ICC 2019

1. Dominant CIR Tap Index Identification for
Wideband Channels
Tadilo E. Bogale1, Xianbin Wang2, and Long B. Le3
North Carolina A&T State University, Greensboro, USA1
Western University, London, Canada2
Institute National de la Recherche Scientific (INRS), Montreal, Canada3
May 2019

2. Presentation outline
Presentation outline
1 System scenario and objective
2 Multipath channel model
3 Dominant Tap Index Identification (DTII)
Motivation
Problem description
Problem formulation and proposed solution
4 Simulation results
5 Conclusions
IEEE ICC 2019 Dominant CIR tap identification May 2019 2 / 12

3. System scenario and objective
System scenario
System scenario
1
IEEE ICC 2019 Dominant CIR tap identification May 2019 3 / 12

4. Multipath channel model
Multipath channel model
Multipath CIR model
Multiuser: Single antenna VEs and N antenna BS
Maximum delay spread Td and sampling period Ts
No of multipath CIR taps L = Td
Ts
¯hkn =[¯hkn1, ¯hkn2, · · · , ¯hknL]T
⇒ ¯Hk =
√
Pk
˜Hk
√
Rk
Assumption:
√
Pk [j],
√
Rk [j] are constant for Cb blocks, ¯hknl:
correlated over time, Pk = diag(g2
k1, g2
k1, · · · , g2
kL)
˜˜Hk = P−1
k
¯Hk Uk D−1
k (Low dimension)
svd(Rk ) Uk Dk UH
k
IEEE ICC 2019 Dominant CIR tap identification May 2019 4 / 12

5. Dominant Tap Index Identification (DTII) Motivation
Dominant CIR Identification
Dominant CIR Identification: Motivation
Motivation
¯Hk is observed with additive noise
Coefficients of Pk may have significant variations.
CIR tap ¯Hk corresponding to g2
ki → 0 contains only noise information
⇒ Including CIR taps corresponding to g2
ki → 0 lead to poor CSI estimation
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
∴ Exclude CIR taps with very small g2
ki when sub-carrier CSI is computed
Question: How do we estimate g2
ki and quantify very small g2
ki?
IEEE ICC 2019 Dominant CIR tap identification May 2019 5 / 12

6. Dominant Tap Index Identification (DTII) Problem description
Dominant Tap Index Identification (DTII)
Problem description
Problem description
Design DTII as the problem maximizing SNR by assuming SISO
(Simple to extend to MIMO)
Exact SNR is not computable due to imperfect CSI
⇒ Formulate problem using lower-bound SNR
SISO System
Recovered signal
ˆxs =
1
|ˆhs|2
ˆh∗
sys = xs +
ˆh∗
s
|ˆhs|2
(esxs + nds) (1)
where ys = hsxs + nds, es = hs − ˆhs, σ2
d and σ2
t are noise variances
Lower-bound SNR
γlb
s =
σ2
x
E
ˆh∗
s
|ˆhs|2
(esxs + nds)
2
= σ2
x
L
i=1 σ2
hi + Lσ2
t
σ2
x Lσ2
t + σ2
d
(2)
IEEE ICC 2019 Dominant CIR tap identification May 2019 6 / 12

7. Dominant Tap Index Identification (DTII) Problem formulation and proposed solution
Design problem and proposed approach
Problem formulation and proposed solution
Design formulation:
˜L0 = max
L
γlb
s = min
L
L +
σ2
d
σ2
t
σ2
x
L
i=1 γhi + L
f0 (3)
γhi =
σ2
hi
σ2
t
is ith CIR path SNR.
Useful property
Objective is convex with L if γhi are sorted in decreasing order.
Remaining issue
How to compute γhi and noise variances
How to get efficient approach to find optimal solution
Proposed approach
Applies a two step approach to address the issues
Step 1: Exploits operating environment to compute noise powers
Step 2: Uses noise information from step 1 to get sorted SNR
IEEE ICC 2019 Dominant CIR tap identification May 2019 7 / 12

8. Dominant Tap Index Identification (DTII) Problem formulation and proposed solution
Proposed solution: Details
Proposed two step solution: Details
Step 1
Exploits operating environment to compute noise
powers from the past OFDM symbols Nb
Employs statistical information to identify the size of
taps (¯L) containing zero CIR powers (i.e., tap
contains only noise)
Step 2
Uses the noise information from Step 1 to get the
sorted SNR.
Employs the average power of each tap to get SNRs
Applies simple bisection search since optimization
problem is integer value
IEEE ICC 2019 Dominant CIR tap identification May 2019 8 / 12

9. Dominant Tap Index Identification (DTII) Problem formulation and proposed solution
Improved solution
Improved solution
Motivation
When γhi γh(i+k), k = 1, 2, · · · , and γhi 1 (i.e.,
very small noise power), ˜L = 1 becomes the optimal
solution.
⇒ Effect of noise would not be averaged (degrades
performance)
Suggested improvement
Set ˜L as the solution of βγlb
s with β ≥ 1 as a tuning
parameter selected based on the noise power
(i.e., set large β when the noise power is small and
vice versa).
IEEE ICC 2019 Dominant CIR tap identification May 2019 9 / 12

10. Simulation results
Simulation parameters
Simulation parameters
Single UE communication
(Extension to multiuser is trivial)
LTE ETU channel environment
No of BS antenna N = 8
Fc = 5.6 GHz, FFT size M = 512, Cb = Sb = 8
Spatial correlation
R =
C
i=1
a(θi )a(θi )H
Temporal correlation
E{( ˜H[i])m,n( ˜H[j])H
m,n} = αij = J0(2πf|i − j|)
J0(.): 0th-order Bessel, f: Normalized Doppler
VE speed V = 30 km/hr
IEEE ICC 2019 Dominant CIR tap identification May 2019 10 / 12

11. Simulation results
SE comparison with and without DTII
Observations
When β = 1 is selected, proposed achieves
better only in low to medium SNR regimes
With properly selected β, we can obtain
improved performance in all SNR regimes
Performance improvement is significant in the
high SNR region
⇒ Proposed design is beneficial for high
modulation transmission
One can expect better performance when β is
optimzed further
No significant SE improvement is observed
when Nb is beyond some value (i.e., around 50)
⇒ Advantageous since smaller Nb reduces
complexity and facilitates proposed design
perform well for a rapidly changing channel.
With and without DTII
-6 -3 0 3 6 9
SNR (in dB)
0.4
0.6
0.8
1
1.2
1.4
1.6
Normalizedlower-boundSE
With DTII (Nb
=200, =1)
With DTII (Nb
=200, > 1)
With DTII (Nb
=50, =1)
With DTII (Nb
=50, > 1)
With DTII (Nb
=10, =1)
With DTII (Nb
=10, > 1)
Without DTII
IEEE ICC 2019 Dominant CIR tap identification May 2019 11 / 12

12. Conclusions
Conclusions
This work proposes a dominant CIR tap index identification
problem
Problem is formulated as a simple convex optimization problem
where its solution is obtained efficiently using bisection search
approach
With the proposed approach, we can achieve more than 50%
improvement in spectrum efficiency (SE) compared to the
conventional design that does not take into account DTII
The proposed approach is simple to realize in practice and can be
adopted in different wireless setups including LTE and WiFi
IEEE ICC 2019 Dominant CIR tap identification May 2019 12 / 12