Fast two-stage spectrum detector for cognitive radios in ... - IEEE Xplore

www.ietdl.org Published in IET Communications Received on 3rd November 2011 Revised on 11th January 2012 doi: 10.1049/iet-com.2011.0751

ISSN 1751-8628

Fast two-stage spectrum detector for cognitive radios in uncertain noise channels P.R. Nair1 A.P. Vinod1 K.G. Smitha1 A.K. Krishna2 1

School of Computer Engineering, Nanyang Technological University, Singapore EADS Innovation Works, EADS Singapore Pte Ltd., Singapore E-mail: [email protected]

2

Abstract: An enormous influx of wireless services and devices coupled with inefficient usage of electromagnetic spectrum has led to an apparent scarcity of usable radio bandwidth. Cognitive radio is leading the trend for increasing the spectrum efficiency by utilising the vacancy in the radio spectrum created by absence of the licensed primary user. This paradigm shift can only take place if the means to detect the primary user are well established so that an ecosystem can be created where both primary and secondary users can co-exist without interfering with each other. In this study the authors propose a two-stage detection mechanism which gives an improved performance over conventional single-stage detectors yet optimises the usage of the second stage, thereby reducing the sensing time as compared to conventional two-stage spectrum sensing algorithms. A hardware implementation of the algorithm has also been done to quantify the area and power consumption values. By utilising the second-stage optimally, the algorithm presented in this study helps in reducing the sensing time by 86% as compared with the conventional two-stage detector. By not activating the second stage at high SNRs, the proposed algorithm saves 0.915 W of dynamic power out of a total of 1.09 W, thus effectively reducing the dynamic power consumption by 84%.

1

Introduction

An apparent scarcity in radio spectrum has been felt for quite some time. More and more wireless devices and standards to satisfy the ever-increasing demand of consumers are coming into the market, which has invariably led to the clogging of the wireless spectrum. A study conducted by the Federal Communications Commission (FCC) revealed the fact that hardly 25% of the allocated spectrum gets utilised [1, 2]. The concept of cognitive radio (CR) manages to precisely address this problem of under utilisation of the spectrum. The ability to sense the spectrum to determine whether the owner of the licensed spectrum, known as the primary user (PU), is active or not, forms an integral part of a CR device. An accurate detection is a prerequisite so that the PU does not face any undue interference from a CR node, also known as the secondary user (SU). Many algorithms which enable detection of the PU have been developed. Some algorithms such as energy detector (ED) and eigenvalue-based detector (EVD) enable blind detection of the PU wherein no knowledge of the PU is required for estimating the presence or absence of the PU. On the other hand, the well-known matched filter algorithm requires complete knowledge of the signal to be detected. Algorithms like cyclostationary feature detector (CFD) require a priori knowledge of some of the characteristics of a signal like its carrier frequency, symbol duration etc. The merits and demerits of each of the above-mentioned algorithms have also been well researched and documented in the literature [3]. In this paper we have focused on the ED and CFD algorithms to investigate how their individual IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

merits can be synergised while at the same time the demerits negated without any impact of the performance of the system as a whole. It is known that though the ED is a very simple detector to design, it suffers from a fundamental limitation as a result of the errors in noise estimation which makes it unsuitable when the signal-tonoise ratio (SNR) falls below a certain threshold known as the SNR wall [4, 5]. On its part, though the conventional CFD algorithm is excellent in its robustness to noise and can work well in low SNR regimes, it is highly computationally complex and takes more time in arriving at a result. In order to facilitate a faster detection of the cyclostationary features of a PU, we investigated the pilotassisted detection (PACD) approach. It has been established that PACD can help in detection of the cyclic properties faster and more accurately [6]. Although the opponents of this scheme say that this leads to alteration in the basic waveform of the PU [7], we feel that in future it would be in the best interest of both PU and the SU to make the spectrum as efficient as possible. In this paper, we have investigated a two-stage sensing scheme wherein the first stage is an ED followed by a PACD. The idea is to use the benefit of cyclostationary analysis to mitigate the problems caused by noise power uncertainty of ED and combine the use of boosted pilot carrier to reduce the computational complexity of the cyclic frequency analysis in the second stage. Some studies have already been conducted on two-stage detectors for spectrum sensing in CR [8, 9]. Our approach differs from these techniques in that we propose an optimum utilisation of the second stage detector. Unlike the scheme mentioned in 1341

