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Chapter 7 Performance of QAM

Chapter 7 Performance of QAM. Performance of QPSK Comparison of Digital Signaling Systems Symbol and Bit Error Rate for Multilevel Signaling. Huseyin Bilgekul EEE 461 Communication Systems II Department of Electrical and Electronic Engineering Eastern Mediterranean University. 0 1 0 1. x.

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Chapter 7 Performance of QAM

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  1. Chapter 7Performance of QAM • Performance of QPSK • Comparison of Digital Signaling Systems • Symbol and Bit Error Rate for Multilevel Signaling Huseyin Bilgekul EEE 461 Communication Systems II Department of Electrical and Electronic Engineering Eastern Mediterranean University

  2. 0 1 0 1 x Rb/2 0 1 1 1 0 0 1 0 cos wct Serial to Parallel Converter BPF + - 90 Rb 1 1 0 0 x Rb/2 Performance of QPSK Im x Decision Regions • Modeled as two BPSK systems in parallel. One using a cosine carrier and the other a sine carrier • Ts=2 Tb x x Re x

  3. Performance of QPSK

  4. Performance of QPSK • Because the upper and lower channels are BPSK receivers the BER is the same as BPSK. • Twice as much data can be sent in the same bandwidth compared to BPSK (QPSK has twice the spectral efficiency with identical energy efficiency). • Each symbol is two bits, Es=2Eb

  5. M-ary Communications • Send multiple, M, waveforms • Choose between one of M symbols instead of 1 or 0. • Waveforms differ by phase, amplitude, and/or frequency • Advantage: Send more information at a time • Disadvantage: Harder to tell the signals apart or more bandwidth needed. • Different M’ary types can be used. Multiamplitude (MASK) +s(t), +3 s(t), +5 s(t),. . ., +(M-1) s(t). Multiple phase (MPSK, QPSK) Multitone (MFSK) Quadrature Amplitude Modulation (combines MASK and MPSK)

  6. M-ary Communications • As M increases, it is harder to make good decisions, more power is used • But, more information is packed into a symbol so data rates can be increased • Generally, higher data rates require more power (shorter distances, better SNR) to get good results • Symbols have different meanings, so what does the probability of error, PE mean? • Bit error probability • Symbol error probability

  7. 10 11 01 00 Multi-Amplitude Shift Keying (MASK) • Send multiple amplitudes to denote different signals • Typical signal configuration: • +/- s(t), +/- 3 s(t), ….., +/- (M-1) s(t) 4-ary Amplitude Shift Keying • Each symbol sends 2 bits • Deciding which level is correct gets harder due to fading and noise • Receiver needs better SNR to achieve accuracy Recived Signal

  8. Average Symbol and average Bit Energy • Transmit Rm M-ary symbols/sec (Tm=1/ Rm) • Each pulse of form: k s(t) • Assume bit combination equally likely with probability 1/M • The average symbol energy is, • Each M-ary symbols has log2M bits of information so the bit energy Eb and the symbol enrgy EpMare related by • Same transmission bandwidth, yet more information

  9. t=Tp s(t)+n(t) r(t) s(T-t) H(f) Threshold Detector r(Tp) +kAp+n(Tp) MASK Error Probability • Same optimal receiver with matched filter to s(t) • Total probability of SYMBOL ERROR for M equally likely signals:

  10. Decision Model 10 01 11 00 • Two cases: • (M-1)p(t) – just like bipolar • Interior cases, can have errors on both sides Ap 3Ap -Ap -3Ap

  11. MASK Prob. Of Error • In a matched filter receiver, Ap/sn= 2Ep/N

  12. MASK Prob. Of Error • In a matched filter receiver, Ap/sn= 2Ep/N

  13. Bit Error Rate • Need to be able to compare like things • Symbol error has different cost than a bit error • For MASK

  14. Error Probability Curves • Use codes so that a symbol error gives only a single bit error. • Bandwidth stays same as M increases, good if you are not power-limited. M=16 M=8 M=4 M=2

  15. Im Re x x Im x x x Re x x x x x M-ary PSK (MPSK) • Binary Phase Shift Keying (BPSK) 1: s1(t)= s(t) cos(wct) 0: s0(t)= s(t)cos(wct+p) • M-ary PSK

  16. MPSK • Must be coherent since envelope does not change • Closest estimated phase is selected

  17. Im x x x x x x x x MPSK Performance • Detection error if phase deviates by > p/M • Strong signal approximation Re

  18. MPSK Waterfall Curve • QPSK gives equivalent performance to BPSK. • MPSK is used in modems to improve performance if SNR is high enough.

  19. ri qi Quadrature Amplitude Modulation (QAM) • Amplitude-phase shift keying (APK or QAM) • The envelope and phases are,

  20. QAM Performance • Analysis is complex and not treated here. • QAM-16 • Upper Bound for general QAM depends on spectral efficiency relative to bipolar signals,

  21. QAM vs. MPSK MPSK QAM • Very power efficient for high signal configurations, but requires a lot of power • Can give inconsistent results for different bit configurations

  22. Multitone Signaling (MFSK) • M symbols transmitted by M orthogonal pulses of frequencies: • Receiver: • bank of mixers, one at each frequency • Bank of matched filters to each pulse • Higher M means wider bandwidth needed or tones are closer together

  23. MFSK Receiver H(w) x Sqrt(2)cos w1t H(w) x Comparator Sqrt(2)cos w2t H(w) x Sqrt(2)cos wMt

  24. MFSK Performance • When waveform 1 is sent, sampler outputs are Ap+ n1, n2 , n3, etc. • Error occurs when nj> Ap+ n1 • Average Probability of error:

  25. MFSK Performance • Channel BW: • BW efficiency decreases, but power efficiency increases • Signals are orthogonal so no crowding in signal space

  26. MFSK vs. MPSK MPSK MFSK

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