SYSC 4607

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SYSC 4607 Lecture 18 Outline

• Review of Previous Lecture
• MIMO Systems
• Advantages of MIMO over SISO
• Parallel Decomposition of MIMO channels
• Capacity of MIMO Channels

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Review of Previous LectureVariable-Rate
Variable-Power MQAM
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Review of Previous LectureSpectral Efficiency in
Rayleigh Fading
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Review of Previous Lecture

• Adaptive MQAM uses capacity-achieving power and
  rate adaptation, with power penalty K.
• Adaptive MQAM comes within 5-6 dB of capacity
• Discretizing the constellation size results in
  negligible performance loss.
• Constellations cannot be updated faster than 10s
  to 100s of symbol times OK for most Dopplers.
• Estimation error and delay can lead to
  irreducible error floors.

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Multiple Antennas Adding Spatial Dimension
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Single-User / Multi-UserSpatial Multiplexing
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MIMO Principles

• Array and diversity gains increase coverage and
  QoS
• Multiplexing gain increases spectral efficiency
• Cochannel interference is reduced and cellular
  capacity increases

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MIMO Principles
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MIMO Principles
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Narrowband MIMO System(Flat Fading Channel)
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Narrowband MIMO System(Flat Fading Channel)
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MIMO Systems (Flat Fading)

• MIMO systems have multiple transmit and receive
  antennas
• With perfect channel estimates at Tx and Rx,
  decomposes into independent channels
• - RH -fold capacity increase over SISO system
• - Demodulation complexity reduction
• - Can also use antennas for diversity and
  beamforming
• - Leads to capacity versus diversity tradeoff
  in MIMO

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MIMO Performance Improvements

• MIMO results in four major Performance
  improvements
• - Array Gain
• - Diversity Gain
• - Spatial Multiplexing Gain
• - Interference Reduction Gain
• In general it is not possible to take advantage
  of all the above improvements due to Conflicting
  demands

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MIMO Performance Improvements

• Array Gain
• - Increase in average SNR due to coherent
  combining
• - Requires channel knowledge of transmitter
  and receiver
• - Depends on number of transmit and receive
  antennas
• Diversity Gain
• - Diversity mitigates fading in wireless
  links
• - MtMr links of independently faded
  channels can lead to MtMr-th order diversity as
  compared to SISO link (diversity order is slope
  of BER curve)
• - Can be achieved in the absence of channel
  knowledge at the transmitter by designing
  suitable transmit signals (space-time coding)

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MIMO Performance Improvements

• Spatial Multiplexing Gain
• - Transmit independent data signals from
  individual antennas
• - Receiver can extract different streams
  under uncorrelated fading channel conditions
  rich scattering
• - A linear increase (in min(Mt, Mr)) in
  capacity for no additional power or bandwidth
  cost is obtained
• Interference Reduction
• - Differentiation between the spatial
  signatures of the desired channel and co-channel
  signals is exploited to reduce interference
• - Requires knowledge of desired signals
  channel (spatial filtering)
• - Smart antenna system Beam-forming at
  transmitter through switched beam or adaptive
  array
• - Aggressive frequency reuse and increase
  in multi-cell capacity.

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Combined Advantages of MIMO
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Capacity of MIMO Systems

• Capacity of multiple antennas at input or output
  (but not both) increases with the log of number
  of antennas, while MIMO capacity can increases
  LINEARLY with number of antennas.
• For a full-rank channel matrix, RH - fold
  capacity increase is possible, where RH
  min(Mt,Mr).

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Capacity of MIMO Systems
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Spatial Multiplexing Gain

• Transmitters use same frequency and modulation
• Sub-streams are independent (no coding across the
  transmit antennas - each sub-stream can be
  individually coded)
• Individual transmit powers scaled by 1/Mt , so
  the total power is kept constant
• Channel estimation burst by burst using a
  training sequence
• Requires nearindependent channel coefficients

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Spatial Multiplexing Gain
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MIMO ChannelParallel Decomposition

• Multiplexing gain is realized through parallel
  decomposition MIMO channel is decomposed to RH
  parallel independent channels.

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MIMO ChannelParallel Decomposition
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MIMO ChannelParallel Decomposition
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MIMO ChannelParallel Decomposition
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Capacity of MIMO Systems

• Is the sum of capacity of parallel channels
• Channel is static or fading
• Channel knowledge CSIR, CSIT, or Channel
  distribution only
• For static channel with perfect channel knowledge
  at TX and RX, waterfilling over space is optimal
  power allocation
• Similar idea in fading, based on short-term or
  long-term power constraint
• Without channel knowledge, capacity is based on
  an outage probability

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Main Points

• MIMO channels greatly improve capacity and
  performance through array gain, diversity gain,
  interference reduction, and spatial multiplexing.
• MIMO channel can be decomposed into RH parallel
  SISO channels, where RH is rank of channel matrix
  H.
• Greatest capacity improvements are obtained under
  rich scattering conditions (H full rank).
• Capacity depends on the degree of channel
  knowledge at transmitter and receiver