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www.ietdl.org [8, 9] where the second stage is activated each time the ED is unable to detect the presence of a signal, we propose an SNRbased decision unit that decides whether to trust the results of the ED or to do another round of sensing using the more robust PACD. Thus, the two-stage detector proposed in this paper helps in optimising the usage of the PACD yet at the same time improves the performance of the CR node in low-SNR regimes. A part of this paper has been published in [10], where we presented a preliminary idea of the two-stage detection algorithm using ED in both the stages of the spectrum sensing algorithm. In this paper, we replace the secondstage ED with the PACD technique so as to make the algorithm robust in the presence of uncertainty in noise power estimation. Also this paper presents the hardware resource requirements for implementing the algorithm and shows the saving in the amount of dynamic power possible because of this algorithm. The rest of this paper is organised as follows. Section 2 describes the conventional approaches to spectrum sensing and the problems thereof. It also describes the advantages of a PACD and how it enables better and faster detection in low-SNR regimes. Section 3 details the proposed two-stage detector and shows its benefits. It also discusses ways to optimise the activation of the second stage and thereby save sensing time as compared with conventional two-stage approaches. Section 4 presents the hardware implementation details of the proposed method. Finally Section 5 concludes our findings and results.

The mean and variance of the test statistic for the ED in the first stage have been shown, using the results in [5] as

m0 = s2n ; m1 = m0 (1 + g);

s2n s0 =  Ns

(4)

 s1 = s0 ( 2g + 1)

(5)

It has been shown in [5] that s2n ¼ N0∗ Ns , where N0 is the noise power density. In an ED, for a given Pf and Pd the required SNR value (critical SNR( gc)), to achieve the target probability of detection and false alarm for a given Ns is given by (6).

gc =

Q−1 (Pf ) − Q−1 (Pd )  Q−1 (Pd ) + Ns

(6)

The fundamental limitation of the ED is that any error in the estimation of the noise power severely degrades its performance. In [4, 5], the authors have shown that there is a lower limit of the SNR beyond which it is impossible for the ED to detect the presence of the PU signal. For an uncertainty in noise power estimation of d, a noise power of s2n can vary from [ds2n, s2n/d] [4]. In the worstcase scenario, this leads to an SNR below which estimation is impossible. This SNR can be derived as

s2s +

2 Performance analysis of conventional spectrum sensing schemes

s2n ≥ ds2n d

(7)

Solving the above equation leads to a minimum SNR of In this section, we present a brief overview of the ED and CFD scheme and also review the conventional two-stage detector models available in the literature. 2.1

ED and noise uncertainty

H0 : y[n] = w[n]

(1)

H1 : y[n] = s[n] + w[n]

(2)

H0 is the hypothesis that the PU is not transmitting and hence s[n] is 0, whereas H1 is the hypothesis that the PU is using the channel for transmission. The test statistic Z( y) for Ns number of samples can be expressed as N

(3)

The CR system makes this decision based on the threshold (l ) and discriminates between the presence and absence of signal. It is this threshold which determines the performance metrics, probability of detection (Pd) and probability of false alarm (Pfa) of the system. We assume that the primary signal and the noise are an independent and identically distributed (iid) random process with zero mean and of variances, s2s and s2n, respectively. The SNR at the receiver ( g) is therefore given as g = s2s /s2n . 1342 & The Institution of Engineering and Technology 2012

(8)

The SNR wall can be expressed as

Let s[n] represents the PU signal and w[n] represents the noise introduced by the transmission channel. Then the signal sensed by the CR can be hypothesised as [3]

s 1  |y[n]|2 Z(y) = Ns 1

  s2s 1 ≥ d − s2n d

gwall

 2   ss 1 D/10 = = 10 log10 10 − D/10 dB s2n wall 10

(9)

We can expand on this result to obtain the SNR in an uncertain environment, denoted as gu , at which the target probability of detection and target probability of false alarm is maintained. With the help of results in [5], we can show that for an uncertainty of d in the estimation of noise power, the SNR required to reach the target performance can be obtained as   l − m0 Pf = Q s0   l − m1 Pd = Q s1

