Sensing Threshold Adaptation Based on Partial Channel State Information for Energy Detection in Cognitive Radio Networks Amanpreet Kaur
Dishant Khosla
Arvind Arora
Electronics & Communication Engineering Department Chandigarh Engineering College, Landran Mohali-140307, Punjab, India
[email protected]
Electronics & Communication Engineering Department Chandigarh Engineering College, Landran Mohali-140307, Punjab, India
[email protected]
University Centre of Instrumentation and Micro-Electronics, Punjab University, Chandigarh-160014, India
[email protected]
Abstract: The spectrum sensing methods have been incorporated in
an essence to fulfill the sensing requirements associated with the detection of primary user in cognitive radio (CR) networks. Energy detection (ED) is the simplest and most commonly employed method to sense the licensed spectrum so that secondary user can make proficient use of it. The conventional energy detector has predefined value of sensing threshold due to which its targeted performance deteriorates considerably with noise uncertainty under severe fading environment at low SNR province. In this paper, we have proposed a novel approach for the adaptation of sensing threshold based on the imperfect knowledge of channel state information (CSI) so that it must be chosen approximately to meet tradeoff between probability of detection and false alarm probability under severe fading. The simulated results are presented to validate that proposed scheme is more robust against noise vagueness. We have compared the performance efficiency of proposed methodology with imperfect CSI, the conventional methodology with full CSI and conventional scheme with imperfect CSI. It has shown that the proposed scheme significantly outperforms the conventional schemes.
Keywords: threshold; adaptation; energy detection; partial; channel state information.
I. INTRODUCTION The use in emerging and innovative technologies with the efficient usage of electro-magnetic spectrum in radio environment is the present demand of wireless communication. The use of radio frequency in every country is governed by their corresponding government agencies as Federal Communication Commission (FCC) in United States. Regulation of wireless network is done by allocated fixed spectrum assignment policy in the traditional approach of spectrum management. This lends towards the dilemma of over consumption and scantiness of spectrum. In 2002, studies based on the field measurement [1] have revealed that large portions of spectrum allocation are impeded. Dynamic
spectrum access [2], with the evolution of cognitive radios (CR), is the motivation to eradicate these problems that can use spectrum with an opportunistic manner instead of static regulation policy. CR is a modern technology that allows unlicensed secondary user to abuse the frequency spectrum of certified incumbent user when it is not self-employing that spectrum [3, 4]. Thus, in spectrum sensing, the most crucial task in CR networks to monitor changes all the time, the busy communication channels as well as free ones are identified by a secondary transciever and it instantly moves into the free channels leaving behind the occupied communication channels under the condition that it should not interfere the licensed terminals. For efficient exploitation of spectrum and sharing of that spectrum, spectrum sensing capabilities are embedded to the prototype of the next generation hand held devices. Spectrum sensing schemes like energy detection, cyclo-stationary detection, matched filter detection and cooperative [2, 5, 6] are available. Each detection method has its own pros and cons, and out of these, energy detection method is the simplest and oldest used technique that doesn’t require any prior knowledge of signal. Due to its simplicity and less complexity over match filtering and cyclo-stationary feature detection scheme, it is more popular. However, the fundamental problems [5-7] associated with it are: (i) susceptibility to noise levels, (ii) inability to distinguish between modulated signal and noise and thus between incumbent user and secondary user (iii) inability to detect the incumbent user’s signal with low signal to noise ratio. Despite these bottlenecks, energy detection outperforms in terms of its low sensing duration than other sensing techniques, which makes it a strong candidate for wideband spectrum sensing. Cooperative spectrum sensing [8, 9] is used to improve the detection performance. The sensing threshold plays noteworthy role in PU signal detection and thus must be chosen appropriately to meet tradeoff between
