Precoding and Massive MIMO - Tohoku University Official ... · PDF filePrecoding and Massive MIMO Precoding and Massive MIMO ... I A full diversity order is equal to the number of

Precoding and Massive MIMO


Jinho ChoiSchool of Information and Communications

GIST

October 2013

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1. Introduction

2. Overview of Beamforming Techniques

3. Cooperative (Network) MIMO3.1 Multicell with a common group of users3.2 Multicell with different groups of users

4. Massive MIMO4.1 Partial cooperation4.2 Pilot contamination in massive MIMO4.3 Pilot contamination precoding

5. Conclusions

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1. Introduction

1. Introduction

I Beamforming with antenna arrays has been studied forwireless communications since early 90s.

I Transmit and receive beamforming have been considered forcellular systems to improve the signal-to-noise ratio (SNR) orextend the coverage.

I A better beamforming gain can be achieved if the number ofantennas in an array is large.

I In cellular systems, as base stations (BSs) can have a numberof antennas, beamforming can be easily employed at BSs.

I In this case, transmit beamforming becomes downlinkbeamforming and receive beamforming becomes uplinkbeamforming.

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1. Introduction

Downlink beamforming = transmit beamforming at BS

Beamforming and Massive MIMO

1. Introduction

Downlink beamforming = transmit beamforming at BS

Beamformer

w1

wL

w2

Data symbols

Beampattern

Dynamic or static

4 / 604 / 64


1. Introduction

I Unfortunately, due to various problems, the number ofantenna elements in an array for downlink beamforming islimited.

I However, in 5G, transmit (or downlink) beamforming has beenconsidered seriously to extend the coverage.

I In this tutorial, we review existing downlink beamformingapproaches and focus on cooperative and noncooperativeapproaches in multi-cell MIMO systems.

I In the end, we wil attempt to highlight the differences betweennetwork MIMO and massive MIMO in multi-cell systems.

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1. Introduction

How transmit beamforming works:

TX 2

1h

2h

TX 1

Let h1 and h2 denote the channel coefficients from TX antennas 1and 2, respectively. If TX antenna k transmits wks, where wk isthe weight and s is the signal to be transmitted, the received signalbecomes

r = h1w1s+ h2w2s+ n = (h1w1 + h2w2)s+ n,

where n is the background noise.

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1. Introduction

The SNR at the receiver becomes

SNR =|h1w1 + h2w2|2Es

N0≤ ||h||

2||w||2EsN0

,

where the equality holds if wk ∝ h∗k.

I A full diversity order is equal to the number of antennas.

I The more transmit antennas, the better performance.

I However, the channel state information (CSI) is required fortransmit beamforming to achieve the maximum SNR.

I If the transmitter does not know the CSI, the receiver has tofeed back it to the transmitter.

I With limited feedback, the number of antennas cannot belarge, which has been one of the major drawbacks of transmitbeamforming, which may not be a drawback in TDD mode(using the channel reciprocity).

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2. Overview of Beamforming TechniquesI There are three different systems where beamforming can be

employed:A. Point-to-point MIMO (single-user beamforming)B. Multiuser (point-to-multipoint) MIMO (multiuser

beamforming)C. Multipoint-to-multipoint (or network) MIMO (cooperative

beamforming)

I We can also consider a different system in which beamformingplays a crucial role:

D. Massive MIMO: this is the case where single-user beamformingis employed in a multi-cell system

I For cellular systems,I single-cell: point-to-point or multiuser MIMOI multi-cell: network MIMO (there is inter-cell interference

problem), massive MIMO

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A. Point-to-point MIMOI To achieve diversity gain:

I beamforming with CSI at transmitterI space-time coding (STC) without CSI at transmitter

I To achieve multiplexing gain:I SVD with CSI at transmitterI BLAST techniques without CSI at transmitter

I There are also other techniques that enjoy the trade-offbetween diversity and multiplexing gains

Ref. Zheng and Tse, “Diversity and Multiplexing: A FundamentalTradeoff in Multiple Antenna Channels,” IEEE TIT, May 2003

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Beamforming for point-to-point MIMO

I It is often known as single-user beamforming

I To maximize the SNR, the principle of matched filtering (MF)can be employed when CSI is available, which is known asmaximal ratio transmission (MRT) scheme in the context ofMIMO.

