Bandpass Modulation and Demodulation Continued, Slides of Digital Communication Systems

Download Bandpass Modulation and Demodulation Continued and more Slides Digital Communication Systems in PDF only on Docsity! 1 Digital Communication Systems Dr. Shurjeel Wyne Lecture 10 CH 4 -Bandpass Modulation & Demodulation 2 Today’s lecture, we are going to talk about:  How to calculate the average probability of symbol error for different modulation schemes that we studied  How to compare different modulation schemes based on their error performances 2 3 Error probability of bandpass modulation  Before evaluating the error probability, it is important to remember that:  Type of modulation and detection ( coherent or non- coherent), determines the structure of the decision circuits and hence the decision variable, denoted by z.           Nr r  1 r  T 0 )(1 t  T 0 )( tN )( tr 1r Nr r Decision Circuits Compare z with threshold. m̂ 4  The matched filters output (observation vector= ) is the detector input and the decision variable, z, is a function of , i.e.  For M-ASK, M-QAM and M-FSK with coherent detection  For M-PSK with coherent detection  For non-coherent detection of M-FSK  We know that for calculating the average probability of symbol error, we need to determine Error probability … )(rfz r r rz rz ||rz  Hence, we need to know the statistics of z, which depends on the modulation scheme and the detection type. sent)|CconditionsatisfiesPr(zsent)| ZinsideliesPr( ii ii ssr  5 -10 -5 0 5 10 15 20 25 10-4 10-3 10-2 10-1 100 Eb/N0 [dB] P E (M ) Binary Modulation BPSK DBPSK BFSK-Coh BFSK-NonCoh Probability of symbol error for different Binary modulations 10  Coherent detection of M-ASK  Decision variable:  T 0 )(1 t ML detector (Compare with M-1 thresholds))(tr 1r m̂ Error probability …. )(1 t 2s1s 0gE3 “00” “01” 4s3s “11” “10” gE gE gE3 4-ASK 1rz  6 11 Error probability ….  Coherent detection of M-ASK ….  Error happens if the noise, , exceeds in amplitude one- half of the distance between adjacent symbols. For symbols at the ends, error can happen only in one direction. Hence:      gMMege gmme ErnPErnP MmErnP   ssss ss 111111 11 Pr)(andPr)( ;1for||||Pr)(            0 2 2 1 log6)1(2)( N E M MQ M MMP bE gbs E MEME 3 )1()(log 2 2   mrn s 11 Gaussian pdf with zero mean and variance 2/0N                            0 1 111 1 2)1(2)()1(2Pr)1(2 Pr M 1Pr M 1||Pr2)(1)( 1 N E Q M Mdnnp M MEn M M EnEnEn M MP M MP g E ng ggg M m meE g s Probability of symbol error for M-ASK 12 Error probability …  Coherent detection of M-QAM  T 0 )(1 t ML detector1r  T 0 )(2 t ML detector )(tr 2r m̂Parallel-to-serial converter s) threshold1 with(Compare M s) threshold1 with(Compare M )(1 t )(2 t 2s1s 3s 4s “0000” “0001” “0011” “0010” 6s5s 7s 8s 10s9s 11s 12s 14s13s 15s 16s “1000” “1001” “1011” “1010” “1100” “1101” “1111” “1110” “0100” “0101” “0111” “0110” 16-QAM 7 13 Error probability …  Coherent detection of M-QAM …  M-QAM can be viewed as the combination of two modulations on I and Q branches, respectively.  No error occurs if no error is detected on either I and Q branches. Hence:  Considering the symmetry of the signal space and orthogonality of I and Q branches: SKM A branches)QandIondetectederrornoPr(1)(1)(  MPMP CE   22 1I)onerrorPr(no Q)onerrorI)Pr(noonerrorPr(nobranches)QandIondetectederrornoPr( MPE                  0 2 1 log3114)( N E M MQ M MP bE Average probability of symbol error for PAMM 14 Error probability …  Coherent detection of MPSK Compute Choose smallest 2 1arctan r r ̂ |ˆ|  i  T 0 )(1 t  T 0 )(2 t )(tr 1r 2r m̂ 3s 7s “110” )(1 t 4s 2s sE “000” )(2 t 6s 8s 1s 5s “001” “011”“010” “101” “111” “100” 8-PSK Decision variable r ̂z 10 19 Probability of symbol error for M-PSK EP dB/ 0NEb Note! • “The same average symbol energy for different sizes of signal space” 20 Probability of symbol error for M-ASK EP dB/ 0NEb Note! • “The same average symbol energy for different sizes of signal space” 11 21 Probability of symbol error for M-QAM EP dB/ 0NEb Note! • “The same average symbol energy for different sizes of signal space” 22 Probability of symbol error for M-FSK EP dB/ 0NEb Note! • “The same average symbol energy for different sizes of signal space”