Beamforming and SpaceTime Coding for AdHoc Networks

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Beamforming and Space-Time Coding for Ad-Hoc
Networks

• Hamid Jafarkhani
• Deputy Director
• Center for Pervasive Communications and Computing
• University of California, Irvine
• Li Liu
• Javad Kazemitabar
• Siavash Ekbatani

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Outline

• Introduction
• Open-loop closed-loop systems
• Co-phase space-time trellis codes
• Connectivity measures for Ad-Hoc Networks
• Summary of results
• Future work

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A Parameterized Class of Space-Time Block Codes

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Set Partitioning for BPSK
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Example (Super-Orthogonal Space-Time Trellis Code)

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Advantages of SOSTTC

• Systematic method for code construction
• Combined coding gain/diversity gain
• Simplified ML decoding
• Closed form performance evaluation
• Extension to SQOSTTC for four transmit antennas

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Block Diagram of a Transmit Beamforming System
Bit stream for Ant-1
Input Bits
Encoder
Bit Stream for Ant-2
Receiver
Transmitter
Receiver
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Shortcomings of Channel Feedback from Receiver

• Channel estimation error at the receiver
• Quantization loss
• The delay between estimation time and the time
  that feedback is used

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Channel Feedback Quality

• If the feedback quality drops too low, the
  beamforming scheme should gradually fall back to
  the non-beamformed scheme.
• Perfect Channel Feedback Beamforming
• No Channel Feedback Space-Time Coding
• What shall we do in between?

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Linear Beamforming Scheme for STBCs
Feedback CSI
STBC Encoder (OSTBC/QSTBC)
Multiply with Beamforming Matrix P
Channel Estimation Linear Proc.
Input Bits
CPC
Decoded Bits
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Advantages and Disadvantages

• Performance improvement through optimal power
  loading
• Complicated implementation (eigen-analysis)
• Beamforming matrix renders high PAPR
• trellis state machine and beamforming scheme
  should be jointly defined

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Co-phase Transmission
Channel phase feedback
Multiply with steering vector w
Maximum ratio combining
Input Bits
L-PSK modulation
ML decoder
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Advantages and Disadvantages

• Easy implementation (no eigen-analysis)
• Easy decoding
• No coding gain, poor performance
• Requires at least M-1 feedback bits

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Motivation

• Designing trellis codes satisfying
• Good performance, (trellis coding gain
  beamforming gain)
• Easy implementation based on phase feedback (no
  eigen-analysis)
• Easy symbol-by-symbol decoding
• Should work for any number of feedback bits as
  well as no feedback scenario
• Low PAPR

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A Simplified SOSTTC Beamforming Scheme
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Strategy

• Beamforming gain directly from code design

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• Channel model
• M transmit antennas, 1 receive antenna

Quasi-static Rayleigh fading channels and AWGN

• Quantized channel phase feedback
• LL2 ? LM bits feedback.
• Lm bits are used to uniformly quantize

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CPSTTC System Block Diagram

• Based on the channel phase information, the
  proper inner code is selected
• A standard M-TCM structure is used as the outer
  code

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Signal Design for Inner Codes

• The rotated version of orthogonal STBCs

• The co-phase designs

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Design Criterion for CPSTTC

• Minimizing conditional PEP
• Defining coding gain metric (CGM) for a pair of
  codewords

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Set Partitioning for Different Signal Designs
(BPSK)
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CPSTTC Example (1 bit feedback)
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Observations

• When b20, the elements from B(c1,c2,0) and
  A(c1,c2,0) attain the smallest intra-CGM. Thus
  B(c1,c2,0) and A(c1,c2,0) build the corresponding
  inner code for b20 case.
• When b21, the elements in B(c1,c2,?) and
  A(c1,c2,0) have the smallest intra-CGM. Thus
  B(c1,c2, ?) and A(c1,c2,0) build the
  corresponding inner code for b21 case.

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CPSTTC Examples (2 bits feedback)
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Advantages of the CPSTTC

• Worst-case pairwise CGM happens for parallel
  transitions
• Low decoding complexity (symbol)
• No eigen-analysis
• Low PAPR
• Combines the advantages of SOSTTC and co-phase
  design

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Simulation Results (2 TX)
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Simulation Results (4 TX)
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Why is it promising?

• Low complexity
• Good performance
• Identical to optimal beamforming for perfect
  channel feedback and identical to space-time
  coding for no channel feedback.
• Adaptive structure for different configurations

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Special Challenges for Ad-Hoc Networks

• Nodes may have different resources
• Power
• Size
• Level of mobility
• Number of antennas
• As a result, nodes may use different modulation,
  coding, and beamforming methods

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Connectivity

• Conventional connectivity measures do not work
  and may not be meaningful.
• There is a need for new connectivity metrics
  specially for hybrid networks that include nodes
  with different number of antennas.

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Geometric Disk Model

• Two nodes are connected if their distance is
  smaller than the transmission radius.
• Drawback Disk models do not reflect the wireless
  networking reality.

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SINR Model

• Two nodes are connected if the signal to noise
  and interference ratio is bigger than a
  threshold.
• Drawbacks
• SINR does not reflect coding/diversity impacts.
• A given SINR translates to different capacities
  and symbol error rates (SERs).

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Sample QPSK SER-SINR Plots
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Capacity as a measure of connectivity

• Channel path gains are random
• We use a probabilistic capacity measure for
  connectivity
• We show how to calculate the above measure for
  each link and different scenarios

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SER measure of connectivity

• One can calculate SER for a given space-time
  code, modulation,
• A probabilistic SER measure for connectivity
• We show how to calculate the above measure for
  each link and different scenarios

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Numerical Results

• Connectivity graphs of a random topology of 200
  nodes in a square domain of 1000 square meters
• bit/sec/Hz
• Power Tx 1 Watt Noise Watt

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Probabilistic Capacity
1x1
2x2
Hybrid
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Largest Cluster Size
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Probabilistic SER
1x1
2x2
Hybrid
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Largest Cluster Size
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Results and Findings

• A new adaptive structure that combines the
  advantages of SOSTTC and co-phase design
• Low complexity
• Good performance
• Identical to optimal beamforming for perfect
  channel feedback and identical to space-time
  coding for no channel feedback
• The design strategy works for any constellation,
  any rate, any number of states, and any number of
  feedback bits

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Results and Findings

• Two new connectivity measures
• Capacity measure
• SER measure
• A classic connectivity measure based on signal
  strength is not capable of accurately capturing
  the connectivity phenomenon
• Employing multiple antenna mobile nodes enhances
  the connectivity of fading ad-hoc networks

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Future Work

• Solutions for time selective channels
• Solutions for frequency selective channels
• Cross layer issues
• Effects of scheduling
• Design issues