Pilot Contamination Mitigation for Wideband Massive MIMO: Number of Cells Vs Multipath

Pilot Contamination Mitigation for WidebandMassive MMO: Number of Cells Vs Multipath

T. E. Bogale+, L. B. Le+, X. Wang++ and L. Vandendorpe+++

Institute National de la Recherche Scientifique (INRS), Canada+

University of Western Ontario (UWO), Canada++

University Catholique de Louvain (UCL), Belgium+++

Dec. 07, 2015 (Globecom 2015)

Presentation outline

Presentation Outline

1 Existing Channel Estimation (Summary)OFDM ApproachNon-OFDM Approach

2 Multicell Channel Estimation and Objective

3 Proposed Channel Estimation and Beamforming: Main Results

4 Proposed Joint Channel Estimation and Beamforming: Details

5 Simulation Results

6 Conclusions

(Globecom 2015) Pilot Contamination Dec. 07, 2015 (Globecom 2015) 2 / 10

Existing Channel Estimation (Summary) OFDM Approach

Existing Channel Estimation: OFDM

Assumptions

Pilot duration Tp, bandwidth B and delay spread Td are known

Existing Channel Estimation Technique:

OFDM Approach (i.e., Frequency domain approach)Non-OFDM Approach (i.e., Time domain approach)

OFDM Approach:

If To is OFDM duration and Tu is useful symbol duration, maximum number of UEs are[Marz TWC 10] and [Fern JSAC 13]

Example: LTE signal with ∆f = 15KHz, Tu = 1∆f = 66.7µs, Tp = To, Td = 4.69µs,

K = TuTd≈ 14 (L = Ns

K sub-carriers per UE)

Assumptions

OFDM Approach:

Existing Channel Estimation (Summary) OFDM Approach

Assumptions

OFDM Approach:

Assumptions

OFDM Approach:

Existing Channel Estimation (Summary) Non-OFDM Approach

Existing Channel Estimation: Non-OFDM

Same settings as OFDM (i.e., Ts = TuNp

, L = TdTs

=NpK multipaths

between k th UE and nth BS antenna hkn = [hk1n, hk2n, · · · , hkLn])

rn =K∑

Xk hkn + wn = Xhn + wn

where X = [X1,X2, · · · ,XK ], hn = [h1n, h2n, · · · , hKn] and

xk1 0 · · · 0 0

xk2 xk1 · · ·...

...xk3 xk2 · · · 0 0...

... · · ·...

...xk(Np−1)

xk(Np−2)· · · xk(Np−L+1)

xk(Np−L)

xkNpxkNp−1 · · · xk(Np−L+2)

xk(Np−L+1)

If K =

NpL = Ns

Np, X is full row-rank (i.e., hn is estimated reliably)

Multicell Channel Estimation and Objective

Existing Channel Estimation: Mult-cell

∴ In Tu duration, CSI of K UE can be learned (i.e., each UE uses L”net” sub-carriers (time-slots) in OFDM (Non-OFDM))

(Same resource in both freq and time domain CSI acquisitions)

Each BS equipped with massive (N →∞) antennas serve K UEs

(i.e., use Tp to learn CSI)

No CoMP transmission is required (Advantageous)

Reusing of CSI pilots over multiple cells: ”Pilot contamination” (each UESINR will be bounded) (Disadvantage)

(i.e., only one cell Nc = 1 can serve its UEs without Pilot contamination)

OBJECTIVE

For fixed B, L, Tp and each cell serves K UEs, can weincrease Nc more than one ensuring that each UEachieve unbounded sub-carrier SINR when N →∞?

(i.e., mitigate (cancel) pilot contamination)

Multicell Channel Estimation and Objective

OBJECTIVE

For fixed B, L, Tp and each cell serves K UEs, can weincrease Nc more than one ensuring that each UEachieve unbounded sub-carrier SINR when N →∞?

(i.e., mitigate (cancel) pilot contamination)

Proposed Channel Estimation and Beamforming: Main Results

Proposed Design (Summary)

Three step approach

Allow pilot transmission in time domain (i.e., Non-OFDM)Express estimate of each sub-carrier channel as linearcombination (LC) of received signal in CSI acquisition phaseOptimize Nc , pilots and LC terms ensuring unbounded SINR

Three step approach

Main Results

Using the proposed design, Nc = L cells can reliably estimate the CSIwhile ensuring unbounded SINR

There is a Non-zero gap between the rate achieved by proposeddesign (i.e., CSI estimation and beamforming) and perfect CSI

⇒ ONLY mitigating pilot contamination

Multipath taps L, analogous to OFDM CP size, increases with B

∴ Wideband massive MIMO helps increase Nc

A total of Np = KNc UEs are served in all cells

∴ Each UE effectively uses one ”net” pilot for any B (interpretation)

Proposed Channel Estimation and Beamforming: Main Results

Three step approach

Main Results

Using the proposed design, Nc = L cells can reliably estimate the CSIwhile ensuring unbounded SINR

