 3 with λopt = 2.5 for both values of γFC. To plot Fig. 4, the target metrics computed according to the second rule was for any value of K, while λopt = 1 if K = 1 and λopt = 4 if K = 5 for both values of γFC, lastly if K = 3, λopt = 2.2758 for γFC = 0 dB and λopt = 2.4117 for γFC = 8 dB. We have adopted PH0 = PH1 = 0.5 in order to simulate the most difficult situation (maximal entropy of the primary user activity).

Fig. 3.Global probabilities of detection and false alarm for the new and the reference schemes. K = 1 left, K = 3 right. First rule adopted for determining target metrics.

Fig. 4.Global probabilities of detection and false alarm for the new and the reference schemes. K = 1 left, K = 3 right. Second rule adopted for determining target metrics.

Notice that the two rules for choosing the decision threshold lead to very similar ROC performances of the proposed scheme, mainly for K = 3. Notice that the graphs on the right of Figs. 3 and 4 present almost equal ROC performances. When K = 1, it can be observed a small advantage of the second rule. For both γFC = 0 dB and γFC = 8 dB, the first rule leads to a minimum value of the global false alarm slightly greater than the second rule. Then, it is possible to conclude that these two rules can be indistinguishably used in the proposed scheme, without significant implications in performance.

It can be also observed from these figures that, when comparing our scheme (new) with the one proposed in [23] (reference), the new scheme overcomes the reference for γFC = 0 dB and the performances are approximately equal when γFC = 8 dB. When K = 3 the performances of both schemes are practically the same for all values of γFC.

We conclude that the new scheme can save energy during the reporting phase without compromising the global decision performance, improving this performance in some cases. This improvement can be explored for reducing the second term of (7), saving even more energy. More details regarding this aspect are given in the next subsection.

It is worth mentioning that the performance results of the reference system as shown in Fig. 3 and Fig. 4 are from simulations because the theoretical results from [23] do not match the simulations for γFC = 0 dB; see Section 2.2.

As for the previous ROCs, each value on the curves from simulations in Fig. 3 and Fig. 4 was obtained from 500,000 Monte Carlo events. The difference from the previous setup in each event, when the new system is considered, is that the SU's decisions are sent to the FC using the proposed censoring technique, and the final decision at the FC is arrived at from the simple threshold-based decision rule. The received SNR at the SUs was arbitrarily set to γSU = -5 dB.

3.3 On the energy consumption of the proposed system

Similarly to what we have done regarding the reference system, we can model the total energy consumption per sensing round for the new system as

recalling that ELS, ER and ET are the energy consumed by a single SU due to local sensing, reporting of the local decisions to the FC and opportunistic data transmission, respectively, M is the number of cooperating SUs, is the average number of SUs with local decision mk = 1 and Pfree is the probability that the FC decides in favor of a free channel. The first term of (16) is constant and has the same value both in (7) and (16). The second term in the reference system is also constant and equal to MEb. However, in the proposed scheme this term depends on where Pmk = 1] = PH0PFA,SU + PH1PD,SU. Therefore, the energy consumption in the reporting phase for the new scheme is

The maximum value of energy consumption in the reporting phase of the new scheme is equal to MEb, a value that is equal to the corresponding one in the reference model and, when all SUs decide by mk = 0, the energy consumption in the reporting phase is zero. However, on the average, the energy consumption in the new scheme will be lower than in the reference scheme. The last term also depends on Pfree, as in the reference model. Recall that the energy consumption of the new scheme is reduced compared to the reference scheme due to a smaller second term of (16).

4. Energy Efficiency Analysis

We present the energy efficiency analysis using two approaches. The first is made considering a scenario in which the global decision performances of the reference and new schemes are equal to one another. The second considers the possibility of different performances. For both approaches we have arbitrarily adopted the second rule for determining the target metrics, since this rule has produced approximately the same results achieved with the first one; refer to Section 3 for more details about these rules.

For the first analysis we consider M = 5, K = 3, γFC = 8 dB and γSU = -5 dB. With these parameters, the global decision performances are approximately the same for the new and the reference schemes, as shown in Fig. 3 and Fig. 4; see Section 3. Therefore, the values of the third term in (7) and (16) are approximately equal. As the first term in these two equations always have equal values, this first analysis will show a comparison in terms of energy consumption mainly due to the reporting phase.

