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lecture14 - EE455/591 EE455/591 Orthogonal Signaling...

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Unformatted text preview: EE455/591 EE455/591 Orthogonal Signaling Orthogonal Signaling Reading: Read Section 7.1 again, 7.3 Reading: Read Section 7.1 again, 7.3 Review: Error Probabilities Review: Error Probabilities Topics: Topics: 1. 1. Orthogonal Signaling Orthogonal Signaling 2. 2. Correlation Type Demodulators Correlation Type Demodulators 3. Geometrical Representation of Orthogonal Signals 3. Geometrical Representation of Orthogonal Signals 4. Bit Error Rate for Orthogonal Signaling 4. Bit Error Rate for Orthogonal Signaling Review: Calculating Error Probabilities • Noise n is a zero mean Gaussian R.V. • Variance σ 2 =N E/2 • Error events –-1 sent but +1 detected – +1 sent but -1 detected = =- <-- ∞- ∫ 2 / 2 2 1 ) ( 2 2 N E Q dx e E n P x E σ σ π = = ≥- ∞ ∫ 2 / 2 2 1 ) ( 2 2 N E Q dx e E n P x E σ σ π 2 / 2 / 2 2 2 1 2 1 ) ( x y x e x dy e x Q-- ∞ < = ∫ π π 1. Orthogonal Signaling • We focused on binary antipodal signaling last lecture • The two antipodal symbols are not orthogonal to each other • Orthogonal signals (e.g. 4PPM) Signals are orthogonal if ∫ T s i (t) s j (t)dt = 0 for i j ≠ A T 2T T 4T 3T 5T 00 10 01 11 11 A T s 1 (t) for bits =01 A T s 2 (t) for bits =10 A T s 3 (t) for bits =11 s (t) for bits=00 1. Examples of Orthogonal Signals 2-PPM 2-Hadamard sine and cosine s 1 (t) s 2 (t) Extension from 2 to 4 4PPM T A t T A t T A t T A t T A t T A t A T A T s 1 (t) for bits =01 A T s 2 (t) for bits =10 A T s 3 (t) for bits =11 s (t) for bits=00 1. Why are these Functions Orthogonal?...
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This note was uploaded on 11/01/2009 for the course EEE 455 taught by Professor Hui during the Spring '09 term at ASU.

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lecture14 - EE455/591 EE455/591 Orthogonal Signaling...

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