Pilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems
1. Pilot Optimization and Channel Estimation for
Multiuser Massive MIMO Systems
Tadilo Endeshaw Bogale
Institute National de la Recherche Scientifique (INRS),
Canada
March 20, 2014
2. Presentation outline
Presentation outline
1 Multiuser Block Diagram
2 Problem Statement
3 Proposed Solution
4 Simulation Results
5 Conclusions
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 2 / 12
3. Multiuser Block Diagram
Communication Scenario and Objective
BS
a1 · · · aM
MS1
MS2
MSK
h
1
h2
hK
Scenario
• MS1, MS2, MSK are separated in space
and no coordination between them
⇒ Downlink Multiuser system
• MS1, MS2, MSK have single antennas
⇒ Downlink Multiuser MISO system
• Channel between Tx and Rx is flat fading
• Transmission is TDD
• M >> K (i.e., Massive MIMO system)
General Objective
• To estimate channels H = [h1, h2, · · · hk ]
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 3 / 12
4. Multiuser Block Diagram
Conventional Channel Estimation (Orthogonal)
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
h3
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 4 / 12
5. Multiuser Block Diagram
Conventional Channel Estimation (Orthogonal)
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
h3
x1
x2
x3
⋄ y1 = h1x11 + h2x21 + h3x31 + n1
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
8. Multiuser Block Diagram
Conventional Channel Estimation (Orthogonal)
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
h3
x1
x2
x3
⋄ y1 = h1x11 + h2x21 + h3x31 + n1
y2 = h1x12 + h2x22 + h3x32 + n2
y3 = h1x13 + h2x23 + h3x33 + n3
⇒ Y = HX + N
where X = [x1 x2 x3]
N = [n1 n2 n3]
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
9. Multiuser Block Diagram
Conventional Channel Estimation (Orthogonal)
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
h3
x1
x2
x3
⋄ y1 = h1x11 + h2x21 + h3x31 + n1
y2 = h1x12 + h2x22 + h3x32 + n2
y3 = h1x13 + h2x23 + h3x33 + n3
⇒ Y = HX + N
where X = [x1 x2 x3]
N = [n1 n2 n3]
⇒ YXH
= H + NXH
ˆhk = hk + NxH
k
⇒ Requires N ≥ K
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
10. Problem Statement
Problem Statement
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Objective : Optimize pilots xk
Estimate channels hk , ∀N, M, K
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 12
11. Problem Statement
Problem Statement
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Objective : Optimize pilots xk
Estimate channels hk , ∀N, M, K
⋄ Assumptions : hk =
√
gk
˜hk
˜hk ∼ CN(0, 1)
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 12
12. Problem Statement
Problem Statement
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Objective : Optimize pilots xk
Estimate channels hk , ∀N, M, K
⋄ Assumptions : hk =
√
gk
˜hk
˜hk ∼ CN(0, 1)
⋄ Problem : Y = HXH
+ N
where H = [h1, · · · , hK ]
X = [x1, · · · , xN ]
N = [n1, · · · , nN]
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 12
13. Problem Statement
Problem Statement
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Objective : Optimize pilots xk
Estimate channels hk , ∀N, M, K
⋄ Assumptions : hk =
√
gk
˜hk
˜hk ∼ CN(0, 1)
⋄ Problem : Y = HXH
+ N
where H = [h1, · · · , hK ]
X = [x1, · · · , xN ]
N = [n1, · · · , nN]
⋄ Represent : hk = WH
k Yuk
ξk = tr{E{|hk − hk |2
}}
= uH
k (
K
i=1 gi xi xH
i + σ2
IN)uk tr{(WH
k Wk )}
+gk IM − (gk xH
k uk )tr{WH
k } − (gk uH
k xk )tr{Wk }
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 12
14. Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Represent : hk = WH
k Yuk
ξk = tr{E{|hk − hk |2
}}
= uH
k (
K
i=1 gi xi xH
i + σ2
IN)uk tr{(WH
k Wk )}
+gk IM − (gk xH
k uk )tr{WH
k } − (gk uH
k xk )tr{Wk }
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairness
minxk ,uk ,Wk
K
k=1
1
gk
ξk
s.t xH
k xk ≤ Pk
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
15. Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Represent : hk = WH
k Yuk
ξk = tr{E{|hk − hk |2
}}
= uH
k (
K
i=1 gi xi xH
i + σ2
IN)uk tr{(WH
k Wk )}
+gk IM − (gk xH
k uk )tr{WH
k } − (gk uH
k xk )tr{Wk }
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairness
minxk ,uk ,Wk
K
k=1
1
gk
ξk
s.t xH
k xk ≤ Pk
⋄ Wk =
gk xH
k uk
K
i=1 gi xH
i
uk uH
k
xi +σ2uH
k
uk
IM .
