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lecture15 - EE455/591 EE455/591 More on Orthogonal...

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Unformatted text preview: EE455/591 EE455/591 More on Orthogonal Signaling More on Orthogonal Signaling Reading: Read Section 7.1 - 7.3 Reading: Read Section 7.1 - 7.3 Review: Geometric Representation of Signals Review: Geometric Representation of Signals Topics: Topics: 1. 1. Hadamard/Walsh Orthogonal Functions Hadamard/Walsh Orthogonal Functions 2. 2. Orthogonal Projection and Signal Distances Orthogonal Projection and Signal Distances 3. Bit Error Rate for Orthogonal Signaling 3. Bit Error Rate for Orthogonal Signaling Review: Examples of Orthonormal Basis 2-PPM 2-Hadamard sine and cosine s 1 (t) s 2 (t) 1 (t) 2 (t) T A t T A t T A t T A t T A t T A t T 1/ T t T t T t T 1/ T t T t T A t (2/T) (2/T)-1/ T (2/T) (2/T) A Review: Projecting Functions onto a Basis Question: How to express 2-Hadamard in the basis of 2PPM? 2-PPM 2-Hadamard s 1 (t) s 2 (t) 1 (t) 1 (t) 2 (t) 2 (t) T A t T A t T A t T A t T 1/ T t T t T t T 1/ T t (2/T) (2/T)-1/ T Answer: 1 (t)= [ 1 (t) + 2 (t)]/ 2 2 (t)= [ 1 (t) - 2 (t)]/ 2 Review: Geometric Representations of Functions 2-PPM 2-Hadamard s 1 (t) w 1 (t) s 2 (t) w 2 (t) Basis 1 (t) 1 (t) 2 (t) 2 (t) T A t T A t T A t T A t T 1/ T t T t T t T 1/ T t (2/T) (2/T)-1/ T 1 2 s 1 =(A (T), 0) s 2 =(0, A (T)) 1 =( T 1 (t) 1 (t)dt, T 1 (t) 2 (t)dt) =(0.707, 0.707) for A=1, T=1 2 =( T 2 (t) 1 (t)dt, T 2 (t) 2 (t)dt) =(0.707, -0.707) 1 2 1. Walsh/Hadamard Functions ( 29...
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lecture15 - EE455/591 EE455/591 More on Orthogonal...

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