Cognitive Radio Techniques for GSM BandBaiju Alexander, R. David Koilpillai

Department of Electrical EngineeringIndian Institute of Technology Madras

Email: {baiju,davidk}@iitm.ac.in

Abstract—Cognitive Radio has generated a lot of interest asa novel approach for improving the utilization of spectrumresource in recent years. Cognitive radios have to reliably sensethe RF environment to co-exist with legacy wireless networks.The critical design problem is to reliably detect the presenceof primary users. In this paper we compare the performanceof different schemes for signal presence detection as applied tothe GSM band. We also propose a hybrid scheme to detect thepresence of GSM signals.

I. INTRODUCTION

Wireless systems today are characterized by static spectrumallocations which are under-utilized [1][2]. GSM systems use890 - 915 MHz [3] band for uplink and 935 - 960 MHz [3]band for downlink. However, in many places some of thesefrequencies may not be used or some of the signal frequenciesmay not be present in a particular area due to RF propagationeffects. It can also happen that there is no signal present dueto lack of GSM deployment, like in remote villages. Theseunused frequencies can then be used by cognitive radios [4] fortheir operations. Cognitive radio can be used only if permittedby the regulatory authority. A possible scenario is that thespectrum owner may deploy equipment which use cognitiveradio techniques to do self configuration and autonomousfrequency planning. Cognitive radios are considered lowerpriority or secondary users of spectrum allocated to a primaryuser. Their fundamental requirement is to avoid interferenceto the primary users in their vicinity. Spectrum sensing hasbeen identified as a key enabling functionality to ensure thatcognitive radios do not interfere with primary users, by reliablydetecting primary users signal.

The first application of spectrum sensing is studied underIEEE 802.22 standard group [5] in order to enable secondaryuse of UHF spectrum for fixed wireless access. In addition,there are a number of indoor and rural applications wherespectrum sensing would increase spectrum efficiency andutilization. Spectrum sensing is often considered as a detectionproblem [6], the key challenge of spectrum sensing is thedetection of weak signals in noise with a very small probabilityof missed detection, which requires better understanding ofvery low SNR regimes [7].

Our goal is to study different detection schemes applicablefor GSM band and to compare these methods based on proba-bility of missed-detection. Some of the detection schemes usedin cognitive radios are matched filter detectors [7], energydetectors [8] and cyclostationary feature detectors [10][11].The following are the topics discussed in this paper.

• Study of energy detection method for GSM signals.• Limitations of the energy detector performance due to

presence of noise level uncertainty and fading.• Study of cross-correlation-based detector.• A hybrid detection scheme for GSM signals.

The paper is organized as follows: Section II reviews the en-ergy detector model, and derives its performance and addressesthe limitations. In Section III, we study the performance ofcross-correlation-based detector. In Section IV, we discuss ahybrid detection scheme for primary signal in GSM band. Thesummary and conclusions are presented in Section V.

II. ENERGY DETECTOR CHARACTERIZATION

We consider the detection of a weak GSM signal in additivenoise, and the effect of multipath fading. The signal power isconfined within an apriori known bandwidth B (200 kHz forGSM) [3], around the carrier frequency fc. We assume thatactivity outside of this band is unknown. A sub-optimal energydetector is adopted, which can be applied to any signal type.An energy detector consists of a low pass filter to reject outof band noise and adjacent signals, A/D converter, square-law device and integrator. Without loss of generality, we canconsider a complex baseband equivalent of the energy detector.The spectrum sensing mechanism is attempting to classify thegiven GSM channel as either “occupied” by a GSM signal oras “vacant”. This is a binary hypothesis testing problem, thetwo hypotheses are summarized below.

H0 : y[n] = w[n] ⇒ signal absent

H1 : y[n] = x[n] + w[n] ⇒ signal present

where n = 0, 1, · · · , N − 1 (N - observation interval).

x[n] = received signal samples

w[n] = noise samples

y[n] = received Samples

The noise is assumed to be additive, white and Gaussian(AWGN) with zero mean and variance σ2

w. The signal samplescan also be modeled as Gaussian random process with varianceσ2

x.A decision statistic for energy detector is:

∆ =1N

N−1∑n=0

y(n)y∗(n)

A. Performance

Performance of energy detector is measured by a resultingpair of probability of detection (Pd) and probability of falsealarm (Pfa). Each pair is associated with the particular thresh-old (γ) that tests the decision statistic:

∆ ≥ γ ⇒ decide signal present

∆ < γ ⇒ decide signal absent

When the signal is absent, the decision statistic has a centralchi-square distribution with N degrees of freedom [8]. Whenthe signal is present, the decision statistic has a non-centralchi-square distribution with the same number of degrees offreedom [8]. If N is large we can use the central limit theoremto approximate the test statistic as Normal(m,σ2) that isGaussian with mean m and variance σ2.

