Optimal Design of Energy-Efficient Multi-User MIMO Systems 1

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1 Optimal Design of Energy-Efficient Multi-User MIMO Systems 1 Is Massive MIMO the Answer? Luca Sanguinetti (UPI/Supélec) luca.sanguinetti@unipi.it Joint work with: Emil Björnson (KTH/Supélec), Jakob Hoydis (Alcatel-Lucent), Mérouane Debbah (Supélec) Network of Excellence in Wireless COMmunications# 1 Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer? To appear IEEE TW Preprint available on arxiv: Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

2 Introduction What are the 5G expectations? Tons of Plenary Talks and Overview Articles Fulfilling dream of ubiquitous wireless connectivity Expectation: Many Metrics Should Be Improved in 5G Higher user data rates Higher area throughput Great scalability in number of connected devices Higher reliability and lower latency Better coverage with more uniform user rates Improved energy efficiency (green cellular networks) Conflicting Metrics! Impossible to maximize all metrics simultaneously Our goal: High energy efficiency (EE) with uniform user rates Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

3 Introduction How to measure energy efficiency? Energy Efficiency in bits/joule EE = Average Sum Throughput [bit/second] Power Consumption [Watt] Conventional Academic Approaches Maximize throughput with fixed power Minimize transmit power for fixed throughput New Problem: Balance Throughput and Power Consumption Crucial: Account for overhead signaling Crucial: Use reasonable power consumption model Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

4 PART I The EE Optimization Problem Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

5 Introduction Multi-user MIMO System #$%&'()*+,-).'/-$,&-01,-). #2'k +, f(x) ()*+,-).'xk!" Multi-User Multiple-Input Multiple-Output (MIMO) One BS with array of M antennas K single-antenna UEs with random locations x k R 2 (in meters) Share a flat-fading carrier Main Question: How should a multi-user MIMO system be designed to maximize energy efficiency? Optimization variables: M,K and R (user rate) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

6 System Model TDD mode!"#$%& '$#()*!"#$%& -./%*0$**$(% +(,%#$%& '$#()* +(,%#$%& -./%*0$**$(%!"#$%& /%%3#58*3* ζ 98#: U +(,%#$%&75 ζ 9;#: /%%3#58*3* U 1(23.3%4356#(4&75U 42/%%3#58*3* TDD mode Uplink pilots enable the BS to estimate the UE channels Channels are considered reciprocal BS uses uplink estimates for precoding Downlink pilots let each UE estimate its effective channel Parameters U = B C T C channel uses B C coherence bandwidth and T C coherence time ζ (ul) and ζ (dl) Ratio of uplink and downlink transmission (ζ (ul) +ζ (dl) = 1) τ (ul) K and τ (dl) K Pilot signaling Rate (in bit/second) per each UE Uplink rate ζ (ul) R Downlink rate ζ (dl) R Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

7 System Model Channel model and linear Processing Channel Model h k C M 1 {h k,n } channel between antenna n and UE k h k CN ( 0 M,l(x k )I M ) Rayleigh small-scale fading distribution l( ) : R 2 R Large-scale channel fading (we keep it generic) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

8 System Model Channel model and linear Processing Channel Model h k C M 1 {h k,n } channel between antenna n and UE k h k CN ( 0 M,l(x k )I M ) Rayleigh small-scale fading distribution l( ) : R 2 R Large-scale channel fading (we keep it generic) Linear processing with perfect knowledge of H = [h 1,h 2,...,h K ]) Uplink (MRC, ZF, and MMSE) H for MRC G = H ( H H H ) 1 for ZF (1) ( HP (ul) H H +σ 2 ) 1H I M for MMSE Downlink (MRT, ZF, and MMSE) H for MRT V = H ( H H H ) 1 for ZF (2) ( HP (ul) H H +σ 2 ) 1H I M for MMSE Setting V = G reduces computational complexity! (But not necessary) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

9 Uplink Achievable rates Under the assumptions of Gaussian codebooks, the achievable uplink rate (in bit/second) of the kth UE is ( ) R (ul) k = ζ (ul) 1 τ(ul) K R (ul) Uζ (ul) k (3) where the pre-log factor R (ul) k ( ) 1 τ(ul) K accounts for pilot overhead and Uζ (ul) = Blog ( 1+ K l=1,l k is the uplink gross rate (in bit/second) of UE k. p (ul) k g H k h k 2 p (ul) l g H k h l 2 +σ 2 g k 2 ) (4) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