There is a Non-zero gap between the rate achieved by proposeddesign (i.e., CSI estimation and beamforming) and perfect CSI

⇒ ONLY mitigating pilot contamination

Multipath taps L, analogous to OFDM CP size, increases with B

∴ Wideband massive MIMO helps increase Nc

A total of Np = KNc UEs are served in all cells

∴ Each UE effectively uses one ”net” pilot for any B (interpretation)

Proposed Joint Channel Estimation and Beamforming: Details

Proposed Design: Details

Rx signal from CSI acquisition (nth antenna in i th BS)

rin =K∑

(Xki hkiin +

Nc∑j=1,j 6=i

Xkj hkjin) + win

Introduce LC vector and express hkiins = rTinvkis

Beamforming phase

yins =K∑

Nc∑j=1

hkjinsdkjs + wins, ⇒ dkis = aHkiisyis

SINR dkis

γkis =E|hH

kiisakiis|2∑(m,j) 6=(k,i) E|hH

mjisakiis|2 + E|wHisakiis|2

MRC Beamforming

MRC receive beamformer akiis

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

X∗mjCmjiXTmj + σ2I

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

where C(.) is related to channel covariance information

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

Observation

X∗mjCmji f∗s fTs CmjiXT

mj : Scales with N2 (dominant)

Other terms scale with N, L or Np (can be ignored for very large N)

⇒ γkis ≈vH

(X∗kiCkii f∗s fT

s CkiiXTki

(∑Km=1

∑Ncj=1,(m,j)6=(k,i) X∗mjCmji f∗s fT

s CmjiXTmj

∣∣∣∣large N

Determination of number of cells Nc

Choose Nc ensuring γkis →∞ as N →∞ (i.e., get no. of cells)

|fTs CkiiXT

kivkis|, s.t fTs CmjiXT

mjvkis = 0,∀(m, j) 6= (k , i)

Using rank analysis, vkis 6= 0 exists iff Nc ≤ L for any C(.) (i.e., if Nc > L,equality constraints may not be satisfied) (see Theorem 1 of paper)

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

Optimization of Pilots and LC terms (Xmj and vkis)

For given Nc , optimize vkis,Xmj to get max ¯γkis(γkis) for arbitrary N

For fixed Nc , Xmj , maxvkis ¯γkis(γkis) is RQ (closed form)Choose noise like orthogonal xmj ∈ CNp×1,∀m, j (suboptimal)(Ensures balanced sub-carrier rate, e.g., random QPSK samples)xmj from Zadoff Chu seq. achieves superior rate (not used in paper)(Zadoff Chu sequences: Flat spectrum and used in LTE Ref. signal)

rin =K∑

(Xki hkiin +

Nc∑j=1,j 6=i

Xkj hkjin) + win

Beamforming phase

yins =K∑

Nc∑j=1

SINR dkis

γkis =E|hH

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

Observation

⇒ γkis ≈vH

s CkiiXTki

(∑Km=1

s CmjiXTmj

∣∣∣∣large N

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

rin =K∑

(Xki hkiin +

Nc∑j=1,j 6=i

Xkj hkjin) + win

Beamforming phase

yins =K∑

Nc∑j=1

SINR dkis

γkis =E|hH

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

Observation

⇒ γkis ≈vH

s CkiiXTki

(∑Km=1

s CmjiXTmj

∣∣∣∣large N

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

rin =K∑

(Xki hkiin +

Nc∑j=1,j 6=i

Xkj hkjin) + win

Beamforming phase

yins =K∑

Nc∑j=1

SINR dkis

γkis =E|hH

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

Observation

⇒ γkis ≈vH

s CkiiXTki

(∑Km=1

s CmjiXTmj

∣∣∣∣large N

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

rin =K∑

(Xki hkiin +

Nc∑j=1,j 6=i

Xkj hkjin) + win

Beamforming phase

yins =K∑

Nc∑j=1

SINR dkis

γkis =E|hH

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

MRC Beamforming

E|wHi akiis|2 =vH

( K∑m=1

Nc∑j=1

E|hHmjisakiis|2 =vH

(X∗mj

[Cmji f∗s fT

s Cmji +K∑

Nc∑v=1,(u,v) 6=(m,j)

Cmjuvis

mj + σ2tr{Cmjis}I)

Observation

⇒ γkis ≈vH

s CkiiXTki

(∑Km=1

s CmjiXTmj

∣∣∣∣large N

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

|fTs CkiiXT

mjvkis = 0,∀(m, j) 6= (k , i)

Simulation Results

2 3 4 5 6 7 8 9 100

Normalized number of antennas (N0)

ProposedLS (Pilot reuse)MMSE (Pilot reuse)LS (Orthogonal pilot)MMSE (Orthogonal pilot)EVD approach in [7]Approach in [9]

2 4 6 8 10 12 14 16 180

Proposed approachPerfect CSI

Rg << c

Rg ≈ c

REREFENCES

[7]: Q. N. Hien and E. G. Larsson,”EVD-based channel estimation in multicellmultiuser MIMO systems with very largeantenna arrays”, in ICASSP, 2012, Kyoto,Japan, 2012, pp. 3249 - 3252.