(10)

(11)

where Q(x) is defined by the complementary distribution function of the standard Gaussian and is given as 1 Q(x) = 2p

1

2

e−u

/2

du

(12)

x

The threshold, l, can vary from ds2n to s2n/d. Hence the IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

www.ietdl.org maximum uncertainty for l can be

l=

ds2n l = d2 l s2n /d

(13)

Substituting (13) into (11) and using (4) and (5), we can show that   Ns (d2 − 1) + d2 Q−1 (Pf ) − g Ns √ Pd = Q (2g + 1)

(14)

corresponding to cyclic frequency a. In other words, (20) represents the cross spectral density of the frequency shifted signals x(t)e−jpat and x(t)e+jpat . When a ¼ 0, (20) reduces to the power spectral density of the signal. It is difficult to do a blind search for the cyclic frequency a and this adds to the computational complexity of the CFD. Also if there is no knowledge about the possible cyclic frequencies of the signal to be detected, it leads to a very high detection time. However, extensive studies have been done to document the cyclic frequencies of signals of practical interests [13, 14]. These cyclic frequency values can be used to reduce the computation time significantly.

Squaring on both sides and solving for g, we can obtain √ d Q (Pf ) − Q (Pd ) 2d2 − 1 2  gu  (d − 1) + Ns 2

−1

2.3

−1

(15)

Thus, we can see how a fundamental limitation of the ED limits its operational deployment as a CR in a practical setup where perfect knowledge of the noise power cannot be guaranteed. 2.2

Cyclostationary feature detector

CFD is robust to noise as noise is assumed to be wide sense stationary that does not exhibit cyclostionarity and thus work well even in low-SNR regimes [11]. Also since the CFD is independent of the estimate of noise variance, the limitation because of errors in the estimation of noise, which cripple the ED, does not affect a cyclostationary analysis significantly. A continuous time random process x(t) is said to be second-order cyclostationary if its mean and autocorrelation show periodicity in time. Mathematically this means that for a cyclic period T, x(t) can be represented as

FFT accumulation method for computing CSD

The computational complexity of computing the CSD of a spectrum and consequently the time taken to arrive at a conclusive result is one of the major disadvantages of the CFD [15]. In [16], the authors developed two seminal algorithms to estimate the CSD. They are classified as fast Fourier transform (FFT)-based accumulation method (FAM) and strip spectral correlation method (SSCA). In this paper we use the FAM algorithm to estimate the CSD since it computes the results faster than SSCA [17]. To obtain the CSD, first the complex demodulates of the input signals are generated. This is done by using a sliding N-point FFT followed by downshifting the frequency to baseband. The generated complex demodulates are as follows. N /2 

XT (n, f ) =

c(k)x(n − k)e−j2pf (n−k)Ts

(21)

c(k)y(n − k)e−j2pf (n−k)Ts

(22)

k=−N /2 N /2 

YT (n, f ) =

k=−N /2

E[x(t)x(t + t)] = E[x(t + T )] R(x, t) = E[x(t)x(t + t)] = E[x(t + T )x(t + T + t)]

(16) (17)

for all t and t. From (17), it can be seen that if the autocorrelation function is periodic then it will have a Fourier representation given by R(x, t) =



Rax (t)ej2pat

(18)

a

The Fourier coefficients of (18) can be expressed as −1 1 N R(x, t)e−j2pat N 1 N t=0

Rax (t) = lim

(19)

Here a is the cyclic frequency of the autocorrelation function and Rax (t) is called the cyclic autocorrelation function (CAF). Thus, a process is called cyclostationary if there exists a = 0, such that Rax (t) = 0 for some values of t. In other words, the cycles of R(x, t) are to be detected for testing the presence of cyclostationarity. By taking the Fourier transform of the CAF, we obtain the cyclic spectral density (CSD) as [12] Sxa (f ) =

+1 

t=−1

Rax (t)e−j2pf t

(20)

Equation (20) represents the frequency spectrum, Sx( f ), IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