∆ ∼ Normal

(σ2

w,(σ2

w)2

N

)under H0

∆ ∼ Normal

(σ2

x + σ2w,

(σ2x + σ2

w)2

N

)under H1

where

N = Number of samples

Then probability of missed detection (Pmd) can be evaluatedas [9]:

Pmd = Q

( √N

σ2x + σ2

w

[(σ2x + σ2

w)− γ]

)(1)

where threshold γ is:

γ = σ2w

(1 +

Q−1(Pfa)√N

)(2)

where the function Q(.) is defined as:

Q(α) =1√2π

∫ ∞

α

e−x2

2 dx (3)

The performance of the energy detector was evaluated usingMonte Carlo simulations. The number of samples used wereN = 568, probability of false alarm was fixed at 10 %,noise power in 200 kHz bandwidth was assumed to be−116 dBm. Detection threshold was calculated using eqn.(2)and simulation was run for different received signal power. Fig.1 shows theoretical curve for probability of missed detectionat different SNR. Theoretical curve was plotted using eqn.(1).Fig. 1 also shows the simulated performance of energy detectorat different SNR. Fig. 2 shows the simulated probability offalse alarm for the energy detector. Fig. 1 also validatesthe Gaussian approximation used to derive theoretical perfor-mance of energy detector as the theoretical missed detectioncurve closely matches with the simulated one for low SNRs.

Fig. 1. Theoretical and simulated performance of energy detector in AWGN,number of samples N = 568

Fig. 2. Probability of false alarm in percentage for energy detector

B. Limitations

In simulating the above results we assumed that the additivenoise is white, and Gaussian, with zero mean and withknown variance. However, the noise term is an aggregationof various sources including, not only thermal noise at thereceiver and underlying circuits, but also interference due tonearby unintended emissions, weak signals from far awaytransmitters etc. Second, we assumed that noise variance isprecisely known to the receiver, so that the threshold can be setaccordingly. However, this is not possible as noise could varyover time due to temperature change, ambient interference,filtering, etc. Even if the receiver estimates it, there is aresulting estimation error due to limited amount of time. Dueto this noise uncertainty, there is a minimum SNR below whichsignal cannot be detected, this minimum SNR level is referredto SNRwall [12]. Performance of energy detector with noiseuncertainity in AWGN channel was simulated for N = 142samples, Fig. 3 shows the simulated missed detection curve of

Fig. 3. Performance of energy detector with noise uncertainity, number ofsamples N = 142

energy detector with noise uncertainity of 1 dB in comparisonwith simulated missed detection curve of energy detector withnoise uncertainity of 0 dB. We can see from Fig. 3 that noiseuncertainity limits the performance of energy detector anddetection of primary signal is not possible below −2 dB SNR.

Up to this point, we have considered spectrum sensingperformed in AWGN-like channels. In fading channels, how-ever, sensing requirements are set by the worst case channelconditions introduced by multipath, shadowing and local inter-ference. These conditions could easily result in SNR regimesbelow the SNRwall, where the detection will not be possible.Fig. 9 shows the probability of missed detection at differentSNRs for energy detector with noise uncertainity of 1 dBin multipath fading environment. For the simulation the hillyterrain model [13] was used and speed was assumed to be lessthan 2 Kmph, the number of samples used for simulation wasN = 64. We consider the hilly terrain model because it has thelongest delay spread when compared to other GSM multipathchannel models. We can see from Fig. 9 that even at high SNRsin range of 8 to 10 dB, the probability of missed detectionis more than 10−2. Performance limitations of simple energydetector necessitate enhanced detection schemes, which arediscussed in the next sections.

III. CROSS CORRELATION BASED DETECTORS

Every GSM timeslot has a training sequence embedded init [14]. These training sequence are known sequence usedfor channel estimation. By cross-correlating received sampleswith training sequence we can detect the presence of train-ing sequence even in very low SNR. Cross-correlation-baseddetector is a coherent detector, coherent detectors have beenstudied earlier for cognitive radio [15]. Cross-correlation oftwo wide sense stationary sequence s1,s2 is given by

R(m) = E [s1(n)s∗2(n−m)]

Where, E[ ] is expectation and m denotes the number ofsamples by which s2(n) is delayed.

