Link Parameters and Definitions
The parameters listed in Table 1 are used to describe the communication link. All parameters and
subsequent calculations are based on SI units. Parameter values for different link scenario
examples are given in Table 2.
Symbol
Pt
BR
At
r

d
AmbIrrad
RBG
dlens
tlens
view
Np
RD
Description
Time average optical transmission power
Bit rate
Diameter of transmitter aperture (collimating lens)
Link range
Transmission wavelength
Effective bandwidth of optical filter at the receiver
Ambient spectral irradiance near 
Reflectivity of background objects in receiver field of view
Diameter of receiver collection lens
Transmission of receiver optics (entire channel transmission is lumped into this
parameter).
Half angle of receiver field of view
Number of pixels in the entire imaging array
Responsivity of detection photodiode
Table 1 – Link parameter definitions
Based on optical diffraction limited by the diameter of the transmitter aperture, the peak optical
intensity along the axis of the transmission beam is given by1
2P   At 
Io  t 2 2 2
r
2
(1)
The factor of two assumes that on-off modulation (OOM) is used and that the transmission power
during an “on” period is equal to twice the average transmission power.
The half angle of the first null in the transmission beam, which is used as a basic measure of
transmission beam divergence, is given by
 null  1.22

At
(2)
Signal Strength
Assuming that active beam steering keeps the transmission beam aligned within the “half-width
half-max” angle, the worst-case intensity at the receiver is one half of the intensity along the
transmission axis, which is given by Equation 1. Also, in the worst case the transmitter is off the
optical axis of the receiver by view, reducing the effective collection area of the receiver as shown
below in Equation 3.
2
d 
Prec  I o    lens   cos( view )  t lens
 2 
1
2
(3)
Ideally, all of this power is focused onto a single photodiode, generating a signal current
isig  Prec  RD
(4)
Optical Noise Limit
The limiting theoretical noise factor is shot noise from the DC current in the photodiode at a
given pixel. This current consists of detected ambient light reflected from background objects in
the receiver field of view as well as leakage current in the photodiode. Leakage current is
typically on the order of femptoamps even in large area CMOS n-well diodes above room
temperature, and is negligible compared to the received ambient signal. Calculation of the
received ambient power proceeds as follows.
Background objects are modeled as Lambertian reflectors, meaning that the intensity of the
reflected light is proportional to the cosine of the angle relative to the surface normal. In the worst
case, the background normal is aligned with the optical axis of the receiver. In this case, the
background area within the field of view of a single pixel is
a pixel
2

r  2 view 

Np
(5)
The total ambient optical power reflected from this area (within the receiver filter bandwidth) is
PREFL  AmbIrrad  a pixel  RBG  d
(6)
AmbIrrad is typically the spectral irradiance of the sun at sea level at wavelength  when
considering the worst case.
The reflected optical power collected by the receiver is
2
PBG
P
d 
 REFL
   lens   t lens
2
r
 2 
(7)
Note that PREFL is proportional to r2, thus the collected background power is independent of the
link range. The impact of view and Np in Equation 5 provide the primary means of reducing
background noise without affecting signal strength. The DC photocurrent generated by the
collected ambient optical power is simply
I BG  PBG  RD
This DC photocurrent generates shot noise which has a uniform spectral density given by
(8)
2
i shot
 2  qe  I BG
f
(9)
where qe is the charge of an electron.
The minimum possible bandwidth of the receiver is approximately equal to one half the bit rate in
order to allow approximately three settling time constants per bit period. Assuming that the small
signal behavior of the receiver is that of a low pass filter with a single pole at one half the bit rate,
the effective noise bandwidth of the receiver is
NBW  12 BR 

(10)
2
and thus the total mean square shot noise current integrated over frequency is
2
ishot
 qe  I BG  BR 

(11)
2
Finally, the optically limited signal to noise ratio (SNR) of the received signal (in decibels) is
given by
2
 i
 isig

