Active Wireless Sensing in Time, Frequency
and Space
IPAM 2007
Mathematical Challenges and Opportunities in Sensor Networks
Akbar M. Sayeed
(joint work with Thiagarajan Sivanadyan)
Wireless Communications Research Laboratory
Electrical and Computer Engineering
University of Wisconsin-Madison
http://dune.ece.wisc.edu
Supported by NSF
Motivation
In-network processing
 Information processing in sensor
Sensor network:
networks
spatio-temporal sampling  Sensors communicate and relay
information among themselves
Disadvantages
 Excess delay: Multiple multihop
transmissions across the network
 Excess energy consumption: Additional
tasks such as routing and coordination
among nodes
Physical spatial
signal field
E.g: Consensus algorithms require
O(n1.5 log n) radio transmissions
(Dimakis et al. IPSN ‘06)
Active Wireless Sensing
Alternative Approach for Rapid Information Retrieval
Downlink:
Space-time
interrogation
waveforms
(high power)
Uplink:
Weak sensor
response
(energy-limited)
Consensus achieved in two channel uses
Wireless
Information
Retriever (WIR)
Other Motivations and Connections

Network to fusion-center communication architecture

Advances in RF technology – reconfigurable RF front-ends
– Source-channel matching - Information retrieval at multiple
spatial resolutions
– New tradeoffs between rate, energy and reliability/fidelity

Connections
– Imaging sensor networks (Madhow) – radar
– Multipath channels, multi-antenna (MIMO) communication
– Joint source-channel communication (Gastpar & Vetterli)
Distributed beamforming (Mudumbai et.al. 2005)
– Distributed time-reversal (Barton et.al. 2005)
– Cooperative/opportunistic relaying (Scaglione)
– Cognitive radio/radar
Overview
 Salient characteristics
– “Dumb” sensors: limited computational power, relatively
sophisticated RF front-ends
– “Smart” Wireless Information Retriever (WIR):
computationally powerful, equipped with an antenna array
 Basic protocol (Line-of-sight communication)
– WIR interrogates sensor ensemble with wideband space –
time waveforms
– Sensors respond to WIR interrogation signals
– WIR exploits the space-time characteristics of sensor
ensemble response for information retrieval
 Interplay between sensing, processing, and communication
– Canonical sensing configurations : spatial scale of signal
correlation and/or network cooperation
– Matched source-channel communication: energy efficiency
and sensing capacity
 AWS over multipath channels
Basic Communication Protocol
s(t)
WIR
t
carrier tone
Sensor 1
T
Sensor 1
receives s(t)
Sensor 2
Sensor 2
receives s(t)
Carrier synch:
The WIR transmits
a carrier tone to
synchronize the
frequency of local
sensor oscillators
Interrogation:
Temporal
The WIR transmits
code
a wideband
acquisition
spatio-temporal
waveform s(t)
- Temporal pseudo
noise (PN) code
by sensors
t
Fixed Delay
t
Sensor transmissions:
sensors modulate the
PN code to transmit
their (compressed)
measurements to the WIR:
- Non-coherent transmission
- Coherent transmission
(sensor phases stable
over two channel uses)
Line-of-Sight Sensing Channel
M-element
array (ULA)
at the WIR
PN code : q(t)
Duration : T
Bandwidth : W
K : number of sensors
or active scatterers
i
: sensor data
i
i
: sensor phase
: sensor delay
i : sensor angle
i
i e
 ji
q(t   i )
Received signal
 r1 (t )  K
 ji


r (t )  
i e a(i )q(t   i )  w(t )

 rM (t )  i 1
Array response vector
1


  j 2 
e

a    


  j 2 ( M 1) 
e

Sensor Resolution in Angle-Delay
 Spatial resolution: resolve the received signals from M fixed
uniformly-spaced directions via receive beamforming
 Delay resolution: resolve the signals in each spatial beam by
correlating with uniformly delayed versions of the PN code
Delay
  1 W
Angle


  1 M
A single sensor in each
resolution bin for large W
Sufficient Statistics:
Angle-Delay Matched Filtering
K
r (t )   i e
 ji
i 1
Uniform
Angle-Delay
Sampling
  1/ M
  1/ W
a(i )q(t   i )  w (t )
 
