beamforming for multiuser massive mimo systems: digital versus hybrid analog-digital

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Beamforming for Multiuser Massive MIMO Systems: Digital versus Hybrid Analog-Digital Tadilo Endeshaw Bogale and Long Bao Le Institute National de la Recherche Scientifique (INRS), Canada Email: {tadilo.bogale, long.le}@emt.inrs.ca OBJECTIVES System Model: Multiuser Massive MIMO (mmWave) Problem: Weighted Sum Rate Maximization Design Hybrid Analog-Digital Beamforming Compare Hybrid and Digital Beamformings Examine effects of # RF chains and ADCs DIGITAL BEAMFORMING (Summary) Settings: The kth UE symbol d k ∈C S k ×1 BS and kth UE # ant, N and M k Received signal : r k = H H k K X i=1 B i d i + n k Estimated signal : ˆ d D k = W H k r k Digital Precoding: K i=1 B i d i ∈C N×1 Digital Estimation: W H k r k ∈C S k ×1 Needs N and M k RF chains at BS and kth UE Too expensive for Massive MIMO (N,M k large) HYBRID BEAMFORMING Goals: Use limited RF chains at BS and UEs (low cost) Employ PSs only for analog beamformer (low cost) Apply hybrid precoding and estimation Achieve same(closer) performance as digital one Main idea: Maintain A K i=1 ˜ B i d i K i=1 B i d i Maintain ˆ d Hy k = ˜ W H k F H k r k W H k r k = ˆ d D k Design ˜ B k C P t ×S k ( ˜ W k C P rk ×S k ) in digital Design A C N×P t (F k C M k ×P rk ) in analog Key Challenges ? Constraints: rank( ˜ W H k F H k ) P rk , |F k(ij) | 2 =1 rank(A[ ˜ B 1 , ··· , ˜ B K ]) P t , |A ij | 2 =1 PROPOSED HYBRID BEAMFORMING Motivation: Good hybrid solution approaches the digital one Choose HB matrix closer to that of DB one Minimize MSE between ˆ d D k and ˆ d Hy k Incorporate weight to ensure fairness Problem Formulation Step 1: Choose a reference DB Block diagonalization DB (simple) ˆ d D k = Z k Q k d k + ˜ U H hk n k (no interference) where Z k , Q k , ˜ U hk depend on H (see paper) Step 2: Design HB to solve WSMSE min A, ˜ B k , ˜ W k ,F k K X k=1 tr{(Z k p Q k ) -1 ξ k (Z k p Q k ) -1 } s.t ξ k =E{( ˆ d Hy k - ˆ d D k )( ˆ d Hy k - ˆ d D k ) H } K X k=1 tr{A ˜ B k ˜ B H k A H } = P max |A (i,j) | 2 =1, |F k(i,j) | 2 =1 Non Convex Objective Constraints PROPOSED ALGORITHM Given: Z k ,Q k , P max Tool: OMP Optimize ˜ W k , F k for all UEs For fixed ˜ W k , F k , k, optimize A, ˜ B k , k jointly FINISH SIMULATION RESULTS INTERESTING PROBLEM: Given an arbitrary reference DB, how many RF chains and PSs do we need ensuring HB=DB ? Simulation Parameter Settings: ULA channel with L k = 16 scatterers and K =4 BS and MS k # ant (RF chain): 128(KP rk ) and 32 (P rk ) -7.5 -5 -2.5 0 2.5 5 7.5 10 12.5 15 17.5 17.5 50 100 150 200 250 300 SNR (dB) Sum Rate (b/s/hz) Digital vs Hybrid: S k =8, P rk =16 Digital Hybrid (P rk =L k =16) 8 10 12 14 16 18 20 60 80 100 120 140 160 180 P rk Sum Rate (b/s/hz) Effect of P rk Digital (SNR = -4 dB) Hybrid (SNR = -4 dB) Digital (SNR = 6 dB) Hybrid (SNR = 6 dB) Huge Gap 2 4 6 8 10 12 20 40 60 80 100 120 140 S k Sum Rate (b/s/hz) Effect of S k Digital Hybrid (P rk = 8) Hybrid (P rk = 16) Big Gap Call for Papers for