10 Uplink Average RF power to guarantee the same R If R (ul) k = R for k = 1,2,...,K then p (ul) = σ 2 (D (ul) ) 1 1 K (5) with g [ D (ul)] k H h k 2 = (2 R/B for k = l, 1) g k 2 k,l gh k h l 2 g k 2 for k l. (6) The average uplink RF power (in Watt) is { } P (ul) TX = σ2bζ(ul) η (ul) E 1 T K (D(ul) ) 1 1 K (7) where 0 < η (ul) 1 is the LPA efficiency at the UEs. The same can be done for the downlink! Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

11 Problem statement EE optimization The EE optimization problem is mathematically defined as: maximize M Z +,K Z +, R 0 K k=1 EE = ( { E R (ul) k } { }) +E R (dl) k P (ul) TX +P(dl) TX +P CP where P CP accounts for the circuit power consumption (missing term so far!). (8) Solvable through exhaustive search: All combinations of K and M (integers) Optimal R for each pair Good only for off-line cell planning Conventional approach P CP = P FIX [1] P FIX is fixed (control signaling, load-independent backhaul, baseband processors...) EE (ZF) if M EE (ZF) if K An accurate model for P CP is very much important! Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

12 Circuit power consumption A realistic (or reasonable) model Our model: where the different terms account for: P CP = P FIX +P TC +P C/D +P BH +P CE +P LP (9) P FIX control signaling, load-independent backhaul, baseband processors... P TC transceiver chains P C/D channel coding and decoding P BH load-dependent backhaul P CE channel estimation (performed once per coherence block) P LP linear processing at the BS Objective: simple and realistic models for how each term depends on (M, K, R)! Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

13 Circuit power consumption Transceiver chains The power consumption P TC can be quantified as [2, 3] 2 P TC = (MP BS +P SYN )+KP UE Watt (10) where P BS [= 1W] circuit components (such as converters, mixers, and filters) P SYN [= 2W] local oscillator P UE [= 0.1W] circuits components of each single-antenna UE 2 [2] S. Cui, A. Goldsmith, and A. Bahai, Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks, JSAC 04. [3] R. Kumar and J. Gurugubelli, How green the LTE technology can be? Wireless VITAE 11. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

14 Circuit power consumption Coding and decoding The power consumption P C/D is proportional to the number of bits per second [4] 3 : P C/D = K ( k=1 E{R (ul) k ) +R (dl) k } (P COD +P DEC ) Watt (11) where P COD and P DEC are the coding and decoding powers (in Watt per bit/s). For simplicity, P COD [= 0.1W/Gbit/s] and P DEC [= 0.8W/Gbit/s] are the same in the uplink and downlink. 3 A. Mezghani and J. A. Nossek, Power efficiency in communication systems from a circuit perspective, ISCAS 11. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

15 Circuit power consumption Backhaul The load-dependent term P BH can be computed as [5] 4 P BH = K k=1 ( { E R (ul) k }) +R (dl) k P BT Watt (12) where P BT [= 0.25W/Gbit/s] is the backhaul traffic power (in Watt per bit/second). 4 [5] S. Tombaz, A. Vastberg, and J. Zander, Energy- and cost-efficient ultra-high-capacity wireless access, Commun. Mag. 11. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

16 Circuit power consumption Channel estimation The power P CE for channel estimation is where P CE = P (ul) CE +P(dl) CE (13) P (dl) CE = B 4τ (dl) K 2 (14) U L UE P (ul) CE = B 2τ (ul) MK 2 (15) U L BS with L BS [= 12.8GFlops/W] and L UE [= 5GFlops/W] being the computational efficiency in flops/watt (reasonably L BS L UE ). Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