I There are also other approaches without CSI or partial CSI:I Blind beamforming (or long-term transmit beamforming) with

statistical properties of channelsI Semi-blind beamforming (with partial CSI)I Diversity beamforming (with channel coding): compared to

blind beamforming, it can achieve a diversity gainRef. J. Choi, “Diversity eigenbeamforming for coded signals,” IEEE

TCOM, June 2008.

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4 6 8 10 12 14 16

10−4

10−3

10−2

10−1

SNR (dB)

BER

Coded

D−eigenEigen − 1Optimized

Performance of blind beamforming (Eigen-1), diversitybeamforming (D-eigen and Optimized)

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B. Multiuser MIMO

I There exists interference due to the presence of multiplesignals to be transmitted to multiple users.

I Dirty paper coding (DPC) can achieve the channel capacityby suppresing known interference. However, itsimplementation is not easy.

I Multiuser beamforming can provide a reasonable performancewith low-complexity.

I A better performance can be achieved with multiuser diversity& user selection

I CSI at BS is required to mitigate the (intra-cell) interference:I No feedback in TDD: channel reciprocity can be usedI Feedback in FDD: excessive overhead

I Resource allocation (including power control) becomes acrucial.

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Capacity of multiuser MIMOI Dirty paper coding: it can achieve the capacity, but difficult

to implement

Csum = EmaxPk

log det(I + HPHH)

≥ E log det(I +Ptotal

KHHH)(equal power)

I Multiuser diversity: it is simple, but overall throughput is low

Cmd = E log(1 + Ptotal maxk||hk||2)

I Multiuser beamforming: if user selection is combined, it itsupper bound is proportional to the number of selected users(scaling law is applied):

Cmb ≤ E∑

k∈Uorthogonal

log(1 + Pk||hk||2)

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0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

25

30

Achievable Rate

Csum (equal power)CmdCmbeam (approx.)

60 users, 4 users are selected in multiuser downlink beamforming

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Conventional Multiuser Beamforming Problem (without userselection)

Mobile terminal

Base station

Mobile terminal

Mobile terminal

I wk: beamforming vector to user k; hk: channel vector to userk, Pk = E[|sk|2]: TX power to user k multiuser beamforming,where sk is the signal to user k

I TX signal:∑K

k=1 wksk15 / 64



Multiuser joint beamforming and power control:

Pk, wk = arg min∑

k Pk

subject to

Pq |hH

q wq |2∑k 6=q Pk|hH

q wk|2+σ2q≥ γq

||wq||2 = 1

I This is an optimization problem to minimize the totaltransmission power subject to SINR constraints.

I Based on the uplink-downlink duality, this problem has beensolved.

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C. Network (or Cooperative) MIMO

I Highly sophisticated systems to deal with intra-cell as well asinter-cell interference (ICI)

I Known techniquesI Cooperative transmissions (e.g., CoMP)I Interference alignment

I Distributed nature

I Backhaul transmissions

I Interference channel models

I There should be the trade-off between performance andcomplexity (or overhead)

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TX

TX

TX RX

RX

RX

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Remarks on beamforming in network MIMO:

I AdvantagesI Easy to implementI Optimal solutions to most beamforming optimization problems

are known (QoS can be guaranteed)I Spatial multiplexing gain with reasonable performances

I DisadvantagesI Not capacity-achieving schemesI Most (downlink) beamforming methods require CSI at BS.I Furthermore, in network MIMO, BSs in cooperation need to

share their CSI.

I Dilemma in FDD modeI Due to limited CSI feedback, it is prohibitive to use large

antenna arrays.I However, with arrays of a few antenna elements, a significant

performance improvement may not be achieved.