Here Ts is the sample duration and c(k) is the data tapering window of length T ¼ N∗ Ts. In order to further increase the efficiency of the estimation, the N-point FFT is hopped over the received data in blocks of L samples. Typically, the value of L is chosen to be N/4 to obtain a reasonable trade-off between maintaining efficiency in computation, minimising cycle leakage and cycle aliasing [16]. After the computation of the complex demodulates, an element-wise product of the XT(n, f ) is done with the conjugate of YT(n, f ). Time smoothing of the resulting data is ensured by means of a second P-point FFT. The values of N and P depend on the frequency and cyclic frequency resolution desired. Thus, for a sampling frequency fs , desired frequency resolution of Df and cyclic frequency resolution of Da, the chosen value of N and P are N=

fs ; Df

P=

fs LDa

(23)

Both N and P are chosen to be power of 2 so that zero padding can be avoided before using the FFT algorithm. From [16] we can see that the CSD using the FAM estimator can be obtained as a +qDx

SXYi T

(nL, fj )Dt =



XT (rL, fk )YT∗ (rL, fl )gc (n − r)e−j2prq/p

r

(24) 1343

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www.ietdl.org gc(n 2 r) is the window operation, q is the index in the range −

PL PL ≤q≤ −1 2N 2N

(25)

k and l range from 1 to N. The FAM approach to compute the CSD is a fast technique to arrive at the result. But the speed of detection can be further increased if the cyclic frequencies to look for are also known a priori. In Section 3 we look at how intentionally embedding cyclostationary features in the transmitted waveform can help in not only improving faster detection and analysis of the spectrum but also enable it to be robust at low SNRs. 2.4

Fig. 2 Comparison of probability of detection for a two-stage detector with conventional single stage detectors as given in [8]

Two-stage detector

With the help of the algorithm in [8] we now discuss and explain the merits of using a two-stage sensing scheme over a single-stage sensing scheme. Fig. 1 shows a generic model of a two-stage detector used conventionally [8, 9, 18, 19]. The ED is chosen as the first stage not only because of its simplicity but also because the ED maintains a constant low probability of false alarm even at low SNR conditions. The second-stage detection can be any of the known techniques like CFD, EVD [20], or fine resolution sensing [21]. As seen from Fig. 1, if the ED computes the total energy (T1) to be greater than the first-stage threshold (l1), then it is hypothesised that the band of spectrum is in use. On the other hand, if T1 is less than l1 , then a second-stage analysis is done to do a fine sensing of the spectrum band. The test statistic of the second stage (T2) is compared with a pre-computed threshold l2 and a final decision is taken accordingly. As discussed in Section 2, ED is beneficial when the SNR is high so that even though there could be some errors in estimation of the noise variance, the ED would work fine as long as the SNR is above the lower bound SNR Wall given by gu . CFD on the other hand is robust to noise and hence is useful when the SNR is low. But CFD leads to a high detection time owing to the high computational complexity in calculating the cyclic frequencies. Thus, an ED-CFD two-stage detector as in [8] appears to be a good choice so that the benefits of both the detectors can be utilised whereas at the same time the disadvantages of one stage can be mitigated by the other. The probability of detection and the time taken to arrive at the results in [8] have been shown in Figs. 2 and 3, respectively. It can be observed that at low SNRs, a twostage detection scheme leads to a high probability of detection as compared with a single-stage detection scheme. The penalty to be paid for this improvement in detection performance is the increase in time taken to arrive at the result. In Fig. 3, we reproduce the mean detection time plot of the two-stage detector as compared to the single-stage

Fig. 1 Model of a conventional two-stage detector 1344 & The Institution of Engineering and Technology 2012

Fig. 3 Comparison of mean detection time of a two-stage detector with conventional single-stage detectors as given in [8]

detector for different SNRs. The plots clearly show that although the mean detection time of the two-stage detector is less than that of the CFD technique, it is very high when compared with the ED technique. The probability of activation (Pact) of the second-stage in a conventional twostage detector is given as Pact = P(H0 )(1 − Pf 1 ) + P(H1 )(1 − Pd1 )

(26)

P(H0) is the probability of the channel being vacant and P(H1) is the probability of the channel being occupied by PU. Pf1 and Pd1 are the respective target probability of false alarm and probability of detection of the ED used in the first stage. It has been shown that in practice the P (H0) can be as high as 80% [22]. Thus, for a Pf1 and Pd1 of 10 and 90%, respectively, for the first-stage ED, (26) computes that the second stage will get activated for 74% of the times on average. Thus, if t1 is the time taken by the ED in the first stage and t2 is the time taken by the stage used for secondary detection, then the total time taken (T ) for arriving at the result can be calculated as T = t1 + Pact xt2