 sig


SNR  10 log
 20 log 
 i2 
 i2
 shot 
 shot




(12)
Communication Scenarios
Three communication scenarios are now evaluated based on the preceding derivations. In all
scenarios, it is assumed that simple n-well/substrate diodes are used as photodetectors. These
diodes offer the highest responsivity in a standard CMOS process by approximately an order of
magnitude, but practically limit communication to a few Mbps due to the slow collection of
carriers generated deep in the substrate. However, recently it has been shown that novel layout
can extend the bandwidth of these diodes to hundreds of Mbps at a cost of reducing their
sensitivity at least two fold2. Although power consumption may become the limiting factor in
high-speed, high-resolution imaging arrays, it should be possible to extend data rates to tens of
Mbps in the future. Of course, Equation 11 shows that operating at higher bit rates will
compromise the SNR. This can be mitigated by higher transmission power, shorter link range,
larger collection lens, etc.
The link parameters for the three scenarios are given below in Table 2. Key parameters that vary
between the scenarios appear in boldface.
Scenario 1 is the typical SALT communication scenario, where two cubic centimeter SALT
nodes are communicating over a 10 km link at 5 Mbps with 5 mW average optical power
transmission beams.
In scenario 2 two cubic millimeter “Smart Dust” motes are communicating with steered laser
beams. The small size of these motes prohibits use of a collection lens, so the receiver only has a
single element detector and a receiver aperture of 200 m.
In scenario 3 a single SALT node is transmitting to a low earth orbit satellite receiver. The
transmitter characteristics the same as those of the typical SALT node described in scenario 1.
However, the receiver is much farther away, but has a much larger collection lens available. The
calculations in this scenario would not be valid for ground-ground communication links where
atmospheric effects would become very significant.
In all three cases the 1 mm aperture of the collimating lens at the transmitter limits the beam
divergence. The value 0.8 W/m2nm for AmbIrrad is the spectral irradiance of the sun at sea level
near 830 nm.
Symbol
Pt
BR
At
r

d
AmbIrrad
RBG
dlens
tlens
view
Np
RD
Scenario 1
(typical SALT)
Scenario 2
(mote-mote)
Scenario 3
(long range)
5
5
1
10
830
10
0.8
0.3
15
0.5
30
3232
0.3
0.1
5
1
0.01
830
10
0.8
0.3
0.2‡
0.5
60
1
0.3
5
5
1
200
830
10
0.8
0.3
600
0.3
2
6464
0.3
Units
mW
Mbps
mm
km
nm
nm
W/m2nm
W/W
mm
W/W

A/W
Table 2 – Specifications for three communication scenarios.
Table 3 lists values derived for each scenario based on the preceding equations.
In the typical SALT scenario the worst-case signal and optically limited r.m.s. noise
currents are approximately 1.3 nA and 160 pA respectively. This provides a high enough
SNR for reliable communication. However, the electronic noise in the receiver must be
commensurate with the optical noise or the SNR will be degraded. Current receiver
designs have approximately 1-2 nA of rms noise current, which may be accommodated
for by reducing the link range to 3 km, for example.
In the second scenario (short range communication between Smart Dust motes) the
shorter communication range more than makes up for the reduced transmit power and
smaller receiver aperture, resulting in a somewhat larger signal current than in the
previous case. The smaller receiver aperture balances the lower array resolution to keep
the ambient photocurrent approximately the same. The result is a higher optically limited
SNR. In such a scenario, constraints on receiver power consumption may demand that the
electrical noise is much greater than the optical noise limit.
In the third scenario (communication from a SALT node or Smart Dust mote) the long link range
is compensated by the availability of a large collection lens at the receiver to achieve adequate
signal strength. The large lens also increases the collected ambient light power. However, using a
high resolution imaging array and a much smaller field of view reduces the ambient light power.
If a smaller lens were used, the optically limited SNR wouldn’t change, but the very low signal
strength would place a much stricter requirement on electrical noise in the receiver.
Scenario 1
(typ. SALT)
Scenario 2
(mote-mote)
Scenario 3
(long range)
Units
1.14
1.01
4.36
1.31
1.07105
257
72.3
21.7
2.28103
1.01
8.95
2.69
439*
1.05*
52.6*
15.8*
1.1410-3
1.01
20.1
6.02
4.76104
114
128
38.6
mW/m2
mrad
nW
nA
m2
kW
nW
nA
Optical RMS shot noise
0.165
0.141*
0.220
nA
Optically limited SNR
18.0
25.6
28.8
dB
Symbol Description
Io
null
PREC
isig
apixel
PREFL
PBG
IBG
2
i shot
SNR
Peak intensity at receiver
Beam null half angle
Worst case received power
Worst case received current
Area in f.o.v. of one pixel
Reflected BG power
Received BG power
Ambient photocurrent
Table 3 – Derived values for the three communication scenarios described in Table 2
*
These values are pessimistic. The equations used assume that background power is
reflected to the receiver along the surface normal. In this case, a single pixel views a
wide angle, and a large fraction of received background power was reflected off the
surface normal, where the reflection intensity is lower.
Max Born and Emil Wolf, Principles of Optics, 7th (expanded) edition, 1999, University Press,
Cambridge, pg. 440.
1
C. Rooman, D. Coppée, and M. Kuijk, “Asynchronous 250-Mb/s Optical Receivers with Integrated
Detector in Standard CMOS Technology for Optocoupler Applications,” IEEE Journal of Solid-State
Circuits, vol. 35, no. 7, July 2000.
2