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D. Massive MIMO

I TDD mode to exploit the channel reciprocity for the CSI atBS and make use of large antenna arrays

I Multi-cell, but noncooperative systems

I Due to noncooperative transmissions, no backhaulcommunications between BSs are required.

I But, systems can suffer from ICI.

I Using massive antenna arrays, ICI can be mitigated.

I Key issues: pilot contamination, array calibration, etc.

I There are other advantages. One of them is that theshort-term fading disappears by the law of large numbers.

I This makes resource allocation easy and reduces the burden ofchannel coding.

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3. Cooperative (Network) MIMO


I Network MIMO is to fully exploit the spatial gain in amulti-cell system

I In network MIMO, intercell interference can be mitigated bycooperation between BSs through backhaul links:

Ref. 1 Karakayali, et al., “Network coordination for spectrally efficientcommunications in cellular systems,” IEEE Comm. Mag.,2006.

Ref. 2 Gesbert, et al., “Multi-cell MIMO cooperative networks: a newlook at interference,” IEEE JSAC, 2010.

I Provided that each BS in cooperation is equipped with anantenna array, cooperative beamforming can mitigate intercellas well as intracell interference in downlink transmissions.

I Regardless of its implementability, it may provide performancebounds.

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BS

BSBS

BSs in cooperation need to share users’ data and/or CSI to theirusers through a backhaul network.

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Levels of cooperation between BSs through backhaul links:

I full cooperation: BSs share all CSI and signals (this isequivalent to the case of a big BS with distributed arrays or asingle big cell)

I partial cooperation 1: BSs share all CSI, but not signals

I partial cooperation 2: BSs share all signals, but not CSI

I partial cooperation 3: each BS has its local CSI and signals(but limited information can be exchanged between BSs forsuch as user allocation)

The cooperation would be limited by backhaul overhead. Thus,effective partial cooperation, not full cooperation, is desirable inpractice.

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3.1 Multicell with a common group of users


1. All BSs in cooperation support a common group of users(these users would be cell-edge users).

2. The cooperation between BSs is limited (if there is nolimitation, this scenario is equivalent to a single-cell).

3. Each BS has local CSI, which is the channel vectors from theBS to all users in a common group, while other BSs’ CSI isunknown.

4. There could be some cooperation between BSs such as userallocation.

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ZF-DPC precoding in a multicell system

Ref. Ho, et al., “Decentralized precoding for multicell MIMOdownlink,” IEEE TWC, 2011.

Assumptions:I There are Q BSs in cooperation and N users per cell (there

are K = QN users in total).I Each BS is equipped with an antenna array of L elements.I The CSI from each BS to all K users (not just N in the cell)

is known by each BS, while the CSI from the other BSs tousers is not known.

I That is, at BS q, the CSI to K users are known, but not theCSI from BS q′ 6= q to K users.

I This partial CSI can allow block diagonalization to suppressintercell interference

I Within a cell, then DPC is used to suppress intracellinterference

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Key variables:Hq: L×K downlink channel matrix from BS q to all K usersGq: L×N submatrix of Hq (channel vectors to users in cell q from BS q)Wq: L×N beamforming matrix at BS qsq: N × 1 signal vector at BS qrq: N × 1 signal vector received by users in cell qnq: N × 1 noise vector received by users in cell q

LetHq = [Gq H−q].

The received signal vector at users in cell q is given by

rq = GHq

Q∑p=1

Wpsp + nq

Block diagonalization to avoid intercell interference:

HH−qWq = 0.

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For block diagonalization, orthogonal projection matrix can beused:

P⊥q = I−H−q(HH−qH−q

)−1HH−q.

The beamforming matrix can be

Wq = ζqP⊥q Gq,

where ζq is the normalization factor that is given by

ζq =

√N

||P⊥q Gq||F

The average power per beamforming vector is unity.

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user 2

G1

G2

Hï1

Hï2

BS1

BS2

W1

W2

user 1

Then, the received signal vector becomes

rq = GHq

Q∑p=1

ζqP⊥p Gpsp + nq

= ζqGHq P⊥q Gqsq + nq.