(27)

Considering the time taken by the second-stage detection (t2) process as observed from Fig. 3, it becomes evident that the cost of improving the detection performance is indeed high. A close look at Fig. 2 reveals a hidden redundancy in the two-stage sensing scheme. We can see that at high SNRs, the improvement in the detection performance of the twostage detector is negligible as compared to an ED stage. Hence at high SNRs, where the ED is not constrained by the SNR wall, sensing the spectrum a second time whenever the ED calculates the energy to be less than the threshold seems to be overkill. In other words, activating the second stage of the CR without considering the SNR of IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

www.ietdl.org the channel the CR is in will lead to an unnecessary evaluation by the time-consuming second stage. The same inference can also be derived by observing the algorithm presented in [9]. The advantage in mean detection time proposed by [9] is due to the fact that at high SNRs the decision is taken at the ED stage itself and the decision does not go to the maximum eigenvalue detector (MED) stage. Since the two-stage method in [9] uses only 104 samples for energy detection while when ED alone is used, 1.1 × 105 samples are used for analysis, the savings in time is due to the reduced number of samples in the method in [9] and not due to the fact that ED – MED twostage detector is being used. Thus, with these insights obtained, in the next section we propose a modification to the conventional two-stage spectrum sensing algorithms to optimise the usage of the second stage.

3 Proposed two-stage spectrum sensing scheme In this section, we put forth a novel two-stage spectrum sensing scheme that seeks to address some of the problems discussed in Section 2 of this paper. 3.1

Pilot-assisted cyclostationary detection

Table 1

fs (k − 1) 32

a = Da[j − (2P ∗ L + 1)]

(29)

where Da = fs /P ∗ L. Thus, using (28) and (29), the exact location, j, of the pilot subcarriers can be determined. In this paper, we have analysed the PACD detector by averaging 50 OFDM symbols which corresponds to approximately 4096 data values. It is observed that the pilot subcarrier with a boost of 6 dB works well even at SNRs as low as 215 dB. We also analysed the ratio of the pilot subcarrier and the data subcarrier at various SNRs for different boosts to the pilot subcarrier. It can be seen from Fig. 4 that the Gaussian noise has a ratio of 1.1 for all SNRs whereas the ratio of the pilot to data subcarrier for the boosted subcarriers remain more than 1.2 even at a SNR of 215 dB. Since a SNR of 215 dB is a fairly low SNR for a CR to operate in, we reason that a boost of 6 dB to the pilot sub-carrier is sufficient to allow normal operations even under low-SNR conditions. As seen from Fig. 4, a pilot to data sub-carrier cyclic frequency ratio of 1.2 is sufficient to discriminate between the presence and absence of the PU. 3.2

CFD is robust against co-channel or adjacent channel interference and performs better than ED, but in the face of uncertainties in frequency selective fading, the CFD has a limitation to its operating SNR regime [4]. Thus, to mitigate these problems faced by a CSD, it has been suggested that pilot tones be embedded into the transmission waveforms of the PU [4, 6, 11, 23]. Although this approach is also not devoid of its share of criticism [7], we believe that embedding pilot tones has multitudes of benefits like negating the effects of SNR wall [4], increases the accuracy of detection even under doppler fading scenario [24], and also enables faster detection [6]. In this paper, we exploit the cyclostationary features arising because of embedding a known signature into the pilot subcarrier of an OFDM symbol. We analysed the performance of the boosted pilot subcarrier OFDM symbol under AWGN conditions. Table 1 briefly lists out some of the relevant parameters of the OFDM symbol used for analysis. Since we are embedding the pilot tones at known locations, the cyclic frequencies can be pre-calculated and the analysis can be restricted to looking for peaks only at the desired cyclic frequencies. In our case, the cyclic frequency of a pilot subcarrier at index ‘k ’ of the 64 subcarrier OFDM symbol can be computed as

