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C5. Improved Cognitive Radio Energy Detection Algorithm Based upon Noise Uncertainty Estimation

Hossam M. Farag1 and Ehab Mahmoud Mohamed2 1Faculty of Engineering, Aswan University, Aswan, Egypt, hossam.farag@aswu.edu.eg.

2Current: Dept. of Information and Communication Technology, Osaka University, Osaka, Japan. 2Permanent: Faculty of Engineering, Aswan University, Aswan, Egypt, ehab@wireless.comm.eng.osaka-u.ac.jp

ABSTRACT Cognitive Radio (CR) is a regulated technique for opportunistic access of idle resources. In CR, Spectrum

sensing is one of its important key functionalities. It is used to sense the unused spectrum in an opportunistic manner. Energy detection constitutes a preferred approach for spectrum sensing in cognitive radio due to its simplicity and applicability. The traditional energy detection technique, which is based upon fixed threshold, is sensitive to noise uncertainty which is unavoidable in practical cases. This noise uncertainty gets the fixed threshold energy detector un-optimized in its performance. In this paper, an efficient energy detector is proposed for optimal CR performance. The proposed scheme is a dynamic threshold energy detection algorithm, in which, two threshold levels are utilized based upon the average energy received from the primary user (PU) during a specified period of observation. Thresholds evaluations are based upon estimating the noise uncertainty factor. These thresholds are used to maximize the probability of detection (Pd) and minimize the probability of false alarm (Pfa). Theoretical analysis and simulation results show the effectiveness of the proposed scheme in comparison to the traditional energy detection method with less increase in complexity.

Keywords: Cognitive Radio, Energy Detection, Noise Uncertainty, probability of detection, probability of false alarm.

I. INTRODUCTION Nowadays wireless communication systems are based basically upon fixed spectrum allocations, which means

that the spectral is fixedly assigned to the authorized users at any time. In consequence, spectral resources are utilized un-efficiently.

Cognitive Radio (CR) [1] has emerged as a promising solution that can effectively address the existing conflicts between spectrum demand growth and spectrum underutilization. CR aims at improving spectrum usage efficiency by allowing some unlicensed (secondary) users (SU) to access in an opportunistic and non-interfering manner some licensed bands temporarily unoccupied by the licensed (primary) users (PU).

A major challenge in cognitive radio is that the SU needs to detect the presence of PU in a licensed spectrum and quit the frequency band as quickly as possible if the corresponding primary radio emerges in order to avoid interference to the PU. This technique is called spectrum sensing. Common methods of spectrum sensing are energy detection, cyclostationary detection and matching filtering detection [2]. The existing techniques provide different trade-offs between required sensing time, complexity and detection capabilities, but their practical applicability depends upon how much information is available about the PU signal. In most generic cases, a CR user is not expected to be provided with any prior information about the nature of the primary signals that may be present within a certain frequency band. When the secondary receiver cannot gather sufficient information, the energy detection technique is the best choice for the sensing work. The main drawback of the energy detection scheme is its sensitivity to the noise power variations, small fluctuations in noise power may cause a sharp decline in energy detection performance due to SNR walls [3], [4]. Most studies on the energy detection techniques are based upon constant noise power [5]-[7], however, the noise is an aggregation of various sources like thermal noise, leakage of signals, aliasing from imperfect front end filters, quantization noise, etc. Therefore, it is non-practical that the average noise power keeps constant in the detection duration; hence the noise uncertainty is unavoidable.

In [3], the problem of using a fixed threshold in the energy detection is highlighted. The authors claimed that noise uncertainty factor highly affects the performance of the fixed threshold energy detectors results in what so

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called SNR walls. Below this SNR wall, which depends upon the value of the noise uncertainty factor, the fixed threshold energy detector fails to be robust, no matter how long it observes the channel.

In [4], the authors theoretically proved that in order to overcome the SNR wall problem (noise uncertainty problem) two different thresholds have to be used. The two thresholds are evaluated using the value of the noise uncertainty factor. One of the two thresholds (the smaller one) is used to maximize the value of Pd and the other (the larger one) is used to minimize the value of Pfa. Hence, their claim is to use two different thresholds for evaluating the Pd and the Pfa. Although of the effectiveness of their theoretical study, they didn’t give any practical methodologies of how we can estimate the noise uncertainty factor or how two different thresholds can be toggled based upon the presence and the absence of the PU in order to maximize the Pd and minimize the Pfa.

