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

3

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

7

)(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

13

14

15

16

• 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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18

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

24

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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28

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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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