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Within rq, there exists intracell interference. Thus, sq has to beDPCed signals.

The sum rate becomes

C =

Q∑q=1

E[log2 det

(I + Ω|ζq|2ΨqΨ

Hq

)]where E[nqn

Hq ] = I, E[sqs

Hq ] = ΩI, and Ψq = GH

q P⊥q Gq.

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3.2 Multicell with different groups of users


I Each BS has its own group of users.

I There are Q BSs and each BS has N users.

I Each BS is equipped with L antennas for beamforming.

I In this case, local CSI at BS is not sufficient to suppress theintercell interference.

I In order to migitate both intercell and intracell interference bybeamforming, SINR could be considered.

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Key variables:

Hq,k: the L×N channel matrix from BS k to the users in cell qWq: the L×N beamforming matrixsq: the N × 1 signal vector from BS q

I Local CSI at BS k is H1,k,H2,k, . . . ,HQ,k.I Wq = [w1;q . . . wN ;q] decides the transmission power if

E[sqsHq ] = I, i.e.,

Pi;q = ||wi;q||2.

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The received signal at cell q is given by

rq =

Q∑k=1

HHq,kWksk + nq.

At user i in cell q, the received signal becomes

ri;q =

Q∑k=1

hHi;q,k

N∑u=1

wu;ksu;k + ni;q

= hHi;q,qwi;qsi;q +

∑u6=i

hHi;q,qwu;qsu;q︸︷︷︸

=intracell

+∑k 6=q

N∑u=1

hHi;q,kwu;ksu;k︸︷︷︸

=intercell

+ni;q

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I The SINR becomes

SINRi;q =|hHi;q,qwi;q|2∑

u6=i |hHi;q,qwu;q|2 +

∑k 6=q

∑Nu=1 |hH

i;q,kwu;k|2 + σ2i;q

In general, any beamforming algorithm that minimizes theSINR requires full CSI, which requires significant backhaultransmissions.

I Define the intercell interference at cell q as

Zi;q =∑k 6=q

N∑u=1

|hHi;q,kwu;k|2.

Note that this interference is not a function of Wq.

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Well-known multiuser beamforming problems:

I Maximization of SINR with power constraints

maxWq SINRi;qsubject to ||Wq||2F ≤ Pq

I Minimization of power with SINR constraints

min∑

q ||Wq||2Fsubject to SINRi;q ≥ Γi;q

I See SINR-based Joint Power Control and Beamformingto solve the above problem

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Interference leakage based approaches are also popular:

I Define the interference leakage from BS q to cell k as

Ik(Wq) = ||HHk,qWq||2F.

I To minimize the leakage to the other cells, we can have thefollowing constraint:

∑k 6=q

Ik(Wq) = tr

WHq

∑k 6=q

Hk,qHHk,q

Wq

≤ Iq,leak.

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Distributed optimization approaches:

I Forming a global optimization problem

I Decompose it into local optimization problems

I Each local optimization problem is solved at a BS and updatevariables through backhaul links

I Do iterations until a satisfactory performance is achieved

I Key references:

I Palomar and Chiang, “A tutorial on decomposition methodsfor network utility maximization,” IEEE JSAC, 2006.

I Chiang, et al., “Layering as optimization decomposition: amathematical theory of network architectures,” Proc. IEEE,2007.

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Example: – Dual decomposition

I The minimization of power with SINR constraints:

min∑Q

q=1Cq(Wq)subject to SINRi;q(Wq) ≥ Γi;q

where Cq(Wq) = ||Wq||2F.