Based upon the work of [3] and [4], in this paper, a practical two threshold dynamic energy detection algorithm for CR applications is proposed. The proposed scheme is based upon predicting the presence and the absence of the PU. This can be done through evaluating the average energy received from the PU during a specified period. This activity profile of the primary user enables us to predict, to some extent, the presence or the absence of the primary user. The thresholds are used to maximize the Pd and to minimize the Pfa, i.e., when the expectation is the presence of the PU the smaller threshold is used, and vice versa. These thresholds are evaluated using an expected value of the noise uncertainty factor, which can be evaluated using the noise variance history, and the noise variance is estimated by the method given in [8].

We prove the effectiveness of the proposed scheme in comparison to the conventional fixed threshold energy detector theoretically and through computer simulations. Computational complexity comparison is also given.

The rest of the paper is organized as follows: Section II reviews the classical fixed threshold energy detector. Section III describes the proposed energy detection technique. Section IV shows the theoretical analysis of the proposed scheme. Performance evaluations are given in Section V followed by the complexity analysis in Section VI, and the conclusion in Section VII.

II. THE CLASSICAL ENERGY DETECTION TECHNIQUE

A. Spectrum Sensing Problem Formulation Spectrum sensing problem can be modeled as the binary hypothesis testing problem where the state of the

PU is defined by the following two hypotheses:

absent) (PU )()(0 nwnyH =⇒ (1) present) (PU )()()(1 nwnxnyH +=⇒ (2)

n=1,…,N where N is the total length of the PU observing period, hypothesis H0 sates that there is no PU in the sensed channel, and hypothesis H1 states that a PU is present. y(n) corresponds to the samples of the received signal, and w(n) corresponds to the samples of the noise process, which is considered to be additive white Gaussian noise (AWGN) with varianceσ 2

n , i.e., w(n)∈ N(0,σ 2n ). x(n) corresponds to the PU signal samples, and

N is number of the received signal samples collected to carry out the detection process. Unfortunately, spectrum sensing algorithms may fall into mistakes in practice, which can be classified into missed detections and false alarms. A missed detection occurs when a primary signal is present in the sensed band and the spectrum sensing algorithm selects hypothesis H0, which may result in harmful interference to primary users. On the other hand, a false alarm occurs when the sensed spectrum band is idle and the spectrum sensing algorithm selects hypothesis H1, which results in missed transmission opportunities and therefore in a lower spectrum utilization. Based upon these definitions, the performance of any spectrum sensing algorithm can be summarized by means of two probabilities: the probability of detection Pd = Pr(H1/H1) and the probability of false alarm Pfa = Pr(H1/H0). Large Pd and low Pfa values would be desirable for good CR performance.

B. The Fixed Threshold Classical Energy Detector The Cognitive Radio system is usually in the shortage of knowledge about the structure and information of the

PU signal. Thus, energy detection is a preferable CR energy detection method because it could detect the PU signal without any prior knowledge about it. Moreover, its implementation is quite simple. Classical energy

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detector measures the energy received on a primary band during an observation interval and declares the current channel state as busy (hypothesis H1) if the measured energy is greater than a properly set predefined fixed threshold, or idle (hypothesis H0) otherwise [9]. The test statistic is given by:

∑=

=N

n

nyyD0

2)()( (3)

where D(y) is the decision variable. The test statistic follows a central (under hypothesis H0) and non-central (under hypothesis H1) chi-square distribution with N degrees of freedom. In low SNR regimes, the number of samples required to achieve a certain performance (certain Pfa and Pd) is always larger than one sample, (N >> 1). Based upon this observation, the central limit theorem can be employed to approximate the test statistic as Gaussian distribution as follows:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++≈

12 22

42

) )(2),((

) 2,()(

HPNPNN

HNNNyD

nn

onn

σσ

σσ (4)

where P is the average signal power. If only AWGN noise is considered, then, the Pfa and Pd can be written as [3]:

)2

()|)((2

2

σ

σγγ

n

norfa

NN

QHyDPP−

=>= (5)

))(2

(()|)((

2

2

1σσγγ

n

nrd

PNPN

QHyDPP++−

=>= (6)

where Q(.) is the standard Gaussian complementary cumulative distribution function and γ is the decision threshold. In the constant false alarm method, a target Pfa is set for the CR system from which the desired detection threshold can be calculated as follows:

] 2 )( [ 12 NNPQ fan += −σγ (7)

it is clearly shown from Eq. (7) that the calculated detection threshold is not only affected by the target Pfa but also by the value of the noise variance σ 2

n , which is not a constant value in practical situations. So, a small fluctuation inσ 2

n will highly affect the calculated threshold which in turns causes unreliable detection of the PU even if we highly increase the value of N results in what so called the SNR wall [3].

III. THE PROPOSED ENERGY DETECTION SCHEME In this section, a new dynamic energy detection algorithm is proposed. The suggested scheme takes into

account the noise uncertainty effect results in more robust with higher performance CR energy detector than the classical fixed threshold one.