a=

For an FAM-based CSD analysis, this translates to

Spectrum sensing using two stages

We have observed from Fig. 2 that at low SNRs, a two-stage detection leads to an increase in the detection performance. However, when the SNR is high, the performance of the single-stage ED and the two-stage detector is observed to be the same. Hence, we feel that the second-stage detection can be deactivated in a two-stage detector if the operating SNR of the CR is high enough to trust the ED stage alone. Fig. 5 shows the proposed modification to the algorithm that can be incorporated to reduce the mean detection time of a two-stage CR at high SNR values. In this algorithm, the first-stage ED computes the energy and compares it with the preset threshold (l1). If the energy is found to exceed the threshold, then the spectrum is assumed to be occupied by the PU However, if the energy is found to be less than the threshold, then the CR estimates the SNR of the channel the device is operating in. The estimation of the SNR can be done by the various known techniques available in the literature such as [25, 26]. It should be noted that the estimate of the SNR is an input to this algorithm. This paper does not deliberate in detail on the techniques to estimate the SNR. This input value of the estimate of the SNR, g, can be compared to the computationally established value of SNR, gu , given by

(28)

Parameters of OFDM symbol

no. of subcarriers no. of pilot subcarriers no. of data subcarriers sampling frequency pilot subcarrier gain cyclic prefix length sub-carrier modulation

64 4 48 20 MHz [0– 14 dB] 16 quadrature phase shift keying (QPSK)

IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

Fig. 4 Ratio of pilot to data sub-carrier cyclic frequencies at low SNRs 1345

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Fig. 7 Probability of detection of the proposed two-stage detector as compared to a single stage ED based detector

Fig. 5 Proposed algorithm of a two-stage detector to reduce the mean detection time

(15) to find out whether the operating SNR of the CR can meet the target Pd and Pf . If g exceeds gu , then the result of the ED stage can be trusted and the channel can indeed be assumed to be vacant. On the other hand, if g is less than gu , then the analysis of ED stage need not be correct and could be a case of miss detection. Hence, the second stage needs to be activated to have a better look at the samples and confirm or overturn the result obtained by the ED in the first stage. The proposed two-stage detector was simulated for detecting the OFDM signal as structured in Table 1. The target Pd and Pf were kept at 90 and 10%, respectively. Also the probability of the channel being vacant, that is, P(H0), was kept at 80%. Fig. 6 shows the comparison between the percentage of the times the second stage is activated in the two-stage detector discussed in [8] and the proposed algorithm. It can be clearly seen that by incorporating an estimate of the SNR of the channel in the model described in [8, 9], the activation of the second stage can be avoided at high-SNR regimes. For the set of parameters used in this simulation, the critical SNR is 210.5 dB and hence we can see that once the SNR of the channel is more than 210.5 dB, the algorithm switches to the ED stage alone. In other words, the algorithm uses both the stages of detection when the SNR is below the critical SNR gu , while it completely switches off the second stage and relies only on the ED in the first stage when the SNR is higher than gu . We can observe that, the second stage gets activated as much as 80% of the time in a conventional two-stage

detector. Thus, in a conventional two-stage detector, at high SNRs, even though the ED correctly determines the spectrum to be vacant, a redundant analysis is done using the time- and power-consuming second stage. In other words, for instance, if this algorithm is implemented on the technique mentioned in [8], at sufficiently high SNRs ( g . gu), we could save the 150 ms required for two-stage analysis and restrict the analysis to the ED stage alone. Thus, the detection time can be brought down to 20 ms thereby saving up-to 86% of the detection time. We can see from Fig. 7 that this strategy does not have any adverse effect on the probability of detection of the proposed two-stage detector. This is because when g is greater than gu , the ED stage is sufficient enough to meet the target Pd for a given Pf and thus the need for a second-stage evaluation is not necessary. From Figs. 6 and 7 we can see that the second stage can be totally switched off at high-SNR regimes without having any impact on the detection performance of the CR system. Also from Fig. 3 it is apparent that the second stage consumes most time for detection and analysis and hence any reduction in the usage of the second stage would lead to substantial savings in the mean detection time of the CR. Mathematically, the reduction in the detection time, Tred , over the conventional two-stage method at high SNRs (g . gu) can be expressed, in terms of the probability of activation Pact , as Tred =

Pact ∗ t2 t1 + Pact ∗ t2

(30)

Here t1 and t2 are the time taken by the first and second stage, respectively. Thus, as the spectral band under consideration becomes more and more sparse that is P(H0) increases, Pact also increases as given by (26). This leads to a reduction in the mean detection time obtained for the proposed method over the method in [8].

