pilot optimization and channel estimation for multiuser massive mimo systems
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Pilot Optimization and Channel Estimation forMultiuser Massive MIMO Systems
Tadilo Endeshaw Bogale
Institute National de la Recherche Scientifique (INRS),Canada
March 20, 2014
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
Multiuser Block Diagram
Communication Scenario and Objective
BS
a1 · · · aM
MS1
MS2
MSK
h 1
h2
hK
Scenario
• MS1, MS2, MSK are separated in spaceand 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
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
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
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
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
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
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
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 + Nwhere X = [x1 x2 x3]
N = [n1 n2 n3]
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 12
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 + Nwhere X = [x1 x2 x3]
N = [n1 n2 n3]
⇒ YXH = H + NXH
hk = hk + NxHk
⇒ Requires N ≥ K
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 5 / 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
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 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)
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 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 + Nwhere H = [h1, · · · ,hK ]
X = [x1, · · · , xN ]N = [n1, · · · ,nN ]
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 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 + Nwhere H = [h1, · · · ,hK ]
X = [x1, · · · , xN ]N = [n1, · · · ,nN ]
⋄ Represent : hk = WHk Yuk
ξk = tr{E{|hk − hk |2}}= uH
k (∑K
i=1 gix ixHi + σ2IN)uk tr{(WH
k Wk )}+gk IM − (gk xH
k uk )tr{WHk } − (gk uH
k xk )tr{Wk}
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 6 / 12
Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h 1
h2
hK
x1
x2
xK
⋄ Represent : hk = WHk Yuk
ξk = tr{E{|hk − hk |2}}= uH
k (∑K
i=1 gix ixHi + σ2IN)uk tr{(WH
k Wk )}+gk IM − (gk xH
k uk )tr{WHk } − (gk uH
k xk )tr{Wk}
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairnessminxk ,uk ,Wk
∑Kk=1
1gkξk
s.t xHk xk ≤ Pk
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h 1
h2
hK
x1
x2
xK
⋄ Represent : hk = WHk Yuk
ξk = tr{E{|hk − hk |2}}= uH
k (∑K
i=1 gix ixHi + σ2IN)uk tr{(WH
k Wk )}+gk IM − (gk xH
k uk )tr{WHk } − (gk uH
k xk )tr{Wk}
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairnessminxk ,uk ,Wk
∑Kk=1
1gkξk
s.t xHk xk ≤ Pk
⋄ Wk =gk xH
k uk∑Ki=1 gi xH
i uk uHk x i+σ2uH
k ukIM .
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h 1
h2
hK
x1
x2
xK
⋄ Represent : hk = WHk Yuk
ξk = tr{E{|hk − hk |2}}= uH
k (∑K
i=1 gix ixHi + σ2IN)uk tr{(WH
k Wk )}+gk IM − (gk xH
k uk )tr{WHk } − (gk uH
k xk )tr{Wk}
⋄ ξk depends on gk ⇒ higher gk higher ξk
⇒ To incorporate fairnessminxk ,uk ,Wk
∑Kk=1
1gkξk
s.t xHk xk ≤ Pk
⋄ Wk =gk xH
k uk∑Ki=1 gi xH
i uk uHk x i+σ2uH
k ukIM .
⋄ ξk = M(
gk − uHk (g
2k xk xH
k )uk
uHk (
∑Ki=1 gi x i xH
i +σ2IN )uk
)
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 7 / 12
Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h 1
h2
hK
x1
x2
xK
⋄ Wk =gk xH
k uk∑Ki=1 gi xH
i uk uHk x i+σ2uH
k ukIM .
⋄ ξk = M(
gk − uHk (g
2k xk xH
k )uk
uHk (
∑Ki=1 gi x i xH
i +σ2IN )uk
)
⋄ ˜ξk = Mgk − Mg2
k xHk A−1xk
where A =∑K
i=1 gix ixHi + σ2I
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 8 / 12
Proposed Solution
Proposed Solution
BS
a1 · · · aM
MS1
MS2
MS3
h 1
h2
hK
x1
x2
xK
⋄ Wk =gk xH
k uk∑Ki=1 gi xH
i uk uHk x i+σ2uH
k ukIM .
⋄ ξk = M(
gk − uHk (g
2k xk xH
k )uk
uHk (
∑Ki=1 gi x i xH
i +σ2IN )uk
)
⋄ ˜ξk = Mgk − Mg2
k xHk A−1xk
where A =∑K
i=1 gix ixHi + σ2I
⋄ minxk tr{Q−1k } − gk xH
k Q−2k xk
1+gk xHk Q−1
k xk
s.t xHk xk ≤ Pk
where Qk =∑K
i=1,i 6=k gix ixHi + σ2IN
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 8 / 12
Simulation Results
Effect of SNR
Parameters: M = 128, N = 16, K = 32, Pk = 1mw, SNR = Pavσ
2
0 2 4 6 8 10 12 14 150.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
SNR (dB)
Nor
mal
ized
WS
MS
E
Existing algorithmProposed algorithm
g =
0.04 0.74 0.81 0.260.70 0.29 0.08 0.870.07 0.74 0.12 0.440.59 0.63 0.53 0.200.67 0.24 0.72 0.400.39 0.41 0.14 0.870.02 0.92 0.63 0.060.63 0.75 0.76 0.06
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 9 / 12
Simulation Results
Effect of Number of pilots (N)
Parameters: M = 128, K = 32, Pk = 1mw, SNR = Pavσ
2
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)
Nor
mal
ized
WS
MS
E
Existing (Orange) and proposed (Blue) algorithms
SNR = 18dB
SNR = 12dB
SNR = 6dB
g =
0.04 0.74 0.81 0.260.70 0.29 0.08 0.870.07 0.74 0.12 0.440.59 0.63 0.53 0.200.67 0.24 0.72 0.400.39 0.41 0.14 0.870.02 0.92 0.63 0.060.63 0.75 0.76 0.06
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 10 / 12
Simulation Results
Convergence speed and effect of initialization
Parameters: M = 128, N = 16, K = 32, Pk = 1mw, SNR = Pavσ
2
5 10 15 20 25 30 35 400.75
0.755
0.76
0.765
0.77
0.775
0.78
0.785
0.79
0.795
0.8
Iteration number
Nor
mal
ized
WS
MS
E
SNR = 0dB
DFT matrix with pilot reuseTruncated DFT matrixRandom matrix
5 10 15 20 25 30 35 400.67
0.68
0.69
0.7
0.71
0.72
0.73SNR = 3dB
Iteration number
Nor
mal
ized
WS
MS
E
DFT matrix with pilot reuseTruncated DFT matrixRandom matrix
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 11 / 12
Conclusions
Conclusions
In this work, we accomplish the following main tasks.
We propose new pilot assignment and channel estimationalgorithm (especially for Massive MIMO system)
The proposed algorithm employs WSMSE as an objective function
To solve the problem, we apply MMSE and Rayleigh quotientmethods
The proposed algorithm achieves the optimal pilot and estimatedchannel when K = N
Tadilo (CISS, Princeton, NJ, USA, Mar. 2014) Channel estimation March 20, 2014 12 / 12
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