A Design of Energy Detector in Cognitive Radio under Noise Uncertainty
Wei Lin, and Qinyu Zhang Communication Engineering Research Center, Shenzhen Graduate School, Harbin Institute of Technology Email: {hitblueghost@hotmail.com, zqy@hit.edu.cn}
CR system being taken into practical use is on the premise that CR system will not cause unbearable interference to primary systems. Designers of CR system need to make a fundamental tradeoff between space and transmission power [3]. In “no-talk” zone around the protected primary receiver, cognitive users must keep silent to allow the primary receiver to decode the received signal correctly. Since the quiet zone is outside the decodable region, cognitive devices are required to have high sensitivity in order to detect the primary signal in low SNR. Device-centric sensing methods mainly used in CR include energy detection, coherent detection, and cyclostationary feature detection [4]. The energy detector (radiometer) can detect any type of unknown primary signal. The coherent detector (matched filter) is the optimal detector for deterministic signal on Additive White Gaussian Noise (AWGN) channel, which can be used to detect the primary signals with a pilot. And the cyclostationary feature detector is suitable for the detection of non-white signal, such as the OFDM signal of DTV system [5]. Compared with other detectors, the performance of energy detector is lower. However, energy detector is most widely used because it doesn’t need any information about the primary signal, and has lower complexity to perform real-time detection. But energy detector totally can not detect the primary signal under a SNR threshold due to the impact of noise uncertainty. In [6], the existence of SNRwall is proved for all the moment detectors including energy detector. To reduce the noise uncertainty, some approaches were proposed, including interference estimation and coordination of CR devices. Although the noise uncertainty itself is harmful for detection, can it be utilized in some ways to help sensing? The paper is related to works [3], [7]-[9]. Our interest is in the difference of the impact of various types of noise uncertainty on the performance of energy detection, and how to exploit the type of noise uncertainty to determine the design parameters of detectors. Without increasing the number of samples, detecting performance can be improved by properly choosing decision threshold of the detector. In some situations the SNRwall can be approached, and even broken through. The rest of the paper is organized as follows. In Section II, the performance analysis of the energy detector is reviewed. In Section III, the model of noise uncertainty is proposed. In

Abstract—Cognitive radio is proposed as an approach to solve the conflict between the spectrum congestion and under-utilization. Energy detector is the detector most widely used in cognitive radio system due to its generality and low complexity. In this paper, the performance of energy detector under noise uncertainty is studied. The discrete form and continuous form of the noise uncertainty model are proposed. The average detection performances of the energy detector are analyzed under various types of noise uncertainty models, based on which a design of energy detector is put forward. Selecting different statistic decision thresholds will result in different detection performance. According to a prior knowledge about the noise variance distribution, a proper threshold can be selected to improve the detection performance as much as possible under the existence of noise uncertainty. Index Terms—cognitive radio, uncertainty, decision threshold energy detection, noise

I. INTRODUCTION With the explosive growth of wireless services, the ireproducible spectrum resource becomes more and more precious and scarce. Evidence to this fact is the crowded nature of spectrum allocation charts. It has been proved that spectrum can’t be utilized effectively with traditional spectrum allocation policies that frequency bands are statically allocated to unique services. How to improve the utilization of spectrum resource to satisfy the increasing demand of the wireless services has become an urgent problem to settle. The FCC tried to solve the problem by sharing spectrum on ISM and U-NII bands, which soon led to congestion in these bands. On the other hand, many surveys have illustrated that most licensed bands are underutilized. It is shown that the average usage rate of spectrum under 3GHz is merely 5.2% according to the report from NRNRT Project [1]. To solve the paradox between the spectrum congestion and under-utilization, cognitive radio (CR) is considered to be a solution to improve the utilization of spectrum resource. CR system searches and finds available spectrum resource in which to operate, without changing existing spectrum allocation. IEEE has already founded a 802.22 workgroup to establish the standards of WRAN based on CR techniques [2].

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Section IV, the design principles of energy detector are explained. Numerical results are presented and discussed in Section V. Finally, conclusions are drawn in Section VI. II. BACKGROUND REVIEW A. Basic Analysis of Energy Detector To detect the primary signal by the energy detector in AWGN channel is to distinguish between the following hypotheses:

§ γ − Nσ 2 · w ¸ Pfa = Q ¨ ¨ 2 Nσ 4 ¸ w ¹ ©

(3)

If there was no limitation about the number of samples, the energy detector could satisfy any given detection and false alarm probabilities. The least number of samples required by the detector is a function of received signal to noise ratio (SNR) by the cognitive radio,

H0 : Y [n] = W [n] n = 1," , N H1 : Y [n] = X [n] + W [n] n = 1," , N , J G where N denotes the number of samples, Y is the received JJ G signal at the cognitive radio, X is the transmitted signal from JJ G the primary transmitter, and W is the zero-mean AWGN with the variance
2

N = 2 ª(Q −1 ( Pfa ) − Q −1 ( Pd )) SNR −1 − Q −1 ( Pd ) º ¬ ¼ 2 2 where SNR = σ x σ w .

2

(4)

The design of detectors usually follows the constant false alarm rate (CFAR) criteria. The decision threshold is set by the number of samples and the given false alarm probability.

σ w2 .

In non-coherent detection, the signal can

γ = Nσ w 2 + Q −1 ( Pfa ) 2 Nσ w 4

(5)

also be considered as a Gaussian random process with the variance σ x . The decision statistic for energy detector is:

B. Impact of Noise Uncertainty Interference is the main cause to the noise uncertainty which makes the energy detector highly non-robust in low SNR. In general, the noise uncertainty can be modeled as a set or a range of noise distribution, such as [σ L , σ H ] , where σ L represents
2 2 2

T = ¦ (Y [n]) 2
N

(1)

the case that there’s no device transmits in the surrounding area, and σ H represents the case that all the surrounding devices
2

The performance of detection is measured by the pair of its detection and false alarm probabilities ( Pd , Pfa ) . Each pair is associated with a threshold

transmit simultaneously. Let the noise uncertainty be xdB, which means σ
2 H

γ

of the decision statistic.

= σ ⋅10 .
2 L 2 2 P . When σ H ≥ σ L + P , the cognitive 1 1

x 10

Suppose the power of the primary signal received at

T >γ T