Fig. 4. Comparison of synchronization burst and normal burst trainingsequence based cross-correlation detectors in AWGN

In practice, an estimator of the cross-correlation that is usedis

R(m) =1N

N−1∑n=0

s1(n)s∗2(n−m) 0 ≤ m ≤ M

where, M is the maximum lag for the cross-correlation.Different types of GSM bursts (normal burst and synchro-

nization bursts) have different length of training sequence[14]. The normal burst has 26-bit training sequence andsynchronization burst has 64-bit training sequence [16]. Toevaluate the performance of cross-correlation-based detector,computer simulations were carried out. Detection threshold(γ) was fixed such that probability of false alarm (Pfa) was10 %. Fig. 5 shows the simulated probability of false alarmfor the cross-correlation-based detector. The detector perfor-mance was evaluated at different SNRs for AWGN and fadingchannels. Fig. 4 compares the probability of missed detectionat different SNRs for cross-correlation-based detector whichuses two different training sequences (of length 26, and 64bits); normal burst training sequence and synchronization bursttraining sequence. It is observed from Fig. 4 that longer thetraining sequence more reliably we can detect the signal in lowSNR. For all subsequent simulations the synchronization bursttraining sequence based cross-correlation detector is used.When compared with energy detector, the cross-correlation-based detector detects the primary signal more reliably inAWGN channel as shown in Fig. 6. The cross-correlation-based detector also perform better than energy detector inmultipath fading environment, Fig. 9 shows the probabilityof missed detection for the cross-correlation-based detectorat different SNRs with multipath fading. For simulating theprobability of missed detection curves for energy detector inFig. 6 and 9, we used N = 64.

IV. HYBRID DETECTION SCHEME

From the previous section we see that cross-correlation-based detector performs better than the energy detector; it can

Fig. 5. Probability of false alarm in percentage for cross-correlation-baseddetector

Fig. 6. Comparison of energy detector and cross-correlation-based detectorusing synchronization burst training sequence, number of samples N = 64

detect weak signals more reliably and is not affected by noiseuncertainty. The main disadvantage of cross-correlation-baseddetector is that it has to scan for longer time to detect thepresence of primary signal. The duration of scanning dependson the training sequence used and type of burst used. Differenttype of bursts have different repeat rate, Normal burst occurs atleast once in 8 timeslots of broadcast carrier and synchroniza-tion burst occurs once in 80 timeslots. In GSM each timeslot(also called burst) has duration of 577 µsec. Cross-correlation-based detection scheme gets further complicated because thedetector is not time synchronized with primary user signal, andhence, the exact location of training sequence is not known tothe detector.

To take advantage of both the detection schemes we proposea hybrid scheme, which uses the energy detector for initialdetection, and uses cross-correlation method for confirmation.The key steps are enumerated below.

1) Energy detector is used in first stage of hybrid detector.

Fig. 7. Block diagram of the hybrid detector

Fig. 8. Probability of false alarm in percentage for hybrid detector

2) The probability of false alarm energy detector is fixedat 10 %.

3) The cross-correlation method is used in the second stage.4) The probability of false alarm cross-correlation detector

is fixed at 10 %.5) Threshold for each detector is fixed based on probability

of false alarm .Block diagram of the hybrid detector is shown in Fig. 7. All thereceived samples first pass through the energy detector, if theenergy detector fails to detect primary signal then the receivedsamples are analyzed using cross-correlation detector. Hybriddetector can make faster decision than cross-correlation-baseddetector because it uses cross-correlation based detector onlywhen energy detector fails to detect the primary signal. Fig. 9shows performance of the hybrid detector in multipath fadingchannel. The overall probabilty of false alarm for hybriddetector was found to be 20 % and the probability of misseddetection of hybrid detector for different SNRs is similarto cross-correlation based detector. For cognitive radios themissed detection probability is more crucial than false alarmprobability so higher false alarm probabilty of the hybriddetector does not degrade the performance. Fig. 8 shows thesimulated probability of false alarm for the hybrid detector.

V. CONCLUSION

In this paper we investigated the performance of the energydetector and the cross-correlation based detector to detect the

Fig. 9. Comparison of energy detector with 1 dB noise uncertainity, cross-correlation based detector and hybrid detector in fading channel, number ofsamples N = 64, Hilly terrain multipath fading model used

presence of the primary user’s signals. We also proposed ahybrid detector and evaluated its performance. We simulatedthe achievable probability of missed detections and probabilityof false alarm, and the minimum detectable signal levels inAWGN and fading channels for different detectors. For energydetector, it was found that the presence of RF propagationchannel uncertainties sets practical limits on minimum de-tectable signal levels, which cannot be further improved bysignal processing. For correlation-based detector we foundthat it can reliably detect low SNR signals but require longersensing time. It is demonstrated that the hybrid detectorrequires lesser sensing time and can also reliably detect lowSNR signals.

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