4 Hardware implementation of the proposed scheme

Fig. 6 Probability of activation of the second stage in the proposed method as compared to a conventional two-stage detector such as in [8] 1346 & The Institution of Engineering and Technology 2012

The proposed two-stage ED-PACD sensing scheme is implemented on Xilinx Virtex xc4vsx35-10ff668 FPGA as shown in Fig. 8. The hardware implementation of the ED assumes that the error function (Q), number of samples (Ns), the SNR (g) and the noise variance (m0) will be supplied as input to the module. Thus, the ED estimates the threshold based on these parameters. The threshold is compared with the detected energy from the input to determine whether the channel is occupied or not. If the channel is not occupied, then g is compared with the SNR wall ( gc) calculated using the ‘SNR wall calculator’ as shown in Fig. 8. IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

www.ietdl.org

Fig. 8 Hardware implementation diagram of proposed scheme (ED-PACD)

If g is greater than gc , then the decision of ED is taken as final as the SNR lies in the reliable limit within the SNR wall. If g is less than gc , then the second stage is activated using ‘second-stage selector’ as shown in Fig. 8. Fig. 8 also shows the hardware realisation of the second-stage, PACD, which is used to compute the spectral correlation density. The figure shows two serial FFT units of 128 and 8 points. The accumulator is used to accumulate the spectral correlation values which are passed to the threshold module. Here the ratio of the pilot subcarrier cyclic frequency and the data sub-carrier cyclic frequency is computed. If this ratio is found to be greater than 1.2, then it is assumed that the input signal is present and that the band is not free for use. The bit stream of the proposed architecture is generated using a Xilinx system generator. The power is calculated using Xilinx Xpower. Table 2 summarises the results of the implementation. It is clear from Table 2 that the implementation of the PACD comes at a huge cost of power required to be available on a platform. Also the number of multipliers (digital signal processing (DSP) 48) required for the PACD techniques is almost three times the requirement for an ED. It can be observed that in cases where the second stage is not activated (because of the SNR wall comparison), the proposed scheme saves 0.915 W out of a total of 1.09 W, Table 2

Total hardware resource utilisation profile

Technique No. of slices ED CFD

2154 3970

DSP48’s (no. of multipliers)

Static power, W

Dynamic power, W

13 38

0.44443 0.47857

0.17833 0.91499

IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751

thus effectively saving 84% of the total dynamic power. Note that the dynamic power required to compute the value of the SNR wall is 0.05536 W, which is just 5% of the total dynamic power consumed by the proposed two-stage sensing scheme. In a portable device such as a CR, the power consumption could be a very important design parameter as this has direct bearing on the capacity of the battery required. The algorithm proposed in this paper addresses this problem by switching off the time- and power-consuming second stage when the ED is sufficient for good detection performance.

5

Conclusion

In this paper, we propose a two-stage detector using ED in the first stage and a boosted pilot subcarrier for cyclic frequency detection in the second stage. The use of cyclic frequency detection aims to mitigate the problems caused by noise uncertainty faced by ED at low SNRs. We pre-compute the lower bound of the SNR at which the ED still works satisfactorily and show that by estimating the SNR of the channel the CR is in, we can switch off the second stage of a two-stage detector when the channel SNR is higher than the lower bound of the SNR level of the ED. We show that this does not cause any loss of performance. If the proposed algorithm is implemented for the technique in [8], it could help in saving the mean detection time by as much as 86% at high SNRs where the ED is sufficient for detection purposes. The hardware implementation of the ED and PACD techniques shows that the dynamic power requirement of the PACD is five times that of the ED. Hence switching off the PACD stage leads to enormous saving in power consumption. Thus, the proposed two-stage 1347

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www.ietdl.org detector not only leads to saving in the mean detection time of the CR, it also lowers the dynamic power of the CR device by 84% which is a limiting factor for any battery-operated device.

6

References

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IET Commun., 2012, Vol. 6, Iss. 11, pp. 1341–1348 doi: 10.1049/iet-com.2011.0751