2. Generalized Likelihood Ratio Test A second communication system sends +V volts for a 1 bit and -V volts for a 0 bit.

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2 Generalized Likelihood Ratio Test A Second Communication System Sends V Volts For A 1 Bit And V Volts For A 0 Bit 1 (128.48 KiB) Viewed 27 times

2. Generalized Likelihood Ratio Test A second communication system sends +V volts for a 1 bit and -V volts for a 0 bit. The clock circuit associated with your receiver synchronizes to the bit stream by detecting the arrival of the bits. (It does not care whether it is a 0 or a 1.) You are to build a bit detector that will detect the arrival of a bit. Because the communication line has an unknown attenuation, you not know the mean of the incoming bits. You do know that the noise will have a mean of O and a variance of 1 and will be Gaussian distributed. Your hypothesis test will not be one-sided and will have the following form: Ho: u = 0 HT: A 0 a) Develop a Generalized Likelihood Ratio Test (GLRT) using N samples. (Assume each sample is Independent and Identically Distributed.) b) Establish the performance of the detector based on a Probability of False Alarm (aka size) a. Specify the answer in terms of a function called Q?chi2, which is the inverse of the right tailed integral for the Chi-squared random variable.