Beamforming and space time coding for ad hoc 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. Outline. Introduction Open-loop & closed-loop systems

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Beamforming and Space-Time Coding for Ad-Hoc 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


Outline

  • Introduction

  • Open-loop & closed-loop systems

  • Co-phase space-time trellis codes

  • Connectivity measures for Ad-Hoc Networks

  • Summary of results

  • Future work


A Parameterized Class of Space-Time Block Codes


Set Partitioning for BPSK


Example (Super-Orthogonal Space-Time Trellis Code)


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


Block Diagram of a Transmit Beamforming System

Bit stream for Ant-1

Input

Bits

Encoder

Bit Stream for Ant-2

Receiver

Transmitter

Receiver


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


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?


Linear Beamforming Scheme for STBCs

Feedback CSI

STBC Encoder (OSTBC/QSTBC)

Multiply with Beamforming Matrix P

Channel Estimation & Linear Proc.

Input Bits

Ĉ=PC

Decoded Bits


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


Co-phase Transmission

Channel phase feedback

Multiply with steering vector

w

Maximum ratio combining

Input Bits

L-PSK modulation

ML decoder


Advantages and Disadvantages

  • Easy implementation (no eigen-analysis)

  • Easy decoding

  • No coding gain, poor performance

  • Requires at least M-1 feedback bits


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


A Simplified SOSTTC Beamforming Scheme


Strategy

  • Beamforming gain directly from code design


Quasi-static Rayleigh fading channels and AWGN:

  • Channel model

    M transmit antennas, 1 receive antenna:

  • Quantized channel phase feedback

  • L=L2+ ┄ + LMbits feedback.

  • Lm bits are used to uniformly quantize:


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


Signal Design for Inner Codes

  • The rotated version of orthogonal STBCs

  • The co-phase designs


Design Criterion for CPSTTC

  • Minimizing conditional PEP

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


Intra-CGM

A

c

,

c

,

0

o

r

π

1

2

(0.0035)

S0

S1

(0.00093)

S00

S01

S10

S11

00

11

01

10

B

c

,

c

,

π

Intra-CGM

B

c

,

c

,

1

2

0

1

2

(0.0018)

Intra-CGM

(0.074)

S0

S1

(0.00047)

S0

S1

(0.038)

S00

S01

S10

S11

00

11

01

10

S00

S01

S10

S11

00

11

01

10

Set Partitioning for Different Signal Designs (BPSK)


CPSTTC Example (1 bit feedback)


Observations

  • When b2=0, 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 b2=0 case.

  • When b2=1, 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 b2=1 case.


CPSTTC Examples (2 bits feedback)

b

0

case

b

1

case

b

2

case

b

3

case

2

2

2

2

B(c1,c2,0)

S0 S1

B(c1,c2,

π

) S0 S1

B(c1,c2,

π/2

) S0 S1

B(c1,c2,

0

) S0 S1

B(c1,c2,

π3/2

) S0 S1

B(c1,c2,

π3/2

) S0 S1

B(c1,c2,

π/2

) S0 S1

B(c1,c2,

π

)

S0 S1

B(c1,c2,0)

S1 S0

B(c1,c2,

π

) S1 S0

B(c1,c2,

π/2

)

S1 S0

B(c1,c2,

0

) S1 S0

B(c1,c2,

π3/2

) S1 S0

B(c1,c2,

π3/2

) S1 S0

B(c1,c2,

π

) S1 S0

B(c1,c2,

π/2

) S1 S0

b

0

case

b

1

case

b

2

case

b

3

case

2

2

2

2

B(c1,c2,0) S0 S1

B(c1,c2,3

π/2

) S0 S1

B(c1,c2,

π

) S0 S1

B(c1,c2,

) S0 S1

B(c1,c2,

π/2

) S1 S0

B(c1,c2,

0

) S1 S0

B(c1,c2,

π

) S1 S0

B(c1,c2,3/2

π

) S1 S0


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


Simulation Results (2 TX)


Simulation Results (4 TX)


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


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


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.


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.


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).


Sample QPSK SER-SINR Plots


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


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


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


Probabilistic Capacity

1x1

Hybrid

2x2


Largest Cluster Size


Probabilistic SER

1x1

Hybrid

2x2


Largest Cluster Size


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


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


Future Work

  • Solutions for time selective channels

  • Solutions for frequency selective channels

  • Cross layer issues

  • Effects of scheduling

  • Design issues


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