17 Circuit power consumption Linear Processing This costs [6] ( P LP = B 1 (τ(ul) +τ (dl) )K U ) 2MK L BS +P LP C Watt (16) where P LP C accounts for the power required for the computation of G and V. With MRT/MRC P (MRT/MRC) LP C = B U 3MK L BS Watt (17) With ZF With MMSE P (ZF) LP C = B ( K 3 ) + 3MK2 +MK U 3L BS L BS Watt (18) P (MMSE) LP C = QP (ZF) LP C Watt (19) where Q is design parameter (number of iterations for fixed point computation). Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

18 System parameters EARTH Project 5 5 G. Auer, O. Blume, V. Giannini, I. Godor, M. Imran, Y. Jading, E. Katranaras, M. Olsson, D. Sabella, P. Skillermark, and W. Wajda, D2.3: Energy efficiency analysis of the reference systems, areas of improvements and target breakdown. INFSO-ICT EARTH, [Online]. Available: Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

19 PART II Optimal EE parameters for ZF processing Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

20 Uplink and Downlink ZF processing If a ZF detector is employed with M K +1, then where α is a design parameter and R (ul ZF) k = R = Blog(1+α(M K)) (20) P (ul ZF) TX = Bζ(ul) σ 2 S x η (ul) αk (21) where S x = E x { (l(x)) 1 } accounts for user distribution and propagation environment. If ZF precoding is used with M K +1, then and R (dl ZF) k = R = Blog(1+α(M K)) (22) Letting η = ( ζ (ul) ) 1 ζ(dl) η (ul) + η (dl) P (dl ZF) TX P (ZF) TX = P(ul ZF) TX = Bζ(dl) σ 2 S x η (dl) αk (23) +P (dl ZF) TX = Bσ2 S x αk (24) η Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

21 EE optimization ZF Processing If ZF is used on UL and DL, then maximize M Z +,K Z +,α 0 ( K 1 (τ(ul) +τ (dl) )K ) R EE (ZF) U = Bσ 2 αs x K +P (ZF) η CP (25) subject to M K +1 (26) where R = Blog(1+α(M K)) and (using our model) 3 2 P (ZF) CP = C i K i +M i=0 i=0 ( D i K i +AK 1 (τ(ul) +τ (dl) )K U ) R (27) Objective: Finding EE-optimal value of (M,K,α) when the other two are fixed. Coefficients {C i } Coefficients A and {D i } C 0 = P FIX + P SYN A = P COD + P DEC + P BT C 1 = P UE D 0 = P BS C 2 = 4Bτ(dl) UL UE D 1 = L B (2 + 1 BS U ) C 3 = B D 3UL 2 = B (3 2τ (dl) ) BS UL BS Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

22 EE optimization Optimal Number of Users (1) Theorem 1 For given values of ᾱ = αk and β = M/K, the number of UEs that maximize the EE metric is K = max K (o) l l (28) where the quantities {K (o) l } denote the real positive roots of the quartic equation where µ 1 = K 4 2U τ (ul) +τ (dl)k3 µ 1 K 2 Uµ 0 2µ 0 K + τ (ul) = 0 (29) +τ (dl) U τ (ul) +τ (dl) (C 2+ βd 1 )+C 1 + βd 0 C 3 + βd 2 and µ 0 = C 0+ Bσ 2 Sx ᾱ η. C 3 + βd 2 Observations on K : Decreases with {P UE,P BS } Increases with {P FIX,P SYN } and coverage area Unaffected by {P COD,P DEC,P BT } Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

23 EE optimization Optimal Number of BS Antennas (1) Theorem 2 For given values of K and α, the number of BS antennas maximizing the EE metric can be computed as M = M (o) with with M (o) = e Bσ 2 Sx α( η W D e 3 C i=0 = C ik i K α+c ) + αk 1 e α +1 +αk 1 (30) 2 and D i=0 = D ik i. (31) K Corollary 3 When α grows large, we have which is an almost linear scaling law. M α ln(α) (32) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

24 EE optimization Optimal RF Power (1) Theorem 4 For given values of K and M, the EE-optimal α 0 can be computed as α = ew ( η Bσ 2 Sx (M K)(C +MD ) ) e 1 +1 e 1 M K (33) with C > 0 and D > 0. Observations on α : Increases with {P BS,P FIX,P SYN,P UE } and coverage area Unaffected by {P COD,P DEC,P BT } Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

