Temporal Spectrum Sensing in Packet-Based Network Using Double Thresholds

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.

Temporal Spectrum Sensing in Packet-Based Network Using Double Thresholds Yingxi Liu

Nikhil Kundargi

Ahmed Tewfik

School of Electrical Engineering University of Minnesota, Twin Cities Minneapolis, MN 55455 Email: [email protected]

School of Electrical Engineering University of Minnesota, Twin Cities Minneapolis, MN 55455 Email: [email protected]

School of Electrical Engineering University of Minnesota, Twin Cities Minneapolis, MN 55455 Email: [email protected]

Abstract—Traditional cognitive radio protocols rely on identifying intervals of time when a channel is available to secondary users. To date, the detection of such opportunities has relied on single threshold based binary hypothesis testing schemes. In this paper, we describe the shortcomings of traditional single threshold transmit opportunity methods. We then propose a hysteresis based detection scheme that uses two different thresholds for detecting that a channel that was unavailable has become available or that an available channel is no longer available. We provide numerical simulation and experimental results to show that the proposed double threshold approach reduces interference to the primary network and enhances the throughput of the secondary network. Index Terms—DSA, spectrum sensing, cognitive radio.

I. I NTRODUCTION Cognitive Radio Networks (CRNs) operate on the principle of Dynamic Spectrum Access (DSA) which involves detection and exploitation of underutilized segments of the radio spectrum without causing interference to the licensed spectrum user. The Cognitive Radio (CR) acts as a Secondary User (SU) that coexists with the licensed Primary User (PU). The field of cognitive radios has developed at a rapid pace in the last decade [1] [2] [3]. Spectrum sensing is the key function in CR. Lots of techniques are applied to spectrum sensing, such as Energy Detection, Cyclostationary Detection, Pilot-Based Coherent Detection, Covariance-Based Detection, etc [4]. Energy detection received a lot of attention in the literature and we will focus on energy detection in this work. As the rapid growth of data services in 3G [5] and WiFi [6] networks, CR faces new challenges in temporal spectrum hole detection in packet-based networks (PBN). Traditionally, energy detection is treated as a binary hypothesis testing problem. The test design problem is usually approached by considering optimization of secondary user throughput with constraints on interference incurred by PU from SU [7]. While this type of approaches optimize the instantaneous benefit of CR, it is not suitable for online spectrum hole detection in PBNs, especially when PU’s signal power are close to SU detector’s noise power. The reason is that in a PBN, once the channel is occupied by PU (“ON” state, “OFF” denoting channel being vacant), it will be “ON” for quite a long time (comparing to CR’s sensing interval). If PU’s signal power and CR’s noise

power are close, it is very likely for CR to observe multiple “OFF” to “ON” (OFF→ ON) and “ON” to “OFF” (ON→ OFF) changes during a single PU’s packet transmission, or during an actual spectrum hole. This approach will either cause large interferences to PU or lose secondary transmission opportunities. And if a PU signal suffers from deep fading, the performance of this method will be even worse. An alternative approach introduced in [8] successfully circumvents this problem by allowing secondary user to transmit constantly with small power, which is controlled by detection of changes in primary network’s packet statistics. However, with small transmission power, this approach can only provide a very limited coverage and data rate. We propose in this paper a double threshold to enhance the operation of cognitive radio networks. Namely, different thresholds are used for detection of OFF→ ON and ON→ OFF changes. When the channel is actually “ON”, CR wants to observe more of the “ON” state in order to protect PUs. Therefore a low threshold is preferable. When the channel is actually “OFF”, CR wants to observe more of the “OFF” state to better use the channel vacant time. Moreover, in a practical primary network, as we explain below, our experimental results show that multiple signal power levels appear on the channel, which makes the detection in this direction easier than in ON→ OFF. Therefore here a high threshold is preferable. Additionally, with certain detection requirements, such as probability of detection in OFF→ ON direction and probability of false alarm in ON→ OFF direction, a proper range of those two thresholds are derived in this paper. And also within the range, it is illustrated that the CR transmission will cause less interference and less transmission opportunity loss. The remainder of this paper is organized as follows. Section II introduces the system model used. Section III explains the double-threshold spectrum sensing scheme. The experimental implementation and numerical results are then covered in Section IV. Finally, Section V concludes the paper. II. S AMPLING - BASED E NERGY D ETECTION A. Sampling of Primary Networks Consider a CR that is surrounded by a number of primaryusers and is trying to detect the temporal spectrum holes.