In the proposed scheme, two threshold levels are carefully calculated to compute the noise uncertainty effect and maximize / minimize the values of Pd / Pfa, respectively.

On important observation can be drawn from Eq. (5) and (6) is that if we can (to some extent) predict the presence/ absence of the PU in the current observation event, we can highly increase/ decrease the values of Pd / Pfa by dynamically decreasing /increasing the used threshold levels, respectively. Therefore, a PU prediction based dynamic threshold energy detection algorithm for CR spectrum sensing can be lunched. Based upon this observation and thanks to the fact that the time required by the PU to change its status (ON/OFF) is negligible to the time the PU remains in certain status (ON/OFF), we propose a dynamic PU status predication based CR energy detector. In the proposed algorithm, given by Fig. 1, the energy history profile of the PU is calculated and based upon these history records, we can expect (to some extent) the presence / absence of the PU. That is, the average received energy of the PU activity is evaluated during L consecutive N periods of observations, including the current observation period in which a decision of the presence / absence of the PU should be taken, see Eq. (8).

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∑=

=L

kkav yD

LD

1

)(1 (8)

where Dav is the PU average received energy over L consecutive N periods of observations. D(y) is the PU received energy. At the same time, we calculate the noise uncertainty factor during these L periods of observations. This can be done by estimating the noise variances of these L periods, and divide the maximum noise variance observed by the average value of the measured noise variances [9], [10] which can be given by Eq. (9).

∑=

≤≤= L

iin

inLi

L 1

2

2

1

1

)(max

σ

σρ (9)

where ρ is the noise uncertainty factor. After calculating the average energy received Dav and the noise uncertainty factor ,ρ Dav is compared with a predefined threshold ,γ which is calculated using the constant false alarm rate method given by Eq.(7). If Dav ,γ≥ then we expect (to some extent) the presence of the PU in the current user activity. In consequence, and in order to decline the noise uncertainty effect which we already estimated by Eq. (9), we use the value of ργ / as a threshold to predict the PU activity during the current observation period. In the opposite side, in case of Dav ,γ< then we expect (to some extent) the absence of the PU in the current observation period and hence we increase the threshold level to be .ργ

Fig.1: The Proposed Energy Detector algorithm.

This dynamic nature of the proposed scheme will highly compensate the noise uncertainty effect in evaluating the PU current activity. Therefore, a highly improved performance is expected compared to the conventional energy detector as will be shown in the subsequent sections.

IV. THEORETICAL ANALYSIS OF THE PROPOSED SCHEME The performance of the proposed scheme is highly affected by the used prediction system. Based upon the

differences between what the algorithm predicts for the current PU activity and the actual PU activity, the theoretical study of our algorithm can be divided into 4 cases as follows:

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Case 1: The system prediction declares H1 and the PU is actually present (H1) (true prediction) as a result, ργγ /=new this will increase the value of Pd compared to the fixed threshold method.

Case 2: The system prediction declares H1 but actually the PU is absent (H0) (false prediction) as a result, ργγ /=new this will increase the value of Pfa compared to the fixed threshold method.

Case 3: The system prediction declares H0 and the PU is actually absent (H0) (true prediction) as a result, ργγ =new this will decrease the value of Pfa compared to the fixed threshold method.

Case 4: The system prediction declares H0 but the PU is actually present (H1) (false prediction) as a result, ργγ =new this will decrease the value of Pd compared to the fixed threshold method.

From the previous discussion, cases 1 and 3 represent the case that PU doesn’t change his status during a long time period, and cases 2 and 4 represent the case that the PU suddenly changes his status from ON to OFF or from OFF to ON, respectively. The proposed scheme outperforms the conventional fixed threshold scheme in the PU steady state situations, in which the PU doesn’t suddenly change his status. Usually in real communication systems, the time of continuous ON or OFF status of a communication device is much larger than the time of state transitions. Therefore, we expect higher performance of the proposed scheme over the conventional fixed threshold scheme in real communication environments. The different seniors of the proposed algorithm are also summarized in Table 1.

Table1: Theoretical Analysis Summary of the Proposed Energy Detection Algorithm

Case Predicted state

Actual state

new Consequence Prediction accuracy

1 H1 H1 ργ / Pd increases Good prediction 2 H1 H0 ργ / Pfa increases Poor prediction 3 H0 H0 ργ Pfa decreases Good prediction 4 H0 H1 ργ Pd decreases Poor prediction

V. PERFORMANCE EVALUATIONS In our simulation, a real communication environment is simulated for the PU using QPSK modulated signal

and including additive white Gaussian noise (AWGN). Mont-Carlo computer simulations are used to prove the effectiveness of the proposed scheme.

