sensor network capacity enhancement through spatial concurrency bharat b. madan and shashi phoha...
TRANSCRIPT
Sensor Network Capacity Enhancement Through
Spatial Concurrency
Bharat B. Madan and Shashi PhohaApplied Research Lab, Penn State University
CH• Nodes need to send their data to the CH (Cluster Head, Fusion Center).
• Single wireless channel (e.g., 802.11) – need to time multiplex a single channel to service multiple sensors.
• Need for concurrency – so that CH can receive data concurrently from high data rate multiple sensors.
1. Multiple frequency channels – CH deploys multiple frequency channels.
2. Spatial concurrency – create multiple channels in space (via beam forming).
Sensor Network Communication
s1 s2 sN
q1
CH Array
BFN
y1 y2
BF2BF1
yN
Space Diversity Processing• Space diversity requires multiple element array antenna.• Duality between time sampling and space sampling.• Optimally control the link (or channel) gain Gij • Assumptions:• CH knows the location (direction) of each sensor node• Sources lie in the far field
1
1 N-10 i
ti
di
q 1
2
3
4
• Problem formulation: Steer null in the direction of nodes 2,3,4 while maintaining constant gain in the direction of node 1
• Possible Solutions1. Constrained optimization 2. Synthesize array response
CH
• Mathematical Model
;
1111
22
*
*
2
*
2
v
vv
s
ss
C
CC
x
xx
NNN M
VSCX *
Constrained Optimization • Minimize total output power
subject to C1*W=1 w0 w1wN-1
S
• In the process of minimizing total power, the array would null out all nodes (except for the contribution of node 1 due to the constraint)
• Spatial parallelism: Have multiple beam-formers running in parallel
• The ith beam-former will maintain contribution of the ith node, while nulling out all other nodes.
CH
Beam Pattern Synthesis• BF1:Maintain fixed response towards the
direction of θ1 while simultaneously generating nulls in the directions θ2, θ3 ,.., θM-1
• Design BF2, BF3, ..,BFM-1 in a similar manner to deal with (M-1) sensor nodes of a cluster
• Computational Issues• In general, C may not be square and
existence of unique solution can not be guaranteed
•Pair wise multi-stage algorithm
Antennaarray
BF1
BF2
BFM-1
y1
y2
yM-1
ee
eeee
MNjMj
Njj
Njj
)1sin()1()1sin(
)2sin()1()2sin(
)1sin()1()1sin(
1111
w
ww
N 1
2
1
0
01
e
e
Nj
j
C)1sin()1(
)1sin(
1
1
CH
Pair Wise Multi-stage Algorithm• Consider only 2-element array and two directional sources
q2
q1
• 2-element array that constrains output due to source1 to a constant level, while simultaneously nulling out source2
w1 w2
S
w1 w2
S
w1 w2
S
w1 w2
S
w1 w2
S
ee
j
j
)sin(
)sin(
2
1
11
01
2
1
ww
e
e
e
j
j
j
w
w
))2sin()(sin(
)2sin(
))2sin()(sin(
12
;11
1
1
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Transmit Side Concurrent Beam-forming
+ + +
+
+
+
+
+
+
BF1
BF3
BF2
1 2 3
•Wireless communication: effectively half-duplex, i.e., not possible to simultaneously receive and transmit (unlike in wired communication collision detection is feasible).•Antenna array (a node) is not capable of transmitting and receiving at the same time (on the same channel).• How to exploit available concurrency?• Accumulate requests for a finite time, i.e., batch processing
tw
s
ss
www
wwwwww
NNNNN
N
N
2
1
21
22221
11211
111
s
ss
ggg
gggggg
NNNNNN
NN
NN
2
1
2211
2222121
1212111
)()()(
)()()(
)()()(
Array Manifold
g ij: Channel gain offered by ith element to signal sj
s1
s2
s3
Beam Pattern SynthesisLet u = sin(θ)• Initialize beam pattern
euPo ujnN
n
onw
1
0
)(
• Synthesis problem: Control the pattern Ps(u), such that
duPsPo uuMSE 22
1 || )()(1
1
won
ewnuj
N
on
1
euPs ujnN
n
snw
1
0
)(
is minimized, subject to
1,..,2,1,0)( MmumPsdukd k
1,..,2,1,0)( MmuPsm
N=17, M=4
Applications• Single hop sensor fusion
CH
1
3
24
• Each nodes sends RTS (in some arbitrary order).
CH
1
3
24
• CH accumulates RTSs and sends CTS concurrently to all nodes.
• Receive/Transmit concurrent beam-former makes the wireless router behave like a wireless Ethernet switch.
• Wireless Ethernet Switch
1
2
3
P1, 1
P2 , 2
P3, 3 1’
2’
3’
P1, j1
P2, j2
P3, j3
• Concurrent Jamming
• Above scenario: node 3 is enemy; 1 and 2 are friends• Alternately, 1, 2 and 3: enemy nodes being suppressed
concurrently
Concurrent Transmit Side Beam-former
1’
2’
3’
T1, j1
T2, j2
T3, j3
Jamming waveform synthesizer
• Mobile command and control.
RTS
CTSCTS
• CH, Wireless router/switch, C2 center, Jammer, etc. not constrained to be stationary
Accumulate RTS/CTS Protocol• k=0,1,..,N number of requests (arrivals) in time window tw
• Associate a reward (penalty) function f(k) with event k
f(k)
k
k’ N
tw
• Linear f(k)
Simulation Results
• New MAC protocol, Accumulated RTS/CTS (A-RTS/CTS)
• N: # array elements• Reward versus arrival rate λ• Concave function behavior
• For a given N, as λ increases, R first increases (due to N degrees of concurrency)
• Beyond certain point, higher value of λ leads to reduced performance (due to the request accumulation window getting filled up quickly hence higher idle time)
Conclusions
• Concurrent beam-forming is a powerful concept for providing spatial concurrency.
• Several possible applications:• Sensor network traffic capacity enhancement.• Wireless Ethernet switch for high speed routing.• Mobile Control & Command Center • Concurrent jamming.• Cellular phone network – cell capacity enhancement.