Chapter 5 Digital transmission through the AWGN channel by Prof.XIAOFENG LI SICE,UESTC UESTC-Digital transmission through the AWGN channel Prof李晓峰 1
Introduction In this chapter,we focus on how to transmit digital info signals with waveforms. The topics include: 1. Geometric representation of sig waveforms; 2.Diff types of waveforms for digital transmissions; 3.Optimal reception; 4. Performance evaluation on the AWGN channel 5. Comparison of the methods. UESTC-Digital transmission through the AWGN channel Prof李晓峰 3
Contents 16 Hrs ■Introduction Geometric rep.of the sig waveforms Pulse amplitude modulation 2-d signal waveforms M-d signal waveforms Opt.reception for the sig.in AWGN Optimal receivers and probs of err UESTC-Digital transmission through the AWGN channel Prof李晓峰 4
5.1 Geometric rep.of the sig waveforms 1.Review of the Vectors and Vector Space Concepts: ·length and direction Geometric representation u+V=(4,+,42+y 。 Coordinates u=(u,42}-----------二7 v=(Vx,V,) ·vector addition, v=(,) 。 length calculation ·dot/inner products 。 basis vectors:i and j 。 Algebraic representation,v=v xi+vx j Dimensions:2-space,3-space,N-space UESTC-Digital transmission through the AWGN channel Prof李晓峰 5
5.1 Geometric rep.of the sig waveforms 1.Review of the Vectors and Vector Space Let B=fe,...,ey}be an orthonormal basis for a N dimensional vector space RV. If v is any vector in the space,then it can be written uniquely in the form V=a1e1+a2e2+…+awev a,...,ay are called the coordinates of v. e2=j a +■，+，+ 02 u=(m V= y=(w, aN e1= UESTC-Digital transmission through the AWGN channel Prof李晓峰 6