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Communications through High Delay Spread x Bandwidth (HDB) Channels: Opportunities and Challenges M. Emami, F. Lee and A. Paulraj Stanford University October 18, 2004 AIM Workshop on Time-Reversal Communications in Richly Scattering Environments

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Agenda What is a HDB Channel and the TR Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User Capacity Equalization Multi User Capacity Equalization Concluding Remarks

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What is a HDB Channel? Delay Amplitude Delay Amplitude Delay High Delay Spread Sparse Channel Few resolved paths Low Delay Spread Many resolved paths High Delay Spread Rich Channel

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HDB Metric The TR effect depends on the number of significant resolvable taps (N) in the channel response Typically, N > 30 represents a good HDB channel

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Time Reversal (TR) Experiment x(t) = s(t) h * (-t) s(t) r(t) = s(t) h * (-t) h(t) TxRx x(t) h(t) r(t) Step 2 Tx h(t) Rx (t) h(t) Step 1

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TR Effects Spatial focusing Temporal focusing Channel hardening Normalized Magnitude Number of Occurrences Original Channel After TR Magnitude PDF of One Tap

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Agenda What is a HDB Channel and the TR Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User Capacity Equalization Multi User Capacity Equalization Concluding Remarks

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Experimental Evidence for TR Effects Indoor (Intel/Stanford) Large office space with cubicles (40 x 60 yards) Bandwidth 2 to 8 GHz (UWB) Channel measured with fixed Tx and Rx in a grid of.5m x.5m at (approx.) every 3 cm Outdoor (Nokia) Bandwidth 100 MHz Underwater Acoustics

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Indoor Wireless: Spatial Focusing Effect NLOS Data Distance in Wavelength Power LOS Data Distance in Wavelength Power Spatial power profile strongly localized at intended receiver location

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Indoor Wireless: Temporal Focusing Effect Tap Index Normalized Magnitude Impulse Response after TR Temporal power profile at intended receiver strongly localized in time Side lobes double channel length Tap Index Channel Impulse Response Normalized Magnitude

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Outdoor Wireless: Temporal Focusing Effect Tap Index Normalized Magnitude Impulse Response after TR Tap Index Channel Impulse Response Normalized Magnitude N 17 for this case

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Underwater Acoustics Distance High N Low N Time (µs)

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Agenda What is a HDB Channel and the TR Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User Capacity Equalization Multi User Capacity Equalization Concluding Remarks

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Characterizing Spatial Focusing Single Ring (SR) Model h(τ,R) is the channel from Tx to r = R r=0 represents center of circle r=0 Tx rmrm d N i.i.d. uniformly distributed scatterers rMrM 1 2

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Spatial Focusing Statistics Space-time (S-T) random field generated by a one shot TR pulse offers multiple characterization Influencing parameters N - HDB metric λ - wavelength BW - bandwidth Δθ = θ 2 -θ 1 (receive angle spread) Define E{ (R )} = [max {s(, R)}] 2 where s(, R) = h * (-, 0) h(, R)

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Spatial Focusing Statistics - Metrics Long range spatial focusing: 3-dB contour of (R ) around Rx (G a and G x are the range and cross-range widths of contour)

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One-Shot Results: Single Tx Antenna Distance in Wavelength GaGa GxGx N = 1 N = 100 Typical one-shot realizations of (R ) around target point Distance in Wavelength

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One-Shot Results: 5 Tx Antennas Typical one-shot realizations of (R ) around target point Distance in Wavelength N=1N = 100 Distance in Wavelength

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Spatial Focalization: E{ (R)} Distance in Wavelength Pulse Bandwidth (MHz) Peak Power (dB)

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S-T Focalization: Empirical Relationships for SR Model

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Agenda What is a HDB Channel and the TR Effect Experimental Data Communications in HDB Channels Single User Capacity Equalization Multi User Capacity Equalization Concluding Remarks

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What is a HDB Communication System? A communication system that exploits the TR effect to improve performance factors. The transmitter uses a pre-filter derived from the time reversed channel for transmission to the intended receiver. Demod. / Decode h( ) Encode / Mod. Tx Rx

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Important Questions for HDB Communications How is capacity affected by HDB channels in single and multi-user scenarios? What are the key communication problems? Equalization for ISI Channel coding Can spatial focusing be preserved Are there any LPI or CCI reduction effects Design tradeoffs

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Agenda What is a HDB Channel and the TR Effect Experimental Data Communications in HDB Channels Single User Capacity Equalization Multi User Capacity Equalization Concluding Remarks

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Capacity of Single User HDB Channels Capacity of a communication channel determines maximum rate of transmission per channel use. HDB channels are frequency selective fading channels. They will suffer a capacity penalty w.r.t. AWGN channels at high SNR. Optimum approach to maximizing capacity is water-filling (WF). TR is close to but not true WF.

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Effect of HDB Channels on Capacity TR rate: Max. achievable rate: Tx power spectral density

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Water-Filling In order to obtain I WF, the input energy must satisfy the water-filling solution:

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Capacity: TR vs. WF Ergrodic capacity of TR is near optimal at low SNR Outage capacity decreases with increase in # of taps Rate (bits/s/Hz) Probability Cumulative Distribution SNR Average Rate (bits/s/Hz) 50 taps

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Equalization Options for HDB Channels Tx EqualizationRx Equalization TRNone LE / DFE / MLSE LENone TRLE THP LE – Linear Equalizer DFE – Decision Feedback Equalizer MLSE – Maximum Likelihood Sequence Estimator – Too complex (exponential) THP – Tomlinson-Harashima Precoding Tx Eq.Rx Eq. h( )

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Equalization HDB = high Inter Symbol Interference Problem Modulation schemes can be used to mitigate ISI problem. e.g. Spread spectrum, OFDM. We discuss Single carrier schemes where the ISI problem is severest.

