1 Constellation Diagram Properties of Modulation Scheme can be inferred from the Constellation Diagram: Bandwidth occupied by the modulation increases as the dimension of the modulated signal increases. Bandwidth occupied by the modulation decreases as the signal_points per dimension increases (getting more dense). Probability of bit error is proportional to the distance between the closest points in the constellation. Euclidean Distance Bit error decreases as the distance increases (sparse).
Constellation Diagram. Properties of Modulation Scheme can be inferred from the Constellation Diagram: Bandwidth occupied by the modulation increases as the dimension of the modulated signal increases. - PowerPoint PPT Presentation
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1
Constellation Diagram Properties of Modulation Scheme can be
inferred from the Constellation Diagram:
Bandwidth occupied by the modulation increases as the dimension of the modulated signal increases.
Bandwidth occupied by the modulation decreases as the signal_points per dimension increases (getting more dense).
Probability of bit error is proportional to the distance between the closest points in the constellation.
Euclidean Distance Bit error decreases as the distance increases (sparse).
2
Linear Modulation Techniques Digital modulation techniques classified
as: Linear
The amplitude of the transmitted signal varies linearly with the modulating digital signal, m(t).
They usually do not have constant envelope. More spectrally efficient. Poor power efficiency Example: QPSK.
Non-linear / Constant Envelope
3
• constant carrier amplitude - regardless of variations in m(t)Better immunity to fluctuations due to fading. Better random noise immunity.
• improved power efficiency without degrading occupied spectrum- use power efficient class C amplifiers (non-linear)
• low out of band radiation (-60dB to -70dB)
• use limiter-discriminator detection- simplified receiver design-high immunity against random FM noise & fluctuations
from Rayleigh Fading
• larger occupied bandwidth than linear modulation
Constant Envelope Modulation
4
Frequency Shift Keying Minimum Shift Keying
Gaussian Minimum Shift Keying
Constant Envelope Modulation
5
Frequency Shift Keying (FSK)
Binary FSK
Frequency of the constant amplitude carrier is changed according to the message state high (1) or low (0)
Discontinuous / Continuous Phase
0)(bit Tt0
1)(bit Tt0
b
b
tffAts
tffAts
c
c
)22cos()(
)22cos()(
2
1
6
Switching between 2 independent oscillators for binary 1 & 0
sBFSK(t)= vH(t) binary 1bH
b
b Tt tfT
E 0)2cos(
21 =
binary 0 sBFSK(t)= vL(t)
bLb
b TttfT
E 0)2cos(
22 =
switch
cos w2t
cos w1tinput data phase jumps
Discontinuous Phase FSK
• results in phase discontinuities• discontinuities causes spectral spreading & spurious transmission • not suited for tightly designed systems
7
single carrier that is frequency modulated using m(t)
sBFSK(t) = ))(2cos(2
ttfT
Ec
b
b
t
FSKcb
b dmktfT
E )(22cos2
where (t) =
t
FSK dmk )(2
• m(t) = discontinuous bit stream• (t) = continuous phase function proportional to integral of m(t)
=
Continuous Phase FSK
8
FSK Example
1 1 0 1
Data
FSK Signal
0 1 1
VCO
cos wct
x
01
a0
a1
modulated compositesignal
9
• complex envelope of BFSK is nonlinear function of m(t)• spectrum evaluation - difficult - performed using actual time averaged measurements
PSD of BFSK consists of discrete frequency components at• fc
• fc nf , n is an integer
PSD decay rate (inversely proportional to spectrum)
• PSD decay rate for CP-BFSK
• PSD decay rate for non CP-BFSK
f = frequency offset from fc
4
1
f
2
1
f
Spectrum & Bandwidth of BFSK Signals
10
Transmission Bandwidth of BFSK Signals (from Carson’s Rule)
• B = bandwidth of digital baseband signal
• BT = transmission bandwidth of BFSK signal
BT = 2f +2B
• assume 1st null bandwidth used for digital signal, B
- bandwidth for rectangular pulses is given by B = Rb
- bandwidth of BFSK using rectangular pulse becomes
BT = 2(f + Rb)
if RC pulse shaping used, bandwidth reduced to:
BT = 2f +(1+) Rb
Spectrum & Bandwidth of BFSK Signals
11
General FSK signal and orthogonality
• Two FSK signals, VH(t) and VL(t) are orthogonal if
0)()(0
dttVtVT
LH
• interference between VH(t) and VL(t) will average to 0 during demodulation and integration of received symbol
0)()(0
dttVtVT
LH
• received signal will contain VH(t) and VL(t)
• demodulation of VH(t) results in (VH(t) + VL(t))VH(t)
0)()(0
dttVtVT
HH
?
?
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))2(2cos())2(2cos( tftfT
Ec
b
b =
))(2cos())(2cos(2
tfftffT
Ecc
b
b vH(t) vL(t) =then
=bT
c
c
b
b
f
ft
f
tf
T
E
04
)4sin(
4
)4sin(
f
fT
f
Tf
T
E b
c
bc
b
b
4
)4sin(
4
)4sin(=
dtfttfT
EdttVtV
bT
cb
bT
LH 00
)4cos()4cos()()( and
vH(t) vL(t) are orthogonal if Δf sin(4πfcTb) = -fc(sin(4πΔf Tb)