In Fig. 5 we present the energy consumption per sensing round for the new and the reference schemes, as respectively obtained from (7) and (16). The results show that the new scheme achieves significant reduction in the energy consumption when compared with the reference. For obtaining these results, the average energy per bit was set to Eb = ET = 1 joule, and the energy spent during the local sensing period was not taken into account, since its value is the same in both systems.

Fig. 5.Energy consumption per sensing round for the new and the reference schemes.

Notice in Fig. 3 and Fig. 4 that, for the parameters under analysis, PFA,FC = 0 implies PD,FC = 0. Therefore, for the reference system, in (7) Pfree = 1 and a secondary user transmits opportunistically with ET = 1 joule. Since in the reporting phase M BPSK symbols with Eb = 1 are transmitted, the energy consumption per sensing round (disregarding the consumption in the local sensing period) will be equal to 5Eb + 1ET = 6 joules, as show in Fig. 5. Under the same condition in the new scheme, Pfree is also unitary PfreeET = 1. However, in the reporting phase there is no transmission of local decision, once PFA,FC = 0 was achieved by a condition in which PFA,SU = PD,FC = 0. Therefore, for the new scheme the energy consumption per sensing round will be 0Eb + 1ET = 1 joule, as can also be observed in Fig. 5. If PFA,SU increases, the total energy consumption in the reference system decreases due to a decrease in Pfree. However, in the new scheme the total energy consumption increases, mainly due to an increase in the probability of a local detection in each SU, P[mk=1]. Lastly, PFA,FC = 1 implies PD,FC = 1 (see Fig. 3 and Fig. 4) and, therefore, Pfree = 0, that is, no SU will transmit opportunistically. Thus, in the reference and in the new schemes, the difference in the total energy consumption will be the just the energy spent during the reporting phase. For the reference scheme, the reporting task always consumes MEb = 5 joules. For the new scheme, PFA,FC = 1 was achieved by a condition where PFA,SU = PD,SU = 1. Therefore, in this condition the energy spent during the reporting phase is joules, as shown in Fig. 5. It is important to notice that expression (16) produces results in perfect agreement with the simulated results for any value of γFC. On the other hand, expression (7) produces results in good agreement with simulations only for γFC ≥ 6 dB, approximately.

A second analysis is made by considering that the global decision performances are not necessarily the same for both systems. In this case, the energetic cost depends on the operating points of the reference and the proposed schemes. In other words, their global decision performances can influence the energy consumption, making a fair comparison between them difficult. Another metric can be incorporated into this comparison, accounting for the correct identification of the unused spectrum, which promotes the opportunistic data transmissions. This metric is the achievable throughput [18]

in which PH0 (1 - PFA,FC) is the probability of correct identification of the unused spectrum, R is the data rate of the SU and Tt is the time interval in which one of the SUs is scheduled for opportunistic data transmission. The energy efficiency, measured in bits per joule, is defined as the ratio between the achievable throughput and the total consumed energy, that is,

Fig. 6 shows the energy efficiency in both schemes, normalized by RTt. The system parameters adopted were M = 5, γSU = −5 dB and γFC = 0 dB and 8 dB. These results show that the new scheme is more efficient than the reference scheme in all analyzed conditions. Notice also that, if it is assumed a global PFA,FC = 0.1, γFC = 0 dB and K = 1, the energy efficiencies will be ηnew = 0.25(RTt) and ηref = 0.08(RTt), meaning a gain of about 212.5% in energy efficiency in favor of the proposed scheme. Similar behaviors were observed for other values of M, K and γFC, but with different efficiency gains.

Fig. 6.Energy efficiencies of the reference and the new schemes.

It is informative to mention that the agreement between the theoretical and simulated energy efficiencies for the reference system is good only for high values of γFC. Inaccuracies in the low γFC regime are inherited from the inaccuracy of the expressions for computing PD,FC and PFA,FC for the reference system in this regime. Last, but not least, it is important to notice that a higher energy efficiency can be obtained in our scheme not only from the reduction in the second term of (16), but also when the new scheme outperforms the reference one in terms of ROC, increasing the achievable throughput.

