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

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 0 1 1 1 0 0 1 0 Serial to Parallel Converter x 90 cos wct + 0 1 0 1 1 1 0 0 Rb Rb/2 - BPF

Performance of QPSK

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

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)

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:

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

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