[9]: T. X. Vu, T. A. Vu, and T. S.Q Quek,”Successive pilot contamination elimination inmulti-antenna multi-cell networks,” IEEEWireless Commun. Letters, Nov. 2014.

PARAMETER SETTINGS

Multipath components L = 4, SNR=0dB

Pilot: Np = 16 (random QPSK symbols)

Number of cells Nc = L = 4, K = 4

Total number of BS antenna N=2N0

All multipath channels are i.i.d with gains

gk1i = 1,gk2i = 0.9,gk3i = 0.6,gk4i = 0.7,∀k

First UE in cell i is the target UE

2 4 6 8 10 12 14 16 18 200

c=5 (v

kis with (11))

Nc=5 (v

kis with (12))

Nc=6 (v

kis with (11))

Nc=6 (v

kis with (12))

REREFENCES

PARAMETER SETTINGS

gk1i = 1,gk2i = 0.9,gk3i = 0.6,gk4i = 0.7,∀k

First UE in cell i is the target UEOBSERVATIONS

Proposed design achieves better rate thanexisting designs in massive MIMO regime

There is a rate gap between proposed andperfect CSI designs even if N →∞

As expected, we have pilot contaminationwhen Nc > L = 4 (i.e., bounded rate)

Also Np = KNc confirms that our designspends only one ”net” pilot per UE irrespectiveof bandwidth (which is reduced by a factor of Lcompared to existing design)

∴ Treating wideband channel as it is helpsincreasing number of cells in massive MIMO

Simulation Results

2 3 4 5 6 7 8 9 100

ProposedLS (Pilot reuse)MMSE (Pilot reuse)LS (Orthogonal pilot)MMSE (Orthogonal pilot)EVD approach in [7]Approach in [9]

2 4 6 8 10 12 14 16 180

Proposed approachPerfect CSI

Rg << c

Rg ≈ c

REREFENCES

PARAMETER SETTINGS

gk1i = 1,gk2i = 0.9,gk3i = 0.6,gk4i = 0.7,∀k

First UE in cell i is the target UE

2 4 6 8 10 12 14 16 18 200

c=5 (v

kis with (11))

Nc=5 (v

kis with (12))

Nc=6 (v

kis with (11))

Nc=6 (v

kis with (12))

REREFENCES

PARAMETER SETTINGS

gk1i = 1,gk2i = 0.9,gk3i = 0.6,gk4i = 0.7,∀k

First UE in cell i is the target UEOBSERVATIONS

Proposed design achieves better rate thanexisting designs in massive MIMO regime

There is a rate gap between proposed andperfect CSI designs even if N →∞

As expected, we have pilot contaminationwhen Nc > L = 4 (i.e., bounded rate)

Also Np = KNc confirms that our designspends only one ”net” pilot per UE irrespectiveof bandwidth (which is reduced by a factor of Lcompared to existing design)

∴ Treating wideband channel as it is helpsincreasing number of cells in massive MIMO

Conclusions

We propose new joint channel estimation and beamformingdesign for multicell massive MIMO systemsThe proposed design exploits multipath components of frequencyselective wireless channelsThe proposed design allows Nc = L cells utilize the sametime-frequency resources while efficiently mitigating pilotcontaminationThe proposed design is applicable for arbitrary channel statisticsboth i.i.d and correlated (see also [Boga TSP 15])The proposed design can also be extended straightforwardly toother channel and beamformings (see [Boga TSP 15] for more details )The proposed design is simple to implement as the maincomplexity arises from Rayleigh quotient problem (similarcomplexity as matrix SVD)

References

T. E. Bogale, L. B. Le, X. Wang, and L. Vandendorpe, Pilot contaminationin wideband massive MIMO system: Number of cells vs multipath, IEEETrans. Signal Process. (submitted) (2015).

F. Fernandes, A. Ashikhmin, and T. L. Marzetta, Inter-cell interference innoncooperative TDD large scale antenna systems, IEEE J. Select. Areasin Commun. 31 (2013), no. 2, 192 – 201.

Q. N. Hien and E. G. Larsson, EVD-based channel estimation in multicellmultiuser MIMO systems with very large antenna arrays, ICASSP, 2012(Kyoto, Japan), 2012, pp. 3249 – 3252.

T. L. Marzetta, Noncooperative cellular wireless with unlimited numbersof base station antennas, IEEE Trans. Wireless Commun. 9 (2010),no. 11, 3590 – 3600.

T. X. Vu, T. A. Vu, and T. S.Q Quek, Successive pilot contaminationelimination in multi-antenna multi-cell networks, IEEE Wireless Commun.Letters (2014), 617 – 620.

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Pilot Contamination Mitigation for Wideband Massive MIMO: Number of Cells Vs Multipath

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