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probability of detection and possibility of false alarm under severe fading. Unlike the conventional energy detector, in few recent reports threshold adaptation techniques have been proposed to control sensing threshold dynamically [11] and on double threshold [13]. The work in [10] an iterative constant false alarm detection rate (CFADR) method with parametric estimation can adjust threshold but requires large number of samples. The work in [12] has limited its performance due to considering uniform SNR throughout the system. In some employed work [14], signal to noise ratio at secondary transmitter is considered to adapt sensing threshold with assumption that it has full knowledge channel state information (CSI). From a practical point of view, it is never possible to have full knowledge about the channel conditions as it is time varying in nature and thus keep changing with time and geographical location. However, to deal with the conflicts, it is considered that channel CSI is known beforehand [15]. The channel dependent dynamic algorithm [16] has been engaged for imperfect channel conditions with significant probability of detection but they require significantly long duration for spectrum sensing and large number of energy samples. This may lead to the reduction of transmission time and thus overall throughput of the system decreases [17]. From the above discussion, it is clear that the selection of sensing threshold deserves the attention for further investigation which defined the efficient performance of energy based spectrum sensing scheme. Therefore, in this paper, it is aimed to examine how the threshold selection process can be optimized with the imperfect knowledge of channel CSI that contributed to the threshold estimation. A novel threshold adaption scheme is proposed that can maintain the performance of CR suited for operational needs of spectrum sensing. The predicted value of partial CSI parameter from channel estimation can adjust the level of threshold which further investigates to calculate the performance metric parameters: probability of detection, missdetection probability, chances of false alarm and sensing error probability. And unlike the available adaptive schemes in literature that worked for high SNR, our proposed methodology scrutinizes the adopted threshold role at low SNR for each metric parameter. The theoretical and simulated results are presented to demonstrate the effectiveness of the anticipated scheme over conventional scheme. The thorough analysis of conventional ED with full CSI and partial CSI is done and then compared with the proposed adaptive threshold based ED in the simulated results. The rest of the paper is organized as follows. Section II provides the System model for energy detection sensing based cognitive radio network (CRN) with channel estimation. Static threshold energy detection scheme with perfect knowledge of channel CSI and analytical modeling of static threshold ED with imperfect CSI is presented. Proposed adaptive threshold ED based on channel estimation of having imperfect CSI is demonstrated in section III. The simulated results with comparison for all three schemes followed by conclusion is discussed in section IV and V respectively II. SYSTEM MODEL
Figure1 Proposed CRN Channel estimation Model
A. CSI Estimation Model We assent to a sensing based CRN channel estimation model with single primary network and secondary network with single pair of both primary and secondary transmitterreceiver as shown in figure1. Channel link assumptions is given as x
Yp- Channel gain between PU-Tx and PU-Rx
x
Ys - Channel gain between SU-Tx and SU-Rx
x
Yps- channel gain between PU-Tx and SU-Tx
x
β - Parameter defined partial CSI feedback from CSI estimator to ED
We have examined the channel links between SU-Tx and SU-Rx such that energy detection based spectrum sensing is proposed in this paper. In this information theoretic work, it is assumed that the secondary channel link is not time varying and fading is a stationary process thus channel is following block fading model with coherence time Tc . Hence, analysis is done with the assumption that channel gain Ys is unchanged for the given time period Tc.The pilot transmission is carried out between SU-Tx and SU-Rx to indicate what amount of information is lost that is how a signal gets faded during transmission and then a channel and CSI estimator can estimate the channel gain from the pilot carrier sense method such that the obtained value of Ys be Y˜s which is equal to g str .This channel CSI estimator provides the channel state information of the channel link from its channel gaingstr such as þ ∝ 1/gstr. The estimated value of CSI has indicated the channel uncertainties under severe fading and noise. The system model has implied with the available CSI from the SUTx and SU-Rx is imperfect or partial. B. Static Threshold ED with perfect CSI In conventional energy detection scheme the transmitted signal power of the incumbent user is sampled over a frequency channel for fixed time duration r. It is assumed that the channel is following block fading model and has exact knowledge of CSI. The samples of energy signal are taken and are compared with predefined threshold Thlevel to determine the presence or absence of incumbent user. Based on the outcomes, we can define two hypothesis i.e. HOand H1. When total energy of the samples is greater than the preset
threshold Th, it represents the presence of the incumbent user and therefore hypothesis is H1, otherwise, the absence of incumbent user is expressed with null hypothesis HO. w(n) HO} y(n) = { x(n) + w(n)H1
(1)