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Page 1: Beamforming for Multiuser Massive MIMO Systems: Digital versus Hybrid Analog-Digital

Beamforming for Multiuser Massive MIMO Systems:Digital versus Hybrid Analog-Digital

Tadilo Endeshaw Bogale and Long Bao LeInstitute National de la Recherche Scientifique (INRS), Canada

Email: {tadilo.bogale, long.le}@emt.inrs.ca

OBJECTIVES

System Model: Multiuser Massive MIMO (mmWave)

Problem: Weighted Sum Rate Maximization

• Design Hybrid Analog-Digital Beamforming

• Compare Hybrid and Digital Beamformings

• Examine effects of # RF chains and ADCs

DIGITAL BEAMFORMING (Summary)

Settings: The kth UE symbol dk ∈ CSk×1

BS and kth UE # ant, N and Mk

⇒Received signal : rk = HHk

K∑i=1

Bidi + nk

Estimated signal : dDk = WHk rk

� Digital Precoding:∑Ki=1 Bidi ∈ CN×1

� Digital Estimation: WHk rk ∈ CSk×1

∴ Needs N and Mk RF chains at BS and kth UE

⇒ Too expensive for Massive MIMO (N,Mk large)

HYBRID BEAMFORMING

Goals:

• Use limited RF chains at BS and UEs (low cost)

• Employ PSs only for analog beamformer (low cost)

• Apply hybrid precoding and estimation

• Achieve same(closer) performance as digital one

Main idea:

• Maintain A∑Ki=1 Bidi ≈

∑Ki=1 Bidi

• Maintain dHyk = WHk FHk rk ≈WH

k rk = dDk

• Design Bk ∈ CPt×Sk(Wk ∈ CPrk×Sk) in digital

• Design A ∈ CN×Pt(Fk ∈ CMk×Prk) in analog

Key Challenges ?

• Constraints: rank(WHk FHk ) ≤ Prk, |Fk(ij)|2 = 1

rank(A[B1, · · · , BK ]) ≤ Pt, |Aij |2 = 1

PROPOSED HYBRID BEAMFORMING

Motivation:

• Good hybrid solution approaches the digital one

∴ Choose HB matrix closer to that of DB one

⇒ Minimize MSE between dDk and dHyk

Incorporate weight to ensure fairness

Problem Formulation

• Step 1: Choose a reference DB

� Block diagonalization DB (simple)

⇒ dDk = Zk√Qkdk + UH

hknk (no interference)

where Zk,Qk, Uhk depend on H (see paper)

• Step 2: Design HB to solve WSMSE

minA,Bk,Wk,Fk

K∑k=1

tr{(Zk√Qk)−1ξk(Zk

√Qk)−1}

s.t ξk = E{(dHyk − dDk )(dHyk − dDk )H}K∑k=1

tr{ABkBHk AH} = Pmax

|A(i,j)|2 = 1, |Fk(i,j)|2 = 1

Non Convex

� Objective

� Constraints

PROPOSED ALGORITHM

Given: Zk, Qk, PmaxTool: OMP

Optimize Wk,Fk

for all UEs

For fixed Wk,Fk,∀k,

optimize A, Bk,∀k jointly

FINISH

SIMULATION RESULTS

INTERESTING PROBLEM:

Given an arbitrary reference DB, how many RFchains and PSs do we need ensuring HB=DB ?

Simulation Parameter Settings:

� ULA channel with Lk = 16 scatterers and K = 4

� BS and MSk # ant (RF chain): 128(KPrk) and 32 (Prk)

−7.5 −5 −2.5 0 2.5 5 7.5 10 12.5 15 17.517.550

100

150

200

250

300

SNR (dB)

Sum

Rat

e (b

/s/h

z)

Digital vs Hybrid: Sk=8, P

rk=16

DigitalHybrid (P

rk=L

k=16)

8 10 12 14 16 18 2060

80

100

120

140

160

180

Prk

Sum

Rat

e (b

/s/h

z)

Effect of Prk

Digital (SNR = −4 dB)Hybrid (SNR = −4 dB)Digital (SNR = 6 dB)Hybrid (SNR = 6 dB)

Huge Gap

2 4 6 8 10 1220

40

60

80

100

120

140

Sk

Sum

Rat

e (b

/s/h

z)

Effect of Sk

DigitalHybrid (P

rk = 8)

Hybrid (Prk

= 16)

Big Gap

Call for Papers for

Wireless Communications Symposium

Scope and Motivation:

The Wireless Communications Symposium covers all aspects related to wireless

communications and its applications, with a focus on topics related to physical layer (PHY),

MAC layer, cross-layer, and physical layer-related network analysis and design. High quality

papers reporting on novel and practical solutions to PHY, MAC, and cross-layer design in

wireless communication systems are encouraged. In addition, papers on field tests and

measurements, field trials and applications from both industries and academia are of special

interest.