W
 0, , L , L   maxW 
,
m
0 a  M
h(m, )  wm,
H

K
  i i  m ,
i 1

m
m 
, m  1, , M
M
T  max
zm , 



 r (t )q  t 

 W
  wm,

 dt

Angle-Delay Matched Filtering
Sensor Angle-Delay Signatures
Angle-delay
Channel
Coefficients
Sensor
Angle-Delay
Signature
K
h(m, )   i i  m ,

i 1
 i  m,
e
 ji
m


g  i 
, i  
M
W

sin( M  ) sin  W
g ( , ) 
sin( )
 W

Sensor Localization
h(m, ) 

iS
S
 ,m

 i  {1,
S ,m  i  {1,
S ,
i  i  m,

,


, K } : i
1
m
1 
 m


,

M
2M M
2M 

, K} : i
1
1 



,


2W W
2W 
W
For sufficiently large W, only one sensor in any angle-delay bin
(m, )  th angle  delay bin  i(m, )  th sensor
h(m, )  i i ( m,
 i  m,   e
 ji
)
 m, 
m


g  i 
, i  
M
W

System Equation – Max Resolution
 z1 
K


z     MεΓβ  w  Mε  γ kk  w
k 1
 z N 
Γ   γ1 ,
γi
, γK 
γi  i (m, )
– Angle-delay signature vector of i-th sensor

– Sensor transmission energy
N  ML  K
– Angle-delay matched filter outputs
Ideal Scenario: Orthogonal Signatures
Delay
Sensor signature
  1 W
Angle
  1 M
Sensor
locations
Angle
Delay
Sampling
ith sensor : i ,  i    m


M W 
,
for some (m, )
γi  Orthogonal  No interference between sensor transmissions
Reality: Inter Sensor Interference
Delay
  1 W
Sensor signature
Angle
  1 M
Sensor
locations
Angle
Delay
Sampling
ith sensor : i ,  i    m


M W 
,
for any (m, )
γi  Non-orthogonal  inter sensor interference
M spatial bins
Space-Time Dimensions in AWS
N  ML  K
angle-delay resolution bins
parallel (interfering) channels
between the sensor ensemble and
the WIR
L < TW delay bins
TW temporal dimensions
(length of spreading code)
Canonical Sensing Configurations
K  Kind K coh
N = K = 108
M=9, L=12
Kind  K  108
# Independent bits
per channel use
K coh  1
# Sensors
transmitting
each bit
K ind  9 K coh  12
Partitioning of Sensor Transmissions and
MF Outputs
1Kcoh 0

1 
0 1Kcoh


β     Uβ  

K 
0 0

 1 
0 



  
1Kcoh   Kind 
0
 z1 
K ind


z
  MεQβ  w  Mε  k q k  w
k 1
z K 
 ind 
Q  ΓU  q1 ,
, q Kind 
qi 

kSCR i
γk
qi
2
 K coh
Effective angle-delay signature
associated with the bit in i-th group
Information Retrieval at Max Resolution
Simplest receiver structure for recovering bit from i-th group
Match filtering to angle-delay signature
 
ˆ
β  sign Re QH z
Pe (i)  Q
SINR(i) 


2SINR(i) , i  1,
2Mε qi
, K ind
4
ε 
K ind
qi   Mε q q k
2

2
k 1
k i
H
i


2
2 qi
4
K ind
q
k 1
k i
H
i
qk
2
MMSE Interference Reception
 
ˆ
β  sign Re Lopt z
Signature-matched
filtering

2
Lopt  arg min E Lz  β  QH R 1
L
Interference suppression
R    zz H   MεQQ H   2 I
BER Performance
Matched Filter:
Error floors
Int. Supp:
No error floors
SNR loss
More bits per channel use
Per sensor
Kind bits per channel use
(dB)
ε
ρ=
σ2
Pe  Q  2M qi ρ 
2


 K
 Q  2M 

 K ind


 
ρ 
 
Source-Channel Matching
What if we could map the identical transmissions from K coh sensors
in each group coherently into one angle-delay bin at the WIR?
Source-channel matching
M=9
Max. resolution
L=12
ML  K  108
K ind  9 K coh  12
Sensor transmissions
Dimension reduction by K coh
Reception at the WIR in
K ind  9 angle-delay bins
System Equation: Source-Channel
Matching
K 1
Kind
z  MεQβ  w  Mε  iqi  w
(max resolution)
i 1
Kind 1
Kind
zsc  MεQHQβ  wsc  MεVβ  w  Mε  i vi  wsc
i 1
V  Q HQ   v1 ,
vi
2
Effective “focussed”
angle-delay signatures
, v Kind 
 K coh qi
2
K
2
coh
Coherent K coh  1 angle-delay “focussing” (coherent MAC)
Max-Resolution Versus Matched SourceChannel Communication