According to the central limit theorem, for number of samples > 30 the sampled signal approximation can be Gaussian distribution [18] and is defined below as Normal( O , o 2O) ) y2 (n) = { 2 Normal( 1, o1 )
HO H1
For number of samples N, substituting the mean μi and varianceoi under hypothesis Hi(i = 0,1)for normal Gaussian distribution, and therefore SNR (ð) is formalized as a ratio of 2 ox signal variance to noise variance,ð = thus distribution 2 on
given as ∑ y2 (n) = {
HO } (1+ (ð ) Normal(Non ð), 2N on + 1) H1 4
2
(2)
The test static of energy detection scheme will be given by 1 P(y) =
N
N
)|y(n)|2
(3)
n=1
Different performance indicators namely, probability of detection (PD) and chances of false alarm(PFÆ), Missdetection probability (PMD) are used to measure the performance of the energy detector where, probability of detection may be definite as the probability of detecting incumbent user signal accurately under fading channel. And probability of false alarm may be the probability of detecting the presence of incumbent user when it is actually not present. The higher PMDdegrades the performance of primary user by causing interference to it and privileged PFAexceed the inefficient spectrum utilization. Thus, both should be as low as possible. The PFÆ and PD in terms of ThandN may be given by Th N PD (Th , N) = Q (( 2 − ð − 1) J ) on 2ð + 1
PD = 0.5erfc [
1
(6)
]
/ ƒ2o1
Th −
O
PFÆ = 0.5erfc [
(7)
] / ƒ2oO
(8)
PMD = 1 − PD
Where Th sensing threshold is based on assumption that full channel CSI is known to the secondary-transmitter beforehand. Hence, the exact knowledge about channel has given sensing without errors. The threshold Thmay be defined by Æ, ९ and ℂ parameters and given by 1 − O ); = o 2 o 2 Æ = ( 1 − 1 ); ९ = ( 1 O 2 2 2 2 oO o1 o1 oO
o1 2 2 O − 1 − 2log ( )) oO2 o12 oO 2 (−९ + √९ + Æℂ)/ (9) Th= Æ Here, it is assumed that channel conditions are perfectly detected and exact information of channel state is available. Since, wireless channel is time varying in nature, it is extremely difficult to estimate it accurately under rigorous fading. Thus, the conventional detection scheme with fixed threshold leads to the erroneous results for given PD and PFA .Then, we have assumed that channel conditions are not accurately estimated and the þ available to secondary transmitter is imperfect. In next section, we look that how the inaccurate channel conditions having CSI parameter þ, can influence the conventional energy detector and can be used to vary the threshold adaptively in proposed work. It will be also shown that changing the threshold in a dynamic manner is a better way to keep the performance metrics appropriate to the operational requirements for energy based spectrum sensing. ℂ= (
Normal(Non2, 2Non4) 2
Th −
C. Static Threshold ED with imperfect CSI When partial CSI information is available, the noise variance of the channel and detection threshold will get modified accordingly. The modified test statistics for conventional energy detection scheme having static threshold will be given by
(4) 2
) y (n) =
Normal(þNo2n ,þ 2Non4)
HO
Normal(No2n(ð + þ–1 ), 2Non4(ð + þ –1) H1
Th PFÆ(Th, N) = Q ((
2 − 1) √N)
on
(10)
(5)
Where Q(. )complementary distribution function, it is evident that energy detector performance deviate significantly by varying sensing threshold and number of samples for received SNR. The expressions of likelihood functions having dependency on threshold for the mean and variance are formalized as
The modifiedA, B and C values given by 2 oO Æ = þ2o12 − þ2 1 2 ९ =( )o − þ o2 O 1 þ O 1 ℂ=
2 2 o − O 1
2 2 o − 1 O
2o2o2 ln (þ2 O 1
o1 ) oO
The sensing threshold can be calculated by substituting these modified values into eq.(9) as T'h = 2
2
2
2 2
2 2 2 oO
2 2
2 2
2 2
2o1
–(oO 1 – O o1 )+J(oO 1 – O o1 ) +(þ o1 – þ2 )( O o1 – 1 oO –2oO o1 ln(þ o )) O 2
o þ2o12– O2 þ
(11) This modified T'h can change eq.(6), (7) and (8) accordingly. To conclude, this is not favorable strategy as fading is not estimated perfectly and the loss in communication can’t be neglected. Hence, the chances of error are increased than conventional ED taken under perfect CSI in previous section. The ambiguities between PD and PFA is also formulated with the error probability. Thus, sensing error probability is defined as the chances that energy detection can perform erroneously in channel conditions and may be expressed as Perror = PK1. PD + PKO. PFÆ
(12)
Where PH1 and PHO are probability of occurrence and nonoccurrence of primary signal. It is obvious that fading awareness is not accurately opted from the channel. Hence, instead of static threshold ED with full CSI and partial CSI, we proposed an adaptive threshold selection scheme for ED with partial CSI that will overcome the degradations in ED performance with fixed threshold and erroneous results due to imperfection in CSI III. PROPOSED ADAPTIVE THRESHOLD ED WITH IMPERFECT CSI We are deriving; a dynamic optimal threshold selection algorithm to overcome the effect of improper channel CSI and postulation of perfect CSI in the energy detector based sensing. As the uncertainty conditions are indirectly expressed β . Thus, higher the value channel CSI, weaker is the channel and lower the value of channel CSI, stronger is the channel with having low level of uncertainties.