I Using Lagrangian multipliers,

min

Q∑q=1

Cq(Wq)−Q∑q=1

N∑i=1

λi;q(SINRi;q(Wq)− Γi;q)

=

Q∑q=1

minWq

(Cq(Wq)−

N∑i=1

λi;q(SINRi;q(Wq)− Γi;q)

)︸︷︷︸

=local optimization

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I At each BS, the local optimiztion is carried out as follows:

Wq = arg minWq

Cq(Wq)−N∑i=1

λi;qSINRi;q(Wq)

I At a higher level (i.e., at a central unit), the master dualproblem is to update λ’s:

minλ

Q∑q=1

gq(λ)−N∑i=1

λi;qΓi;q, λ ≥ 0,

where

gq(λ) =

N∑i=1

λi;qSINRi;q(Wq)− Cq(Wq).

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I To update λ’s at a higher level, the following gradient methodcan be used:

λi;q(t+ 1) =[λi;q(t)− α

(SINRi;q(Wq)− Γi;q

)]+,

where [x]+ = max0, x and α > 0 is the step-size.

I Thus, BSs need to send their SINRs to a central unit and thiscentral unit sends λ’s to BSs.

I This approach would have a slow convergence rate, but itdoes not require excessive backhaul transmissions betweenBSs and a central unit.

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Example – Minimization interference leakage problem with SINR

min∑Q

q=1

∑Qk=1 Ik(Wq)

subject to SINRi;q(Wq) ≥ Γi;q

A direct decomposition can be considered. At each BS,

min∑

i wHi Xwi

subject to|hH

i wi|2∑q 6=i |hH

i wq |2+Zi≥ Γi

I X←∑

k 6=q Hk,qHHk,q

I wi ← wi;q

I hi ← hi;qI Zi ← Zi;q + σ2i;qI Γi ← Γi;q

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Since the ICI Zi;q(W−q) in the SINR depends on the otherbeamforming matrices, an iterative algorithm is required to solvethe NML beamforming problem, which consists of the followingtwo key steps.

I Solving the local minimization problem (at BS q):

W(`)q = arg minCq(Wq)

subject to|hH

i;q,qwi;q |2∑u6=i |hH

i;q,qwu;q |2+Zi;q(W(`−1)−q )+σ2

i;q

≥ Γi;q

I updating the ICI:

Zi;q(W(`)−q) =

∑k 6=q

N∑u=1

|hHi;q,kw

(`)u;k|

2,

which is fed back by the users (not by other BSs) to BS q.

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Low-Dimensional Beamforming

I Consider the following eigendecomposition:

X =∑k 6=q

Hk,qHHk,q + αI = EΛEH,

where E = [e1 . . . eL] and Λ = diag(λ1, . . . , λL).

I The local cost function becomes

Cq(W) =∑k 6=q

Ik(W) = tr(WHXW

)I The complexity can be reduced if a subspace of E used as

wi ≈ wi = EΛ−1/2vi,

where E = [e1 . . . eM ] and M < L.

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I With vi of size M × 1, we have

Cq(W) ≈N∑i=1

||vi||2

I The local optimization at BS q is carried out to minimizeCq(W) through vi of size M × 1.

I The subspace beamforming with optimized vi (not wi) can

reduce the complexity by a factor of(LM

)2.

I For highly correlated channels, this approximation may notresult in a significant loss.

I The complexity of the eigendecomposition of X may not besignificant if second order statistics are used:

X→ E[X] =∑k 6=q

E[Hk,qHHk,q] + αI = EΛEH.

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Simulation Results

I Three different approaches are used:I Approach A: The cooperative min-power beamforming with

target SINRI Approach B: The NML beamforming with target SINRI Approach C: The noncooprative minimum total power (NMP)

beamforming with the following cost function:

Cq(Wq) = ||Wq||2F,

which is to reduce the transmission power rather thaninterference leakage (an egoistic approach).

