Multi-Element Array Antennas for
Free-Space Optical (FSO) Networks
Node 1 Node 2
Node 1
D/N
D
…
Repeater 1 Repeater 2 Repeater N-1
Node 2
Jayasri Akella, Murat Yuksel, Shiv Kalyanaraman
Rensselaer Polytechnic Institute (RPI), ECSE akellj@rpi.edu
, yuksem@ecse.rpi.edu
, shivkuma@ecse.rpi.edu
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
1

 Background and Motivation
 Introduction to free-space optical communication using 2-dimensional arrays
 Inter-channel interference in 2-dimensional arrays
 Channel capacity between arrays
 Bandwidth-Volume product
 Audio Mixing Experiment with a 2-Channel FSO system
 Conclusions
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
2





Why FSO Arrays?
High aggregate bandwidth: spatial reuse (multiplexing space): ~ to RF-MIMO
Link robustness due to spatial diversity leverage & spatial channel coding
Optical transceivers are capable of operating at bandwidths greater than 100 Mbps.
 With each transceiver operating at a speed of 100 Mbps, a 10
×
10 array will give 10 Gbps in aggregate capacity.
 Use inexpensive off –the-shelf opto-electronic components
But… cross talk due to inter-channel interference
Node 1
Rensselaer Polytechnic Institute
D
3
Node 2
Shivkumar Kalyanaraman




Lateral distance ‘ Y, from the axis of the laser beam
Horizontal distance ‘ Z’
Received Intensity here is given by I(Y).
I ( Y )

I
0 e
 2 Y
2

( Z )
2
 Thus intensity drops off exponentially with Y .
 => motivation to closely pack transceivers on the 2-d array.
Rensselaer Polytechnic Institute
4
Shivkumar Kalyanaraman

Rensselaer Polytechnic Institute
5
Shivkumar Kalyanaraman

2-Dimensional FSO Arrays: Parameters
 Parameters of the array:
 Package density of the optical transceivers ‘ ρ ’
 Distance between the arrays ‘ d ’
 Angle of the transceiver
‘ θ ’
Rensselaer Polytechnic Institute
6
Shivkumar Kalyanaraman

2-D FSO arrays (contd)
 Consider the transmission from the transceiver T
0
T A
0 to T
0 on the array A, on the array B, T B
0
 A cone from the transceiver T A
0 onto the array B defines field of view.
 The cone not only covers the intended receiver T B
0
, but also
T B
1
, T B
2
, T B
4
, T B
7
.
=> possible interference, cross-talk r
 d tan

Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
7

2-D FSO arrays (contd)
 Similarly T B
0 receives the signal from T A
1
, T A
2
, T A
4
, T A
7
.
=> potential interferers .

For ‘
N
’ interferers, cross talk occurs at T B
0 if the intensity from them exceeds I
T
.
 Because the intensity across the laser is Gaussian distributed, all the potential interferers may not be contributing to cross talk.
Rensselaer Polytechnic Institute
8
Shivkumar Kalyanaraman

 

Rensselaer Polytechnic Institute
9
Shivkumar Kalyanaraman

Inter-channel interference in 2-dimensional arrays
 Define a lateral distance on the array
Y
T st.
I
Y
T

I
T
 The transceivers on the array must be spaced more than .
T
 I
T
1
2
I
0
;



Distance is 100 meters,
Transceiver angle of 1 mrad
=>
Y
T is about 40 cms.
 => We cannot pack the optical transceivers too closely on a compact array.
Rensselaer Polytechnic Institute
10
Shivkumar Kalyanaraman

 Let the spacing on the arrays be
Y
Sep

Y
T
 Let there be N potential interferers for the transceiver T B
0
 Crosstalk occurs at T B
0 when
NI
Y
Sep

I
T
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
11

 Interference happens when a subset of these potential interferers transmit when T A
0 is transmitting. The probability that such an event occurs gives the error probability due to crosstalk.
p e

( 1


 
 r
Y
Sep  j

 
 p
0

Y
Sep
2
 j
2 
( j

1 )
2

) p
0
 Where p
0 is the probability that a ZERO is transmitted.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
12

Package density (

)

=> Error Probability

But, distance (d)
 allows
 package density (

)
Rensselaer Polytechnic Institute
13
Shivkumar Kalyanaraman

Tighter beams (
 divergence angle

) =>
 package density

Rensselaer Polytechnic Institute
14
Shivkumar Kalyanaraman



Error due to inter-channel interference occurs only when a
ZERO is being transmitted by T A
0 to T B
0
, so the interference channel is asymmetric. [ON/OFF Keying]
Thus, the cross talk for the channel between two arrays can be modeled as a Binary Asymmetric Channel (BAC).
0
1-p e p e
X
1
Y
0
1
1
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
15

 The capacity of such a BAC is given by
C
 max p ( x )
H ( p
0
.
p e
)
 p
0
H ( p e
)
 The maximizing input distribution can be found by plotting the above for various p e.
Rensselaer Polytechnic Institute
16
Shivkumar Kalyanaraman

The capacity of array drops with increasing package density.
The drop is more rapid at larger distances.
Rensselaer Polytechnic Institute
17
Shivkumar Kalyanaraman

The capacity of arrays drops with package density and divergence angle of the transceivers.
Rensselaer Polytechnic Institute
18
Shivkumar Kalyanaraman

All is not gloomy…


Though per-channel capacity decreases with (
 package density,
 distance and
 divergence angle)…
For specific points on the capacity curve, …
 … the aggregate capacity of array is higher than a single channel
 Example:
 5 channel array, each channel @ 100 Mbps => an aggregate bandwidth of 0.5 Gbps.
 In same space, 10 channels, each operating at 3/4 ths of its capacity and with an aggregate bandwidth of 0.75 Gbps.
 We introduce a metric to measures the effectiveness of the 2-D array: “
Bandwidth-Volume Product
”.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
19

 We define the performance of an FSO communication channel by three design parameters:



Number of channels per array
The capacity of each of the channel in bits per second (determined by packing density, distance, angle etc)
The distance over which the arrays can communicate with that capacity.

