Beamforming and Space-Time Coding for Ad-Hoc Networks

1. 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

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

3. A Parameterized Class of Space-Time Block Codes

4. Set Partitioning for BPSK

5. Example (Super-Orthogonal Space-Time Trellis Code)

6. 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

7. Block Diagram of a Transmit Beamforming System Bit stream for Ant-1 Input Bits Encoder Bit Stream for Ant-2 Receiver Transmitter Receiver

8. 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

9. 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?

10. 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

11. 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

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

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

14. 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

15. A Simplified SOSTTC Beamforming Scheme

16. Strategy • Beamforming gain directly from code design

17. 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:

18. 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

19. Signal Design for Inner Codes • The rotated version of orthogonal STBCs • The co-phase designs

20. Design Criterion for CPSTTC • Minimizing conditional PEP • Defining coding gain metric (CGM) for a pair of codewords

21. 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)

22. CPSTTC Example (1 bit feedback)

23. 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.

24. 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

25. 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

26. Simulation Results (2 TX)

27. Simulation Results (4 TX)

28. 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

29. 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

30. 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.

31. 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.

32. 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).

33. Sample QPSK SER-SINR Plots

34. 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

35. 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

36. 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

37. Probabilistic Capacity 1x1 Hybrid 2x2

38. Largest Cluster Size

39. Probabilistic SER 1x1 Hybrid 2x2

40. Largest Cluster Size

41. 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

42. 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

43. Future Work • Solutions for time selective channels • Solutions for frequency selective channels • Cross layer issues • Effects of scheduling • Design issues