ARC Future Fellow at The University of Melbourne Sessional Lecturer at Monash University
August 22, 2022
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 1 / 20
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ECE5884 Wireless Communications Week 5: Digital Modulation and Detection
Course outline
This week: Ref. Ch. 5 of [Goldsmith, 2005]
● Week 1: Overview of Wireless Communications
● Week 2: Wireless Channel (Path Loss and Shadowing)
● Week 3: Wireless Channel Models
● Week 4: Capacity of Wireless Channels
● Week 5: Digital Modulation and Detection
● Week 6: Performance Analysis
● Week 7: Equalization
● Week 8: Multicarrier Modulation (OFDM)
● Week 9: Diversity Techniques
● Week 10: Multiple-Antenna Systems (MIMO Communications) ● Week 11: Multiuser Systems
● Week 12: Guest Lecture (Emerging 5G/6G Technologies)
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Communication system
Figure 1: Block diagram of a digital communication system.
● The source encoder converts information waveform (text, audio, image, video,..) to bits.
● The decoder converts bits back to waveform.
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Channel coding
Figure 2: Block diagram of channel coding.
● The channel encoder converts bits to signal waveform.
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Digital communications
1 Convert digital bits into electromagnetic signals, i.e., transmit a few 0s/1s at a time (microseconds between transmissions).
2 Benefits: higher spectral efficiency, powerful error correction techniques, resistance to channel impairments; better security and privacy; etc.
Figure 3: Communication system model.
3 Digital modulation is the process of encoding a digital information signal into the amplitude, phase and/or frequency of the transmitted signal.
s(t ) = A cos (2πf t + θ)
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Digital modulation
Figure 4: Digital modulation schemes – ASK, FSK and PSK.
https://www.researchgate.net/figure/Digital- modulation- schemes- ASK- FSK- and- PSK_fig3_303471153
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Example: QPSK or 4-PSK
Figure 5: Phase-Shift Keying (PSK) digital modulation.
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Digital modulation/demodulation
● Challenges of communications/Research problem:
1 Transmit as much data as possible per second (1G-6G+) – Modulation
2 Estimating the original bit sequence based on the signal received over
the channel -Detection/Demodulation
● Digital modulation technique – high data rate; high spectral efficiency (minimum BW occupancy); high power efficiency (minimum required transmit power); robustness to channel impairments (minimum probability of bit error); and low power/cost implementation.
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Amplitude and Phase Modulation
1 Over a time interval of Ts,
K = log2(M)bits per symbol time Ts
are encoded into the amplitude and/or phase of the transmitted
signal s(t),0 ≤ t < Ts.
2 There are three main types of amplitude/phase modulation:
● pulse amplitude modulation (MPAM) – information encoded in amplitude only;
● phase-shift keying (MPSK) – information encoded in phase only;
● quadrature amplitude modulation (MQAM) – information encoded in
both amplitude and phase.
3 M for M-ary transmission, usually M = 2K .
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Pulse Amplitude Modulation (MPAM)
1 all of the information is encoded into the signal amplitude Ai . The transmitted signal over one symbol time is given by
si(t) = R{Aig(t)ej2πfct} = Aig(t)cos(2πfct),0 ≤ t < Ts
Figure 6: Gray encoding for MPAM
2 The minimum distance between constellation points is
dmin =min∣Ai −Aj∣=2d. i,j
3 Gray code mapping: all adjacent symbols differ by a single bit.
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Pulse Amplitude Modulation (MPAM)
1 The ith constellation has energy Esi = A2i , and the average energy is ̄1M2
Es = M ∑Ai i=1
Figure 7: Decision regions for MPAM.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022
Phase-Shift Keying (MPSK)
1 All of the information is encoded in the phase of the transmitted signal. The transmitted signal over one symbol time is given by
si(t) = R{Ag(t)ej2π(i−1)/Mej2πfct}, i = 1,...,M
Figure 8: Gray encoding for MPSK (Constellation diagram).
2 The minimum distance between constellation points is
dmin =min∣Ai −Aj∣=2Asin(π/M). i,j
where A is typically a function of the signal energy.
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Phase-Shift Keying (MPSK)
1 All possible transmitted signals si (t ) have equal energy: ̄1M22
Es=M∑A =A i=1
Figure 9: Decision regions for MPSK.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022
Quadrature Amplitude Modulation (MQAM)
1 The information bits are encoded in both the amplitude and phase of the transmitted signal. MQAM is more spectrally efficient than MPAM and MPSK in that it can encode the most number of bits per symbol for a given average energy.
2 The transmitted signal over one symbol time is given by si(t) = R{Aiejθi g(t)ej2πfct}, i = 1,...,M
Figure 10: 4-QAM and 16-QAM constellations.
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Quadrature Amplitude Modulation (MQAM)
1 Theenergyinsi(t)isEsi =A2i ,andthusEs = M1 ∑Mi=1A2i . 2 The distance between any pair of symbols:
3 The minimum distance between signal dmin = 2d.
dij =∣∣si −sj∣∣=
(si1 −sj1)2 +(si2 −sj2)2.
Figure 11: Decision regions for MQAM with M = 16.
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Average power
● For BPSK:
● For 4-QAM:
̄1M2 P = M ∑Ai
1√ P ̄=22A2=A2⇒A= P ̄
̄122 P ̄ P=44(2A)=2A ⇒A= 2
● Signal model (kth sample):
rk= Pt(√ ̄xk)h+nk
P Conventionally, we can assume P ̄ = 1.
● Thus,A=1forBPSK;andA=1/ 2for4-QAM.
ECE5884 Wireless Communications @ Monash Uni.
August 22, 2022
Decision regions
Received signal ∶ r = h si + n AWGN channel ∶ r = si + n
Figure 12: Decision regions for 4-PSK and 8-PSK.
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Receiver structure
● Maximum likelihood receiver: is simple to implement because the decision criterion depends only on vector distances.
sˆ=arg min∣∣r−si∣∣ (9) si ,∀i
● Matched filter receiver: This structure makes use of a bank of filters matched to each of the different basis functions. If a given input signal is passed through a filter matched to that signal then the output SNR is maximized.
Figure 13: Matched filter receiver structure.
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References
A. Goldsmith, Wireless Communications, Cambridge University Press, USA, 2005.
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Thank You! See you again
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