25 EE optimization Optimal RF Power (2) Corollary 5 The optimal α is approximately given by α M ln(m) (34) when M grows large. If M becomes large, then α /M the RF power emitted per BS antenna (and per UE if we let K scale linearly with M) decays as 1/ln(M) RF amplifiers can be gradually simplified with M. Much slower than the scaling laws 1/M and 1/ M observed in [7] and [8] 6. 6 [7] J. Hoydis, S. ten Brink, and M. Debbah, Massive MIMO in the UL/DL of cellular networks: How many antennas do we need? JSAC13. [8] H. Ngo, E. Larsson, and T. Marzetta, Energy and spectral efficiency of very large multiuser MIMO systems, TCOM13. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

26 EE optimization Joint sequential optimization Ultimate goal: Joint Global Optimum Too complex only for off-line cell planning Alternating Optimization Algorithm 1 Assume that an initial set (K,M,α) is given; 2 Update the number of UEs K (and implicitly M and α) according to Theorem 1; 3 Replace M with the optimal value from Theorem 2; 4 Optimize the RF power through α by using Theorem 4; 5 Repeat 2) 5) until convergence is achieved. Convergence: A local optimum is achieved for any initial set (K, M, α) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

27 PART III Numerical results Matlab code available for download Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

28 Numerical results ZF processing &'()*+,&--./.('/+, (9 %" %! $" $! #" #! "! $!! #"! #!! "!!! F862A8,BC3.;7;G M = 165, K = 104 &&= "! #!! #"! :7;2(),6-,<=()=,>K? M = 165 K = 104 Massive MIMO! α = , SE = bit/s/hz (per UE) Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

29 Numerical results MMSE processing %" %! $" $! #" #! "! $!! #"! #!! &'()*+,-.,345*4460,1M2 "!!! M = 145, K = 95 77= 30.3 =):5>? "! #!! #"! &'()*+,-.,/0*+0,1K2 M = 145 K = 95 Massive MIMO! Same EE of ZF Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

30 Numerical results MRT/MRC processing #$ #! ' & % $! $!! #"! #!! ()*+,-./0.567,6682.3M4 "!!! DB/+8B.EF7<*)*G M = 81, K = 77 99= 9.86?+<7@A "! #!! #"! ()*+,-./0.12,-2.3K4 M = 81 K = 77 Massive number of BS antennas but not Massive MIMO! Lower EE compared to ZF and MMSE Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

31 Numerical results MRT/MRC processing in our previous work [9] 8 ;8./<=0;22>?>.8?=0@A->94BC1+D.E ) "'( " &'( &!'( FD1-:D0GH9>,+,I M = 4, K = 1 &!!! %! $! #! *+,-./ :405M6 "!!! $! #! "! *+,-./ /405K6 Single-user transmission was optimal for MRT Different power consumption model As compared to [9], we have increased P BT (based on [10]) and made P C/D proportional to the rates instead of K. 8 Designing multi-user MIMO for energy efficiency: When is massive MIMO the answer? in Proc. IEEE Wireless Commun. and Networking Conf. (WCNC), Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

32 Numerical results ZF processing with imperfect CSI %! $" $! #" #! "! $!! #"! #!! &'()*+,-.,345*4460,1M2 "!!! M = 185, K = = =):5>? "! #!! #"! &'()*+,-.,/0*+0,1K2 M = 185 K = 110 Still Massive MIMO! But lower EE with respect to perfect CSI Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

33 Numerical results Average RF power vs. M #! $ +.5)*16)+7,8)*+9:; #! # #!! #!!# F,01G+EC+D,8)* E1HI10)H+D,8)* D)*+J=+1/0)//1 >>K,D0I'1G+D,I/02 <<=>+37)*-)?0+@=A4 BC+37)*-)?0+@=A4 BC+3A'D)*-)?0+@=A4 <EF+37)*-)?0+@=A4 #!!" +! "! #!! #"! $!! %&'()*+,-+./0)//12+3M4 RF power of 100 mw/antenna with ZF and MMSE RF power of 23 mw/antenna with MRT Much smaller than for macro BSs (40 W/antenna [11]) EE-optimal solution can be deployed with low-power UE-like RF amplifiers! Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

