Emerging Technologies Beyond 4G: Massive MIMO, Dense Small Cells, Virtual MIMO, D2D and Distributed Caching

Transcription

1 International Workshop on Emerging Technologies for LTE-Advanced and Beyond-4G Emerging Technologies Beyond 4G: Massive MIMO, Dense Small Cells, Virtual MIMO, D2D and Distributed Caching Giuseppe Caire University of Southern California, Viterbi School of Engineering, Los Angeles, CA Globecom 2012, Anaheim CA, Dec. 3, 2012

2 Wireless operators nightmare b 100x Data traffic increase, due to the introduction of powerful multimedia capable user devices. Operating costs trends not matched by revenue trends. 1

3 Possible answers Release of new wireless spectrum: today, cellular + Wifi accounts for 500 MHz of bandwidth. Releasing new spectrum will at most double the available overall spectrum (at most x2 increase with same technology). Following current technology trend: LTE... painstakingly slow, incremental gain due to backward compatibility. Disruptive technology approach: Massive MIMO, Dense Small Cells, Virtual MU-MIMO, D2D, Wireless Caching. What Can We Expect? 2

4 MU-MIMO Cellular Networks (- 2,4) (0,3) (2,2) (4,1) (6,0) (8,- 1) (- 3,4) (- 1,3) (1,2) (3,1) (5,0) (7,- 1) (- 2,3) (0,2) (2,1) (4,0) (6,- 1) (8,- 2) (- 3,3) (- 1,2) (1,1) (3,0) (5,- 1) (7,- 2) (- 2,2) (0,1) (2,0) (4,- 1) (6,- 2) (8,- 3) (- 3,2) (- 1,1) (1,0) (3,- 1) (5,- 2) (7,- 3) (- 2,1) (0,0) (2,- 1) (4,- 2) (6,- 3) (8,- 4) (- 3,1) (- 1,0) (1,- 1) (3,- 2) (5,- 3) (7,- 4) (- 2,0) (0,- 1) (2,- 2) (4,- 3) (6,- 4) (8,- 5) (- 3,0) (- 1,- 1) (1,- 2) (3,- 3) (5,- 4) (7,- 5) (- 2,- 1) (0,- 2) (2,- 3) (4,- 4) (6,- 5) (8,- 6) (- 3,- 1) (- 1,- 2) (1,- 3) (3,- 4) (5,- 5) (7,- 6) Multiuser MIMO cooperative upper bound: ( C = W M 1 M ) log SINR + O(1), T were M = min{m, KN, T/2}. Fundamental dimensionality bottleneck: channel state estimation overhead (information theoretic upper bound). See also high-snr saturation effect in Fundamental Limits of Cooperation, [Lozano, Heath, Andrews, arxiv: ]. Per-user throughput vanishes as O( 1 K ). 3

5 Network MIMO: A Large-System Analysis 4

6 Discretization of the Users Distribution BS BS user group 1 user group user group 4 user group user group 6 user group 5 cell 1 cell 2 We assume that the users are partitioned in co-located groups with N singleantenna terminals each. We have A user groups per cluster, and clusters of B cells. We have M = γn base station antennas per cell. 5

7 Cluster of Cooperating Base Stations Modified path coefficients β m,k = α m,k σ k taking into account the ICI power. Cluster channel matrix H = β 1,1H 1,1 β 1,A H 1,A..... β B,1 H B,1 β B,A H B,A. Reference cluster channel model y = H H x + z where y = C AN, x = C γbn, and z CN (0, I). 6

8 Linear ZF Downlink Beamforming We consider the weighted rate sum maximization for given channel matrix: maximize subject to A k=1 N i=1 W (i) k R(i) k R R lzfb (H) where W (i) k denotes the rate weight for user i in group k, and R lzfb (H) is the achievable instantaneous rate region of LZFB for given channel matrix H. 7

9 Some Simplifying Assumptions The scheduler picks a fraction µ k of users in group k by random selection inside the group. LZFB precoder obtained by normalizing the columns of the Moore-Penrose pseudo-inverse of the channel matrix. Let µ = (µ 1,..., µ A ) denote the fractions of active users in groups 1,..., A, respectively. For given µ, the corresponding effective channel matrix is given by Hµ = β 1,1H 1,1 (µ 1 ) β 1,A H 1,A (µ A ).., β B,1 H B,1 (µ 1 ) β B,A H B,A (µ A ) 8

10 LZFB parallel channels Letting Vµ = H + µ Λ1/2 µ, we obtain the parallel channel model yµ = H H µvµq 1/2 u + zµ = Λ 1/2 µ Q1/2 u + zµ. Theorem 1. For all i = 1,..., µ k N, the following limit holds almost surely: lim N Λ(i) k (µ) = Λ k(µ) = γ B m=1 β 2 m,kη m (µ) where (η 1 (µ),..., η B (µ)) is the unique solution in [0, 1] B of the fixed point equations A η m βm,q 2 η m = 1 µ q q=1 γ B l=1 η, m = 1,..., B lβl,q 2 with respect to the variables η = {η m }. 9

11 Channel Estimation and Non-Perfect CSIT We assume that the channels are constant over time-frequency blocks of size W T complex dimensions. For each such block, γ p BN dimensions are dedicated to downlink training. Since the channel vectors are Gaussian, linear MMSE estimation is optimal with respect to the MSE criterion. The MMSE can be made arbitrarily small as σk 2 ICI) if and only if γ p γ. 0 (vanishing noise plus The ratio γ p /γ denotes the pilot dimensionality overhead. 10