From Fig. 6 it is also possible to notice that ηnew is more prone to variations with variations of the system parameters than ηref. However, in all analyzed scenarios the energy efficiency of the new scheme is larger than the one achieved with the reference scheme. It is also important to notice that, for the new scheme, when γFC increases the energy efficiency decreases. This behavior is more pronounced when K = 1 and PFA,FC ≤ 0.2 : analyzing this specific case, assuming PFA,FC = 0.1, one can observe in Fig. 4 that the global detection probability is higher in the case when γFC = 8 dB. Inverting (9) it is possible to notice that higher values of PD,SU are also achieved when γFC increases. Therefore, an increase in the total energy consumption is expected due to an increase in the energy consumption during the report phase. Since PFA,FC is the same for both SNRs, the throughput D is kept unchanged. Therefore, from (18) it can be concluded that the energy efficiency decreases when γFC increases.

5. Comparison between the New System and the System of [22]

This section presents a comparison between our fusion scheme and the efficient decision fusion based on the OR rule proposed in [22]. The reason for this comparison is the similarity between them in one specific configuration of the scheme of [22].

The OR rule is a particular case of K-out-of-M rule when K = 1. In this case, the FC will decide for the presence of the PU if at least one of the SUs decides in favor of H1. To reduce the energy consumption, a censoring rule is applied in [22] during the report phase. Therefore, only those SUs that have local decisions in favor of H1 will be able to transmit their decisions, using a continuous wave signaling. To increase the bandwidth efficiency, these SUs transmit the same signal at the same time slot. If the FC detects the signal in that time slot, this indicates that one or more SUs have local decision H1. Therefore, a global decision H1 will be the final decision, based on the OR rule. Otherwise, it will be H0.

Assuming that U is associated to the duration of the time slot for signaling, the u-th discrete-time instant (u = 0, 1, …, U – 1) of the continuous wave used to transmit the local decision from the i-th SU to the FC, i = 1, 2, …, M, is formulated as [22]

where HL,i is the local decision of the i-th SU, Ai and θi are, respectively, the peak amplitude and phase of the continuous wave.

In [22], power and phase controls were proposed to increase the detection performance of the secondary network. Then, to carry out a fair comparison with our proposed system, the power and phase controls shall not be considered. In this case, named DFn,n in [22], the amplitude and phase components assume the values Ai = 1 and θi= 0.

For a pure additive white Gaussian noise (AWGN) reporting channel, the received signal at the FC at the u-th instant is

where M* is the number of SUs that declared the presence of the PU signal.

The test statistic T proposed in [22] is formed according to

The FC decides for the presence of the PU signal if the test statistic is greater than a pre-defined decision threshold λG. Otherwise, the FC decides for the absence of the PU signal. In [22], the threshold λG is chosen to satisfy the target global false alarm probability

Both the new scheme proposed here and the OR rule scheme proposed in [22] use the censoring concept with simultaneous transmission of local decisions. The main difference between these two schemes lies in the decision fusion strategy. In the new scheme it is possible to use the K-out-of-M rule, while the scheme in [22] is limited to the OR rule that is based on a sort of energy detector implemented at the FC. In other words, our decision fusion scheme can estimate how many SUs have transmitted their local decisions, which renders our scheme more generic.

In [22], the signal-to-noise ratio (SNR) is defined as where αi is the report channel gain between the i-th SU and the FC, and σw2 is the variance of the zero-mean white Gaussian noise at the input of the FC. For AWGN report channels αi = 1.

In our scheme, the SNR is defined as γFC = Eb / N0, where Eb is the average energy per transmitted bit and is the unilateral noise power spectral density.

At the end of the report period, in the new scheme we have a single sample r at the FC, which can be seen as a sample at a correlator output. On the other hand, in [22] there are U samples {y(u)} which are used in the computation of the test statistic T given in (21).