Main Topics of Interest:

To ensure complete coverage of the advances in wireless communications technologies for

current and future wireless systems, the Wireless Communications Symposium cordially invites

original contributions in, but not limited to, the following topical areas:

Advanced equalization, channel estimation and synchronization techniques

Broadband wireless access techniques and systems

Channel and network interference characterization and modeling

Channel state information feedback techniques

Coexistence in unlicensed spectra

Cross-layer design and physical-layer based network issues

Device-to-device and machine-to-machine communications

Digital video broadcasting (DVB) and digital audio broadcasting (DAB) techniques

Distributed multipoint, relay assisted, and cooperative communications

Field tests and measurements

Heterogeneous and femtocell networks

Hybrid wireless communication systems (e.g. satellite/terrestrial hybrids)

Interference management, alignment and cancellation, inter-cell interference coordination

(ICIC), and coordinated multi-point transmission (CoMP)

Localization techniques

MIMO, multi-user MIMO, and massive MIMO

Page 2: Beamforming for Multiuser Massive MIMO Systems: Digital versus Hybrid Analog-Digital

Beamforming for Multiuser Massive MIMO Systems:Digital versus Hybrid Analog-Digital

Tadilo Endeshaw Bogale and Long Bao LeInstitute National de la Recherche Scientifique (INRS), Canada

Email: {tadilo.bogale, long.le}@emt.inrs.ca

HYBRID BEAMFORMING (Block Diagram) [1]

Source Tx (Digital part) RF Chain Tx (Analog part)

Freq. Dom.

data source

d1

d2

dK

••

Freq. Dom.

digital BF

1

2

Pt

••

IFFT (row)

& add CP

1

2

Pt

••

RF1

analog

RF2

analog

RFPt

analog

••

AnalogBF

AnalogBF

AnalogBF

••

N

N

N

••

2

2

2

1

1

1

1

2

N

••

••

••

••

••

••

H

1 Discard CP& take FFT

d1 Decoded1

2 Discard CP& take FFT

d2 Decoded2

K Discard CP& take FFT

dK DecodedK

••

d B Ark = hH

k ABd+ nk

If OFDMA

If OFDMA

HYBRID BEAMFORMING [1]

Settings: K single antenna UEs and N >> K

⇒ rk = hHk Bd + nk [Digital]

• For any B, rank(B) ≤ K

• UQ = svd(B), with UHU = IK , Q ∈ CK×K

⇒ rk = hHk UQd + nk

Goal

• Step 1: Design Q in Digital (K RF Chains OKEY)

• Step 2: Design U in Analog with PSs only (HOW ?)

since Umn = amnejθmn , amn ≤ 1, |Umn| 6= 1 if amn 6= 1

Key Result:

• Theorem 1 of [1]: amn = ej cos−1( amn

2 ) + e−j cos−1( amn

2 )

⇒ Umn = ej(cos−1( amn

2 )+θmn) + e−j(cos−1( amn

2 )−θmn)

⇒ Umn ≡ 2PSs (U can be implemented with 2NK PSs)

∴ B = Q and A = U

Given an arbitrary reference DB, how many RF chains andPSs do we need ensuring HB=DB ?

� MISO System: Maximum of K RF chains and 2NK PSs

PSs can be reduced (see [1] for details)

RF chains can be reduced if B is low rank [1]

� MIMO System: Can be extended like in [1]

REREFENCES

1. T. E. Bogale, L. Le, and A. Haghighat, Hybridanalog-digital beamforming: How many RF chains andphase shifters do we need?, IEEE Trans. (Submitted),http://arxiv.org/abs/1410.2609.

