Probability and Random ProcessesAnderson Darling Test

Institute of Engineering and Technology

Anonymous

Group members:Harshil Prajapati 131013Kavi Pandya 131020

Maninder Sambhi 131024Saumil Shah 131044

Shailee Sutariya 131047Urvika Sonar 131060

May 9, 2015

Institute of Engineering and Technology (IET) AD Test May 9, 2015 1 / 5

Outline

1 Description and System Model

2 Algorithm

3 Result

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Description and System Model

Description and System Model

For spectrum sensing, it is always preferable to use non-parameterisedsensing method than parameterised sensing method for general purposescenario. We may not know about the parameters for every signal. At lowSNR, for unknown parameters the performance of the tests based onparameterised sensing methods is degraded. So non-parameterised basedtests like AD test are preferred over parameterised tests like ED test.

AWGN System Model

y =√qxh + n

y : Recieved Signal√q : Square root of SNR

x ⇒ 1 : Transmitted Signalh ⇒ 1 : AWGN modeln : Noise (Randomly Generated)

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Algorithm

Algorithm

Step 1: Determine the critical point t0 according to a given false alarmprobability α

Step 2: Sort the observations in increasing order. Suppose the sortedobservations are Y1 ≤ Y2 ≤ . . . ≤ Y2.

Step 3: Calculate the value A2c according to the formula

A2c = -

∑ni=1(2i − 1)(ln(Zi ) + ln(1− Zn+1−i )

n- n

Step 4: Reject the null hypothesis H0 in favor of the presence of signaltransmission if A2

c > t0; otherwise, declare that the channel is not in use.

Reference: Spectrum Sensing in Cognitive Radio Using Goodness of Fit Testing, Haiquan Wang

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Result

Result

Figure : ROC Curve

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