BVP is similar to the “Bandwidth-Distance Product” metric of a fiber-optic link.


In a fiber-optic link, the fiber dispersion adversely effects the aggregate capacity, …
… whereas in the multi-channel FSO link, it is interference
& cross-talk
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
20

Bandwidth-Volume Product vs Package density and
Inter-Array Distance
Rensselaer Polytechnic Institute
21
Shivkumar Kalyanaraman

 BVP is a useful metric that integrates all the design parameters of the multielement 2-D array system.
 The curve (BVP vs package density) gives us design guidance regarding which parameters to choose for the 2-D array communication.
 For example, for a 200 meter range,
 the optimal package density
 ~25 channels per square meter (2.5Gbits),

… at a transceiver angle of 1.5 m rad.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
22

a) Two transmitters on different channels
Rensselaer Polytechnic Institute
23 b) Single receiver and circuit for both the channels
Shivkumar Kalyanaraman

Rensselaer Polytechnic Institute
24
Shivkumar Kalyanaraman

Rensselaer Polytechnic Institute
25
Shivkumar Kalyanaraman

 2-dimensional arrays give an very good bandwidth performance over short range (100s of meters) free-space optical communications.
 To use these arrays over long distances outdoors, very narrow beams coupled with auto-aligning mechanisms are needed.
 We are experimenting with new optical (hardware) modules to manage the critical 2-d array parameters
 Multi-hop transmission is a natural way to extend range.
 Bandwidth-Volume product is a useful metric that provides design guidance on the optimal implementation of the 2-D arrays.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
26

Students:
Jayasri Akella, sri@networks.ecse.rpi.edu
Dr. Murat Yuksel (post-doc): yuksem@ecse.rpi.edu
Ps: Online free videos of all my advanced networking classes
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
27

Rensselaer Polytechnic Institute
28
Shivkumar Kalyanaraman

A typical FSO communication system
 Free-space as medium of transmission
 ON OFF keying digital modulation of the light beam at the transmitter.
 The receiver is a threshold detector. Outputs a ONE if the received intensity I > I
T
, and a pre-set threshold intensity level.
ZERO if I < I
T
. where I
T is
 Typically duplex communication
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
29

Inter-channel interference continued
 We define the package density for which there is o no crosstalk such that

Y
2
T

0

1

  potential interferers
” for a

N
 πρr 2
πρ
 d tan
θ

2
 N transceivers, includes T A
0 interferers for T B
0.
Rensselaer Polytechnic Institute
30 and N-1 potential
Shivkumar Kalyanaraman





Let us assume that these N-1 transceivers are distributed along J circles around T A
0
. We can calculate the error probability in terms of each of these
J circles either being ON (transmit a ONE) or OFF (transmit a ZERO).
The number of circles for a transceiver spacing of Y
Sep is given by
J



 r
Y
Sep
The radius of the j th circle r j r
 jY
The number of transceivers on the j th circle is a function of the package density and is given by:
K j
  r j
2 
K j

1
K
0

1



Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
31





Crosstalk can happen only when the transceivers on each of the J circles are such that
K j
I r j

I
T
Consider the following cases:
1.
2.
3.
4.
T A
0 transmits a ‘0’ and K j
T A
0 transmits a ‘0’ and K j
T A
0 transmits a ‘1’ and K j
T A
0 transmits a ‘1’ and K j transmit a ‘0’ transmit a ‘1’ transmit a ‘0’ transmit a ‘1’
Interference happens only in the above Case2, since only then T B
0 receives a false threshold. The probability of such an event is given by:
Where p
0 p e

( 1

J  p
0 k j ) p
0 j is the probability that a ZERO is transmitted.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
32

Design guidelines for 2-D arrays




As the package density increases, the error probability increases and hence the capacity decreases.
The specific package density at which the capacity drops is a function of the distance between the arrays, and the angle of the transceivers and the specific arrangement of the transceivers on the array. The figures demonstrate the behavior of the capacity for a uniformly spaced transceiver configuration.
We can choose the package density such that each channels operates at a full capacity. Alternatively, we choose a package density wherein each channel operates at a lower capacity point and gets a higher aggregate bandwidth due to multiple operating channels.
For example, we can choose an array with 5 transceivers, each operating at 100 Mbps each, with an aggregate bandwidth of 0.5 Gbps.
Alternatively, we can pack 10 transceivers, each operating at 3/4 ths of its capacity and with an aggregate bandwidth of 0.75 Gbps.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
33

Bandwidth-Volume Product

“Bandwidth” denotes the capacity of a single channel, i.e. the unit of
Bandwidth is Mbps . “Volume” describes the 2-dimensional nature of the array and the distance over which they can communicate. The volume is simply multiplication of the number of channels on the array and the communication distance, i.e. the unit of the Volume here is meter . This means unit of BVP is Mbps-meter
 The advantage of BVP is that it provides an integrated performance evaluation measure to aid the decision process for choosing various parameters (e.g. d , θ) of the multi-element FSO system. The distance of operation, number of channels should be carefully chosen to achieve the desired capacity.
 Even if each of the channel is not operated at full capacity, one can still achieve high bit rates due to the presence of multiple simultaneous transmissions.
Shivkumar Kalyanaraman
Rensselaer Polytechnic Institute
34