2. T. E. Bogale and L. B. Le, Beamforming for multiusermassive MIMO systems: Digital versus hybridanalog-digital, in Proc. IEEE Global CommunicationsConference (GLOBECOM), Austin, Tx, USA, 10-12 Dec.2014.

3. O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R.W. Heath, Spatially sparse precoding in millimeter waveMIMO systems, IEEE Tran. Wirel. Com., Jan. 2014.

4. S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A.Thomas, and A. Ghosh, Millimeter wave beamforming forwireless backhaul and access in small cell networks, IEEETrans. Commun., vol. 61, no. 10, Oct. 2013.

5. X. Zhang, A. F. Molisch, and S-Y. Kung,Variable-phase-shift-based RF-Baseband codesign forMIMO antenna selection, IEEE Trans. Signal Process.,vol. 53, no. 11, pp. 4091 4103, Nov. 2005.

6. J. Tropp and A. Gilbert, Signal recovery from randommeasurements via orthogonal matching pursuit, IEEETran. Info. Theory Dec. 2007.

7. T. Yoo and A. Goldsmith, On the optimality ofmultiantenna broadcast scheduling using zero-forcingbeamforming, IEEE Trans. Sel. Area. Commun., vol. 24,no. 3, pp. 528 541, Mar. 2006.

SOME SIMULATION RESULTS [1]

OPEN PROBLEM

For any H and reference DB, how to reduce RFchains < K while ensuring HB=DB ?

Simulation Parameter Settings:

� Downlink MISO and Flat fading ULA channel

� ZF reference DB, N = 64 and K = 16

� NPS denotes # PSs and SNR = 10dB

2 4 6 8 10 120

10

20

30

40

50

60

70

80

Ave

rage

sum

rat

e (b

/s/h

z)

Pt=16 RF chains

Number of scatterers (Lk)

DBHB in [1] (N

PS=98)

HB in [1] (NPS

=40)

HB in [1] (NPS

=20)

HB in [2] (NPS

=64)

HB in [3] (NPS

=64)

Antenna selection DB

2 4 6 8 10 1230

35

40

45

50

55

60

65

70

75

80

Number of scatterers (Lk)

Ave

rage

sum

rat

e (b

/s/h

z)

Pt=24 RF chains

DBHB in [1] (N

PS=98)

HB in [1] (NPS

=40)

HB in [1] (NPS

=20)

HB in [2] (NPS

=64)

HB in [3] (NPS

=64)

Antenna selection DB

CONCLUSIONS

• DB achieves the best performance

• Significant performance loss is incurred in HBapproaches of [2] and [3] when Lk is large (e.g.,Rayleigh fading)

• HB approach of [1] uses the lowest RF chains andPSs, and achieves same performance as DB

• Number of PSs can be reduced with negligibleperformance loss [1] (see also the above plot)

Call for Papers for

Wireless Communications Symposium

Scope and Motivation:

The Wireless Communications Symposium covers all aspects related to wireless

communications and its applications, with a focus on topics related to physical layer (PHY),

MAC layer, cross-layer, and physical layer-related network analysis and design. High quality

papers reporting on novel and practical solutions to PHY, MAC, and cross-layer design in

wireless communication systems are encouraged. In addition, papers on field tests and

measurements, field trials and applications from both industries and academia are of special

interest.

Main Topics of Interest:

To ensure complete coverage of the advances in wireless communications technologies for

current and future wireless systems, the Wireless Communications Symposium cordially invites

original contributions in, but not limited to, the following topical areas:

Advanced equalization, channel estimation and synchronization techniques

Broadband wireless access techniques and systems

Channel and network interference characterization and modeling

Channel state information feedback techniques

Coexistence in unlicensed spectra

Cross-layer design and physical-layer based network issues

Device-to-device and machine-to-machine communications

Digital video broadcasting (DVB) and digital audio broadcasting (DAB) techniques

Distributed multipoint, relay assisted, and cooperative communications

Field tests and measurements

Heterogeneous and femtocell networks

Hybrid wireless communication systems (e.g. satellite/terrestrial hybrids)

Interference management, alignment and cancellation, inter-cell interference coordination

(ICIC), and coordinated multi-point transmission (CoMP)

Localization techniques

MIMO, multi-user MIMO, and massive MIMO