MIMO Time Reversal Communications Hee-Chun Song, W.S. Hodgkiss, and W.A. Kuperman Marine Physical Laboratory/Scripps Institution Oceanography University of California, San Diego 9500 Gilman Drive, La Jolla September 14, WUWNet 2007, Montreal, Canada

Outline Underwater Acoustic (UWA) Channel Time reversal mirror (TRM) Application to communications Multi-user communications: Experiments Downlink (active) Uplink (passive) Summary

Radio vs. Underwater Acoustic Channel

Challenges in UWA Channel Delay Spread (ISI) Doppler Spread Stojanovic et al., “Phase-coherent digital communications for underwater acoustic channels,” IEEE J. Oceanic Eng., Commercial modem: Incoherent FSK (Frequency shift keying) Research community: Multi-channel DFE with 2 nd order PLL

BACKGROUND: TRM CLAY AND PARVELESCU (underwater acoustics) 1965 ZEL’DOVICH (non-linear optics): Phase Conjugation 1972 Retrograde antenna (microwave) 1964 BUCKER (underwater acoustics - mfp) 1976 TAPPERT et al. (underwater acoustics - “retrograde …”) FINK et al. (ultrasonics): Laboratory experiment 1989 JACKSON AND DOWLING (underwater acoustics) 1991,1992 Marine Physical Laboratory and SACLANTCEN (implementation of TRM in ocean) present

FAF-99: 3.5 kHz SRA (TRM)VRA

Multi-focus

3.5 kHz tranceiver 3.5 kHz SRA (’99 and ’00) L = 78 m N = 29

Probe Source Pulse Normal Time-Reversal Communications Application to Acomms Self-equalization ACTIVE (downlink)

TR: Self-Equalization Process Channel complexity (number of multi-paths) Number of array elements Spatial distribution (spacing and aperture) TR + Equalization 1. Remove the residual ISI 2. Compensate for time variations in the channel

Performance Comparison: Theory Stojanovic, JASA (2005) TR TR+EQ Output SNR Input SNR Song et al., JOE (2006) Song et al., JASA (2007) Channel Model TR+EQ

FAF04: Active Time Reversal + DFE TRM Only TRM+DFE SNR 0 =13.7 dB SNR 0 =26.3 dB Song et al., IEEE JOE (2006)

PASSIVE ACTIVE Song et al., JASA (2006) SIMO MISO

Multi-channel DFE w/ implicit matched filter Passive time reversal Followed by a single Channel DFE Time Reversal Yang, JOE (2005) Correlation-based DFE

Multi-User MISO (Active Time Reversal) Downlink Song et al., IEEE JOE 31, 2006

MIMO Implementations: Round Robin

FAF03: MISO 3-User Acomm (QPSK) 25.5 dB Range = 8.6 km 27.7 dB 29.7 dB

Multi-Access SIMO (Passive Time Reversal) Uplink Song et. al., JOE (2007)

FAF05: SIMO Multi-user Acomms (3-4 kHz)

FAF05: Multi-Access SIMO, R=4 km Receiver Co-channel interference LFM

FAF05: Single User SIMO, R=4 km ISI: 45 symbols Single User 96-m

FAF05: Multi-Access SIMO, R=4 km 6 Users 3 Users

Co-Channel Interference 6 Users

FAF05: Multi-Access SIMO, R=20 km (SRA-VRA2)

CIR R=4 and 20 km R=4 km, ISI: 45 symbolsR=20 km, ISI: 10 symbols Use bottom 20 elements for processing

FAF05: Multi-Access SIMO, R=20 km 3 Users 1 User

Summary Time reversal mirrors, either active or passive, exploit spatial diversity to achieve temporal and spatial focusing in complex environments (e.g., acoustic waveguide) Temporal focusing mitigates ISI while spatial focusing enables a straightforward extension to multi-user MIMO communications. Active (downlink) and passive (uplink) time reversal is equivalent mathematically with the communications link being in the opposite direction. Time reversal approach provides optimal performance in theory when combined with adaptive channel equalization. At-sea experimental results in shallow water have demonstrated the effectiveness of time reversal communications.

Performance Prediction: FAF05, QPSK M=2 Fractionally-sampled DFE Theory: Stojanovic, JASA (2005) Song et al., JASA (2007)

Time Reversal Communications (11-19 kHz)

FAF06: f =15 kHz, W=7.5 kHz 16 kbits/s at 2 km range15 kbits/s at 5 km range ISI:120 symbols ISI:100 symbols

Passive Time Reversal + DFE

L R Array Resolution: Free Space Rayleigh diffraction limit

cc V)V)  ee LeLe LcLc cc ee S B S B S B S B S B B S Array Resolution: Waveguide

Mobile hydrophone Time reversed signals Spatial focusing of the time reversed wave Distance (mm) Amplitude Fink et al

Single Channel Communication w/ a Moving Source LFM, 100-ms, 2-4 kHz T = 1-ms, 3 kHz, N=9002 symbol

Time Reversal vs Equalizer MLSE MMSE LE DFE Song et al., IEEE JOE 31, 2006 Song et al., JASA 120, 2006 Yang, JOE 29, 2004

FAF04: Pianosa Island (SW of ELBA) Shallow Water Experiment Depth: 50 m Range: 2 km