100311-lecture10 - 1 EE522 Communications Theory Mar 11,...

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Unformatted text preview: 1 EE522 Communications Theory Mar 11, Spring 2010 Instructor: Hwang Soo Lee Lecture #10 – Optimum Receiver Structures for Digital Modulation 2 Announcements ¡ Project Proposals ¢ Graded on a scale of 0 to 5 ¡ Midterm Exam Thursday 3/25, 10:30-13:30 ¢ Covers material through Thursday 3/18 ¢ Bring: calculator, one page of notes ¡ HW #3 Due Today ¡ HW #4 handed out ¢ Due Thursday, March 18 ¡ Handouts ¢ Course Notes #10 ¢ HW #4 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 correlation and matched filter. ¡ We now turn to calculating performance. 4 Problem Statement ¡ We transmit a signal , where is nonzero only on . ¡ Let the various signals be transmitted with probability: ¡ The received signal is corrupted by noise: ¡ Given , the receiver forms an estimate of the signal with the goal of minimizing symbol error probability . ) ( t s ) ( ) ( ) ( t n t s t r + = ) ( t s ) ( t r ) ( ˆ t s 5 Final Form of MAP Receiver ¡ Multiplying through by the constant : ¡ 6 Interpreting This Result ¡ weights the a priori probabilities...
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100311-lecture10 - 1 EE522 Communications Theory Mar 11,...

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