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TR at Tx – No Receive Processing This channel has a severe ISI problem. Power of main tap = Power in ISI taps. TR does not solve the ISI problem. Mitigation: Rate back-off ISI

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Rate back-off (RB) Rate back-off refers to signaling at symbol rate < 1/BW. This effectively sub-samples the channel, reducing the effective ISI while capturing full diversity Normal Channel after TREffective Channel with RB = 2 Peak ISI

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ISI vs. Rate back-off for TR Assuming the channel taps are i.i.d. Gaussian, the ratio of peak to ISI power is related to rate back-off as follows: Plot of γ TR for No Rate back-off (RB = 1) Theoretical Intel Indoor Data

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Rx-Only Equalization: LE and DFE sk'sk' H(z) sksk nknk C(z) 1–B(z) sk'sk' F(z) H(z) sksk nknk LE DFE PerformanceComplexity LEPoor (Noise enhancement) Time domain: O(n) Frequency domain: O(log 2 n) DFEClose to MLSE at high SNR (Error propagation negligible) Time domain: O(2n) Frequency domain: O(n) + O(log 2 n)

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Tx-Only Equalization: LE Minimize mean square error (MSE) subject to power constraint: is the delay of the equalizer and the channel is for removing the bias We investigate

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TR vs. Tx-LE: Effect of Rate back-off Rate back-off improves effective SNR SNR eff (dB) SNR MFB (dB) RB=25 RB=5 RB=2 RB=1

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Joint Tx & Rx Equalization: TR & LE TR performs near-optimal WF while LE & rate back-off mitigate ISI For further complexity reduction, only the largest 10 or 20 taps in impulse response after TR and rate back-off are used to design LE

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TR & LE: Performance Results (Full impulse response after TR contains 499 taps) LE only uses largest 20 taps of impulse response after TR LE only uses largest 10 taps of impulse response after TR RB RB = Rate-back-off Factor

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Joint Tx & Rx Equalization: THP Modulo operator at transmitter limits average & peak power of x k Better BER performance than DFE, especially at low SNR, since there is no error propagation Capacity penalty of 0.255 bits/transmission at high SNR compared to DFE (shaping loss) H(z) 1–B(z) mod sksk xkxk nknk sk'sk' F(z)

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Effect of HDB on LE & THP

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Effect of Equalization on Spatial Focusing Rx-only equalization: No spatial focusing Tx-only equalization TR: Shown previously (use as reference) LE: Similar to TR with a small penalty

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Spatial Focusing: Simulation Results 100 i.i.d. Gaussian taps (N=100) We have that for both MMSE and TR

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TR vs. Tx-LE: Effect of Multiple Antennas SNR eff (dB) SNR MFB (dB) Effective SNR increases with # of Tx antennas (M T )

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Single-User MIMO Systems The capacity for a frequency selective MIMO channel is given by: λ i is the energy of space-frequency mode i of the channel + + +

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Multi-User Systems Assumption Each user has 1 antenna Base station (BS) has M T antennas Key questions What is the effect of HDB on capacity regions? What are the appropriate equalization techniques for HDB channels? H( ) User 1 User K... BS...

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Capacity Regions of Multiple Access Channels R1R1 R2R2 R1R1 R2R2 R1R1 R2R2 Flat Single Antenna Multiple Antennas No ISI ISI R1R1 R2R2 Flat

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Broadcasting Channels Dirty Paper Coding (DPC) Examples of practical DPC schemes THP Trellis precoding Flexible precoding Lattice coding w 2 nR snsn znzn ŵ(y n ) ynyn x n (w,s n ) interferencenoise

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Tx Equalization for Broacast Channels + + +

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THP for Broadcast Channels s1's1' mod I - B HF sK'sK' mod n x y1y1 yKyK... mod sksk Element-Wise Operation Feedback Filter (Triangular) Channel (Flat or ISI) Feedforward Filter Joint (vector/matrix) processing at BSIndividual (scalar) processing for each user

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THP for Broadcast Channels Equivalent to VBLAST at Rx No error propagation Sources of capacity loss relative to optimum DPC Shaping loss induced by modulo operation Symbol-by-symbol encoding Secure communication possible Difficult for one user to decode other users data based on its own received signal

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Performance Example: [2] 2-Tap ISI Channel with Equal Power, # of Users = 4 M T = 4 M T = 5 M T = 6 Simulation Theoretical Approximation

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References [1]R. Schober and W. H. Gerstacker, On the Distribution of Zeros of Mobile Channels with Application to GSM/EDGE, IEEE JSAC, July 2001. [2]L. U. Choi and R. D. Murch, A Pre-BLAST-DFE Technique for the Downlink of Frequency-Selective Fading MIMO Channels, IEEE Trans. Commun., May 2004.

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Publications of TR Group [1]M. Emami, et al., Predicted Time Reversal Performance in Wireless Communications Using Channel Measurements, to appear in IEEE Commun. Letters. [2]J. Hansen, et al., Design Approach for a Time Reversal Test Bed for Radio Channels, Special Session on MIMO Prototyping, 12th European Signal Processing Conference, Sept. 2004. [3]C. Oestges, et al., Time Reversal Techniques for Broadband Wireless Communications, European Microwave Week, Oct. 2004. (Invited Paper) [4]T. Strohmer, et al., Application of Time Reversal with MMSE Equalizer to UWB Communications, to appear in GLOBECOM04. [5]M. Emami, et al., Matched Filtering with Rate Back-off for Low Complexity Communications in Very Large Delay Spread Channels, to appear in Asilomar Conference on Signals, Systems, and Computers, Nov. 2004.

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