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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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)
• 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)