 K
Pe  Q  2M 

 K ind

 
ρ 
 
versus
Pe,sc
2




K


 Q  2M 
 ρ

 K ind  


How do we do Source-Channel Matching?
Highest resolution
Source-channel matching
Array reconfiguration
Distributed time-reversal to line up sensor delays in each group
Distributed beamforming in each group
Alternative Approach
Decreasing antenna spacing  decreasing carrier frequency
Alternative to time-reversal: decreasing signaling bandwidth
Distributed beamforming in each low-resolution bin
fc
3
W
W
4
fc 
Sensing Capacity
C  K ind ,    K ind log 1  SINR    
L

TW  L
Fraction of temporal
dimensions used
Angle-delay
Parallel channels
Ideal case: SINR  SNR
bps/Hz
Received SINR
per parallel
channel
Capacity: Max Resolution (Ideal)
  K
C  K ind ,    K ind log 1  

  K ind
Coherence gain


 M 


L

TW  L
Array gain
Sensing capacity increases monotonically with Kind
Kind  K :
Cmax  K log 1  M
K ind  1:
Cmin   log 1  MK
Maximum parallel channels
Minimum SNR per parallel channel
Minimum parallel channels
Maximum SNR per parallel channel
Capacity: Source-Channel Matching
  K 2

Csc  K ind ,    K ind log 1  
M 

  K ind 



Coherent “beamforming” in each group/parallel channel
Each parallel channel is a K coh 1 coherent MAC
Multiplexing gain versus received-SNR tradeoff (AS & Raghavan 2006)
MK 2
K ind,opt    
2

ε
2
Capacity-maximizing
configuration
Sensing Capacity Comparison: With or
Without Source-Channel Matching
Kind  K
SNR

Max. resolution

Source-channel matching
(adaptive resolution)
AWS over Multipath
c
Scatterer
Sensor Ensemble

LOS Path
WIR
Scattered Path
50c
50c
AWS over Multipath: Multiple Bounce
c
Scatterer
Sensor Ensemble

LOS Path
WIR
Scattered Path
50c
50c
System Equation
K
LOS:
z  MεΓβ  w  Mε  γ ii  w
i 1
Multipath:
Γ   γ1 ,
, γ K   Γlos  Γmp U
Effective signature of i-th sensor:
Average received per-sensor SNR:
NK
N  Np
Np  K
Ensemble
Signature
Matrix
(low rank)
Scatterer
Signature
Matrix
(full rank)
EnsembleTo-Scatterer
Coupling
Matrix
(full rank)
γ i  γ i,los  Γ mp ui

M 1  N p  2p

Impact of Multipath
Signal dispersion in space and time
Pros:
• Higher capture of transmitted sensor energy
• Higher spatio-temporal diversity
• Distinct sensor signatures for denser ensembles
• Distinct sensor signatures with smaller arrays and bandwidths
Cons:
• Sensor localization information lost
• Fading
Sensor Signatures – Line-of-Sight (LOS)
Paths
K = 108 sensors in 3 angle – 4 delay bins
Scatterer Signatures
108 Scatterers
27 Scatterers
Scatterer Positions
Signatures Induced
by a Single Sensor:
Single Bounce Scattering
Signatures Induced
by a Single Sensor:
Multiple Bounce Scattering
Dimensions Induced by Sensor Ensemble
27 Scatterers
Scatterer Positions
Single Bounce Scattering
Multiple Bounce Scattering
(Angle=9, Delay = 18)
(Angle=9, Delay = 38)
Dims = 102
108 Scatterers
(Angle=9, Delay = 24)
Dims = 118
Dims = 142
(Angle=9, Delay = 46)
Dims = 228
Effective Sensor Signatures
Single Bounce Scattering
Multiple Bounce Scattering
Eigenvalues of the Coupling Matrix
Single Bounce Scattering
Multiple Bounce Scattering
Sum of Eigen Values: LOS - 42.12
Sum of Eigen Values: LOS - 42.12
27 Scat. – 2651 ; 54 Scat. – 5307
27 Scat. – 2982 ; 54 Scat. - 5944
108 Scat. – 10318 ; 162 Scat. – 15704
108 Scat. – 11590 ; 162 Scat. - 17587
Conclusions and Challenges

Flexible architecture for information retrieval in sensor networks
– Complementary to in-network processing (latency, energy efficiency)
– Reconfigurable wideband multi-antenna RF front ends
– X-fertilization between space-time wireless communications, radar,
and sensor networks
– Cognitive wireless communications and sensing

Distributed source-channel matching
– Multi-resolution space-time sensing and communication
– New tradeoffs involving energy, information rate, fidelity

Challenges and future research
– AWS over multipath – sensor addressing via space-time reversal
– Interplay with in-network processing
– Optimization for inference applications
– Learning unknown signal fields and channels