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Fig. 2: Single Threshold Spectrum Sensing

Fig. 1: Network Environment for Spectrum Sensing

The APs are located at varying as shown in Fig. 1. Such deployments can typically arise in IEEE 802.11 network environments. The signal observed by CR can be a signal from one PU or a superimposed version of signals from different PUs, in the case when a collision occurs. Let the sampled received signal be y(i), where i is the discrete time index. Usually when a CR is sampling at a high rate, the received samples behave irregularly due to sampling imperfections. The energy detection based on one sample is highly unreliable and to mitigate this effect a preprocessing of averaging is performed, N 1  |y((n − 1)N + i)|2 , r(n) = N i=1

B. Single Threshold Spectrum Sensing As illustrated before, single threshold spectrum sensing performs a simple binary hypothesis test to detect the status of the channel: (2) (3)

The test is performed by: H1 r(n) ≷ η s , H0

r(n) ∼ N (m, σ 2 ),

r(n) ∼ N (M1 , σ12 ).

(6)

With single threshold spectrum sensing, the detection of channel status is just a binary hypothesis test based on (5) and (6). The test is of the form in (4). For detection of the direction OFF→ ON, the designed probability of detection and false alarm for a particular threshold η s are: = Q( pdesired d

η s − M1 ), σ1

(7)

ηs − m ), σ

(8)

and pdesired = Q( f

where Q( ) is the Marcum-Q function. However, as mentioned earlier, there also exist other signal power levels from different PUs. Fig. 3 is a real-life signal power metric obtained from samples in a 802.11 environment similar to that described in Fig. 1. As we can see, there are roughly 3 to 4 signal power levels during the observation period. Let us consider the case where in the network there are 3 signal power levels, and they follow Gaussian distribution N (M1 , σ12 ), N (M2 , σ22 ) and N (M3 , σ32 ) with M1 ≤ M2 ≤ M3 ; the noise power level follows the distribution N (m, σ 2 ), m ≤ M1 . The probability of appearance of these three levels given channel is “ON” are p1 , p2 , p3 , and p1 + p2 + p3 = 1. Then the actual probability

(4)

where η s is the threshold for single-threshold spectrum sensing. Fig. 2 is an example of the single threshold spectrum sensing performance in the case of a typical 802.11 channel capture. The dashed line in the figure is the threshold. If the average signal energy is above the threshold, it detects

(5)

and the metric of the smallest signal power level:

(1)

where N is the length of averaging window. Note that N is often set to an optimal value to ensure that no primary packet is averaged out with noise, while still being long enough for r(n) to be approximated as Gaussian distributed random variable as per Central Limit Theorem.

H1 : Channel occupied by one of the PUs H0 : Channel not occupied by any PU

a primary signal; otherwise it classifies the channel as vacant. It is seen that if the noise power and signal power are far apart, they can be easily separated by the single threshold. However, when the signal power is comparable to noise power, like in the circled part, it is difficult for CR to correctly detect the channel status for the whole packet duration. Here in this work we do not adopt (1) to find the distribution of noise power and signal power, but instead, without loss of generality we assume that the metric of noise follows:

Fig. 3: Sampling metric of a practical 802.11 network

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TABLE I: Notation pmin01 d pmax10 f D η01 D η10 ηs D01 Tw S01 Tw TiD10 TiS10

Minimum required probability of detection in OFF→ ON Maximum allowable probability of FA in ON→ OFF Threshold in OFF→ ON detection Threshold in ON→ OFF detection Threshold in ST spectrum sensing Transmission opportunity loss in OFF→ ON using DT Transmission opportunity loss in OFF→ ON using ST Interfering time in ON→ OFF using DT Interfering time in ON→ OFF using ST

of detection of the test is:

Fig. 4: Transmission time loss and interfering time

η − M1 )+ σ1 η s − M2 η s − M3 p2 Q( ) + p3 Q( ), σ2 σ3

=p1 Q( pactual d

s

(9)

and pactual = pf . With M1 , M2 and M3 far apart, it is f reasonable to claim that pactual ≥ pdesired . d d III. D OUBLE THRESHOLD SPECTRUM SENSING Since from (9) we have pactual ≥ pd , therefore there d is a little margin in probability of detection that we can increase η s so that pf is decreased. The reason to decrease pf in the OFF→ ON direction is that secondary user will be more likely to observe channel vacant time for transmission, hence increasing secondary system throughput. However, if η s is increased, for the detection in the ON→ OFF direction, probability of false alarm is increased, and this translates into increased interference to the PU when the secondary user transmits. Also whenever the primary user signals suffer from deep fading, it is even more likely that false decisions are made. Since it is difficult to satisfy constraints in both directions, we introduce the use of an additional threshold to detect when the channel changes from “ON” to “OFF”. Since the detection in ON→ OFF and OFF→ ON directions is independent, the two thresholds can be determined separately. D D be threshold for the OFF→ ON direction and η10 Let η01 for the ON→ OFF direction. The secondary user tracks the channel status as follows. When the channel is “OFF”, it waits D and then changes the channel for the metric to exceed η01 status to “ON”; when it is “ON”, it waits for the metric to D and then changes the channel status to “OFF”. drop below η10 In the rest of this section, we are going to illustrate how to D D and η10 from minimum required pmin01 in OFF→ obtain η01 d max10 in ON→ OFF direction, and propose ON direction and pf the conditions under which the transmission opportunity loss and interfering time can be reduced. The notations used are summarized in Table I. A. OFF → ON Detection In this section we will assume the same setup as in Section II. In the direction of OFF→ ON, we have shown in the previD can be increased to make the probability ous section that η01 of false alarm smaller. If the minimum desired probability of

