coherent detection primary advantage primary disadvantage

ECE 4710: Lecture #35 1

Coherent Detection Primary Advantage

Has better BER for same Eb / N0 compared to non-coherent detection

OR Has lower Eb / N0 for same BER compared to non-coherent detection

Primary Disadvantage Coherent reference signal must be derived from noisy signal at Rx input

» Complex & expensive circuitry» Noisy reference signal means BER formulas are best case

Actual performance is slightly worse Many applications choose non-coherent detection for simplified circuitry

and lower cost» Sacrifice Eb / N0 for lower cost/reduce complexity circuitry


Non-Coherent Detection

Non-Coherent Rx Circuitry Simple & cheap No carrier recovery for coherent reference Widely used for OOK and BFSK modulation methods

» Non-coherent OOK Rx is most widely used method in fiber optic communication systems

Can’t be used for BPSK, QPSK, OQPSK, QAM carrier recovery required for measurement of absolute phase of Rx signal

BER equations Derivation much more complicated than coherent detection


Non-Coherent OOK Detection

Bandpass Filter : 1) Filter BW = Bp must be large enough to capture most of signal power to preserve signal waveshape (envelope) at output, 2) Eliminate noise PSD outside of signal BW output noise, n(t), will be bandlimited gaussian noise

Envelope Detector : Replaces product detector in coherent Rx no carrier reference and synchronization circuitry needed

Sample & Hold + Threshold Device : Same function as in coherent Rx


OOK Bandpass Waveforms

Received Signal + Noise

Bandpass AWGN represented by

)"0"binary (0,0)()"1"binary (0,)2cos()(

2

1

TttsTttfAts c

)"0"binary (0,)()()"1"binary (0,)()2cos()(

2

1

TttntrTttntfAtr c

)2sin()()2cos()()( ncnc tftytftxtn

n uniformly distributed random phase




BER for equally likely 1’s and 0’s

What are conditional PDF’s at output of envelope detector??

For s2 the input to envelope detector is only bandlimited AWGN “noise only” case Output “noise only” PDF has a Rayleigh distribution

T

T

V o

V

oe drsrfdrsrfP 0201 )|(21)|(

21

0 for )|( )2/(2

020

220 rersrf r

Envelope detector output is always

positive



For s1 the input to envelope detector is sinusoidal bandpass signal + bandlimited AWGN Signal + noise case PDF is Rician

2 is variance of noise PDF at input to envelope detector

Io(A) modified Bessel function (zero order)» Io(A) = 1 for A = 0 Rician PDF reduces to Rayleigh when no signal

is present noise only

0 for )|( 20

0)2/()(

20

10

2220

rArIersrf Ar

pp BNBN 002 2)2/(



RicianRayleigh

When A / » 1 Rician PDF Gaussian PDF


Non-Coherent OOK BER

Bit Error Rate is

Cannot be solved in closed form Using A / » 1 an approximate solution can be found

or

T

T

V

rV Are drerdrArIerP 0

)2/(2

002

00

)2/()(2

0 220

2220

21

21

1 for 21 )8/( 22

AeP A

e

4for

21

0

)/(]2/1[ 0 pbNETBe

TBNEeP bp


Non-Coherent FSK Detection

FSK Signal Spectrum“1”“0”

Bandpass Filter BW = 2B = 4R Main lobe + 1st sidelobe Envelope detector produces waveshape that is rectangular



“1”

“0”

For signal only at Rx input:

)"0"binary (0)()"1"binary (0)(

0

0

TtAtrTtAtr

Dual OOK RF Rx

0 Optimal

TV


Assume a “1” is transmitted s1 Upper channel input is signal energy + bandlimited

AWGN Output PDF of envelope detector is Rician

» Same as OOK with signal “On” “1”

Lower channel input is bandlimited AWGN only Output PDF of envelope detector is Rayleigh Lower channel Rayleigh noise added to upper channel

signal + noise Effectively doubles noise power compared to OOK



For OOK the average energy per bit is

Note that for “1” bit

For FSK the average energy per bit is

Twice the bit energy compared to OOK


40

221 22 TATAEb

“1” “0”

22221 222 TATATAEb

“1” “0”

dttfAdttfAET

c

T

cb 0

2

0

22 )4cos(1)2(cos2

1

2|)4sin(

21|

21 2

2200

TAtfAtAETT

cb


FSK vs. OOK Double the noise power and Double the signal power BER vs. Eb / No performance is the same!!

Non-coherent FSK BER is the same as non-coherent OOK BER

Note that coherent FSK and coherent OOK also had same BER for matched filter case:


4for

21

0

)/(]2/1[ 0 pbNETBe

TBNEeP bp

)/( 0NEQP be


BER vs. Eb / N0

CoherentOOK & FSK

Non-CoherentOOK & FSK

For Pe < 10-3 Non-cohererntOOK & FSK

require only 1 dB more than coherent

OOK &FSK1 dB

Non-cohererntOOK & FSK require 4 dB

more than coherentBPSK & QPSK

BPSK orQPSK


OOK & FSK Rx

Coherent OOK and FSK require carrier recovery & synchronization circuitry Complexity adds significant cost to Rx Only gives 1 dB improvement for BER vs. Eb / N0

Almost all OOK and FSK Rx’s are non-coherent Reduced cost/complexity relative to coherent Rx Only small difference in BER performance

Coherent Rx : BPSK/QPSK has significantly better performance (3 or 4 dB) compared to OOK/FSK Use complexity and $$ for better performance


DPSK Detection

Coherent Rx required for BPSK & QPSK Differentially encoded BPSK DPSK can be

detected using partially coherent Rx Partially Coherent?

» **No carrier recovery circuitry**» Use 1-bit period delayed version of incoming Rx signal to provide

reference signal for product detector» Tx carrier oscillator must be stable from one-bit period to next

Delayed carrier input to product detector able to detect phase change (not absolute phase value) Input data must be differentially encoded


DPSK Detection

For optimal detection bandpass matched filter BER is Much better than OOK or FSK Only slightly worse than BPSK & QPSK ( 1 dB)

DPSK widely used since BER is almost as good as BPSK but no carrier recovery circuitry is required

Effectively a compromise between noncoherent OOK/FSK and coherent BPSK/QPSK

)/(21 0NE

ebeP


BER vs. Eb / N0

CoherentOOK & FSK

Non-CoherentOOK & FSK

For Pe < 10-3 DPSK requires

only 1 dB more than

BPSK or QPSK1 dB

DPSK has3 dB better

Eb / No comparedto non-coherent

OOK/FSK

BPSK orQPSK

DPSK

coherent detection primary advantage primary disadvantage

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