An Efficient Dynamic Thresholds Energy Detection Technique for Cognitive Radio Spectrum Sensing Hossam M. Farag
EhabM.
Dept. of Electronics & Communications Engineering Aswan University Aswan, Egypt
[email protected]
Abstract- Cognitive Radio (CR) is an intelligent 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 conventional 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 based upon a dynamic threshold energy detection algorithm, in which, the decision threshold is toggled between two levels 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 conventional energy detection method with less increase in complexity. Keywords-Cognitive Radio; Noise uncertainty; Probability of false alarm; Probability of detection.
I.
INTRODUCTION
Most wireless communication systems are based upon fixed spectrum allocations, which in tum get the spectral resources to be un-efficiently utilized. Cognitive Radio (CR) [1] has been proposed as a dynamic spectrum reuse technology to increase the efficiency of the spectrum utilization by allowing a secondary user (SU) to access in a non-interfering manner some licensed bands which are temporarily not occupied by their licensed primary user (PU). One of the most important challenges in CR network is that the SU needs to reliably detect the presence of PU in a certain band in order to guarantee interference-free spectrum access. This is called spectrum sensing. Common methods of spectrum sensing are energy detection, matched filter and cyclostationary feature detection [2]. Among these techniques, energy detection has been a preferred approach due to its simplicity and applicability. The main drawback of energy detection is its sensitivity to noise power fluctuations, small variations in noise
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Dept. of Information & Communication Technology Osaka University Osaka, Japan e
[email protected] _
power may cause a sharp degradation in energy detection performance due to SNR wall [3], [4]. Most studies on energy detection technique are based upon constant noise power [5]-[7]; however, the noise is an aggregation of various sources like thermal noise, aliasing from front end filters and leakage of signals. Therefore, using constant noise power during the detection period is non practical approach; hence the noise uncertainty is not avoidable. In [3], the authors claimed that the noise uncertainty factor highly affects the performance of the conventional energy detector results in what so called SNR wall. Below this SNR wall, which depends on the noise uncertainty factor, the conventional energy detector fails to be robust, no matter how long it observes the channel. In [4], a theoretical study proved that in order to mitigate the noise uncertainty problem two different thresholds should be used. One of the two thresholds (the smaller one) is used to maximize the value of the probability of detection (Pd) and the other (the larger one) is used to minimize the probability of false alarm (Pja). These two thresholds are evaluated based
upon the noise uncertainty factor. However, this study didn't
provide any practical methodologies of how the noise uncertainty factor is estimated or how the two thresholds are toggled in a certain manner in order to maximize Pd and minimize Pja. Based upon the work of [3] and [4], in this paper, a practical two dynamic thresholds energy detection algorithm is proposed. The proposed algorithm is based upon predicting the PU activity profile (presence/absent) during the current observation period. This can be done by evaluating the average energy of the PU during a specified period. The two thresholds are toggled in a dynamic manner to maximize Pd and minimize Pja such that; when the PU is predicted to be present the smaller threshold is used and vice versa. The two dynamic thresholds are evaluated based upon the noise uncertainty factor which can be estimated using the noise variance history and the noise variances are estimated as [8]. We prove the effectiveness of our proposed algorithm over the conventional energy detector theoretically and through computer simulations. Computational complexity comparison between the proposed algorithm and the conventional one is also given.
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The rest of this paper is organized as follows: Section II reviews briefly the system model of the conventional energy detector. Our proposed energy detection algorithm is described in Section III. Analytical equations of the proposed scheme are investigated in Section IV followed by the performance evaluations in Section V. Complexity comparison is given in Section VI and finally the conclusion in Section VII. II.
SYSTEM MODEL
Spectrum sensing can be modeled as a binary hypothesis testing problem as follows:
Ho HI
� yen)
� y(n)
= l1{n)
= x(n) + l1{n)
(PU absent)
(1)
(PU present)
(2)
n=1,2,....., N where N is the number of collected samples
during the observation interval, hypothesis Ho sates that there is no PU in the sensed channel, and hypothesis Hi states that a PU is present, (n ) corresponds to the samples of the received signal, w(n) corresponds to the samples of the noise process, which is considered to be additive white Gaussian noise (A WGN) with variance a� and x(n) corresponds to the PU signal samples.
y
Conventional energy detector measures the energy received on a PU band during an observation interval and declares the current channel state as busy (hypothesis HI) if the received energy is greater than a predefined threshold or idle (hypothesis Ho) otherwise [9]. The test statistic is given as follows:
D(y) = Ly(ni N
(3)
11=0
where D(y) is the decision variable. The test statistic follows a central (under Ho) and non-central (under HI) chi-square distribution with 2N degrees of freedom. For low Signal-to Noise ratio (SNR) conditions, to achieve a certain performance (certain Pja and Pd), N is usually large, so the central limit theorem can be employed to approximate the test statistic as Gaussian.
D(y)""
{
Based upon the Constant False Alarm Rate (CFAR) approach, the decision thresholdr is set to satisfy a certain Pja for the CR system. Solving (5) forr gives: (7) we can see that the decision threshold is not only affected by the target Pja, but also by the value of the noise variance a� which is not constant in practical situations, so small fluctuations in a� will highly affect the value of r which in turn will cause unreliable detection of the PU even if we highly increase the value of N which is defined as SNR wall [3]. III.
