1. Data Communications to Train From High-Altitude Platforms
Andy Wang

2. Paper
George P. White, Yuriy V. Zakharov, “Data Communications to Trains From High-Altitude Platforms”, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO 4, pp , July 2007
Other reference:
Lecture note of “Signal Detection and Estimation” from website
Lecture note of “Direction of Arrival Estimation” from website

3. Summary
Analyze communications to multiple moving trains from High-Altitude Platform (HAP) and proposed array signal processing techniques
Direction-of-Arrival (DOA) estimation
Proposed SIC based Root-MUSIC DOA method
DOA tracking with Extended Kalman Filter (EKF)
Multiple train scenarios (crossing/passing/shadowing)
Compare Conventional BF and Null-steering BF

4. Outline Background DOA EKF UL Beamforming Simulation Results
Conclusions

5. Background
Existing high data rate service to train combine satellite and terrestrial cellular link
Higher speed Line-of-Sight (LoS) connections through satellite link
Lower speed connection maintenance with multiple terrestrial cellular links
In stations or tunnels

6. High-Altitude Platform (HAP)
Airplanes or airships positioned at stratospheric altitudes (17-22km) providing wide area wireless coverage
31/28 GHz band
Elevation angle 0 ≦ θ ≦ π/3
Azimuth angle 0 ≦ Φ ≦ 2π

7. To discuss DOA estimation required to create LoS link
Nondata-aid method preferred
Consider multiple train scenario
Tracking using Kalman Filtering
To reduce DOA estimation variance
Uplink beamforming technique
To reduce interference while train-crossing/passing

8. DOA Estimation Correlation-based Method
Multiple Signal Classification (MUSIC)
Root-MUSIC
Source (train) number estimation
Proposed SIC-based Root-MUSIC approach 1 2 M
sensor array d N
signals θm
Delay=(m-1)dsinθm
Output of the sensor array
r(k)=As(k)+n(k), k=1…K (snapshot)
A=[a1,…..,aN]: direction matrix
an=[1,e-j(2π/λ)dsinθn,…, e-j(2π/λ)(M-1)dsinθn]T:
Direction vector for the nth source

9. Correlation-based Method
Define received signal r(k), k: snapshot (or sample)
Steering vectors
Correlation-based method (Bartlett’s method) 1 2 M
sensor array d N
signals θm
Delay=(m-1)dsinθm

10. MUSIC: Principle Correlation matrix of array data R=ARsAH+σ2I
Eigen-decomposition on R
R s: signal correlation matrix
σ2: noise variance
Output of the sensor array
r(k)=As(k)+n(k), k=1…K (snapshot)
A=[a1,…..,aN]: direction matrix
an=[1,e-j(2π/λ)dsinθn,…, e-j(2π/λ)(M-1)dsinθn]T:
Direction vector for the nth source
signal subspace
noise subspace 1 2 M
sensor array d N
signals θm
Delay=(m-1)dsinθm
Since signal subspace⊥noise subspace,
DOAs are the peak locations of
MUSIC spectrum

11. K: snapshot (or samples)
MUSIC: Steps N
M-N v vH
Form the correlation matrix of array output
K: snapshot (or samples)
Perform eigen-decomposition to yield noise eigenvectors
vN+1,….,vM
Find the peak locations of the MUISC spectrum through
exhausted search (by changing a(θ) )
* note: number of source N is unknown (to be discussed later)

12. RM-MUSIC concept Polynomial-based method Let z=ej(2π/λ)dsinθ1 2 M
sensor array d N
signals θm
Delay=(m-1)dsinθm
Polynomial-based method
Let z=ej(2π/λ)dsinθ
peak in correspond to roots of C(z) 
There are (M-1) pairs zeros. Choose the N closest to the unit circle

13. RM-MUSIC Steps
Form the correlation matrix R of array output and find its eigen-decomposition R=QΛQH
Partition Q to yield the noise subspace Qn. Find C=Qn(Qn)H
Obtain Cl by summing the l–th diagonal of C
Find the (M-1) pairs zeros. Choose the N closest to the unit circle (zn, n=1,…N)
Θn=sin-1[angle(zn)]
* note: both these two method need to figure out signal/noise subspace

14. Source (train) number estimation
Use minimum Description Length (MDL) criteria
Number of array element N = (number of signal d) + (number of noise eigen-values)
Estimate the closeness of the eigen-values to figure out the number of signal
MDL penalty function
* Reference

15. Proposed SIC-RM approach
Estimate number of signal first
Extend RM approach
to X- and Y-axis
Substrate noise of
estimated signal

16. DOA tracking with EKF Kalman Filter (KF)
Extend KF (EKF) to non-linear model

17. T= measurement period = 5 seconds in this paper
Kalman Filter
Estimate the state at each time in the sense of minimum mean square error
Linear, IIR filter. Optimum if noises and initial state are all Gaussian.
Kalman State Vector
Motion update matrix
Position in X- & Y-axis
Velocity in X- & Y-axis
T= measurement period = 5 seconds in this paper
* Please refer to course “Adaptive Signal Processing” CH9 for more detail

18. Measurement Model
Cost function

19. Extended to non-linear model
Since measurement model (DOA) is non-linear, we need to extend kalman filter through determining the Jacobian transformation

20. Kalman Prediction Kalman prediction is defined as
And Kalman gain is derived by
Assume constant velocity
Assume constant velocity
Innovation sequence
Kalman gain
Kalman state error covariance matrix
process noise
measurement error covariance matrix
Innovation process
covariance matrix

21. UL Beamforming
Two approaches rely on the estimated steering vectors determined by the DOA estimation method were discussed
Bartlett BF (DOA-steering)
Capon BF (null-steering)
*Output of beamformer y(t)=wHx(t)
Reference/Figure source: “Convex Optimization-Based Beamforming”
Reference

22. Bartlett BF (Conventional BF)
Bartlett BF (DOA-steering)
The weights were designed to maximum the mean output power
signal
Steering vector
Signal in look direction
Signal after beamformer
Mean output power P(w)=E [y(t) y*(t)]

23. Capon BF (null-steering)
Cancelling the wave from known direction
Minimize the co-variance matrix
The true co-variance matrix
J: snapshot or samples
Recal that output of beamformer y(t)=wHx(t) 
 solution is

24. Performance evaluation
The author derive the SINR equation for trains base on the link-budget parameters of HAP. And simulation shows that the Capon BF (null-steering) acquire better performance in train crossing/passing scenarios.
Beam-pattern gain
Noise power
Boltzman constant
Antenna noise
Rx noise figure
Bandwidth
Received
signal
power

25. Simulation scenarios Position estimation
Single train DOA
Multiple train DOA+EFK with
Train crossing/passing
Train in/pass tunnel and station
Prediction and Convergence situation
UL SINR with 2 BF scheme and 2 position estimation scheme (DOA only v.s. DOA+EKF)
Influence of BS motion in HAP
Today we will not show these simulation results

26. DOA estimation simulation
One train with v=300km/h
RM-DOA estimation interval: 5 s

27. Conclusions
Analysis of DOA estimation, tracking and UL beamforming scheme in HAP
Proposed SIC based RM-DOA estimation
Simulate with DOA-EKF tracking
Simulation shows that null-steering technique result better performance in UL multiple train scenario
Simulate various kind of scenario
Based on HAP UL link budget

28. Thank You!