J. Appl. Environ. Biol. Sci., 7(9)89-94, 2017 | ISSN: 2090-4274 |
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Fizza Irfan1, Aamir Zeb Shaikh2, Shabbar Naqvi3, Talat Altaf4
1Network Engineer, Habib Bank Limited, Karachi 2Assistant Professor, Dept. of Telecommunications Engineering, NED University of Engineering & Technology, Karachi 3Associate Professor, Dept. of Computer Systems Engineering, Balochistan University of Engineering & Technology, Khuzdar, Pakistan. 4Professor, Dept. of Electrical Engineering, Sir Syed University of Engineering & Technology, Karachi, Pakistan
Received: March 2, 2017 Accepted: June 30, 2017
ABSTRACT
Energy detection algorithm for sensing of white spaces is a preferred technique in cognitive radio applications due to its blind nature as well as simple implementation. Test statistic for Conventional Energy Detectors (CED) is computed by squaring the received signal samples. In [1], author has proposed an improved energy detector (IED) that computes decision test statistic by using an arbitrary constant replacing the squaring operation. Additionally, it is also shown that the detector performance can be improved under different values of Detection Probability, False Alarm Probability, Signal to Noise ratios and Number of Samples [1]. The detection performance of a CED is highly compromised under environments with noise uncertainty. This happens because the threshold (decision) is set on the basis of received noise variance. An investigation is presented into this paper that assumes IED under exponential noise uncertainty. It is also shown using simulation results that the best detector under exponential noise uncertainty is CED. Additionally, the detection probability is also simulated against received SNR. KEYWORDS: spectrum sensing, improved energy detector, exponential noise uncertainty
Energy detector is a preferred strategy to identify white spaces for cognitive radio applications [2-4].Due to the fact that they don’t require any a prior information for detection of signals. Besides, this RF sensing strategy is used under both licensed and unlicensed bands [2]. Detection of Primary User (PU) activity under licensed bands is a straight forward method in comparison to unlicensed bands. Because the transmission standards of licensed users such as GSM, WCDMA, Wi-Fi, Wi-Max and FM are a prior known to the cognitive sensor. Furthermore, transmission parameters such as signal to noise ratio (SNR), modulation type, carrier frequency, bandwidth, coding rate, duty cycle and data mask are also an a prior knowledge to the Cognitive Sensor. Hence, a coherent receiver-structure for specific transmitters can be found in literature [5]. For Cognitive Radio applications, Matched Filter Detector and Feature detectors are two preferred structures to identify the presence of a PU activity for a known transmitter [4, 6]. Thus, signature based detection algorithms are also recommended for spectrum sensing (for white spaces) purpose in the first standard allowing the secondary use of RF spectrum i.e. IEEE 802.22 [7]. Because, the first cognitive radio standard for air interface does not mandate the specific spectrum sensing algorithms. The details of ISM bands can be given by: 26 MHz band (902-928 MHz), 83 MHz (2.4 to 2.4835 GHz) and 125 MHZ (5.725 to 5.850 GHz). Furthermore, Unlicensed NII bands are typically located at 5 GHz [8]. These bands are typically overcrowded [9]. The operators on these bands include wireless lan i.e. Wi-Fi (IEEE 802.11a, b, g, n), Bluetooth (It is a wireless standard for transmission of data over short distances) also known as IEEE 802.15, Cordless phones, Zigbee users IEEE 802.15.4 – Typically Sensor communications in industries, Microwave ovens, radio-location and amateur satellites. Detection of all these users separately using matched filter architecture is a difficult task due to complexity of receiver structure [10]. Due to these reasons, energy detection based receiver structure is recommended for cognitive radio. Furthermore, ED based sensor has simplest structure [11]. However, in case of unlicensed bands, PU technologies and transmission parameters are un-known to cognitive sensing devices. In such cases, non-coherent spectrum detection algorithms with suboptimal detection performance are selected. Energy detection for spectrum sensing is also