D detection pmin01 is given, η01 can be numerically found by d solving: D η01 η D − M2 − M1 ) + p2 Q( 01 )+ σ1 σ2 η D − M3 p3 Q( 01 ). σ3

=p1 Q( pmin01 d

(10)

When the channel is vacant, but the secondary user observes D , it will claim that that the sensing metric is larger than η01 the channel is occupied and stop its transmission. Decreasing D decreases the transmission opportunity loss TwD01 . Once η01 D , the channel is labeled by the metric goes higher than η01 secondary user to be occupied until the metric goes below D . This is illustrated in Fig. 4. If we further assume that η10 samples are independent from each other, the length of wasted opportunity follows the following distribution: P r{TwD01 = k} = D ηD − m η D − m k−2 η10 −m )Q )(1 − Q( 10 )). (11) Q( 01 ( σ σ σ The long-term expected value of transmission opportunity loss when channel is vacant is: E{TwD01 }

=

D η01 −m ) σ . D −m η10 η D −m Q( σ ))Q( 10σ )

Q(

(1 −

(12)

The expected value of transmission opportunity loss in single threshold spectrum sensing TwS01 is: E{TwS01 } =

1 . s 1 − Q( η −m σ )

(13)

D D Generally, we are interested in the case where η10 ≤ η s ≤ η01 . D D D η01 is obtained through (10). For a given η10 , η01 has to satisfy: D D D ≥ max{η10 , 2m − η10 } η01

(14)

to ensure E{TwS01 } ≥ E{TwD01 }. Proof of (14) is omitted due to limited space. B. ON → OFF Detection In the ON→ OFF direction, the primary goal is to reduce the probability of false alarm, i.e., reduce the chance to interfere with the primary users. Unlike in OFF→ ON direction,

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here we constrain the desired probability of false alarm to , which should be less than the probability of false be pmax10 f alarm given by using η s : η s − M1 η s − M2 )) + p2 (1 − Q( ))+ σ1 σ2 s η − M3 p3 (1 − Q( )). (15) σ3

≤p1 (1 − Q( pmax10 f

D Again, η10 has to be numerically solved by: D η10 η D − M2 − M1 )) + p2 (1 − Q( 10 ))+ σ1 σ2 η D − M3 p3 (1 − Q( 10 )). (16) σ3 Fig. 4 also shows the time of interference: when the channel D , is “ON”, and the signal metric suddenly drops off below η10 the CR will mistake it as being switched to “OFF” until it D . For simplicity, we assume that it only goes back to above η01 happens when the channel is at the lowest signal power level. Then the length of interference TiD10 follows the distribution:

=p1 (1 − Q( pmax10 f

D D Fig. 5: Allowable region for η01 and η10

P r{TiD10 = k} = (1 − Q(

D D η10 η D − M1 k−2 η01 − M1 − M1 ))(1 − Q( 01 )) Q( ), σ1 σ1 σ1 (17)

TABLE II: Example parameters m 1

σ 2

p1 0.4

M1 3

σ1 2

p2 0.3

M2 6

σ2 2.5

p3 0.3

M3 10

σ3 6

and the expected time of interference is: E{TiD10 }

=

D η10 −M1 )) σ1 . D D −M η01 −M1 η01 Q( σ1 ))Q( σ1 1 )

p1 (1 − Q( (1 −

(18)

The expected time of interference when channel is “ON” with η s is: p1 . (19) E{TiS10 } = η s −M1 Q( σ1 ) It is found that E{TiS10 } ≥ E{TiD10 } requires: D D D η10 ≤ min{η01 , 2M1 − η01 }.

