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Beamforming and Space-Time Coding for Ad-Hoc Networks

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Hamid Jafarkhani

Deputy Director

Center for Pervasive Communications and Computing

University of California, Irvine

Li Liu

Javad Kazemitabar

Siavash Ekbatani

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

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

Bit stream for Ant-1

Input

Bits

Encoder

Bit Stream for Ant-2

Receiver

Transmitter

Receiver

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

- 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?

Feedback CSI

STBC Encoder (OSTBC/QSTBC)

Multiply with Beamforming Matrix P

Channel Estimation & Linear Proc.

Input Bits

Ĉ=PC

Decoded Bits

- 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

Channel phase feedback

Multiply with steering vector

w

Maximum ratio combining

Input Bits

L-PSK modulation

ML decoder

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

- 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

- 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:

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

- The rotated version of orthogonal STBCs

- The co-phase designs

- 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

- 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.

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

- 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

- 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

- 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

- 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.

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

- 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).

- 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

- 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

- 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

1x1

Hybrid

2x2

1x1

Hybrid

2x2

- 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

- 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

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