Lecture 7 - 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 7: February 9, 2010 Outline: Minimum-distance detection The matched filter The correlation receiver The projection receiver Complex signal space l j t i i Complex projection receiver 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 The Gram-Schmidt Orthonormalization Procedure , , , set waveform a Start with 2 1 t s t s t s M le whi to 1 For t e M m m end rest he renumber t and waveform this discard t e t e t m m m end where i m i i mi m m s ,s t s t s t s t e 1 1 2 m m i mi 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 Signal Vectors Consider an N-dim linear subspace S with ON basis Associate with each signal in S the N-dim vector of expansion coefficients t t t N , , , 2 1 N i i t s t s s s s 2 1 s i 1 N s 3 t s s t 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 How Does Inner Product Simplify? Consider two waveforms s j ( t ) and s k ( t ), both in the subspace S . How does the inner product < s j ( t ), s k ( t )> simplify? t s t s t s t s M jM j j j 2 2 1 1 t s t s t s t s M kM k k k j j j j 2 2 1 1 M kM k k M jM j j k j t s t s t s t s t s t s t s t s 2 2 1 1 2 2 1 1 , , n m n m n m kn jm M m m m km jm M m M n n m kn jm t t s s t t s s t t s s , , * 1 * 1 1 * , , , k k j j M m km jm s s s s s s 2 1 2 1 1 * , 4 kM jM s s 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 Generalized Parsevals Theorem k j k j dt...
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This note was uploaded on 03/14/2011 for the course STAT 614 taught by Professor Marymeyer during the Spring '10 term at Colorado State.

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Lecture 7 - ECE 614: Principles of Digital Communications,...

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