In order to perform a fair comparison, we have defined that the duration of the time slot, defined by U, must be equal to the time needed for the correlator to output the sample r, leading to Eb = U (recall that Ai = 1). Therefore, the following mapping must be made:

Numerical results in terms of ROC curves regarding these two schemes are shown in Fig. 7. To plot these results we have arbitrarily assumed N = 100, M = 5, K = 1 (OR rule) and K = ⎾ M / 2 ⏋ = 3 (majority voting rule) for the new scheme, γSU = -5 dB and γFC = 0 dB (left) and 8 dB (right), leading to γ'FC = 3 dB and 11 dB. The results for K = M = 5 (AND rule) were omitted, since in this case the ROC curves for the AND rule exhibit a bounding (saturation) effect in the probability of detection and the ROC curves for the system proposed in [22] exhibit the bounding effect in the probability of false alarm, making it difficult a fair performance comparison. Each value on the simulated ROC curves was obtained from 500,000 Monte Carlo events. Each event corresponds to computing PD,SU and PFA,SU for a given decision threshold and signal-to-noise ratio.

Fig. 7.Global probabilities of detection and false alarm for the new and the OR rule scheme of [22]. γFC = 0 dB left, γFC = 8 dB right. First rule adopted for determining target metrics.

In the case of the system proposed in [22], the SUs decisions in favor of H1 are sent to the FC using continuous wave. In this case, a unitary vector with length U is used to reproduce the signal xi(u) during the report round. At the FC, all {xi(u)} samples are added according to (20), with the noise w(u) generated as The value of the test statistic T is computed using (21), and then compared with the threshold λG previously calculated to yield the target global false alarm The final decisions at the FC are used for computing false alarms (if the PU is off) and detection (if the PU is on) rates, which are the estimates of the associated probabilities. Repeating the above procedure, by varying the decision threshold at the SUs, the ROC curves are traced out.

According to the results, it is possible to notice that the performances of the OR rule of [22] and the new schemes are similar when γFC = 0 dB and K = 1. In this situation, the energy consumption of these two schemes is the same during the report and the opportunistic transmission phases. Therefore, it is correct to state that, in this condition, the energy efficiency will be the same in both schemes. When γFC = 0 dB and K = 3, the performance of the new scheme is superior to the OR rule scheme of [22]. In this situation, the energy consumption during the report phase is equal to one another for both schemes. However, the achievable throughput of the new scheme is greater than OR rule scheme of [22]. Therefore, the energy efficiency can be increased in the proposed scheme by only changing the decision fusion rule to majority-voting, contrasting with the limitation of the OR decision fusion rule of [22]. For values of γFC > 0 dB, it can be noticed that the new scheme outperforms the OR rule of [22] for both K = 1 and K = 3. This can be observed in Fig. 7 (right), where the numerical results for simulations with γFC = 8 dB are shown. In this situation, for the OR rule of [22], it is observed a significant increase (from approximately 0.7 to 0.9) in the global detection probability at the point where the global false alarm is 0.1. However, the increased performance of the proposed scheme is considerably higher. Therefore, it can be concluded that, for γFC = 8 dB, the energy efficiency of the new scheme is greater than the one achieved by the OR rule scheme of [22] for K = 1 and K = 3, due to the higher achievable throughput in the first scheme.

6. Conclusions

The new fusion scheme proposed in this article provides a large increase in the energy efficiency when compared with the scheme proposed in [23], maintaining the bandwidth efficiency. A significant energetic gain was observed when values of practical interest are considered for the global false alarm and detection rates at the fusion center. Besides being more energy-efficient, the new scheme can achieve better performances than the reference one, in terms of ROC, mainly when the signal-to-noise ratio in the report channels is low, a situation that is of great practical appeal. It was also verified that the expressions derived in this article provide results with good agreement with simulations, for any of the parameters analyzed. Moreover, it was demonstrated that the new decision fusion scheme exhibits an energy efficiency that is equal to or greater than the energy efficiency of the decision fusion strategy proposed in [22], a conclusion that can be drawn due to the fact that the performance of the new scheme is better than or approximately equal to the one unveiled by the scheme of [22] in terms of ROC, for the system configurations under which both schemes can be fairly compared. The contributions reported in this article allows for the implementation of a cooperative spectrum sensing system that simultaneously cares about the bandwidth and the energy efficiency, aspects of paramount importance in wireless communication systems.