I Approach A is cooperative, while Approaches B and C arenoncooperative (i.e., no backhaul communications betweenBSs)

I The elements of channel matrices are independent Gaussian(no spatial correlation is considered)

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Feasibility results: The NMP beamforming (Approach C) cannotachieve target SINR, but both cooperative min-power beamformingand NML beamforming (Approaches A and B) can achieve targetSINR

4 6 8 10 12 14 16 18 202

4

6

8

10

12

14

16

18

20

Target SINR (dB)

Achi

eved

SIN

R (d

B)

CooperativeNoncoop. (min−power)Noncoop. (min−leakage)

L = 30, Q = 3, N = 5, and M = L = 3045 / 64




Approach A performs better than Approaches B and C, butrequires backhaul communications between BSs

4 6 8 10 12 14 16 18 2010

20

30

40

50

60

70

80

Target SINR (dB)

Tota

l tra

nsm

issi

on p

ower

(dB)

CooperativeNoncoop. (min−power)Noncoop. (min−leakage)

L = 30, Q = 3, N = 5, and M = L = 30

46 / 64




I Low-complexity versions of Approach B (NML): tradeoffbetween complexity and performance

I If M ≥ 20, no performance degradation is observed (note thatuncorrelated channels are used in simulations)

5 10 15 20 25 3024

26

28

30

32

34

36

M

Tota

l tra

nsm

issi

on p

ower

(dB)

L = 30, Q = 3, N = 5, and Γ = 10 dB47 / 64


4. Massive MIMO

4. Massive MIMO

I Proposed by Marzetta in 2010 to effectively mitigate ICIwithout any cooperation between BSs

I A massive MIMO system consists of BSs with large antennaarrays.

I The number of antenna elements is about 100.I Frequency reuse factor is 1 and orthogonal channels within a

cell (no intra-cell interference)I TDD to exploit the channel reciprocity.I The channel vector, h, from a BS to a user can be factorized

ash =

√βu,

where β is a parameter for large-scale fading andu ∼ CN

(0, 1

LI)

is a random vector for small-scale fading,where L 1.

48 / 64


4. Massive MIMO

Large Array

user user

Base Station

narrow beam

In each cell, each user has an orthogonal channel (i.e., no intra-cellinterference) and hk,q denotes the channel vector from BS q to theuser in cell k.

49 / 64


4. Massive MIMO

For a large L, the matched-filter (MF) beamforming can be used.The beamforming vector is given by

wk =hk,k||hk,k||

.

Since the received signal at the user in cell k is

rk = hHk,kwksk +

∑q 6=k

hHk,qwqsq + nk,

the SINR becomes

SINRk =Pk||hk,k||2∑

q 6=k Pq|hHk,qwq|2 + σ2k

.

50 / 64


4. Massive MIMO

ICI can be mitigated as L→∞ as the inner product of tworandom vectors, x = hk,k and y = hk,q, k 6= q, approaches 0.

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

|<x,

y>|2

L: number of antennas

This is the key idea of massive MIMO. That is, without anycooperation between BSs, it is possible to mitigate ICI byincreasing L (similar to CDMA). 51 / 64


4. Massive MIMO

Approximation for a large L:

I ||hk,q||2 → βk,qI uH

k,qwq ∼ CN (0, 1/L)⇒

∑q 6=k

Pq|hHk,qwq|2+σ2k =

∑q 6=k

Pqβk|uHk,qwq|2+σ2k ≈

1

L

∑q 6=k

Pqβk,q+σ2k.

I The approximate SINR is

SINRk =LPkβk,k∑

q 6=k Pqβk,q + Lσ2k

I In SINR, small-scale fading terms disappear – the SINR ismuch less fluctuated over time.

52 / 64


4. Massive MIMO

4.1 Partial cooperation


I Since the frequency reuse factor is 1, there exists ICI althoughit may not be significant for a large L (as shown in the SINRexpression).

I ICI can be further mitigated if ZF or MMSE beamforming canbe used in cooperation with adjacent BSs as in networkMIMO .

I However, it requires massive CSI exchange, which wouldprovide a marginal gain at the expense of excessive backhaulcommunications.

I There might be a tradeoff between ICI mitigation (high ICI fora small L) performance and the backhaul overhead (a largeoverhead for a large L) in the case of cooperation.

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4. Massive MIMO


I In order to improve the performance further, partialcooperation can be considered.