PROPOSED ENERGY DETECTION ALGORITM
In this section, a new dynamic energy detection algorithm is introduced. The proposed algorithm takes into account the noise uncertainty effect when arriving at a final decision about the current status of the PU which results in a robust energy detector with better sensing performance than the conventional energy detector. From (5) and (6), we can observe 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 value of Pd/Pja by dynamically decreasing/increasing the value ofr, respectively. Based upon this observation and thanks to the fact that the time required by the PU to change his status (ON/OFF) is negligible compared to the time it remains at a certain status (ON/OFF), a PU status prediction based CR energy detector algorithm can be lunched.
L-I
In our proposed algorithm, PU activity profile is formed by storing the consecutive received PU energies (L is a configurable parameter) D(y){t), 1::; i::; L -1. Based upon these energy records, we can predict, to some extent, the current PU status by evaluating the average energy of the L consecutive energies including the energy of the current observation event D(yJrL) as follows:
D av
WeN a�,2N a:)
=
I �D ()y L fr
(i)
(8)
(4)
where Dav is the average energy of the L consecutive stored energies.
where P is the average PU signal power, then Pja and Pd can be given as [3]:
At the same time, noise variance history is created by storing the estimated noise variances a�(i), 1::; i::; L -1 of these
2 W(N(P+a2n),2N(P+an) ) 2
a 7//; '� J 2N �l a�
the noise variance of the current observation eventa:'(L)' the
Pfo = P(D(y» rIH) = J , 0
r - P+a:') Pd = P(D (Y» rIH) I = J N( ,
�l J2N(p+a:.)
L-I periods. Using the stored noise variance history including
(5)
)
noise uncertainty factor p can be estimated as follows [10], [11]:
(6) (9)
where Q() is the standard Gaussian complementary cumulative distribution function andr is the decision threshold.
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Then, Dav is compared with the fixed decision threshold y. If
Dav� Y then we expect, to some extent, the presence of the PU
Gaussian random variables, it is also considered to be normally distributed.
in the current PU activity. In consequence, a new decision threshold Yn"" for the final decision, is set to equal Y / p, which results in maximizing Pd. On the other hand, if Dav< Y then we expect, to some extent, the absence of the PU in the current observation period L, so Yn,,,is set to equal py, which in turn results in minimizing Pja'
(10) where J.Lmg and a�,g are given by [12]:
By comparing D(Y)(L) with Yn,,,, the final decision about the existence (H/Ho) of the PU during the current observation can be reliably made. With this simple dynamic threshold selection mechanism, in which, we just make use of the previous measured PU energies along with the previously estimated noise variances, the proposed algorithm can reliably compensate the noise uncertainty effect and highly outperforms the conventional energy detector as will be shown in the subsequent sections. Fig. 1 shows the details of the proposed energy detection algorithm. IV.
THEORITICAL ANALYSIS OF THE PROPOSED ALGORITHM
The measured energy values D(Y)(i) can be assumed to be normally distributed (see (4)) and mutually independent since they represent the energy of the sensed signal at time instants separated by time intervals much greater than the sensing period N over which the signal energy is computed. Since Dav is the average of independent and identically distributed (i.i.d.)
Proposed energy detection algorithm Input: y, N, L Output:
DecisionE {HI, Ho}·
for each sensing event i do: Calculate and store D(Y)i � Energy of N samples. Calculate and store
a�(i)
�
Estimation of the noise variance.
(11)
4 M 2 L-M 2' anog = --:; 2N (P +an) + --, - 2Nan L' L
(12)
[0, ]
where M E L is the number of sensing events where PU is actually present . Based upon the proposed algorithm and the distribution of
D(y)1 and Davg, the new probability of false alarm r;;w and the new probability of detection p�'" will be as follows:
Pfo�= {P,(Da",� r, D(Y)L � r I P)}HO + {P,(Da", < r, D(Y)L � py) }110 = {P,(Da",� r)}lIo'{p,(D(Y)L � rip) I P,(Da",� r)}lIo +
(13)
{P,(Da", < r)}lIo'{p,(D(Y)L � py) I P,(Da", < r)}lIo
F':J�= {P,(Da",� r, D(Y)L � yl P)}HI + {P,(Da", < r, D(Y)L � py) }Hl = {P,(Da",� r)}HI·{P,(D(Y)L � rip) I P,(Da",� r)}HI +
Algorithm:
M ' L-M 2 J.La,g=TN(P+an) +--N an L
(14)
{P,(Da", < r)}HI·{p,(D(Y)L � py) I P,(Da", < r)}HI
Davg is calculated over a representative number of stored PU energy values (L) to accurately estimate the current activity profile of the PU. Since the average of a relatively large set of values is not significantly affected, in general, by the value of a single element, it is reasonable, for L sufficiently large, to assume that Davg is approximately independent of D(y)L regardless of the actual channel state. So, for L sufficiently large we have:
end for
P,(D(Y)L � Y I p)IPr(Davg � y) ==Pr(D(Y)L � Y / p)
(15)
Pr(D(Y)L �PY�Pr(Davg < Y)==P,(D(Y)L �py)
(16)
Using (15) and (16), (13) and (14) will be as follows:
, an(m"x) , P=
-
(J'1I(avg)
�
' uncertamly . " Estlmate lactor. ' d nOIse
P"fo' == +
Dmg
