Channel estimation for orthogonal time frequency space (OTFS) massive MIMO

1. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 1/17
BEIJING
INSTITUTE
OF
TECHNOLOGY
Channel Estimation for
Orthogonal Time Frequency
Space (OTFS) Massive MIMO
1Wenqian Shen, 2Linglong Dai, 3Shuangfeng Han, 3Chih-Lin
I,
and 4Robert W. Heath, Jr.
1School of Information and Electronics, Beijing Institute of Technology
2Department of Electronic Engineering, Tsinghua University
3Green Communication Research Center, China Mobile Research
Institute
4Department of Electrical and Computer Engineering, The University of
Texas

2. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 2/17
1.
2.
4.
3.
System Model
Delay-Doppler-Angle 3D Channel
Simulation Results
3D-SOMP Based Channel Estimation
Outlines

3. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 3/17
OTFS SISO Modulation
 OTFS modulation at the transmitter is
composed of an OTFS pre-processing block and
a traditional frequency-time modulator such as
OFDM.
 The OTFS pre-processing block maps the 2D
data block in the delay-Doppler
domain to the 2D block in the
frequency-time domain by using the inverse
symplectic finite Fourier transform (ISFFT).
IS
FFT
Input
DD
X ISFFT
X S
Transmit
Windowing
OTFSPre-processing
M-point
IDFT
FT
X
Add CP
OFDM Modulator
Parallel to
S
erial
CP
vec{ }

s A S
CP
A S
M N
 M N
 M N
  
CP
M N N
   
CP 1
M N N
 
M N

DD M N


X £
FT M N


X £

4. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 4/17
OTFS SISO Demodulation
 OTFS demodulation at the receiver is composed
of the traditional OFDM demodulator and an
OTFS post-processing block.
 The OTFS post-processing block maps the
received signals in the frequency-time
domain to the 2D block in the delay-
Doppler domain by using the SFFT.
FT M N


Y £
DD M N


Y £
FT
Y
Receive
Windowing
DD
Y
S
FFT
OTFSPost-processing
r
FT,W
Y
Output
Equaliza
tion
Channel
Estimation
M-point
DFT
Remove
CP
OFDM Demodulator
S
erial to
Parallel
CP
R R unvec{ }

R r
M N
 M N
 M N
 M N
 M N

 
CP
M N
N

  
CP 1
M N N
 

5. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 5/17
OTFS Input-Output Relation
 Lemma 1: The received data is given by the
phase compensated 2D periodic convolution of
the transmit data with the delay-Doppler
channel impulse response (CIR) , which
is shown as follows:
where , , and are the -th
element of YD , , and ( ,
).
 
1, 1 / 2
k N
  
l
DD
Y
DD
X
DD
,k
Xl
0,1, , 1
M
 
l L / 2, ,0, , / 2 1
k N N
  
L L
DD
,k
Y
l
1
1 2
DD DD DD DD
, , , , ,
0
2
,
N
M
N
k k k k k k k
N
k
Y X H w V



    
  
 
 
 
l l l l l l
l
DD
,k
Hl
DD M N


H £
DD
X DD
Y DD
H
CP
2 ( 1)
DD
, ( 1)( ) 1,( )
1
M
k
N j i
N
k i M N
i
H h e

 
  

 
l l
Time-variant CIR ,
h l

6. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 6/17
OTFS Massive MIMO
 OTFS working in massive MIMO systems can
further increase the spectrum efficiency by
using multi-user MIMO.
 The main challenge for OTFS massive MIMO is
the downlink channel estimation due to the
required high pilot overhead.
s
TF
,
n m
Y DD
,
k
Y l
Precoding
Input
Mapping
Mapping
AntennaPorts
OTFSPre-
processing
Block
Time-
frequency
Modulator
OTFS
Pre-processing
Time-
frequency
Modulator
OTFS
Pre-processing
Time-
frequency
Modulator
DD
,
k
X l
DD
,
k
X l
OTFSModulation
TF
,
n m
X
TF
,
n m
X
Resource
Element
Mapping
Time-
frequency
Demodulator
OTFS
Post-processing
Demapping
r
Equalization
OTFSDemodulation
Channel
Estimation
TF
,
n m
Y DD
,
k
Y l
Resource
Element
Mapping
Time-
frequency
Demodulator
OTFS
Post-processing
Demapping Equalization
OTFSDemodulation
Channel
Estimation
OTFSModulation
Base S
tation
User 1
User U
Output
Output
s
r

7. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 7/17
Delay-Doppler-angle 3D Channel
 The time-variant CIR associated with the -th
antenna can be expressed as
 Then, the delay-Doppler-angle 3D channel is
given by
( 1)
p 
p s
s
2 2
, , rc s
1 1
p ( ) ,
s s
i i
i
i
N N
j T j p
p s i
i s
h e T e
   
  

 
 

l l
Path
gain
Doppler
frequency
Spatial AoD
Time delay
   
DDA
, ,
p s
,
rc s t
t
1
1
p ( ) ( )
k r
N N
H s N s M i N s
i i i
s
i i
NT k T r N
   



  

  
l l
( 1) /
sin( )
( )
sin( / )
j N x N
N
x
x e
x N







8. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 8/17
3D Sparsity of Delay-Doppler-angle
Channel
 The 3D channel is sparse along the delay
dimension, block-sparse along the Doppler
dimension, and burst-sparse along the angle
dimension. Doppler
Delay
Angle

9. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 9/17
Training pilots in the delay-Doppler
Domain
 To reduce the overall pilot overhead in OTFS
massive MIMO systems, we propose the non-
orthogonal pilot pattern, i.e., pilots transmitted
at different antennas completely overlap.
Doppler (N)
Data Guard
Pilot
Delay
(M)
g
M
M

g
M
/ 2
g
N N
/ 2
g
N
The training sequences at
different antennas are
independently generated

10. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 10/17
Formulation of OTFS Channel Estimation
 Based on the OTFS input-output relation, the
received pilots can be expressed as
 Rewrite it into the vector-matrix form as
g
t
g
t g
1 1
1
2 2
DDA
, , , , , , ,
0
2 2
N
N
M
k k k r k k r k
N N
r k
y w H z v
 

     
  

 
 
  
l l l l l l l
l
DFT of the
transmit pilots
 
y Ψh v
This is a sparse signal recovery problem.

11. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 11/17
3D-SOMP Algorithm
Reshape the correlations as the
same size of the 3D channel matrix
The delay index of the 𝑖-th
dominant path
The Doppler support of the 𝑖-th
dominant path
Transform the burst-sparsity to the
block-sparsity and obtain the angle
support of the 𝑖-th dominant path

12. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 12/17
Simulation Results
 For comparison, we also simulate the traditional
impulse-based channel estimation method and
traditional OMP-based channel estimation
method.
 System parameters for simulations:

13. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 13/17
Simulation Results
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
10
-2
10
-1
10
0
Pilot overhead ratio ()
NMSE
Traditional impulse based technique
Traditional OMP based technique
Proposed 3D-SOMP based technique
To achieve a constant NMSE, the required pilot overhead of the
proposed method is smaller than that of its traditional
counterparts.
 NMSE vs. Pilot overhead

14. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 14/17
Simulation Results
10 20 30 40 50 60
10
-2
10
-1
10
0
10
1
Number of BS antennas (Nt
)
NMSE Traditional impulse based technique
Traditional OMP based technique
Proposed 3D-SOMP based technique
 NMSE vs. # of BS antennas
The proposed method works well with a large number of BS
antennas.

15. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 15/17
Simulation Results
 BER vs. SNR
The proposed method achieves satisfying BER performance,
which is very close to the case with perfect CSI in OTFS
systems.
0 5 10 15 20 25 30
10
-4
10
-3
10
-2
10
-1
10
0
SNR
BER
OFDM under ICI
OFDM with perfect CSI
OTFS with Impulse
OTFS with 3D-SOMP
OTFS with perfect CSI

16. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 16/17
Conclusions
Propose a 3D-SOMP
algorithm for channel
estimation in OTFS massive
MIMO systems
Derive the discrete-time
formulation of OTFS
modulation/demodulati
on
Show the 3D
sparsity of delay-
Doppler-angle
channel
Doppler
Delay
Angle
1
1 2
DD DD DD DD
, , , , ,
0
2
,
N
M
N
k k k k k k k
N
k
Y X H w V



    
  
 
 
 
l l l l l l
l
10 20 30 40 50 60
10
-2
10
-1
10
0
10
1
Number of BS antennas (Nt
)
NMSE
Traditional impulse based technique
Traditional OMP based technique
Proposed 3D-SOMP based technique

17. IEEE ICC’2019——Channel Estimation for Orthogonal Time Frequency Space (OTFS) Massive 17/17
Contact Information
Thank you for your attention !
Wenqian Shen
Beijing Institute of Technology
wshen@bit.edu.cn
http://oa.ee.tsinghua.edu.cn/dailinglong/members/wenqians
hen