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 / 18
Copyright By PowCoder代写 加微信 powcoder
ECE5884 Wireless Communications Week 5 Workshop: 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)
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 2 / 18
Course Information – Assessments
● The assessments in this unit are divided into two parts:
1 Continuous assessment (Quizzes, Assignments and Labs), which
accounts for 50% of the mark
2 Final assessment, which accounts for the rest 50% of the mark
● This unit contains hurdle requirements:
● You are required to achieve at least 45% in the total continuous
assessment component.
● You are required to achieve at least 45% 45% in the final assessment
component.
Assessment Item
Weekly Quizzes (×12) Assignments (×3) Labs (×5)
Final Exam
Weight Due Data
12 End of each week
18 Each (roughly) fourth week
20 Each second week, excl. Week 1 50 TBA
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 3 / 18
Communication system
Figure 1: Block diagram of a digital communication system.
● The source encoder converts information waveform to bits. ● The source decoder converts bits back to waveform.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 4 / 18
Channel coding
Figure 2: Block diagram of channel coding.
● The channel encoder converts bits to signal waveform.
● The channel decoder converts signal waveform back to bits.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 5 / 18
Digital communications
Figure 3: Communication system model.
1 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)
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.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 6 / 18
Example: QPSK or 4-PSK
Figure 4: Phase-Shift Keying (PSK) digital modulation s(t ) = A cos (2πfc t + θ).
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 7 / 18
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
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 8 / 18
Signal and system model
1 Over a time interval of Ts , the system sends K = log2 (M ) bits.
2 Data rate is R = K /T bits per second (bps).
3 For M-ary Tx, there are M = 2K possible sequences of K bits.
4 Each bit sequence of length K comprises a message mi .
Figure 5: s(t) = s1(t) + s2(t − T) + s1(t − 2T) + s1(t − 3T)
How do we represent s(t) for a large signal set si (t) ∈ S = {s1(t), ⋯, sM (t)}? ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 9 / 18
Geometric representation of signals
1 Gram–Schmidt orthogonalization procedure: Any set of M real signals S = {s1(t),⋯,sM(t)} defined on [0,Ts) with finite energy can be represented as a linear combination of N ≤ M real orthonormal basis functions {φ1(t),⋯,φN(t)}.
φi(t)φj(t)dt = 0; i ≠ j 2 Basis function representation:
basis function φj (t ).
si(t)φj(t)dt (2) sij isarealcoefficientrepresentingtheprojectionofsi(t)ontothe
si(t) = ∑sijφj(t), 0 ≤ t ≤ Ts where sij = ∫ j=1
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022
Receiver structure
● Matched Filter (MF) receiver: If a given input signal is passed through a filter matched to that signal then the output SNR is maximized.
Figure 6: Matched Filter (MF) receiver structure.
● Maximum likelihood receiver: Decision depends only on distances.
sˆ=arg min∣∣r−si∣∣ si ,∀i
● Decisionregions{Z1,…,ZM}aresubsetsofthesignalspaceRN. ● When known CSI at Rx, MF does: h′ ⋅r
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022
Pulse Amplitude Modulation (MPAM)
1 All of the information is encoded into the signal amplitude Ai . si(t) = R{Aig(t)ej2πfct} = Aig(t)cos(2πfct),0 ≤ t < Ts
Figure 7: Gray encoding and decision regions for MPAM
2 The minimum distance: dmin = mini,j ∣Ai − Aj ∣ = 2d.
3 The ith constellation has energy Esi = A2i , and the average energy is ̄1M2
Es = M ∑Ai (4) i=1
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
si(t) = R{Ag(t)ej2π(i−1)/Mej2πfct}, i = 1,...,M
Figure 8: Gray encoding and decision regions for MPSK.
2 The minimum distance: dmin = mini,j ∣Ai − Aj ∣ = 2A sin(π/M).
3 All possible transmitted signals si (t ) have equal energy:
Es=M∑A =A (5)
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:
2 E ̄ s = M1 ∑ Mi = 1 A 2i .
dij =∣∣si −sj∣∣=
(si1 −sj1)2 +(si2 −sj2)2;anddmin =2d.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 14 / 18
si(t) = R{Aiejθi g(t)ej2πfct}, i = 1,...,M
Figure 9: 4-QAM and 16-QAM constellations.
3 The distance between any pair of symbols:
Average power
● For BPSK:
● For 4-QAM:
̄1M2 P = M ∑Ai
P ̄=22A2=A2⇒A= P ̄ √
̄122 P ̄ P=44(2A)=2A ⇒A= 2
● Signal model (kth sample):
rk= Pt(√ ̄xk)h+nk
Conventionally, we can assume P ̄ = 1.
ECE5884 Wireless Communications @ Monash Uni.
August 22, 2022
Decision regions
Received signal ∶ r = h si + n AWGN channel ∶ r = si + n
Figure 10: Decision regions for 4-PSK. ECE5884 Wireless Communications @ Monash Uni.
August 22, 2022
References
A. Goldsmith, Wireless Communications, Cambridge University Press, USA, 2005.
ECE5884 Wireless Communications @ Monash Uni. August 22, 2022 17 / 18
Thank You! See you again
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com