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Channels and Models
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accept H0 assume average risk average-sample-number function Bayes estimator binary channel gain channel model Chap communication systems compute consider correlator covariance covariance matrix cross-correlation data samples decision boundary decision interval decision rule decision-directed measurement defined density detection Discrete sampler encoder envelope detector error probabilities error rate example filter output frequency gaussian noise Hence Hilbert transform IRE Trans learning observations likelihood ratio likelihood-ratio tests linear log p(X|S matrix maximum-likelihood estimator measurement strategy multipath noise samples non-decision-directed measurement normal distribution Note number of samples obtain operating-characteristic function optimum receiver orthogonal priori information prob probability of error probability ratio test problem ratio test Rayleigh distributed received data received signal receiver structure sample function sequence sequential probability ratio shown in Fig signal si(t signal waveform signal-to-noise ratio signaling interval statistically independent tap gains theory threshold tion transmitted signals unconditional estimator unknown parameter variance vector waveform zero mean