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**M. Emami, F. Lee and A. Paulraj**

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 Concluding Remarks

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**What is a HDB Channel? Few resolved paths Low Delay Spread**

Amplitude Delay Amplitude Delay Amplitude Delay Few resolved paths Low Delay Spread High Delay Spread Sparse Channel Few resolved paths 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) Tx Rx x(t) h(t) r(t) Step 2 (t) Step 1

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**Magnitude PDF of One Tap**

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 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**

LOS Data NLOS Data Distance in Wavelength Power Power Distance in Wavelength Spatial power profile strongly localized at intended receiver location

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**Indoor Wireless: Temporal Focusing Effect**

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

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**Outdoor Wireless: Temporal Focusing Effect**

Tap Index Normalized Magnitude Impulse Response after TR Channel Impulse Response N 17 for this case

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Underwater Acoustics High N Low N Time (µs) Distance

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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 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 rm d N i.i.d. uniformly distributed scatterers rM 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 = θ2 -θ1 (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 (Ga and Gx are the range and cross-range widths of contour)

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**One-Shot Results: Single Tx Antenna**

Distance in Wavelength Ga Gx N = 1 N = 100 Typical one-shot realizations of (R ) around target point

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**One-Shot Results: 5 Tx Antennas**

Typical one-shot realizations of (R ) around target point Distance in Wavelength N=1 N = 100

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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 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 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 IWF , 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**

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

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**Equalization Options for HDB Channels**

Tx Eq. Rx Eq. h() Tx Equalization Rx Equalization TR None LE / DFE / MLSE LE THP LE – Linear Equalizer DFE – Decision Feedback Equalizer MLSE – Maximum Likelihood Sequence Estimator – Too complex (exponential) THP – Tomlinson-Harashima Precoding

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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 TR Effective 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 γTR for No Rate back-off (RB = 1) Intel Indoor Data Theoretical

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**Rx-Only Equalization: LE and DFE**

sk' H(z) sk nk C(z) LE 1–B(z) sk' F(z) H(z) sk nk DFE Performance Complexity LE Poor (Noise enhancement) Time domain: O(n) Frequency domain: O(log2n) DFE Close to MLSE at high SNR (Error propagation negligible) Time domain: O(2n) Frequency domain: O(n) + O(log2n)

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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**

SNReff (dB) SNRMFB (dB) RB=25 RB=1 RB=2 RB=5 Rate back-off improves effective SNR

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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**

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

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**Joint Tx & Rx Equalization: THP**

H(z) 1–B(z) mod sk xk nk sk' F(z) Modulo operator at transmitter limits average & peak power of xk Better BER performance than DFE, especially at low SNR, since there is no error propagation Capacity penalty of bits/transmission at high SNR compared to DFE (shaping loss)

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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**

SNReff (dB) SNRMFB (dB) Effective SNR increases with # of Tx antennas (MT)

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**Single-User MIMO Systems**

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

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**Multi-User Systems Assumption Key questions . . . . . .**

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

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**Capacity Regions of Multiple Access Channels**

Single Antenna Multiple Antennas R1 R2 R1 R2 Flat No ISI R1 R2 R1 R2 Flat ISI

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**Broadcasting Channels**

Dirty Paper Coding (DPC) Examples of practical DPC schemes THP Trellis precoding Flexible precoding Lattice coding w2nR sn zn ŵ(yn) yn xn(w,sn) interference noise

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**Tx Equalization for Broacast Channels**

+ + +

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**THP for Broadcast Channels**

mod I - B H F sK' n x y1 yK . . . sk Element-Wise Operation Feedback Filter (Triangular) Channel (Flat or ISI) Feedforward Filter Joint (vector/matrix) processing at BS Individual (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 MT = 4 MT = 5 MT = 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 [3] C. Oestges, et al., “Time Reversal Techniques for Broadband Wireless Communications,” European Microwave Week, Oct (Invited Paper) [4] T. Strohmer, et al., “Application of Time Reversal with MMSE Equalizer to UWB Communications,” to appear in GLOBECOM’04. [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

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