James Zeidler, PI Haichang Sui, Jittra Jootar and Adam Anderson, GSRs

1. James Zeidler, PIHaichang Sui, Jittra Jootar and Adam Anderson, GSRs Quantifying Performance Improvements Due to Spatial-Temporal Diversity in MIMO Spread-Spectrum Mobile Ad-hoc Networks

2. Summary of the Main Results • Coherent systems • We studied the effect of Doppler and multipath/spatial diversity in DS-CDMA systems with time-varying channels and noisy CSI • Trade-off among various system parameters are analyzed • Critical Doppler spread and pilot power are obtained to characterize when noncoherent signaling is preferable. • Noncoherent systems • The performance of Differential Unitary Space-Time Modulation (DUSTM) in time-varying channels with advanced detection is analyzed. • DUSTM with offset modulation is studied. • A coded Frequency Hopping Spread Spectrum system based on DUSTM is proposed. Erasure insertion is studied to alleviate PBI/MAI in the proposed system. • Experimental results based on data from BYU

3. Publications • J. Jootar, J. R. Zeidler, and J. G. Proakis, "Performance of Convolutional Codes with Finite-Depth Interleaving and Noisy Channel Estimates," submitted to IEEE Transactions on Communications, April 2005 • J. Jootar, J. R. Zeidler, and J. G. Proakis, ``Performance of Alamouti Space-Time Code in Time Varying Channels with Noisy Channel Estimates,'' in Proceedings of the IEEE WCNC (New Orleans), pp 498-503, Mar. 2005 • J. Jootar, J. R. Zeidler, and J. G. Proakis, ``Performance of Finite-Depth Interleaved Convolutional Codes in a Rayleigh Fading Channel with Noisy Channel Estimates,'' in Proceedings of the IEEE 61st Vehicular Technology Conference (Stockholm), June 2005 • A. Anderson, J. R. Zeidler, and M. A. Jensen, "Differential Space-Time Coding with Offset Quadrature Phase-Shift Keying", Proceedings of the IEEE Workshop on Signal Processing Advances in Wireless Communications (New York, N. Y.), June 2005 • H. Sui and J.R. Zeidler, "Erasure Insertion for Coded MIMO Slow Frequency-Hopping Systems in the Presence of Partial Band Interference", accepted by IEEE Globecom, December 2005 • H. Sui and J. R. Zeidler, "An explicit and Unified Error Probability Analysis of Two Detection Schemes for Differential Unitary Space-Time Modulation", submitted to the IEEE Asilomar Conference, November 2005 • H. Sui and J. R. Zeidler, “Erasure Insertion for Coded MIMO Slow Frequency-Hopping Multiple-Access Networks”, in preparation

4. Coherent Systems • Assumptions: • We focus on DS-CDMA (channel estimation is harder in FH-CDMA due to hopping). • Time-varying channel. • Pilot signal is used to estimate the channel. • Noisy CSI estimates. • Scenarios: • 1) Convolutional codes with finite-depth interleaving. • 2) Alamouti space-time codes.

5. Research Background (coherent systems) • Diversity from space/multipath/Doppler can be jointly exploited (e.g. Giannakis et al 03,05 for a receiver with perfect CSI and block ML detection). • Estimation-Diversity trade-off in block-fading channel is studied by Stark et al from an information-theoretic viewpoint • We study this trade-off under the following assumptions: • The CSI is estimated from pilots (cf. J. K. Caver et al) • Continuously time-varying channel instead of block fading channel • Convolutional codes with finite interleaving depth are accounted. Previous work assumes either perfect interleaving or perfect CSI. • We consider Direct Sequence spread spectrum since it allows simpler channel estimation than Frequency Hopping spread spectrum

6. Coherent Systems: Scenario 1(Convolutional Codes with FD Interleaving) • System Model • DS-CDMA with BPSK modulation. • Pilot and data channels are transmitted with different orthogonal codes. • Channel estimator is an FIR filter. • The effect from interleaving is approximated as separations of consecutive error symbols by interleaving depth I.

7. Coherent Systems: Scenario 1(Convolutional Codes with FD Interleaving) • Results Pairwise error probability as a function of pilot SNR for various values of Doppler spread and interleaving depth Data SNR = 2.22 dB, pilot SNR = 0.97 dB, 11-tap FIR filter, interleaving depth = 23, code rate 1/3, dmin = 18, 220 info bits per block

8. Coherent Systems: Scenario 1(Convolutional Codes with FD Interleaving) • Comparison of between perfect CSI, perfect interleaving and realistic cases when both are imperfect • Effects of pilot SNR, interleaving depth, and Doppler frequency can be observed • Curves are close to perfect CSI performances at moderate SNR (10dB) and low Doppler frequency • Curves converge to perfect interleaving at high Doppler frequency, even if the interleaving depth is low.

9. Coherent Systems: Scenario 1(Convolutional Codes with FD Interleaving) • Conclusions • System performance has been shown to be a function of • Autocorrelation function of the fading coefficients • Multi-path profile • Pilot to noise ratio • Data to noise ratio • Parameters of the channel estimator (#taps, tap coefficients) • Interleaving depth • Coding characteristic • The optimal Doppler spread which gives the best combination of diversity and CSI accuracy has been determined as a function of the above parameters.

