The Physics of MultipleAntenna Channels

1
The Physics of Multiple-Antenna Channels

• Ada Poon and Bob Brodersen
• Berkeley Wireless Research Center
• University of California, Berkeley

2
Why Multiple Antennae?

• Improve range

Network
A
B
C
A
B
C
D

• Minimize interference

MAC
TX
RX

• Increase data rate
• Improve reliability
• Reduce multipath

PHY
3
But its costly

• Demand intensive matrix computation.
• E.g. a division-free, deflation-type and
  LMS-based SVD algorithm (Poon00)
• Direct-mapped power and area estimates 5.86 mW
  and 63.6 mm2.
• Based on 1 V, 1 MHz, 16 bits and 0.25 ?m CMOS
  technology, assume each operation is pipelined
  20 interconnect overhead.

4
How many antennae do we really need?

• Information theorists would say
• Half-wavelength antenna spacing regardless the
  physical environment, as long as theres no hole
  in proof.
• Im lazy, I want less computation!
• Given physical environment of application and
  size of wireless device, find the total spatial
  degrees of freedom in
• Single-user channel
• Interference and relay networks.

5
How to measure physical environment?
Cluster of scatterers
From Intel data
From Intel data
6
Clustering Channel Response

• Physical environment is modeled by
• Note its array-independent
• Its scattering intensity is measured by the solid
  angles

and
7
Signal Dimensions in Array Response

• Continuous arrays with tripole antenna elements.
• Radiated electric field in the direction and d
  distance away due to a point source applied at p
  is
• Far-field response for spherical array of radius
  R is
• Define the effective aperture

(Green function)
8
Wavevector-Aperture-Polarization Product

• A factor of 2, A and W are the respective
  constraints over the polarization, array and
  wavevector signal dimensions.
• Total spatial degrees of freedom
• Combined with time-bandwidth product, the total
  degrees of freedom over time/frequency/space is
  2A WW T.

9
Choosing the No. of Antennae

• Capacities sustained by real environments are far
  below the ideal one.
• At Wt number of transmit and Ar Wr number of
  receive antennae suffice.

10
Physical Interpretations
W2
Physical environment (array-independent)
W3
W1
Grating lobes occur, but its fine!
11
A Design Example

• Physical environment
• Indoor, 3 cluster with cluster angle of 20 ? W
  0.67.
• Wireless device
• 30 cm long ? 5? _at_5 GHz, that is, L 5
• Number of antennae 3
• Half-wavelength antenna spacing requires 10
  antennae.
• When will we need more antennae?

12
Users as a Signal Dimensions

• Scatterers users are interchangeable.
• Should throughput scales with the number of users
  indefinitely?

13
Choosing the No. of Antennas (contd)

• Insensitive to physical environment.
• Size of array dominates.

14
Physical Interpretations
W2
Physical environment
W3
W1
Grating lobes matter now!
15
A Two-Stage Low-Dimension Transceiver
TX Beamformer
RX Beamformer
Space-timeprocessing
SpatialChannelDecoupling
ClusteringChannel
InterferenceSuppression
Spatial Interpolation
Spatial Decimation
RelayingProcessing
ChannelEstimation
From RX
SVD
PhysicalEnvironmentLearning
To TX

• Physical environment learning
• Simple no. of clusters and cluster angle, no. of
  relay users and having interferers or not.
• Sophisticated cluster boundaries, directions of
  users.

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Impact of Scattering

• Relate n to a and LW.
• Trade-offs among range, multiplexing and
  diversity gains.