Coherent Detection Primary Advantage Primary Disadvantage
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Transcript of 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
ECE 4710: Lecture #35 2
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
ECE 4710: Lecture #35 3
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
ECE 4710: Lecture #35 4
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
Non-Coherent OOK Detection
ECE 4710: Lecture #35 5
Non-Coherent OOK Detection
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
ECE 4710: Lecture #35 6
Non-Coherent OOK Detection
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/(
ECE 4710: Lecture #35 7
Non-Coherent OOK Detection
RicianRayleigh
When A / » 1 Rician PDF Gaussian PDF
ECE 4710: Lecture #35 8
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
ECE 4710: Lecture #35 9
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
ECE 4710: Lecture #35 10
Non-Coherent FSK Detection
“1”
“0”
For signal only at Rx input:
)"0"binary (0)()"1"binary (0)(
0
0
TtAtrTtAtr
Dual OOK RF Rx
0 Optimal
TV
ECE 4710: Lecture #35 11
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
Non-Coherent FSK Detection
ECE 4710: Lecture #35 12
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
Non-Coherent FSK Detection
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
ECE 4710: Lecture #35 13
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:
Non-Coherent FSK Detection
4for
21
0
)/(]2/1[ 0 pbNETBe
TBNEeP bp
)/( 0NEQP be
ECE 4710: Lecture #35 14
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
ECE 4710: Lecture #35 15
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
ECE 4710: Lecture #35 16
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
ECE 4710: Lecture #35 17
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
ECE 4710: Lecture #35 18
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