10. Coherent Systems: Scenarios 2(Alamouti Open Loop STC) • System Model • DS-CDMA system with BPSK modulation • Two pilot channels (one from each transmit antenna) use different orthogonal codes. • Two data channels use the same orthogonal code, thus, the signals are combined at the receiver. • The channel estimators are FIR filters. • Alamouti space-time codes • Decoding scheme • Linear combining scheme space-time decoder • ML space-time decoder

11. Coherent Systems: Scenario 2(Alamouti Open Loop STC) • Results Sequence error probability when the linear combining scheme is used (circles are simulation results) Sequence error probability when the ML space-time decoder is used (circles are simulation results)

12. Coherent Systems: Scenarios 2(Alamouti Open Loop STC) • Comparison between no transmit diversity, and Alamouti STC with the linear combining scheme when CSI is noisy and channels are time-varying

13. Coherent Systems: Scenarios 2 • Conclusions • The linear combining scheme, which is the simple receiver suggested by Alamouti, performs well when the CSI is accurate and the channels are quasi-static. • When the CSI is not accurate or the channels are fast fading, the linear combining scheme may be outperformed by the system without transmit diversity. • ML space-time decoder is much more robust at large Doppler than the linear combining scheme space-time decoder.

14. Noncoherent Space-time Signaling • The study on coherent systems suggests that when the channel has high time-variation or the pilot is weak, we have to consider more robust systems by using noncoherent signaling. • Two forms of noncoherently detectable space-time signaling are Unitary ST Modulation (USTM) and Differential Unitary ST Modulation (DUSTM). Both can offer full spatial diversity, if properly designed • The USTM is designed for channels varying from block to block independently • The DUSTM is appropriate for continuously time-varying channels • Our focus is on DUSTM.

15. Research background(Noncoherent ST signaling) • Traditional DUSTM design is based on the assumption that the current and the previous received space-time signals experience the same channel. Also, in previous studies, only linear modulations are considered for symbols. • We extend the investigation of DUSTM in two aspects: • We obtain closed-form expressions for the performance of DUSTM signals in the general time-varying channels with multiple-symbol decision feedback detection. The traditional design criteria is validated in this general setting. • We study the use of offset modulation for symbols in DUSTM signals. Offset modulation avoids 180°degree phase transition in the transmitted signal and also achieves additional advantage in rate or diversity over non-offset DUSTM.

16. Noncoherent System • We study a Frequency-Hopping Spread Spectrum system with DUSTM (DUSTM-FHSS) as a possible physical layer for tactical ad hoc networks • FHSS is relatively insensitive to the near-far problem and more easily operated in non-continuous spectrum than DS-CDMA • Frequency diversity is achieved by hopping under proper coding and interleaving • Channel estimation is hard in FHSS and noncoherent modulation is more practical

17. Research background (DUSTM-FHSS system) • We study the erasure insertion decoding at the receiver for a Reed-Solomon coded DUSTM-FHSS system. This extends previous work (e.g. Pursley et al) on RS-coded FSK-FHSS systems: • DUSTM can offer higher spectral efficiency than FSK and spatial diversity • Acquiring and tracking the time-varying statistics of both channels and asynchronous interferences are studied. Those statistics are often assumed constant and known for each dwell in current literature.

18. System Model

19. Receiver Design • Goal: To reduce decoding error probability • Basic idea: Erasure insertion • Block ECC can correct twice as many erasures as errors ( ) • Demodulator outputs an erasure when the ML estimate is regarded as unreliable (e.g. when a dwell is hit by strong PBI/MAI or experiences deep fade) • Can be viewed as a simple, hard-decision based joint demod/decoding • Approaches • Bayesian erasure insertion: optimal • Likelihood Ratio Test (LRT): suboptimal, low-complexity

20. Simulation Results • Setting: ; Jakes’ model; the noise consists of thermal noise ( ) and PBI, which is present with probability and distributed as ; two Tx antenans and two Rx antennas, RS(16,4) code

21. BYU Data • Experimental data can be approximated as Gaussian random variables with time-varying means. • Prior to analysis and simulation, the time-varying means are found and removed from the experimental data. • The real and imaginary parts of fading coefficients are correlated and do not have identical distributions. Therefore, the analysis was modified to take into account these behaviors. Use the statistics to find the system performance Find channel statistics Compare analytical and simulation results BYU data Use the fading coefficients in Monte Carlo simulations Performance is found through simulations

22. BYU Data • Results Comparison between analytical and simulation results using BYU experimental data

23. QualNet Simulator Source Application Real network data Transport Modify QualNet to: • Allow insertion of network layer solutions • Accurately simulate time-varying channel • Perform bit-level PHY layer operations Routing Network MAC PHY Zeidler: PHY layer diversity Swindlehurst: Optimal training for CSI Channel Jensen: Time-varying channel data and models

24. Conclusion • The available physical layer diversity depends on the availability of CSI. We have studied systems where the receiver has noisy CSI or no CSI. • The trade-off between estimation errors and space/time/frequency diversity are studied in detail. Critical Doppler spread and pilot power beyond which noncoherent transceiver is preferable are characterized. • DUSTM in continuously-varying channels with advanced detection is analyzed and being extended to offset modulation. • A coded DUSTM-FHSS system is proposed for tactical ad hoc networks’ physical layer. Erasure insertion decoding technique is studied for interference rejection. • Some analysis results are verified using data collected at BYU.

25. Future Work • Closed-loop transmit diversity (or feedback beam-forming) in addition to Alamouti STC. • Extend the non-convolutionally coded analysis of Alamouti STC and CLTD to convolutionally coded analysis to take into account the effect of channel variation, interleaving depth, pilot SNR, data SNR, channel estimator, and coding characteristic. • Compare using multiple antennas for diversity and for multiplexing in a FHMA network. • Protocol design and throughput analysis for ad hoc network based on FHSS. • Determine the relative effectiveness of beamforming and STC in various ad-hoc networking environments • Further exploitation of channel modeling with the help of BYU. • Cross-layer simulation environment.