100318-lecture12 - 1 EE522 Communications Theory Spring...

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Unformatted text preview: 1 EE522 Communications Theory Spring 2010 Instructor: Hwang Soo Lee Lecture #12 - The¡Union¡Bound¡ 2 Announcements ¡ HW #4 is due Thursday 3/18. ¡ Handouts: ¢ Lecture Notes #12 ¢ HW #5 – Due Thursday 3/30 3 Modulation ¡ Modulation is used to transmit digital data over a channel. ¡ Gramm-Schmidt procedure allows vector representation of any signal constellation. ¡ Optimal receiver consists of a correlator, weighted to adjust for signal energy and a priori probabilities. ¡ Receiver implementation can be simplified with reduced correlations and matched filter. ¡ Receiver decision rule corresponds to decision regions in signal space. 4 Performance Evaluation ¡ Probability of error can be calculated by integrating probability density function of received signal vector over decision regions. ¡ This integration can become extremely complicated. ¡ Today we explore a simpler method for error probability calculations called the Union Bound. 5 The Union Bound ¡ In theory, we can compute any error probability by integration over the appropriate regions....
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100318-lecture12 - 1 EE522 Communications Theory Spring...

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