favored for detection purpose in first stage or quick detection purpose in the first IEEE 802.22 framework [12]. Besides, many benefits offered by CED, the detection performance is compromised under noise uncertain environments. Furthermore, under low SNR, detector may hit SNR Wall [13]. It is a received signal power limit, below which the detector is unable to sense the presence of a licensed user, operating into the environment, even under longer listening periods [14]. In [15], authors investigate and analyze the CED performance considering the presence of uniformly distributed noise uncertain environment. In [16], authors derive, investigate and analyze Generalized Energy detectors performance under uniformly distributed noise uncertain environment. Furthermore, authors also show that the SNR Wall is independent of the operation
*Corresponding Author: Aamir Zeb Shaikh, Assistant Professor, Dept. of Telecommunications Engineering, NED University of Engineering & Technology, Karachi
Irfan et al.,2017
performed on the received signal samples, i.e. SNR wall does not change under CED or IED operation. In [17], authors investigate the performance of CED under Log-Normal noise uncertainty. In [18], authors analyze the detection performance under different noise uncertainty models both in continuous and discrete time. In this paper, an investigation and analysis for IED detection of spectral bands is presented that considers the received signals with exponential noise uncertainty. It is due to the dynamic nature of wireless medium. Furthermore, probability distribution for uncertainty is assumed as exponential. It is also shown that the detection performance under assumed scenario is not related with the operation performed on received signal samples. Furthermore, it is also shown that the best performing detector under exponential noise uncertainty is CED model. This paper is organized as follows. Section II presents the system model for IED sensor under exponential noise uncertainty; Section III presents the analytical expressions for the proposed detector. The simulation and numerical results along with discussion is presented in section IV. Paper is concluded in section V.
Cognitive radio users opportunistically transmit their data in addition to periodically sensing for unused spectral bands [19]. Furthermore, it is also their responsibility to avoid creating any harmful interference for PU. Because, otherwise RF bands will be useless for all the users including primary and secondary. The performance of spectrum sensors operating under secondary license can be described by a binary hypothesis testing rule i.e.
⎧ε () k ; H
0
() =⎨
yk xk +ε k ;
⎪
1
(1)
In equation (1), it is assumed that the detector computes the presence of a spectral hole or absence of PU activity under H0 and presence of a PU under hypothesis H1. Thus, under null hypothesis, cognitive radio uses the spectrum in secondary fashion, while under H1 it avoids any transmissions as it finds the presence of a licensed user in specific band.
The decision test statistic for the IED can be given from [1]:
1 Kp
∆TIED =∑ | ()
yk | (2)
K
k =1
In the above equation, K shows number of samples required to compute test statistic. P is any arbitrary constant > 0. For p=2, the proposed detection rule can be converted into CED. The decision is taken on the basis of test statistic .The test statistics for CED and GED are given in [16]. For the case under consideration, under both hypotheses, mean and variance for received signal samples is given by [1], shown in equation (3) and (4):
2p/2 p +1 p
Γ()σ ,i = 0
⎪
⎪ π 2
µi =
p/2 p/2
2 (1 +γ ) p +1 p
Γ()σ ,i = 1
⎪
⎩ π 2
(3) p
2 2p+1 1 2p+1 2p
Γ( )- [Γ ( )σ ,i =0
⎥
π 2π2 ⎦2
σ= ⎨
i 2p(1+ γ) p 2p+1 1 2 2p+1 2p
Γ( )Γ ( )σ ,i=1
⎥
π 2 π2 (4)
Assuming very large number of samples, Correct detection of a primary user and false alarm rate for the same can be given by following equations [16].
⎛
⎜η −µ1 ⎟
Pd= Q
⎟
⎜σ 1 ⎟
K ⎠
• Part of this paper is submitted to FYP at TC, NED University, Khi.
(5)
J. Appl. Environ. Biol. Sci., 7(9)89-94, 2017
⎛
⎜η −µ0 ⎟
P = Q
(6)
faσ ⎟
⎜
0 ⎟
K In the above equations, η represents value of threshold, µ0 and µ1 represent mean value of received signal under both null and alternative hypotheses, while σ0 and σ1 are the value of standard deviation under both hypotheses HA and HB respectively.
