Impact of Spatial Correlation and Distributed Antennas for Massive MIMO Systems

Transcription

1 Impact of Spatial Correlation and Distributed Antennas for Massive MIMO Systems Kien T. Truong* and Robert W. Heath Jr. Wireless Networking & Communication Group Department of Electrical & Computer Engineering The niversity of Texas at Austin * MIMO Wireless Inc. The Wireless Networking and Communications Group This work was supported by Huawei Technologies

2 What is Massive MIMO? hundreds of BS antennas tens of users N t 1 N t 1 A very large antenna array at each base station An order of magnitude more antenna elements in conventional systems A large number of users are served simultaneously An excess of base station (BS) antennas Essentially multiuser MIMO with lots of base station antennas Pioneered by Marzetta, Larsson, others see e.g. [Mar10], [LarEtAl13], [RusekEtAl13] 2

3 Problem Statement Massive MIMO requires many antennas for best performance Yet co-locating large antennas is challenging Massive MIMO analysis often assumes uncorrelated antennas Yet spatial correlation is likely present when the arrays are packed Objectives Explore potential gains achieved with MRC & MMSE strategies Establish the potential of massive MIMO in distributed antenna systems Investigate performance improvement with remote radio unit selection 3

4 The Wireless Networking and Communications Group System Model

5 System Model Nt 1 E AMRC r,bu = tr 2 bbu 2 MRC Br,bu = b tr bbu pr X MRC Cr,bu = tr Rbck bbu (c,k)6=(,bu) MRC Dr,bu = X c6=b tr 2 N1 bcu E =I t Nt 1 Nt 1 Nt 1 Nt 1 Nt 1 E Central station b Nt 1 Nt 1 Central station c ucells share the same frequency, i.e. universal frequency reuse Each cell has one BS with antennas & C single-antenna users gbcu [n] CN (0, INt ) px yr,b = pr Hbcxr,c +nr,b c=1 Time-division duplexing (TDD) protocol MIMO operation is multiuser rather than single-user transmission BSs estimate inst. channels based on L (training) signals 5

6 Pilot-based: plink Training N t R bcu Nt 1 x r,ck x r,ck Central station b Orthogonal pilot sequences within a cell Central station c Cells share a common set of pilot sequences C MMSE channel estimation based on the observation at BS b x r,c := [x r,c1,,x r,c ] Training stage in pilot-based methods causes spectral efficiency loss 6

7 Signal Model - L Data Transmission Nt 1 x r,bu h bcu [n] :=R 1/2 bcu g bcu[n] Central station b 1 Central station c Transmit signals from users in cell c is Base station b observes W b 2 C N t Base station b applies a linear detector The linear detector is designed based on estimate of channels to

8 Channel Model with Spatial Corr. L channel vector from user u in cell c to base station b MRC r,bu = 2 b tr bbu 2 pr tr bbu + P (c,k)6=(b,u) tr Rbck bbu + P c6=b = Br,bu MRC as tr : fast fading, uncorrelated WSS complex Gaussian bcu 2 u: deterministic Hermitian positive definite matrix may include several effects Pathloss and shadowing Spatial correlation due to inefficient antenna spacing This model facilitates analysis of distributed antenna systems as A MRC r,bu + CMRC r,bu + DMRC r,bu is a (block) diagonal matrix 1 (Block) diagonal entries correspond to cluster spatial correlation matrices Spatial correlation matrices of clusters have different AoA/AoD and pathlosses 8

9 The Wireless Networking and Communications Group Rate Calculations

10 General plink Achievable Rate Treating as a SISO channel with known channel of Channel est. error & intf. are treated as uncorrelated noise=> worst case Ergodic post-processing SINR for user u in cell b R bu = E[log (1 + 2 bu )], (ug) bku channel estimation error interference local noise ar det plink ergodic 8achievable rate for user u in cell b < ĥ bbu, : Ĥbb T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Tran. Wireless Commun., vol. 9, no. 11, pp , Nov J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath, Pilot contamination and precoding in multi-cell TDD systems, IEEE at Trans. Wireless Commun., bas vol. 10, no. 8, pp , Aug

