1. 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

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

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

6. 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)

7. 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

8. 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 10 11 01 00
Recived Signal

9. 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 EpM are related by
Same transmission bandwidth, yet more information

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

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

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

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

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

15. 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

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

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

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

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

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

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

22. QAM vs. MPSK M 2 4 8 16 32 64 hM=Rb/B Eb/NO for BER=10-6 M hM=Rb/B
0.5 1
1.5
2.5 3
Eb/NO for BER=10-6
10.5 14
18.5
23.4
28.5
MPSK M 4 16 64
256
1024
4096
hM=Rb/B 1 2 3 5 6
Eb/N o for BER=10-6
10.5 15
18.5 24 28
33.5
QAM
Very power efficient for high signal configurations, but requires a lot of power
Can give inconsistent results for different bit configurations

23. 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

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

25. 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:

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

27. MFSK vs. MPSK M 2 4 8 16 32 64 hM=Rb/B Eb/N for BER=10-6 M hM=Rb/B
0.5 1
1.5
2.5 3
Eb/N for BER=10-6
10.5 14
18.5
23.4
28.5
MPSK M 2 4 8 16 32 64
hM=Rb/B
0.4
0.57
0.55
0.42
0.29
0.18
Eb/N for BER=10-6
13.5
10.8
9.3
8.2
7.5
6.9
MFSK