Lecture 11 Outline: Digital Modulation - Stanford University · Lecture 11 Outline: Digital...
8
Lecture 11 Outline: ASK/PSK Demod, Quadrature Modulation, FIR Filter Design l Announcements: l Georgia’s office hours this week are Th 12-1 instead of Th 4-5. l Optional reading on ASK/PSK/QAM Modulation posted l Midterm announcements next week l Review of Last Lecture l Demodulation of ASK and PSK l Quadrature Modulation: MQAM l Introduction to FIR Filter Design l Impulse Response Matching
Transcript of Lecture 11 Outline: Digital Modulation - Stanford University · Lecture 11 Outline: Digital...
Lecture 11 Outline: ASK/PSK Demod, Quadrature
Modulation, FIR Filter Design
l Announcements:l Georgia’s office hours this week are Th 12-1 instead of Th 4-5. l Optional reading on ASK/PSK/QAM Modulation postedl Midterm announcements next week
l Review of Last Lecture
l Demodulation of ASK and PSK
l Quadrature Modulation: MQAM
l Introduction to FIR Filter Design
l Impulse Response Matching
l Broadcast AM has s(t)=[1+kam(t)]cos(wct) with [1+kam(t)]>0l Demodulator uses an envelope detectorl No need to recover phase f, very simple receiver design
l Quadrature modulation sends independent AM signals modulated onto the sin and cosine carriers
l FM encodes information in frequency of carrier (extra topic) l Digital communication systems modulate bits onto baseband
signal m(t), then use passband modulation on m(t)l May also preprocess bits with compression and codingl Analog information signals converted to bits via ADC
l Baseband digital modulation: ON-OFF (ak=A,0), POLAR (ak=±A)
l Passband digital modulation for ASK/PSK:
Review of Last Lecture
)cos()()( jw +=å ttmts c
)()()(*)()()( bk
kbk
k kTtatxfortrecttxkTtrectatm -==-= åå¥
-¥=
¥
-¥=
d
ASK and PSK
l Amplitude Shift Keying (ASK)
l Phase Shift Keying (PSK)
îíì
==
==)"0("0)(0)"1(")()cos(
)cos()()(b
bcc nTm
AnTmtAttmts
ww
1 0 1 1
AM Modulation
AM Modulation
m(t)
m(t)
îíì
-=+=
==)"0(")()cos()"1(")()cos(
)cos()()(AnTmtAAnTmtA
ttmtsbc
bcc pw
ww
1 0 1 1
Assumes carrier phase f=0, otherwise need phase recovery of f in receiver
A
-A
A
-A
ASK/PSK Demodulationl Similar to AM demodulation, but only need to choose
between one of two values (need coherent detection)
l Decision device determines which of R0 or R1 that R(nTb) is closest tol For ASK, R0=0, R1=A, For PSK, R0=-A, R1=Al Noise immunity DN is half the distance between R0 and R1
l Bit errors occur when noise exceeds this immunity
s(t) ´
cos(wct+f)
ò ×bT
b
dtT 0
)(2
nTb
Decision Device
“1” or “0” r(nTb)
R0
R1
a0
r(nTb)
r(nTb)+N
Integrator (LPF)
DN
Quadrature Digital Modulation: MQAM
l Sends different bit streams on the sine and cosine carriersl Baseband modulated signals can have L>2 levels
l More levels for the same TX power leads to smaller noise immunity and hence higher error probability
l Sends 2log2(L)=M bits per symbol time Ts, Data rate is M/Ts bpsl Called MQAM modulation: 10 Gbps WiFi has 1024-QAM (10 bits/Ts)
10 11 00 01
t
mi(t)m1(t)cos(wct)+m2(t)sin(wct)+
n(t)
X
-90o
cos(wct)
sin(wct)
X
ò ×bT
b
dtT 0
)(2
ò ×bT
b
dtT 0
)(2
Decision Device
“1” or “0”
R0
R1
a0
rI(nTb)+NI
Decision Device
“1” or “0”
R0
R1
a0
rQ(nTb)+NQ
A
-A
A/3
-A/3
Ts
Data rate: log2L bits/TsTs is called the symbol time
Introduction to FIR Filter Design
l Signal processing today done digitallyl Cheaper, more reliable, more energy-efficient, smaller
l Discrete time filters in practice must have a finite impulse response: h[n]=0, |n|>M/2l Otherwise processing takes infinite time
l FIR filter design typically entails approximating an ideal (IIR) filter with an FIR filterl Ideal filters include low-pass, bandpass, high-passl Might also use to approximate continuous-time filter
l We focus on two approximation methodsl Impulse response and filter response matchingl Both lead to the same filter design
Impulse Response Matchingl Given a desired (noncausal, IIR) filter response hd[n]
l Objective: Find FIR approximation ha[n]: ha[n]=0 for |n|>M/2 to minimize error of time impulse response
l By inspection, optimal (noncausal) approximation is
[ ] ( )W« jdd eHnh
[ ] [ ] [ ] [ ] [ ] 2/||,0][since,
2
2
2
22 Mnnhnhnhnhnhnh aMn
dMn
adn
ad >=+-=-= ååå>£
¥
-¥=
eDoesn’t depend on ha[n]
[ ] [ ]îíì
>£
=2/02/
MnMnnh
nh da
Exhibits Gibbs phenomenonfrom sharp time-windowing
W
( )Wja eH
p- p0
Main Pointsl Demodulation of ASK/PSK downconverts, integrates, and then
uses a decision device to determine if a “1’’ or “0’’ was sentl Downconversion must be coherent; requires acquisition of phase fl Noise can cause decision device to output an erroneous bit
l MQAM modulation sends independent bit streams on cosine and sine carriers where baseband signals have L=ÖM levelsl Leads to data rates of M/Ts bps (can be very high)
l FIR filter design entails approximating an ideal discrete or continuous filter with a discrete filter of finite duration
l Impulse response and frequency response matching minimizes time/frequency domain error; have same noncausal designl Optimal filter has M+1 of original discrete-time impulse response valuesl Sharp windowing causes “Gibbs” phenomenon (wiggles)