11 Deterministic Equivalent Analysis ypost-processed uplink r,b SINR for linear MRC detector [HoyEtAl13] N (m) t local noise traditional interference log(1 + MRC r,bu ) Assumes MMSE estimation interference due to pilot contamination J. Hoydis, S. T. Brink, and M. Debbah, Massive MIMO in the L/DL of cellular networks: How many antennas do we need? IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp , Feb K. T. Truong and R. W. Heath, Jr., Effects of channel aging in massive MIMO systems, J. Commun. Networks, vol. 15, no. 4, pp , Aug

12 DAS and ser Grouping The Wireless Networking and Communications Group

13 DAS without Spatial Correlation RR k Nt 1 bkcu E Central station b Central station c Spatial correlation is not considered to focus on impact of DAS Each cell has K remote radio units (RRs) Nt and are divisible by K, denote bkcu Ñ t = N t /K; Ũ = /K : large-scale fading coefficient from user u in cell c to RR k in cell b Base stations (or RRs) use linear MRC detector The same pilot-based channel estimation as before 13

14 Full M-MIMO Strategy for DAS RR m bmbu {z } X RR k bkbu N t 1 {z } RRs in each cell coordinate with each other for detection Deterministic equivalent SINR of user u in cell b R in cell as Central station b (ug) 2 bku = h bkbu 2b P 1 Ñ t p r + bkcv (c,v)6=(b,u) herrs achievable in cell b far sum-rates from user u do of not thecontribute users inmuch cellto bits insinr this X X Small large-scale fading channel gain & large channel estimation error i bu = 8 w buĥbbu 2 h E wbu hbbu h bbu + P i. (c,k)6=(b,u) h bckgbck + r 2 p r I Nt w bu Ĥ bb bku + P c6=b 2 bkcu 14

15 2 b ser-grouped Strategy for DAS RR m Each RR serves an equal number of users ( users) in the cell se its own linear MRC detector to detect signals from users it serves SINR of user u served by RR k in cell b for any user grouping Central station b Nt RR k N 1 t 1 (full) bu = PK p r Ñ t k=1 bkbu bku PK 2 k=1 bkbu bku + 1 P K P Ñ t k=1 bku + P c6=b bkcv bkbu (c,v)6=(b,u) PK k=1 bkbu bkcu bku = 2 C r p p + X c=1 2. bkuis an increasing isfunction a diagonal of large-scale matrix fading channel wgain Ũ bu = 8 bkcu. w buĥbbu 2 h E wbu hbbu h bbu + P i. (c,k)6=(b,u) h bckgbck + r 2 p r I Nt w bu Ĥ bb bkbu 15

16 Greedy ser Grouping Alg. for DAS Initialization Randomly permute the user indices to obtain Initial set of available RRs is K b = {1, 2,,K} b = {u 1,u 2,,u } Iteration n =1, 2,, 1 Among the available RRs, find the RR that maximizes the large-scale fading channel gain from itself to user in the same cell (i.e. cell b) u n k n = arg max k2k b bkbu n Assign the found RR (i.e. RR k n ) to serve user If the found RR has been assigned to serve users (including user ), then remove the index of the found RR from K b = K b \ k n Ũ K b u n u n 16

17 Simulation Setup user Base station (BS) Hexagonal cells with antennas per base station sector R bcu =E[h bcu [n]h bcu[n]] users dropped randomly in each sector 17

18 Simulation Parameters Parameters Description Number of sectors per cell 1 Number of users per cell 12 Inter-site distance Pathloss model Penetration loss Antenna array configuration at users Channel estimation method Angle spread ser dropping Shadowing model ser assignment BS antenna gain BS antenna spacing BS total transmit power Thermal noise density BS noise figure (L) MS noise figure (DL) 500m PLNLOS = log10(d), where d > 0.035km is the trans. distance 20dB 1 antenna omni with 0dBi gain MMSE 10 degrees niformly distributed within a cell Not considered Each user is served by the BS in the same cell 10dBi 0.5, 1, 1.5, and 2 wavelengths 40 watts or 46dBm -174dBm/Hz 5dB 9dB 18

