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 2
5.4 Multi-d signal waveforms Sets of multiple dimensional signals are used to transmit M-ary symbols. Common types are 1.Orthogonal signals; 2.*Bi-orthogonal signals; 3.Simplex signals; 4. Binary coded signals; UESTC-Digital transmission through the AWGN channel Prof李晓峰 3
5.4.1 Orthogonal signal waveforms Consider a space with orthonormal basis of{Ψ1，Ψ2，，Ψw},forM-ary transmission And,construct signal set s,s2,,s such that, s,=VE,业1，S,=VE,业，，sw=VEΨu They are,1)orthogonal,2)M-dimensional,3)having equal energies. For convenience of graphing,take M=3 in our discussion. The coordinates and constellations are, 2(04 s=(VE,0,0） dnm=小sm-snl s,=(0VE,0) 2e, =WEE s=(0,0,VE e, =√2E,=2ls p() UESTC-Digital transmission through the AWGN channel Prof李晓峰 4
5.4.1 Orthogonal signal waveforms S=VE,Ψ，s,=E,Ψ2，Sw=VEyu For Binary(M=2) 49) 44() Baseband examples /7 IT "Left"=signals which are completely overlapped 9(t) A4() "Right"=signals which are completely 1/T non-overlapped UESTC-Digital transmission through the AWGN channel Prof李晓峰 5
5.4.1 Orthogonal signal waveforms For M-ary(M=4) S=E,Wir S2 =E.W2 S=E.Wx s (n Baseband examples "Left"=signals which are completely 4320 overlapped 50 24- "Right"=signals which are completely T/2 non-overlapped T/4 Th T(I In practical, The "Left"is usually generated by a famous procedure called Hardamard/ T/23T/4 Walsh-Hardamard Transform(WHT). The "Right"is often called PPM (Pulse 5() position modulation),which are pulses with diff.position. 3T74T UESTC-Digital transmission through the AWGN channel Prof李晓峰 6