The effectiveness of our proposed scheme is illustrated based upon the receiver operating characteristics curve (ROC) which plots Pd versus Pfa [2].

Figures 2 and 3 adjust the value of L, the past records of the PU. In these figures, the ROC curves of the PU are simulated under different values of L, i.e. L=5, 10, 15 and 20 using different Signal to Noise Power Ratios (SNR) of -20 dB and -18 dB, respectively. N is set to 1000 samples during all the simulations.

From these figures, and based upon the trade-off between performance and complexity, we choose the value of L=15 as an optimal L value for the proposed scheme.

Figures 4 and 5 show the performance comparisons between the proposed scheme and the conventional fixed energy detection scheme under different values of SNR. From these figures, we can confirm the higher performance of the proposed scheme compared to the conventional method under different SNR values. This high performance results from the optimized dynamic mechanism used in the proposed algorithm, which flexibly adapts the value of used threshold to increase / decrease the values of the Pd / Pfa, respectively by decreasing the noise uncertainty effect. On the other hand, the conventional energy detector doesn’t have such adaptive behaviour, which results in poor ROC performance compared to the proposed scheme.

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Figures 6 and 7 show the effect of the SNR wall on the traditional fixed threshold detector using different simulated SNR values. As it is clearly appeared, at low SNR values, the conventional energy detector has poor ROC performance, as the system won’t be able to distinguish between the PU signal and noise. Therefore, the system can’t robustly detect the PU signal even if the value of N is highly increased.

Figures 8 and 9 show how the proposed scheme can effectively overcome the SNR wall effect compared to the conventional detector. This SNR wall mitigation comes from the proposed scheme dynamic structure, in which the detection thresholds are dynamically evaluated using the average PU activity in conjunction with the noise uncertainty effect.

Due to the prediction-dynamic nature of the proposed algorithm, and by taking into account the noise uncertainty effect during thresholds evaluations, the proposed scheme has large performance improvements by increasing the value of N even for very low SNR values. Therefore, the proposed algorithm can with high confidence overwhelm the SNR wall effect, which is the major problem facing the traditional fixed threshold method.

Fig. 2: ROC curves of the proposed scheme under different values of L with N = 1000 and SNR = -20dB.

Fig. 3: ROC curves of the proposed scheme under different values of L with N = 1000 and SNR = -18dB.

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Fig. 4: Performance comparison between the proposed scheme and the fixed threshold scheme using L = 15, N = 1000 and

SNR = -20dB.

Fig. 5: Performance comparison between the proposed scheme and the fixed threshold scheme using L = 15, N = 1000 and

SNR = -18dB.

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Fig. 6: ROC curves of the fixed threshold scheme with SNR = -22dB.

Fig. 7: ROC curves of the fixed threshold scheme with SNR = -20dB.

Fig. 8: ROC curves of the proposed scheme with L = 15 and SNR = -22dB.

Fig. 9: ROC curves of the proposed scheme with L = 15 and SNR = -20dB.

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VI. COMPLEXITY ANALYSIS The main concern of any proposed algorithm is the complexity- performance trade off, how much we should

trade the complexity to get better performance. The most efficient algorithms obtain significant increase in the performance with a little or no increase in the complexity. Table 2 shows the rough computational complexity comparison between the traditional fixed threshold and the proposed energy detectors. In this comparison, we only consider the average calculation process in the proposed scheme.

Table 2: The Computational Complexity Comparison

Operation Fixed threshold New scheme

Sum N-1 L(N-1)

Products N LN

From Table 2, the computational complexity of the proposed scheme is higher than the conventional method by a value of L. Actually, the exact increase of the computational complexity will be higher than that because of the noise uncertainty factor evaluations. Although of this small increase in the computational complexity (the optimal value of L is 15 and the usual value of N is 1000), the increase in sensing performance reaches about 3.5 times in case of SNR = -18dB and Pfa = 0.1 (which are the rated CR design parameters).

VII. CONCLUSION In this paper, we have proposed a dynamic threshold energy detection algorithm for CR spectrum sensing. The

proposed algorithm is based upon predicting the current PU activity. Based upon this prediction, dynamic thresholds are evaluated taken into account the noise uncertainty effect. These thresholds are carefully calculated to increase / decrease the values of the Pd / Pfa, respectively. We optimized the performance of the proposed scheme against its parameters. Then, we proved its efficiency in CR spectrum sensing in comparison to the conventional fixed threshold energy detector. In addition, we confirmed the efficiency of the proposed scheme in solving the SNR wall problem. Computational complexity analysis was done upon the suggested scheme, and we proved that although of its little increase in computational complexity, the proposed scheme enhances the sensing performance by about 3.5 times using regular CR design parameters. Further investigations upon the proposed scheme will be done in the near future.

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