(20)

Proof is omitted. Also notice that (20) is not exact because it is assumed that false alarm happens only when the PU signal is at the lowest level. The red region in Fig. 5 shows the D D and η10 determined by (14), (20) and allowable region for η01 D D η01 > η10 . C. Summary Thus for a desired CR with pmin01 and pmax10 , we can d f D D proceed by first calculating η01 and η10 from (10) and (16). D and Then check if (20) and (14) holds for the computed η01 D η10 . IV. N UMERICAL R ESULTS A. Theoretical Simulation Results Table II shows the parameters are used in the simulation: The numerical result of (10) are in Fig. 6 The numerical result of (16) is plotted in Fig. 7 As we can see from Fig. 6 and Fig. = 0.8, we can have pmax10 roughly from 7, if required pmin01 d f 0 to 0.2 such that inequalities (14) and (20) are satisfied.

D Fig. 6: Numerical calculation result of η01 given pmin01 d

Let pf = 0.13, pd = 0.67, Fig. 8 shows the expected D D ≤ η s ≤ η01 . It’s wasted time and interfering time with η10 obvious from the simulated results that using double threshold does reduce the transmission opportunity loss and interferis required for both double-threshold ing time. If pmax10 f sensing and single-threshold sensing, we can compute the D from (14) and (20) and Fig. 5 for the maximum allowable η01 double-threshold sensing. The transmission opportunity loss for double-threshold and single-threshold is shown in Fig. 9. is required for both doubleOn the other hand, if pmin01 d threshold sensing and single-threshold sensing, we can also

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D Fig. 7: Numerical Calculation Result of η10 given pmax10 f

Fig. 9: Transmission opportunity loss for DT and ST vs pmax10 f

Fig. 8: Expected transmission opportunity loss and expected = 0.13, pmin01 = 0.67 interfering time given pmax10 f d

Fig. 10: Interfering time for DT and ST vs pmin01 d

D compute η10 . The interfering time for double-threshold and single-threshold is shown in Fig. 10

B. Double Threshold Spectrum Sensing on Experimental Data The spectrum sensing is performed using a USRP working on the 802.11b channel 11 (2.462GHz). The USRP is located in a common study area with several other laptops surrounded. The sampling rate of the USRP is 1 M samples/s, the averaging window size is N = 30. The Gaussian Mixture Model (GMM) is used to estimate the signal power levels. Fig. 11 is the piece of spectrum sensing metric from captured samples. Those high peaks are signals either from 802.11 beacon signals or other type signals from Access Points (AP). Fig. 12 is the GMM estimate result for a one-second long channel observation. Originally there are four levels. But one of them has really large mean value compared to the others, therefore it is discarded since its probability density function

Fig. 11: Experimental spectrum sensing metric from captured samples

(PDF) will not overlap with others, and it has only a few samples, which means that it does not take a substantial portion of the time when channel is “ON”. Also the noise

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D Fig. 14: Sensing metric together with the thresholds η10 = 0.9, D = 2.5 and η s = 1.8 η01

Fig. 12: GMM estimation result with the first two signal power levels

but double-threshold successfully avoids them; however, there is this yellow-circled region where double-threshold failed to recognize it as a primary signal but single-threshold finds it out.

PDF is omitted here. The estimation results of the first two signal levels and the noise power level are M1 = 2.6536, σ1 = 1.0199, M2 = 9.1398, σ2 = 5.2342, m = 0.9393, σ = 0.0389. And a rough calculation gives p1 = 0.56, = 0.04, pmin01 = 0.66 we p2 = 0.44. With pmax10 f d D D calculate that η10 = 0.9, η01 = 2.5. The expected transmission opportunity loss and expected interfering time is shown in Fig. 13. With this threshold setting, the expected transmission time loss is essentially 0, comparing to 1 with large single threshold (it goes to infinite when η s is small); the expected interfering time is 0.2 comparing with 1 ∼ 1.7 with single threshold. Fig. 14 shows a 0.1 second long piece of the D D = 0.9, η01 = 2.5 metric together with the thresholds η10 and η s = 1.8. The black-circled regions are the places where single-threshold mistakes them as changes of channel state,

V. C ONCLUSION Spectrum sensing in cognitive radio is a tough task, especially when the medium is observed from the physical layer. In this work, we recognize that the spectrum sensing when channel is “ON” and “OFF” are actually different by observing a practical 802.11b wireless network. By performing spectrum sensing with different thresholds in OFF→ ON and ON→ OFF directions, it is illustrated that CRs are able to reduce the time of interfering with primary users and the time lost when there is a transmission opportunity. With desired minimum probability of detection in OFF→ ON direction and maximum tolerable probability of false alarm in ON→ OFF direction, D D and η10 is given, and also a numerical way of computing η01 the conditions of them to reduce transmission time loss and interfering time are given. Theoretical and practical results supports that the double-threshold sensing scheme outperforms single-threshold. R EFERENCES

Fig. 13: Expected wasted transmission time and expected interfering time with practical data

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