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Lecture 20 - ECE 614 Principles of Digital Communications...

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Unformatted text preview: ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2010 ng 2010 Lecture 20: April 6, 2010 Outline: Channel Coding Soft and Hard Detections 1 ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2010 ng 2010 Compare BW Requirements W 1 PAM M T W T rthogonal 1 etc. PSK, QAM, 2 T W 2 Orthogonal K T space. signal l dimensiona with , 1 rate symbol Assume K W T K W valued,- complex are symbols If 2 valued,- real are symbols If 2 T ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2010 ng 2010 Power vs Bandwidth for Orthogonal 3 ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2010 ng 2010 Shannon Limit when W= as dB 6 . 1 2 ln 1 2 N R v v N E b v b Can show (see section 7.1.3) that gap for M-ary orthogonal modulation goes to What happens to Gap as M ? zero as M On an AWGN channel with unconstrained BW, M-ary orthogonal modulation with M achieves Shannon limit of E b / N =-1.6 dB 4 ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2010 ng 2010 Exact P e for Orthogonal Modulation Orthogonal modulation ML detector is max-correlation detector (And i-th correlation is ) , ransmitt ecision rrect r j i r E y 1 1 1 2 1 1 ed, transmitt | and Pr ed, transmitt | decision correct Pr M M r r r r r r r r s s 2 1 N r Q ransmitt ror r ror r M 1 1 1 ed transmitt | correct Pr 1 ed transmitt | error Pr error Pr s s dr N r Q r f r 2 1 1 1 2 E r 5 1 where 1 N r e N r f ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins...
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