In this section, the performance of GED sensor is presented in analytical form for the case of noise uncertainty with exponential distribution. As the noise is aggregation of various unintentional signals such as thermal noise, interference signals the users operating on adjacent spectral bands [20]. Thus, noise variance varies significantly. These variations in the noise power result in noise uncertainty. Exponential distribution can be represented by its probability density function (PDF) as [21]:
−λ x
f () =λ (9)
xe , x>0
Assuming noise uncertainty factor ‘β’ is exponentially distributed in range of [0, L] in this case i.e. [0, 10], the probability density function of noise uncertainty factor can be written as:
α () = e −αλ λ α < 10 (10)
F α ,
Under noise uncertainty, the mean and variance of received signal samples is given by [16] :
2p/2 p + 1 p
Γ()σ ,i = 0
⎪
⎪ π 2 w µ , =
p/2 p/2
i nu 2 (1 + αγ ) p + 1 p
Γ()σ w ,i = 1
⎪
⎩ π 2
(11)
p 22 p
2 2 p + 11 p + 1 ⎤
Γ() −
[Γ () σ ,i = 0
w⎢
π 2 π 2 ⎦σ 2, =
pp
i nu 2 (1 + αγ ) 2 p + 11 22 p + 1 2 p
Γ() − Γ () σ ,i = 1
w
⎢
π 2 π 2
(12)
The
and
are defined as [16]: 2p/2 P +1
A =
(13)
Γ ⎟
p π 2 2p ⎡ 2P+1⎞ 12 P+1
Γ
Γ (14)
⎢ ⎟⎥
p π 2 ⎠ π 2
The probabilities of correct detection and false alarm for fixed noise uncertainty factor α are given as [16]:
p/2 p/2
⎡⎤
kα− A (1 +αγ )
⎥
P = Q N / B (15)
Dp/2 p
⎥
(1 +αγ )
⎣
p/2
P = Q ( kα− A ) N / B (16)
FA pp
Averaging the probabilities of detection and false alarm for exponential noise uncertainty case.
Irfan et al.,2017
p/2 p/2
L
⎡( kα− Ap (1 +αγ )) PD =∫Q p/2 N / Bp fα () x dx
0 (1 +αγ ) ⎥ (17)
p/2 p/2
L ⎡( kα− Ap (1 +αγ )) PD = Q N / Bp −αλ λ α
ed
∫ p/2
(1 +αγ ) 0 ⎣ ⎥ (18)
L p/2
⎤
PFA =∫ Q ⎢⎣(kα− Ap ) N / Bp ⎥Fα (α )dα (19)
⎦
0
L p/2
−αλ λ
P = Q (kα− A ) N / Be dα (20)
FA ∫ ⎢ pp ⎥
⎦
0
In this section, the numerical results of the proposed setup are computed and plotted.
Pfa
Figure 1. ROC for GED at ASNR=-15db and N=10000
Figure 1 shows the Receiver operating Characteristic for GED under exponential noise uncertainty factor. The numerical values used for the simulation are as under: p=2, 3 and 4. P represents the operation of conventional energy detector for p=2 and all the other values of p show improved energy detectors. ASNR=-15db, N=10000. Ap and Bp can be calculated using equation (13) and (14). The results show that maximum PD is achieved at p=2. This result demonstrates that under the exponential noise uncertainty factor, the best detector for GED case is CED.
J. Appl. Environ. Biol. Sci., 7(9)89-94, 2017
Figure 2. Detection Probability and ASNR, at PFA=0.1 and N=10000
In Figure 2, Detection probability is computed for various values of ASNR ranging from -16 dB to -10 dB. False Alarm for this case is considered to be 0.1. The results clearly show that CED outperforms IED under given scenario. And also an obvious result is observed that the increasing SNR results in increased value of detection probability.
GED performance of IED for cognitive radio under exponential noise uncertainty is investigated. The performance is also compared with CED. The results show that the CED outperforms IED under given detection scenarios.
ACKNOWLEDGEMENT
The authors are highly thankful to the NED University of Engineering & Technology that provided all the useful resources that were necessary for the successful completion of this paper.
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