Pilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems
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The document presents a new pilot assignment and channel estimation algorithm for multiuser massive MIMO systems, aiming to enhance performance in downlink communication scenarios. It details the system model, problem statement, proposed solutions, and simulation results demonstrating improvements in channel estimation accuracy, particularly with the use of weighted mean squared error (WSMSE) as an objective function. The findings indicate that the algorithm is optimal when the number of users matches the number of pilots.
![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](https://image.slidesharecdn.com/ciss2014slide4-140607140721-phpapp01/85/Pilot-Optimization-and-Channel-Estimation-for-Multiuser-Massive-MIMO-Systems-3-320.jpg)
![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](https://image.slidesharecdn.com/ciss2014slide4-140607140721-phpapp01/85/Pilot-Optimization-and-Channel-Estimation-for-Multiuser-Massive-MIMO-Systems-8-320.jpg)
![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](https://image.slidesharecdn.com/ciss2014slide4-140607140721-phpapp01/85/Pilot-Optimization-and-Channel-Estimation-for-Multiuser-Massive-MIMO-Systems-9-320.jpg)
![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](https://image.slidesharecdn.com/ciss2014slide4-140607140721-phpapp01/85/Pilot-Optimization-and-Channel-Estimation-for-Multiuser-Massive-MIMO-Systems-12-320.jpg)
![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](https://image.slidesharecdn.com/ciss2014slide4-140607140721-phpapp01/85/Pilot-Optimization-and-Channel-Estimation-for-Multiuser-Massive-MIMO-Systems-13-320.jpg)
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
- 6. 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
- 7. 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
- 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
- 19. Simulation Results Effect of SNR Parameters: M = 128, N = 16, K = 32, Pk = 1mw, SNR = Pav σ2 0 2 4 6 8 10 12 14 15 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 SNR (dB) NormalizedWSMSE Existing algorithm Proposed algorithm 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 9 / 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