Topic: SciencesStatistics

Last updated: August 19, 2019

1) BINARY HYPOTHESIS TESTING 22) COMPOSITE HYPOTHESIS TESTING 23) SEQUENTIAL TESTING 34) REFERENCE BETWEEN THEM 35) DIFFERENCE BETWEEN COHERENT AND NON-COHERENT SENSING TECHNIQUE 41) BINARY HYPOTHESIS TESTINGIn spectrum sensing, hypothesis testing is widely used to test the sensing result for the presence of PUs to efficiently utilize the spectrum.

We first explain binary hypothesis. In Binary hypothesis testing it sense either 0 or 1, 0 represents PU is not available and 1 represent PU available. It is widely used when parameters are known so, it requires also prior knowledge of known parameters. Based on fixed number of samples which means it has fixed sensing time. Binary hypothesis are further divided into two types.? Neyman-Pearson testIn Neyman Pearson (NP) test, objective is to maximize the detection probability (Pd) than false alarm probability (Pf) which means Pd is always greater than Pf. LRT (likelihood Ratio test) is equivalent to NP test which shown below; f (y|H1)NP= __________ f (y|H0)If NP > ? it represents H1 (PU available), otherwise H0 (PU isn’t available).? Bayes testIn Bayes test, objective is to minimize the expected cost called Bayes Risk.

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Used to reduce the sum of all probabilities cost from probabilities of two incorrect decision cases.Miss detection represented by P (H0 | H1)False alarm represented by P (H1 | H0)Probability detection represented by P (H1 | H1) So, the Fusion Center minimize the Bayes risk by declaring H1 and H0 conditions.2) COMPOSITE HYPOTHESIS TESTING As we mentioned above, Binary hypothesis testing is used when both hypotheses are known. In Composite hypothesis testing, it is widely used when there are unknown parameters in PDF’s. It doesn’t require prior knowledge of unknown parameters which is also called GLRT. The method which is commonly used to find the unknown parameters is by MLE (Maximum likelihood ratio). GLRT methodology is used because of its robustness and it is easy to implement. ? Another test, which is Rao test is typically used to detect the weak PUs at Fusion center.

By the help of data fusion type (i.e. soft decision). Rao test is generally same like GLRT but doesn’t require MLE for unknown parameters. ? Another test, is linear test comes under Composite hypothesis testing is Linear test statistics, which is used to finding the unknown PUs as well as unknown channels . ? Third one is Statistic LMP detector is derived, when channel statistics are known. This model provides robustness to the interferences in Primary User signal also in channel gain. Also it is much reliable than NP- based LRT.

3) SEQUENTIAL TESTINGAs previous hypotheses based on fixed number of samples and fixed sensing time, it is much different than both. Sequential testing is typically used to utilize spectrum by reducing sensing time, and requires variable number of samples. Sequential Probability Ratio Test (SPRT) is proposed by Wald, which minimizes the sensing time as per detection performance.In SPRT, samples are taken in sequence and then compared with both thresholds ?0 and ?1. ?0 ?1, FC decides H1If likelihood ratio < ?0, FC decides H0When ratio falls between two thresholds, it takes again observations until and unless it achieve final decision.

The pros of SPRT is it requires fewer samples, less energy consumption, to achieve same detection performance.4) REFERENCE BETWEEN THEMBINARY HYPOTHESIS TESTING? Based on known parameters? Fixed samples? Fixed sensing time? Sense Either 1 or 0? Requires prior knowledge? Easy to implement? Less expensiveCOMPOSITE HYPOTHESIS TESTING? Based on unknown parameters? Determine unknown parameter by MLE? Fixed samples? Fixed sensing time? Doesn’t require prior knowledge ? Robust , easy to designSEQUENTIAL TESTING ? Reduce sensing time? Less energy consumption? Much complex? Expensive? Have two thresholds? Better performance 5) DIFFERENCE BETWEEN COHERENT AND NON-COHERENT SENSING TECHNIQUECOHERENT SENSING TECHNIQUE? In coherent sensing technique, it need prior knowledge of primary user signal to determine whether the signal channel is occupied or not. ? Need reference signal ? Types of coherent sensing technique• Cyclostationary feature detection• Matched filter detectionNON-COHERENT SENSING TECHNIQUE? In non- coherent sensing technique, it doesn’t need any prior knowledge of primary user signal to determine whether the signal channel is occupied or not. ? No need of reference signal ? Types of coherent sensing technique• Energy detection• Wavelet detection• Compressed sensing

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