estimator at the SU-Rx, the feedback path is given back to the adaptation block of energy detection in SpSe of SU-Tx end so that presence or absence signal can be identified accurately at secondary receiver as shown in figure 2. This threshold T'hsettlement works out in accordance with the output from CSI estimator. The proposed work is focused to make the energy based sensor of SpSe attentive about the noise uncertainty in channel so that it can amend its threshold level according to the imperfect CSI. The estimated value of CSI parameter from CSI estimator is E. A slightly greater value þ∗ than the estimated value þ is taken to adjust T'hdue to the chances of erroneous conditions in feedback channel link. According to the channel inversion method, if the channel CSI factor is þ∗, we can switch the threshold value adaptively from minimum to maximum with the þ∗. The maximumthreshold, (ThMIN) and minimum threshold, (ThMAX) are modified and studied in two cases as follows: Case 1: If there is deep fading due to high noise uncertainty or bad channel conditions then channel CSI is high and hence the threshold will be lowered down by an amount of þ∗ accordingly and opt minimum value of modified threshold given by ThMIN =
T'h/ þ∗
(12)
Case 2: If shallow fading and low noise uncertainty is estimated due to good channel conditions then channel CSI is low, the threshold will raise its value β* times and hence the opted value is expressed by ThMAX = T'hþ
∗
(13)
Now, we can get the improved closed form expressions for performance parameters with the adopted sensing threshold using eq. (12) and (13) as ThMIN − 1 (14) ] / PD = 0.5 erfc [ ƒ2o1 PFÆ
−
= 0.5 erfc [ThMAX
PMD = 1 − [0.5erfc (
O
/ ƒ2oO ThMIN −
Perror = PK1. [0.5erfc (
(15)
]
1
ƒ2o1 ThMAX −
1
ƒ2o1
+ PKO. [0.5erfc ( Figure 2 Block diagram for proposed work between SU-Tx and SU-Rx
Under fading channel conditions, detection threshold plays a very important role, as it deteriorates the detection performance severely if not chosen properly. From the channel
(16)
)] )] ThMIN −
O
)]
(17)
ƒ2oO
The formalized expressions are evaluated in next section to be evidence for the performance of proposed scheme. The comparison between proposed with partial CSI and Conventional with CSI is also shown in results.
0.95
Probabilit y of Detection, PD
N=30 & CSI= 1.4 0.35 Static Threshold with Full CSI Static THreshold with Partial CSI Proposed Ada ptive Threshold with partial CSI
0.3
0.25
Probability of miss-detection, P
N=30 & CSI= 1.4 1
0.9
0.85
0.2
0.15
0.1
0.05 0.8 0 0.75 Static Threshold with full CSI
0.7
0.65
0
1
2
3
4
5 6 SNR in dB
7
8
9
10
It is seen that assuming perfection and imperfection in channel, PD can demote its chances from 84.8% to 68.9% .But this proposed dynamic threshold scheme can make achievable possibility to detect primary signal when knowledge of channel conditions is incomplete. An inference drawn from eq. (14) that level of threshold is adjusted to be down so that desirable detection possibility should be achieved as consequently illustrated in the fig 3.
1
2
4
5 SNR in dB
6
7
8
9
10
It is inferred from the graph in fig.5 that, at 0 dB the PMD is lower down as compared to conventional under ideal and partial scenario of channel estimation by 0.1 and 0.26 respectively. This parameter is improved by 83.7% with respect to predefined threshold technique with channel estimation. In fig.6, the chances of occurrence PK1 and nonoccurrence PK0 of incumbent signal is supposed to be 0.5 for demonstration. N=30 & CSI= 1.4, PH0 =0.5, PH1 =0.5 0.7 Static Threshold with Full CSI Static Threshold with Partial CSI Proposed Adaptive Threshold with partial CSI
0.6
error
Error Probability, P
Static Threshold with Full CSI Static Threshold with Partial CSI Proposed Adaptive Threshold with partial CSI
0.3
0.4
0.3
0.25
0.2
0.2
0.1
0.15
0
0
1
2
0.1
3
4
5 6 SNR in dB
7
8
9
10
Figure 6 Perror verses SNR
0.05 0
3
0.5
N=30 & CSI= 1.4 0.4 0.35
0
Figure 5 PMD verses SNR
Static Threshold with Partial CSI Proposed Adaptive Threshold with partial CSI
Figure 3 PD verses SNR
False alaram-Probability, P FA
threshold and its probability approximately becomes zero after 3 dB. This shows the effectiveness of threshold adjustment for imprecisely estimated channel because of high noise uncertainty. Moreover, conventional static threshold ED performance becomes worsen due to 25.7 % increase in PFA on acclimatizing from proper to improper CSI. Hence, this graph reveals that threshold control is the performance up-grading strategy with error reductions during partial CSI estimation in energy based spectrum sensing.
