©1997 BG Mobasseri 3 04/20/23
NONCOHERENT DETECTION
Handling Phase Sync Problems through
Differential Encoding
©1997 BG Mobasseri 4 04/20/23
PHASE SYNCHRONISM
Coherent detection requires precise phase
sync between the received signal and local
oscillator.
Ak cos ωct+θk( )
Ac cos ωct+θc( )
AkAc cos θk−θc( )LPF
phase error
©1997 BG Mobasseri 5 04/20/23
DIFFICULTY ESTABLISHING ABSOLUTE PHASE REFERENCE
What is the phase of the RF pulse seen on the
scope?
©1997 BG Mobasseri 6 04/20/23
CONVENTIONAL ENCODING
Take a 4-phase modulation, known as
Quadrature Phase Shift Keying(QPSK)
90
180
270
000
01
10
11
Es cos 2πfct( )
Escos2πfct+π2
⎛ ⎝
⎞ ⎠
Escos2πfct+π( )
Escos2πfct+3π2
⎛ ⎝
⎞ ⎠
©1997 BG Mobasseri 7 04/20/23
DIFFERENTIAL ENCODING
Although the absolute phase of the incoming
signal varies, by as much as 50o, phase
transitions across symbols are very stable
Instead of mapping symbols into absolute
phases, they are encoded by phase
transitions
©1997 BG Mobasseri 8 04/20/23
MAPPING DATA TO PHASE CHANGES: BINARY EXAMPLE
Data is encoded such that a digit 1 causes a
180 phase shift relative to the previous phase
but 0 causes no phase shift
Receiver will in turn look for phase changes
rather than absolute phases
©1997 BG Mobasseri 9 04/20/23
DIFFERENTIAL ENCODING FOR BPSK
Encode 1 0 1 1 0 1 in BPSK and differential
PSK (DPSK)
π
1 0 1 1 0 1
π π πPSK
phase
phase(reference
π
1 0 1 1 0 1
DPSK
π π
©1997 BG Mobasseri 10 04/20/23
DECODING
1 0 1 1 0 1
πphase change
symbol
Data
π π π
1 0 1 1 0 1
DPSK
π πphase
©1997 BG Mobasseri 11 04/20/23
QPSK WITH GRAY CODING
0 0.5 1 1.5 2 2.5 3 3.5 4-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1absolute phase: 0,90,180,270 - 00 01 11 10
00->001->9011->18010->270
00 01 11 10
©1997 BG Mobasseri 12 04/20/23
DQPSK
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Differential QPSK : 11 01 11 10
bits change00 001 9011 18010 270
11 01 11 1090
arbitrary ref.
270 0 180 90
©1997 BG Mobasseri 14 04/20/23
A BIT OF HISTORY
Early modems designed in the 1950’s used
Frequency Shift Keying(FSK) at 300 bps over
public switched phone lines
In the 1960’s equalized bandwidth increased
to 2400Hz thus allowing bit rates of 2400 bps.
©1997 BG Mobasseri 15 04/20/23
FIRST MILESTONE:V.26
The first 2400 bps modem was made available
in 1962 using 4-PSK (actually, differential
PSK, DPSK)
This was followed in 1967by 8-DPSK at 4800
bps
Note that to achieve higher rates, one has to
go to larger constellation sizes:
BM-ary=Bbinary/logM=4800/3=1600 Hz
©1997 BG Mobasseri 16 04/20/23
BAUD vs. BITS
Baud is the number of symbols/sec.
Bauds and bits are related by logM, where M
is the number of modulation levels– R=Rb/logM
Commercial modems are rated by bits/sec
even though the box says “baud”
©1997 BG Mobasseri 17 04/20/23
9600 bits/sec: V.29/V.32
The first 9600 bps modem was introduced in
1976 using 16-QAM constellation
Baudrate=bandwidth=2400 Hz
Requires adaptive channel equalization to
reduce intersymbol interference
©1997 BG Mobasseri 18 04/20/23
QAM MODEMS
All modern modulation techniques used in
modems are based on the Quadrature
Amplitude Modulation (QAM) method
16-QAM
©1997 BG Mobasseri 19 04/20/23
NON-DIFFERENTIAL GRAY CODING
01010001
0000 0100
1101 1001
1100 1000
1110
1111
1010
1011
0010 0110
0011 0111
©1997 BG Mobasseri 20 04/20/23
L-fold AMBIGUITY
An L-fold rotationally symmetric constellation
maps onto itself for a rotation of +/-K.(2pi/L)
The receiver is unable to resolve a number of
possible carrier lock positions
00
01
10
1100
01
10
11
©1997 BG Mobasseri 21 04/20/23
DIFFERENTIAL QAM
Divide the signal space into L equal pie-
shaped sectors
For 16-QAM, L=4, differentially Gray encode
sectors by 00, 01, 11, 10
Gray encode the remaining 2 bits within each
sector.
©1997 BG Mobasseri 22 04/20/23
DQAM CONSTELLATION
00010011
0010 0000
0111 0101
0110 0100
1111
1110
1101
1100
1011 1001
1010 1000
©1997 BG Mobasseri 25 04/20/23
ENCODING THE REMAINING 3 BITS
The remaining 3 bits are differentially Gray
coded:
Q2 Q3 Q4 Phase Change
0 0 1 0
0 0 0 45
0 1 0 90
0 1 1 135
1 1 1 180
1 1 0 225
1 0 0 270
1 0 1 315
©1997 BG Mobasseri 26 04/20/23
FALL BACK RATE
If conditions demand, transmission falls back
to 8-QAM at 7200 bps. Bit Q1 is permanently
set to zero limiting the amplitudes.
0
90
180
270
45135
225 315
33
3
2
32
©1997 BG Mobasseri 27 04/20/23
V.33
V.33 is a transmission standard at 14,400 bps.
Modulation is 128-QAM constellation
Carrier frequency is 1800 Hz.
Signaling rate is 2400 baud.
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