pilot optimization and channel estimation for multiuser massive mimo systems

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 ]



Conventional Channel Estimation (Orthogonal)

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

h3




BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

h3

x1

x2

x3

⋄ y1 = h1x11 + h2x21 + h3x31 + n1




BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

h3

x1

x2

x3

⋄ y1 = h1x11 + h2x21 + h3x31 + n1

y2 = h1x12 + h2x22 + h3x32 + n2




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




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]




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


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


Problem Statement

Problem Statement

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK



⋄ Assumptions : hk =√

gk hk

hk ∼ CN (0,1)


Problem Statement

Problem Statement

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK




gk hk

hk ∼ CN (0,1)

⋄ Problem : Y = HXH + Nwhere H = [h1, · · · ,hK ]

X = [x1, · · · , xN ]N = [n1, · · · ,nN ]


Problem Statement

Problem Statement

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK




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}


Proposed Solution

Proposed Solution

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK



k (∑K




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


Proposed Solution

Proposed Solution

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK



k (∑K




k xk )tr{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 .


Proposed Solution

Proposed Solution

BS

a1 · · · aM

MS1

MS2

MS3

h 1

h2

hK

x1

x2

xK



k (∑K




k xk )tr{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

)


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


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


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


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


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


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


pilot optimization and channel estimation for multiuser massive mimo systems

Engineering

gk hk hk cn0

hk tadilo ciss

nxh hk

gk im gk xh

h2 hk x1 x2 xk objective

h2 hk scenario ms1

gk higher gk higher

ms1 ms2 ms3 h