Baseband Modulation Techniques - Air University
Transcript of Baseband Modulation Techniques - Air University
Baseband Modulation Techniques
Non-coherent Detection
Lecture 08
4.5.1 Detection of Differential PSK
• DPSK refers to a detection scheme classified as noncoherent because it does not require a reference in phase with the received carrier
• Therefore, if the transmitted waveform is:
• The received signal can be characterized by:
α is an arbitrary constant ; assumed to be uniform random variable distributed between 0 and 2π
n(t): AWGN process
Mi
Tttt
T
Ets io
si
,....1
0)](cos[
2)(
Mi
Tttntt
T
Etr io
s
,....1
0)(])(cos[
2)(
2
• If we assume that α varies slowly relative to two period times (2T), the phase difference between two successive waveforms θj(T1)and θk(T2) is independent of α;
• Basis for differentially coherent detection of differentially encoded PSK (DPSK) is:
– Carrier phase of previous signaling interval is used as phase reference for demodulation
– It requires differentially encoded message signal at the transmitter since information is carried by difference in phase between successive waveforms
)()()()()( 21212 TTTTT ijkjk
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4.5.2 Detection of Binary PSK• Binary DPSK is regarded as the non-coherent version of binary PSK
• Data is encoded in the phase shift between successive symbols rather than the actual value of the phase
• The Basic Idea of DPSK
– If ak = 0, then shift carrier phase by 180o
– If ak = 1, then no shift in carrier phase
• In DPSK, the carrier phase of the previous data bit can be used as a reference
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Sample Index,k 0 1 2 3 4 5 6 7 8 9 10
Information Message, ak 1 1 0 1 0 1 1 0 0 1
Differentially Encoded
message (first bit
arbitrary), dk
1 1 1 0 0 1 1 1 0 1 1
Corresponding phase
shift, θk
0 0 0 π π 0 0 0 π 0 0
Differential Data Encoding
kkk add 1
kkk add 1
Encoding Scheme
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Sample Index, k 0 1 2 3 4 5 6 7 8 9 10
r(k) 1 1 1 0 0 1 1 1 0 1 1
1 1 0 1 0 1 1 0 0 1
Sample Index, k 0 1 2 3 4 5 6 7 8 9 10
r(k) 0 0 0 1 1 0 0 0 1 0 0
1 1 0 1 0 1 1 0 0 1
)(ˆ ka
1ˆ
kkk rra
Decoding Scheme
Advantage • Phase ambiguity can be resolved• Non-coherent detection techniques can be used
)(ˆ ka
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)(ˆ ka
Sample Index,k 0 1 2 3 4 5 6 7 8 9 10
r(k) 1 1 1 1 0 1 1 1 0 1 1
1 1 1 0 0 1 1 0 0 1
2-bits in error
Drawback of Differential Encoding/Decoding:
• When single bit errors occur in the received data sequence due to noise, they tend to propagate as double bit errors
• Since the decoder is comparing the logic state of current bit with previous bit, and if the previous bit is in error, the next decoded bit will also be in error
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Demodulation of DPSK
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Differentially Encoded PSK (DEPSK) Modulation Different from DPSK, as ak encoded differentially but coherently detected The encoded sequence {dk} is used to phase-shift a carrier with phase
angle 0 and π representing symbols 1 and 0 respectively
Method for the detection of DEPSK Coherent detection of PSK followed by differential decoder (dk is
equivalent to rk in the previous slides)
This scheme is used to account for the sometimes 180 phase shift by PLL 10
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Two dimensional modulation (M-QAM)
• M-ary Quadrature Amplitude Mod. (M-QAM)
ici
i tT
Ets cos
2)(
tT
ttT
t
Mitatats
cc
iii
sin2
)( cos2
)(
,,1 )( )()(
21
2211
12
)(1 t
)(2 t
2s1s 3s
4s“0000” “0001” “0011” “0010”
6s5s 7s 8s
10s9s 11s 12s
14s13s 15s 16s
1 3-1-3
“1000” “1001” “1011” “1010”
“1100” “1101” “1111” “1110”
“0100” “0101” “0111” “0110”
1
3
-1
-3
16-QAM
• A MQAM signal can be considered as the sum of two 𝑀 −ASK signals along I and Q branches
I Branch ASK mapping
00 -3
01 -1
11 1
10 3
Q Branch ASK mapping
00 3
10 1
11 -1
01 -3
Two dimensional modulation (M-QAM)
I Branch ASK mapping
00 -3
01 -1
11 1
10 3
Q Branch ASK mapping
00 3
10 1
11 -1
01 -3
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• Coherent detection of M-QAM
T
0
)(1 t
ML detector1z
T
0
)(2 t
ML detector
)(tr
2z
m̂Parallel-to-serialconverter
s) threshold1 with (CompareM
s) threshold1 with (CompareM
Two dimensional modulation (M-QAM)
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4.7.2 Probability of Bit error for coherently detected Differentially Encoded BPSK
00
21
22
N
EQ
N
EQP bb
B
Fig 4.25
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4.8 M-ary Signaling and Performance
4.8.1 Ideal Probability of Bit Error Performance
• Typical probability of error versus Eb/N0 curve has a waterfall like shape
• The ideal curve displays the characteristics as the Shannon limit
• The limit represents the threshold Eb/N0 below which reliable communication cannot be maintained
• Ideal Curve:
– For all values of Eb/N0 above the Shannon limit of -1.6db, PB is zero
– Once Eb/N0 is reduced below the Shannon limit, PB
degrades to worse case value of ½ 20
Figure: 4.27 Ideal PB versus Eb/N0
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4.9 Symbol Error Performance For M-ary Systems
4.9.1 Probability of Symbol Error for MPSK
• For large energy to noise ratios, the symbol error performance PE(M), for equally likely, coherently detected M-ary PSK signaling:
where PE(M) : is the probability of symbol error
Es=Eb(log2M) : is the energy per symbol
M=2k : is the size of the symbol set
• Symbol error performance for Non-coherent detection of M-ary DPSK (for large Eb/N0) is :
MN
EQMP s
E
sin
22)(
0
MN
EQMP s
E2
sin2
2)(0
22
Figure 4.35: Symbol
error probability for
coherently detected
multiple phase
signaling
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4.9.2 Probability of Symbol Error for MFSK
• The symbol error performance PE(M), for equally likely, coherently detected M-ary orthogonal signaling can be upper bounded as:
where:
Es = Eb(log2M): is the energy per symbol
M: is the size of the symbol set
• The symbol error performance PE(M), for equally likely, non-coherently detected M-ary orthogonal signaling is:
0
)1()(N
EQMMP s
E
02exp)
2
1()(
N
EMMP s
E
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Figure 4.36: Symbol error probability for coherently detected M-ary
orthogonal signaling25
Figure 4.37: Symbol error probability for noncoherently detected M-ary
orthogonal signaling26
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Assignment 04
• Chapter 4
• Problems: 4.1, 4.2, 4.3
• Deadline: Monday, 13th August, 2018
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Quiz 04
• Lecture 07
• Monday, 13th August, 2018
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