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
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
5.6.10 Comparison of modulations 1)Efficiency,Rb 2)Reliability,Pb Recall a general block diagram of digital communication {,-1,0,a41H s,(t) n() {,an} Mod. Channel Recv 1R,=1/T Digital communication system It is natural to evaluation the whole systems in 2 aspects: 1)Efficiency,how fast?Rs 2)Reliability,how many errors?Pe More generally,we talk about the bit-rate Rb and bit-err Pb respectively We see that,1)R=kR,=(log2 M)R,,k=log:M 2)B=?P.With Gray code,we have P=P/k. UESTC-Digital transmission through the AWGN channel Prof李晓峰 4
5.6.10 Comparison of modulations 1)Efficiency,Rb 2)Reliability,Pb In the physical channel,Electrical waveforms,such as pulses and carriers, are used to transmit info in the physic media. {,an} 人，an,} s.() r(t)= Recv W s (t)+n(t) Specifically, Baseband(BB):pulses of diff amps(PAM),or orthogonal pulses(PPM); 。 Passband(PB):Carriers with amp/phs/freq mod.(ASK/PSK/FSK),QAM The essential physical features of the waveform is the 1)The BW:denoted by W; 2)The energy:denoted by Es (if unequal,Eav),or Eb=Es/k; UESTC-Digital transmission through the AWGN channel Prof李晓峰 5
5.6.10 Comparison of modulations 1)Efficiency,Rb~W,or n 2)Reliability,P~Eb/No In the physical chaRefer to the BW of a waveform,we simply conclude that, are used to transm BB pulse:W=R/2 PB signals:W=Rs {,am,} For M-D signals, BB pulse:W=MR/2 PB signals:W=MRg We define the normalized data rate (alse called spectral Specifically, efficiency)as ·Baseband(BB) Rp 7= 。 Passband(PB) W kR.(bps/Hz) k=l0g2 M The essential physical features of the waveform is the 1)The BW:denoted by W; 2)The energy:denoted by Es (if unequal,Eav),or Eb=Es/k; UESTC-Digital transmission through the AWGN channel Prof李晓峰 7
5.6.10 Comparison of modulations 10 Note that there are two typical applications: A-16 QAM M-4 PAM M=64 QAM M=8 PAM(SSB) 1)Band-limited which demands high (SSB) PSK special efficiency,QAM is the best, ZH/(s/Sq)M/ M=16 3 for its required Eb/No is relatively 8 small. M=4 PSK M=2 PAM Bandwidth-limited 2)Power-limited which demands low (SSB) -1.6 region energy,FSK is an option,for its M-2 10 15 2025 required Eb/No can be very small. Asymptote! PM=8 SNR per bit,P=/No(dB) Shannon 0.5 Power-limited Limit M=16 R region:帝< 0.3 M=32 Fig 5.66 on p341. -0.2 M=64 Orthogonal signals Coherent detection 0.1 UESTC-Digital transmission through the AWGN channel Prof李晓峰 8