I Not exchange the CSI of fast-fading, but the CSI ofslow-fading, which is βk for large-scale fading.

I Then, the joint power control is carried out to minimize thetotal power of BSs in cooperation with SINR constraints.

I This partial cooperation can guarantee target SINR in massiveMIMO.

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4. Massive MIMO


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

target SINR (dB)

aver

age/

min

imum

SIN

R (d

B)

Average SINR (equal power)Average SINR (opt. power)Minimum SINR (equal power)Minimum SINR (opt. power)

Arrays of L = 100 elements, 3-cell, 4 users per cell

55 / 64


4. Massive MIMO

4.2 Pilot contamination in massive MIMO


I A main issue of massive MIMO is pilot contamination.

I As the coherence time is limited and the number of users percell can be large, the same set of orthogonal pilot sequencescan be used in all cells, which results in interference fromadjacent cell during the uplink training.

I The estimated uplink channel can be contaminated by theinterference and the performance of beamforming can bedegraded.

I This problem is called the pilot contamination. To mitigatethis problem, we can

I take into account interfering pilot signals from adjacent cells inestimating uplink channels;

I adjust precoding vectors to reduce the interference.

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4. Massive MIMO


Two-cell example (TDD: channel reciprocity)

I Assume that MRT precoding vectors are used from estimatedchannels.

57 / 64


4. Massive MIMO

4.3 Pilot contamination precoding


I For a large L, statistical precoding can be used to mitigatethe intercell interference resulting from pilot contamination.

I This scheme is called the pilot contamination precoding(PCP).

I Assume that there are K cells. The estimated channel vectorat the BS in cell k is

hk =

K∑q=1

hq,k + nk.

I The MF beamforming vector is used as:

wk =hk

||hk||.

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4. Massive MIMO


I Received signal at the user in cell k:

xk =

K∑q=1

hHk,qwqsq + vk

=

K∑q=1

sqαq

K∑t=1

hHk,qht,q + vk,

where αk = ||hk||.I Since hk,q =

√βk,quk,q and uk,q are iid, we have

uHk,qut,q → δk,q as L→∞ w.p. 1

I Thus, as L→∞, we have

xk =

K∑q=1

sqαqβk,q + vk.

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4. Massive MIMO


I Staking xk’s:

x = [x1 . . . xK ]T

=

[βk,qαq

][s1 . . . sK ]T + [v1 . . . vK ]T

= As + v,

where [A]k,q =βk,qαq

.I To avoid the interference, s can be replaced with

s→ Bs,

where B = A−1. This means that the BSs need to exchangethe channel information (elements in A) for precoding.

I The resulting received signal is

x = s + v.

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4. Massive MIMO


I Since each BS needs to estimate βk,q and αq = ||hq||, whichare related to slow fading coefficients only, their estimationcan be done precisely, and their exchange through a backhaulnetwork may not result in a heavy overhead.

I Note that the transmission power depends on B = A−1.

I DPC or VP technique can help reduce the total transmissionpower when precoding is used.

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4. Massive MIMO


Improvement by partial cooperation against pilot contamination

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

without PCP with PCP

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5. Conclusions

5. Conclusions

I Beamforming is a simple and effective means to increase SNRor coverage, which can be employed in more complicatedsystems as follows:

I Network MIMOI Cooperation between BSs with not too big arraysI More controls (for better performance)I Backhaul overhead for cooperation might be a critical issueI Distributed optimization will play a key role in reducing

backhaul overheadI Massive MIMO

I Noncooperation, each BS with a big array might be robustenough against ICI

I Less controls (for implementation)I There exists ICI, and due to it, there is difficulty to guarantee

certain performance in terms of SINR.I As a remedy, partial cooperation could be considered.

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5. Conclusions

I Network MIMO versus Massive MIMO:I Network MIMO is to reduce cooperation (full to partial

cooperation)I Massive MIMO is to introduce cooperation (no cooperation to

partial cooperation)

I In the end, network MIMO meets massive MIMO.

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