34 Numerical results Area Throughput vs. M 2.-5/9:.0*;:<*4/=>,?4@6@A+ $ B (! '! "! &! %! $! #! CCDE/7F-.1-G4/HDI8 JK/7F-.1-G4/HDI8 JK/7I+<-.1-G4/HDI8 CL9/7F-.1-G4/HDI8 EEM0<4?+5N/<0?346 /!/! "! #!! #"! $!! )*+,-./01/ /7M8 3 fold improvement in EE for ZF and MMSE vs. MRT/MRC. 8 fold improvement in area throughput for ZF and MMSE vs. MRT/MRC Massive MIMO with proper interference-suppressing precoding (ZF or MMSE) can achieve great EE and unprecedented area throughput. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

35 Extension to multi-cell Symmetric scenario Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

36 Numerical results ZF in the symmetric multi-cell case ' & % $! $!! #"! #!! ()*+,-./0.567,6682.3M4 "!! DB/+8B.EF7<*)*G M = 123, K = 40 99= 7.58?+<7@A! "! #!! #"! ()*+,-./0.12,-2.3K4 Optimal EE value is smaller Mainly due to inter-cell interference M = 123 K = 40 Massive MIMO is still the EE-optimal architecture. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

37 Conclusions Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

38 Conclusions and outlook How should a multi-user MIMO system be designed to maximize energy efficiency? Need: Reasonable throughput model Need: Reasonable power consumption model Is Massive MIMO The Answer? YES! Deploying M = 100/200 with ZF or MMSE a relatively large K is EE-optimal using today s circuit technology. RF power decreases with M: Low-power UE-like equipment can be used at the BS Things change fast! Code available for download (to enable simple testing of other circuit power coefficients) Circuit power coefficients will decrease over time Higher EE with fewer UEs, fewer BS antennas, less RF power, but more advanced processing. Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

39 References [1] G. Auer, O. Blume, V. Giannini, I. Godor, M. Imran, Y. Jading, E. Katranaras, M. Olsson, D. Sabella, P. Skillermark, and W. Wajda, D2.3: Energy efficiency analysis of the reference systems, areas of improvements and target breakdown. INFSO-ICT EARTH, ver. 2.0, [Online]. Available: [2] S. Cui, A. Goldsmith, and A. Bahai, Energy-efficiency of MIMO and cooperative MIMO techniques in sensor networks, IEEE J. Sel. Areas Commun., vol. 22, no. 6, pp , [3] R. Kumar and J. Gurugubelli, How green the LTE technology can be? in Proc. Wireless VITAE, [4] A. Mezghani and J. A. Nossek, Power efficiency in communication systems from a circuit perspective, in Proc. IEEE Int. Symp. Circuits and Systems (ISCAS), 2011, pp [5] S. Tombaz, A. Västberg, and J. Zander, Energy- and cost-efficient ultra-high-capacity wireless access, IEEE Wireless Commun. Mag., vol. 18, no. 5, pp , [6] S. Boyd and L. Vandenberghe, Numerical linear algebra background. [Online]. Available: [7] J. Hoydis, S. ten Brink, and M. Debbah, Massive MIMO in the UL/DL of cellular networks: How many antennas do we need? IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp , [8] H. Ngo, E. Larsson, and T. Marzetta, Energy and spectral efficiency of very large multiuser MIMO systems, IEEE Trans. Commun., vol. 61, no. 4, pp , [9] E. Björnson, L. Sanguinetti, J. Hoydis, and M. Debbah, Designing multi-user MIMO for energy efficiency: When is massive MIMO the answer? in Proc. IEEE Wireless Commun. and Networking Conf. (WCNC), [10] S. Tombaz, K. Sung, and J. Zander, Impact of densification on energy efficiency in wireless access networks, in Proc. IEEE Global Commun. Conf. (GLOBECOM), [11] Further advancements for E-UTRA physical layer aspects (Release 9). 3GPP TS , Mar Luca Sanguinetti (UPI/Supélec) OULU, 25 Nov / 38

Scientific Challenges of 5G

Scientific Challenges of 5G Mérouane Debbah Huawei, France Joint work with: Luca Sanguinetti * and Emil Björnson * * * University of Pisa, Dipartimento di Ingegneria dell Informazione, Pisa, Italy * *