Lecture 18 - 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 2008 ng 2008 Lecture 18: April 1, 2008 Outline: Power-vs-Bandwidth trade-off for PSK Union Bound Approximation UBA for QAM UBA for PSK 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 2008 ng 2008 M-PSK ( ) ( ) ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + = M m t f t g E E t s g m π π 2 1 2 cos 2 ( ) t s 1 ( ) t s 5 2 ( ) t s 2 ( ) t s 3 ( ) t s 4 ( ) t s 6 ( ) t s 7 ( ) t s 8 ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 M-PSK, View #2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = − = = M m M m E s s t f t g E t t f t g E t m m g g π π π φ π φ 2 1 sin 2 1 cos 2 sin 2 , 2 cos 2 2 , 1 , 2 1 s In terms of 3 Signal vectors for M =8 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s E ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 M-PSK Projection of r ( t ) onto signal space yields: 1 s 2 s 3 s 4 s 5 s E n s r + = m 4 6 s 7 s 8 s ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 , ~ i.i.d. are and where 2 1 N N n n ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 Distance between Points ( ) ( ) ( ) M E M E M E E e E d M j π π π π 2 2 2 2 sin 4 2 cos 2 1 2 1 4 2 cos 2 2 1 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = − = − = 5 ⇒ ( ) M E d π sin 2 = ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 P e for M-ary PSK E ( ) M E d π sin 2 = 6 ( ) 2 2 2 P d Q P e − = σ ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 P e for M-PSK ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ≈ ≈ − = M N E Q d Q P d Q P e π σ σ sin 2 2 2 2 2 2 2 = E E But 7 ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⇒ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ≈ ⇒ − M M P Q N E M N E M Q P M e b b e b π π 2 2 2 1 2 2 sin log 2 2 sin log 2 2 log ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins Spri Spring 2008 ng 2008 Power-vs-Bandwidth 8 ECE 614: Principles of Digital Communications, Colorado State University, Fort Collins...
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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 18 - ECE 614 Principles of Digital Communications...

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