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
16. Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Represent : hk = WH
k Yuk
ξk = tr{E{|hk − hk |2
}}
= uH
k (
K
i=1 gi xi xH
i + σ2
IN)uk tr{(WH
k Wk )}
+gk IM − (gk xH
k uk )tr{WH
k } − (gk uH
k xk )tr{Wk }
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairness
minxk ,uk ,Wk
K
k=1
1
gk
ξk
s.t xH
k xk ≤ Pk
⋄ Wk =
gk xH
k uk
K
i=1 gi xH
i
uk uH
k
xi +σ2uH
k
uk
IM .
⋄ ˜ξk = M gk −
uH
k (g2
k xk xH
k )uk
uH
k
( K
i=1 gi xi xH
i
+σ2IN )uk
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
17. Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Wk =
gk xH
k uk
K
i=1 gi xH
i
uk uH
k
xi +σ2uH
k
uk
IM .
⋄ ˜ξk = M gk −
uH
k (g2
k xk xH
k )uk
uH
k
( K
i=1 gi xi xH
i
+σ2IN )uk
⋄ ˜˜ξk = Mgk − Mg2
k xH
k A−1
xk
where A =
K
i=1 gi xi xH
i + σ2
I
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 8 / 12
18. Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h
1
h2
hK
x1
x2
xK
⋄ Wk =
gk xH
k uk
K
i=1 gi xH
i
uk uH
k
xi +σ2uH
k
uk
IM .
⋄ ˜ξk = M gk −
uH
k (g2
k xk xH
k )uk
uH
k
( K
i=1 gi xi xH
i
+σ2IN )uk
⋄ ˜˜ξk = Mgk − Mg2
k xH
k A−1
xk
where A =
K
i=1 gi xi xH
i + σ2
I
⋄ minxk
tr{Q−1
k } −
gk xH
k Q−2
k
xk
1+gk xH
k
Q−1
k
xk
s.t xH
k xk ≤ Pk
where Qk =
K
i=1,i=k gi xi xH
i + σ2
IN
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 8 / 12
20. Simulation Results
Effect of Number of pilots (N)
Parameters: M = 128, K = 32, Pk = 1mw, SNR = Pav
σ2
16 18 20 22 24 26 28 30 32
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Number of pilot symbols (N)
NormalizedWSMSE
Existing (Orange) and proposed (Blue) algorithms
SNR = 18dB
SNR = 12dB
SNR = 6dB
g =
0.04 0.74 0.81 0.26
0.70 0.29 0.08 0.87
0.07 0.74 0.12 0.44
0.59 0.63 0.53 0.20
0.67 0.24 0.72 0.40
0.39 0.41 0.14 0.87
0.02 0.92 0.63 0.06
0.63 0.75 0.76 0.06
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 10 / 12
21. Simulation Results
Convergence speed and effect of initialization
Parameters: M = 128, N = 16, K = 32, Pk = 1mw, SNR = Pav
σ2
5 10 15 20 25 30 35 40
0.75
0.755
0.76
0.765
0.77
0.775
0.78
0.785
0.79
0.795
0.8
Iteration number
NormalizedWSMSE
SNR = 0dB
DFT matrix with pilot reuse
Truncated DFT matrix
Random matrix
5 10 15 20 25 30 35 40
0.67
0.68
0.69
0.7
0.71
0.72
0.73
SNR = 3dB
Iteration number
NormalizedWSMSE
DFT matrix with pilot reuse
Truncated DFT matrix
Random matrix
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 11 / 12
22. Conclusions
Conclusions
In this work, we accomplish the following main tasks.
We propose new pilot assignment and channel estimation
algorithm (especially for Massive MIMO system)
The proposed algorithm employs WSMSE as an objective function
To solve the problem, we apply MMSE and Rayleigh quotient
methods
The proposed algorithm achieves the optimal pilot and estimated
channel when K = N
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 12 / 12