1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. Underwater Acoustics
High N
Low N
Time (µs)
Distance

13. 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

14. 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

15. 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)

16. 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)

17. One-Shot Results: Single Tx Antenna
Distance in Wavelength Ga Gx
N = 1
N = 100
Typical one-shot realizations of (R ) around target point

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

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

20. S-T Focalization: Empirical Relationships for SR Model

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

22. 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

23. 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

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

25. 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.

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

27. Water-Filling
In order to obtain IWF , the input energy must satisfy the water-filling solution:

28. 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

29. 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

30. 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.

31. 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

32. 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

33. 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

34. 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)

35. 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

36. 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

37. 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

38. 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)

39. 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)

40. Effect of HDB on LE & THP

41. 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

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

43. TR vs. Tx-LE: Effect of Multiple Antennas
SNReff (dB)
SNRMFB (dB)
Effective SNR increases with # of Tx antennas (MT)

44. 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 +

45. 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?

46. Capacity Regions of Multiple Access Channels
Single Antenna
Multiple Antennas R1 R2 R1 R2
Flat
No ISI R1 R2 R1 R2
Flat
ISI

47. Broadcasting Channels
Dirty Paper Coding (DPC)
Examples of practical DPC schemes
THP
Trellis precoding
Flexible precoding
Lattice coding
w2nR sn zn
ŵ(yn) yn
xn(w,sn)
interference
noise

48. Tx Equalization for Broacast Channels+ + +

49. 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

50. 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

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

52. 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.

53. 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