19 Antenna Clustering Configurations BS antenna cluster Distributed with 03 clusters Collocated or 01-cluster Note: distributed antennas are equallyspaced on a ring of 2/3 of cell radius Distributed with 08 clusters 19

20 Spatial Correlation Model AoA (angle-of-arrival) AoD (angle-of-departure) (m) scattering cluster user 1 Circular Array Y p,b = p X C p p H bc + N p,b, c=1 user 2 No standardized multi-user spatial correlation model se single cluster model, with randomly located cluster Employ low complexity model for LA and circular array Parameters Random AoA or AoD for each user Laplacian power azimuth spectrum, angle spread of 10 degrees Note: Spatial correlation is independent of mobility in our model A. Forenza, D. J. Love, and R. W. Heath, Jr., ``Simplified Spatial Correlation Models for Clustered MIMO Channels with Different Array Configurations,''IEEE Trans. on Veh. Tech., vol. 56, no. 4, part 2, pp , July

21 Impacts of Spatial Correlation ncorrelated: MRC Spatially correlated: MRC ncorrelated: MMSE Spatially correlated: MMSE Number of antennas at a base station Impacts of spatial correlation depend on reception strategies MRC: uncorrelated channel model is preferred MMSE: spatial correlated channel model is preferred 21

22 Effects of Antenna Distributions cluster, MMSE 03 clusters, MMSE 08 clusters, MMSE 01 cluster, MRC 03 clusters, MRC 08 clusters, MRC Number of antennas at a base station Distributing antennas over cell areas bring considerable gains Saturation is not observed at not-so-large numbers of antennas 22

23 Effects of ser Grouping in DAS Random user grouping Distributed with 03 clusters Number of antennas at a base station 12 users in each cell are evenly divided into 3 groups, Each group is served by a dedicated cluster Greedy user grouping outperforms full M-MIMO strategy Random user grouping is much worse than the other strategies 23

24 Conclusions Massive MIMO and spatial correlation Impact depends on deployed detector Massive MIMO and distributed antennas Provide high performance versus centralized solutions Remote radio unit selection offers high gain Further investigation Connections to power control? Performance with non MMSE estimation? Asymptotic performance trends? 24

25 References [LarEtAl13] E. G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, Massive MIMO for next generation wireless systems, to appear in IEEE Commun. Mag., [RusEtAl13] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors and F. Tufvesson, Scaling up MIMO: Opportunities and challenges with very large arrays, IEEE Signal Processing Mag., vol. 30, no. 1, pp , Jan [HoyEtAl13] J. Hoydis, S. T. Brink, and M. Debbah, Massive MIMO in the L/DL of cellular networks: How many antennas do we need? IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp , Feb [TruHea13] K. T. Truong and R. W. Heath, Jr., Effects of channel aging in massive MIMO systems, J. Commun. Networks, vol. 15, no. 4, pp , Aug [GaoEtAl11]X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, Linear pre-coding performance in measured very-large MIMO channels, in Proceedings of IEEE Veh. Tech. Conf., Sep. 2011, pp [ForEtAL07] A. Forenza, D. J. Love, and R. W. Heath, Jr., Simplified spatial correlation models for clustered MIMO channels with different array configurations, IEEE Trans. Veh. Tech., vol. 56, no. 4, pp , Jul [3GPPLTE] 3GPP TR , Further advancements for E-TRA physical layer aspects, Mar [Mar10] T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Tran. Wireless Commun., vol. 9, no. 11, pp , Nov [Ver98] S. Verdu, Multiuser Detection. Cambridge niversity Press, [JosEtAl11] J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath, Pilot contamination and precoding in multi-cell TDD systems, IEEE Trans. Wireless Commun., vol. 10, no. 8, pp , Aug