Noise and detection: A binary intensity receiver

1
Noise and detection A binary intensity receiver
Received SignalNoise
1
Opt. BPF
El. LPF
PD
h(t)
0

• Noise is additive in the optical domain
• Signal phase information is lost
• In principle, multi-level signals can be
  recovered by introducing multiple thresholds

2
Noise and detection Commentaries

• In principle, optimal detection could be achieved
  with matched filtering in the optical domain.
• In reality, due to technological constraints,
  matched optical filtering is not easily
  achievable and most of the filtering occurs in
  the electrical domain.
• Thermal noise at the receiver is negligible
• Useful analytical approximations

• Optical bandwidth much larger than electrical B
  gtgt Be so that the optical filter does not affect
  the data signal, but only limits the noise.
• Integrate and dump electrical receiver h(t) so
  that the

decision is made on the basis of
, which is the optical energy
within the symbol interval
3
Noise and detection An integrate and dump
receiver
1 or 0
The transmitted signal
Generic, well defined pulses with no ISI
Individual bit detection
4
Noise and detection Error-rate analysis
Degrees of freedom (DOF) and the sampling theorem
(Shannon) The number of orthogonal complex
waveforms that are contained in a time interval T
and whose spectrum is contained in a frequency
interval B, is limited to BT.
A set of BT orthogonal complex functions
Since
and since
is still approximately white
,
so that nk is a Gaussian variable with a variance
equal to the spectral density of n(t) and sk is
the component of the clean waveform along the
base function
D. Slepian and H.O. Pollak, The Bell System
Technical Journal, p.43, January 1961
5
Noise and detection Error-rate analysis
Consequently
The probability distribution of V is well
known1 When a zero is transmitted, sk 0, V is
a Central Chi square variable with 2BT DOF When a
one is transmitted V is a Non-central Chi
square variable with 2BT DOF
Abramowitz and Stegun, Handbook of Mathematical
Functions
6
Noise and detection Error-rate analysis and the
Q factor
0.8
zero
0.6
Probability density
one
0.4
0.2
0
Vth
0
5
10
15
V
The threshold is set at the crossing point and
the Error-rate is ½ times the shaded area
Q factor is defined by the error-rate
Often expressed in dB
7
Noise and detection Error-rate and the Gaussian
approximation
0.4
0.8
BT2
BT10
0.3
0.6
Q 4dB
0.2
Probability density
0.4
(Q-QGauss) dB
0.1
0.2
0
-0.1
0
0
5
10
15
20
25
0
5
10
15
V
Q dB
Although distributions and threshold values are
significantly different the error probabilities
are remarkably similar1
Another good approximation is given by
P.B. Humblet and M. Azizoglu, J. Lightwave
Technol. Vol. 9, p.1576, 1991