MD
IV. PERFORMANCE ANALYSIS WITH NUMERICAL RESULTS MATLAB environment is used to carry out simulations. For Numerical Analysis, some assumptions are made such that N = 30, the SNR ranging from 0 dB to 10 dB furthermore β and β* are assumed to be equivalent to 1.4 and 1.5 respectively. The resultant figures illustrate sensing performance of proposed scheme is analyzed along with the conventional for full and partial CSI comparisons. Figure 3 show that under similar inaccurate channel conditions, proposed threshold amendment algorithm has higher detection performance of 94.8% than fixed threshold existing scheme at low SNR value of 0 dB
0
1
2
3
4
5 SNR in dB
6
7
8
9
10
Figure 4 PFA verses SNR
The fig.4 plotting has cleared that false detections lowered with 0.9% at 0 dB with the dynamic selection of sensing
The curves for conventional method with ideal channel state estimation and for static threshold energy detector with β are varying from 50% to 55% for the diversity of SNR which shows chances of error during incumbent signal detection becomes at half of its peak value and thus are showing poor performance as shown in fig.6. For proposed method the value of Perroris 0.03 at lowest SNR and decreases to approximately
0 after SNR of 5 dB. It is an evident that our suggested work is more robust to changing erroneous channel conditions. CSI= 1.3 80 Static Threshold with full CSI Static Threshold with Partial CSI Proposed Adaptive Threshold with partial CSI
70
No. of samples required, N
60 50
V Conclusion
40 30 20 10 0
0
1
2
3
4
5 SNR in dB
6
7
8
9
10
Figure 7 Requisite N verses SNR
The number of samples requirement plots with respect to SNR dB with an assumption of achieving target PDequals to 0.9 and PFA equivalent to 0.1. The graph plots for the given value 1.3 of þ and has trimmed down N from 70 to 8 as shown in fig.7. It is also seen that the adaptive nature of threshold with inaccurate channel conditions is performing better by reducing N from 15 to 8 than static nature with accurate channel environment. The table1 has shown the evaluation of parametric values obtained for two conventional and proposed. Table.1. Parametric Valuation at 0 dB SNR Static threshold ED with Full CSI
Static threshold ED with partial CSI
Proposed Adaptive Threshold with partial CSI
PD PFA PMD Perror N
0.84 0.12 0.15 0.52 15
0.68 0.39 0.31 0.54 70
0.94 0.009 0.05 0.03 8
N=30 19 18.5
Threshold, Th in dB
18 17.5 17 16.5 16 Conventional with Full CSI 15.5
Covnenional with partial CSI=1.4 Proposed with partial CSI=1.5 0
1
2
3
Figure 8 Threshold verses SNR
4
5 SNR in dB
In this paper, we have shown that keeping threshold fixed at low SNR can cause significant deterioration in the performance of conventional energy detection based on channel conditions with perfect and imperfect CSI. Our proposed scheme in which threshold is made adaptive based on the incomplete CSI estimation can enhance the performance of energy detector in the best possible way. The simultaneous analysis of all three has come up with the increase in detection probability and decrease in chances of miss-detection and false alarm for proposed scheme. The vigor of proposed work is also shown in varying erroneous circumstances with the minimum error probability over conventional schema. The requirement of number of samples is also notably less over accurate and inaccurate channel conditions with static threshold. The time variant communication scenario due to dynamic nature of wireless channel will be the possible future drive to extend the proposed technique. REFERENCES
Parameters
15
The comparison curves in figure 8 has demonstrated that Th has snootier value for the conventional with β = 1.4 as compared to same with ideal and proposed with partial. It is shown that even when channel conditions are made more worsen than conventional for our anticipated method, it is behaving nearly close to the conventional without exacerbate conditions. It is also seen that proposed Th can fluctuate its value to perform better than accurate channel knowledge based energy detector.
6
7
8
9
10
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