coherent techniques

7/30/2019 Coherent Techniques

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@G. Gong 1

A. Noncoherent Orthogonal Modulation

Scheme. For a binary signaling scheme that involves the use of twosignals

T t t st s 0),(),( 21which are orthogonal with equal energy,

let T t t gt g 0),(),( 21

denote the phase-shifted version of , res. , whichremain orthogonal and of equal energy. This scheme is referred to asnoncoherent orthogonal modulation .

)(),( 21 t st s

3. Noncoherent Binary Modulation Techniques

A digital communication receiver with no provision make for carrier phaserecovery is said to be noncoherent.


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At the receiver, the received signal x(t ) can be expressed as follows

+

+=T t t st nt g

T t t st nt gt x

0sent,)( ),()(

0sent,)( ),()()(

22

11

The receiver tries to discriminate between s1(t ) and s2(t ),regardless of the carrier phase. This goal can be achieved by thefollowing receiver structure:

)( t x Comparisondevice

1l

)( choose

If

)( choose

If

2

21

1

21

t s

ll

t s

ll

Figure 1. Binary receiver for noncoherent orthogonal modulation

Matchedto 1(t )

Envelopedetector

2lMatchedto 2(t )

Envelopedetector

Sampleat t = T

Sampleat t = T


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An noncoherent matched filter may be viewed as being equivalent to aquadrature receiver, as illustrated below. The quadrature receiver itself hastwo channel (recall that QPSK receiver).

)(t x

)(t i

T dt 0

T dt 0

+ Squarerooter2il

Let 1(t ) and 2(t ) be the orthonormal set of s1(t ) and s2(t ) and be theversion of that results from shifting the carrier phase by -90degrees . The quadrature receiver is shown in Figure 2 where i = 1, 2.

In-phase channel

Qradrature channel

)(~ t i

)(t i

Square-law

device

Square-lawdevice

2

Ii x

2Qi x

Figure 2)(

~t i


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Remark. The average probability of error for thenoncoherent receiver, Figure 1, or equivalentlyFigure 2, is given by a simple formula

=

02exp

21

N E

Pe

where E is the signal energy per symbol and N 0 /2 is the noisespectral density. We list this result here without proof. Theproof can be found the text book.

(1)


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B. Noncoherent BFSK

For the binary FSK case, the transmitted signal is

2,1 0 ),2cos(2

)( == iT t t f T E

t s bib

bi 2,1 ,integer, ==

+= inT

in f c

b

ci

i.e.,

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11

frequencyusing)(0

frequencyusing )(1

f t s

f t s

Thus the noncoherent binary FSK is a special case of noncoherentorthogonal modulation with and , where T b is the bitduration and E b is the signal energy per bit. From (1), we have the averageprobability of error (bit error rate) for noncoherent BFSK is

bT T = b E E =

=

02exp

21

N E

P be


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)(t xComparison

device

1l

0 choose

If

1 choose

If

21

21

ll

ll

Figure 3. Noncoherent receiver for BFSK

Matched to Envelopedetector

2lEnvelopedetector

Sampleat t = T b

Sampleat t = T b

t f T b 12cos / 2

bT t 0

Remark. When comparing the error performance of noncoherent FSK with

coherent PSK, it is seen that for the same P e, noncoherent FSK requiresapproximately 1 dB more E b / N 0 than does BFSK (for ) , becausecoherent reference signals need not be generated. Therefore, almost all FSKreceivers use noncoherent detection. In the following, we will see that thesame phenomenon occurs for noncoherent DPSK and PSK.

410eP

Matched tot f T b 22cos / 2

bT t 0


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}{ k b 1 1 0 1 0 1 1 0 0 1

Table 1. Illustrating the generation of DPSK signal

index k : 0 1 2 3 4 5 6 7 8 9 10

Differentiallyencodedsequence

}{ k d ref. bit 1 1 1 0 0 1 1 1 0 1 1 k k k bd d = 1

Correspondingphase shift

)}({ k 0 0 0

Decisiondevice

bT dt

0

Delay

T b

)(t r k b

DPSK Receiver (differentially detection)


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Remark. 1. DPSK is an another example of noncoherent orthogonal modulation, when it is

considered over two bit intervals. In this case, from (1)we get the average probability of error for DPSK is

=

0

exp21

N E

P be

since T = 2 T b and E = 2 E b. Thus, for the same P2, DPSKrequires approximately 1 dB more Eb/N0 than doesBPSK.

2. It is easier to implement a DPSK system that a BPSK(or general M-ary PSK), since the DPSK dose not needphase synchronization (but less efficient than PSK).


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Remark. When comparing the error performance of (2) withthat of coherent PSK, it is seen that for the same P e, DPSKrequires approximately 1 dB more E b / N 0 than does BPSK

(for ). It is easier to implement a DPSK system thana PSK system, since the DPSK receiver does not need phasesynchronization.

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coherent techniques

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