12 From the well-known MMSE decomposition, the channel matrix H can be written as H = Ĥ + E, where Ĥ = β 1,1 H 1,1 β1,a H 1,A.. β B,1 H B,1 βb,a H B,A, with and where with E = β m,k = β m,k = β 2 m,k 1/p + β 2 m,k β 1,1 E 1,1 β1,a E 1,A.. β B,1 E B,1 βb,a E B,A β 2 m,k β 2 m,k =, β m,k, 1 + pβm,k 2 and the blocks E m,k and independent with i.i.d. CN (0, 1) elements., 11

13 Achievable rate lower bound Theorem 2. Under the downlink training scheme described above and assuming genie-aided CSIT feedback, the achievable rate of users in group k is lower bounded by ( ) Λ k (µ)q k R k log B β m=1 m,k 2 P m where Λ k (µ) = γ B β 2 m,kη m (µ) m=1 where (η 1 (µ),..., η B (µ)) is the unique solution with components in [0, 1] of the fixed point equation η m = 1 A q=1 η m β2 m,q µ q γ B l=1 η β, m = 1,..., B l l,q 2 with respect to the variables η = {η m }. 12

14 Degrees of freedom and cost of training [ ] The system spectral efficiency must be scaled by the factor 1 γ pnb W T, that + takes into account the downlink training overhead, i.e., fraction of dimensions per block dedicated to (downlink) training. N W T In particular, letting τ = denote the ratio between the number of users per group, N, and the dimensions in a time-frequency slot, we can investigate the system spectral efficiency for fixed τ, in the limit of N. The ratio τ captures the dimensional crowding of the system. 13

15 Linear cellular layout Example: linear cellular layout with M = 8 cells BS 1 BS 2 BS 3 BS 4 BS 5 BS 6 BS 7 BS 8 BS 7 BS 8 BS 7 BS 8 M = B = 1 cell cooperation BS 1 BS 2 BS 3 BS 4 BS 5 BS 6 M = B = 2 cell cooperation BS 1 BS 2 BS 3 BS 4 BS 5 BS 6 M = B = 8 cell cooperation H. Huh (USC) Large System Analysis of Multi-cell MIMO Downlink May 12, / 52 14

16 Comparison with finite dimensional systems Group rate (bps/hz) Fin dim, N=2 Fin dim, N=4 Fin dim, N=8 Asymptotic B= B=2 B= Group location (km) User group rate in finite dimension (N = 2, 4, and 8) for cooperation clusters of size B=1, 2, and 8, with perfect CSIT. M = 8 cells and K = 64 user groups. 15

17 Cost of CSIT and choice of network MIMO architecture (1) B=1 B=2 B=8 Cell sum rate (bps/hz) γ Cell sum rate versus the antenna ratio γ for cooperation clusters of size B=1, 2, and 8. M = 8 cells and K = 192 user groups. 16

18 Cost of CSIT and choice of network MIMO architecture (2) Cell sum rate (bps/hz) B=1, τ=1/64 B=2, τ=1/64 B=8, τ=1/64 B=1, τ=1/32 B=2, τ=1/32 B=8, τ=1/ γ Cell sum rate versus the antenna ratio γ for cooperation clusters of size B=1, 2, and 8. M = 8 cells and K = 192 user groups. 17

19 Large cooperating clusters? γ=1, τ=1/64 γ=2, τ=1/64 γ=4, τ=1/64 γ=8, τ=1/64 Cell sum rate (bps/hz) B Cell sum rate versus the cluster size B for the antenna ratio γ=1, 2, 4, and 8 γ p = γ, M = 24 cells and K = 192 user groups and τ = 1/64. 18

20 Large cooperating clusters? γ=1, τ=1/32 γ=2, τ=1/32 γ=4, τ=1/32 γ=8, τ=1/32 Cell sum rate (bps/hz) B Cell sum rate versus the cluster size B for the antenna ratio γ=1, 2, 4, and 8 γ p = γ, M = 24 cells and K = 192 user groups and τ = 1/32. 19

21 FDD versus TDD Channel State Information at Transmitters (CSIT) downlink uplink common training θ ctr-dl feedback η fb beamforming dedicated training θdtr Frequency-division duplex (FDD) data transmit ζ data Estimation error Training overhead proportional to the number of transmit antennas common training beamforming dedicated training data transmit Estimation error downlink uplink θ ctr-ul θdtr ζ data Training overhead proportional to the number of served users Time-division duplex (TDD) H. Huh (USC) Large System Analysis of Multi-cell MIMO Downlink May 12, / 52 20

22 Marzetta s Massive MIMO Scheme No BS cooperation, each cell on its own. On each slot, a fraction T tr /T is dedicated to uplink training, and (1 T tr /T ) is dedicated to downlink data transmission. Single-user downlink beamforming: transmit with the Hermitian transpose of the estimated channel matrix. Marzetta considers the limit for a finite number K of users per cell, and the number of BS antennas M. In this regime, intra and inter cell interference and noise disappear, except for the inter-cell interference due to PILOT CONTAMINATION. 21

23 What happens for finite M/N? We partition the user population in bins of co-located users. Users in the same bin are (roughly) statistically equivalent. For each bin we consider an optimized MU-MIMO scheme. Scheduling over the user bins to maximize a desired Network Utility Function. 1-dimensional layout BS b BS b 2-BS cluster b BS b x x x -x SN users split btw {b- x, b+x} SN users split btw {b+x, b+1- x} 2-dimensional layout BS (0,1) BS (0,1) BS 0 BS (- 1,1) BS (1,0) 3-BS cluster 0 (pattern 1) BS (0,0) BS (0,0) 3-BS cluster 0 (pattern 2) 22

24 Frequecy reuse f = 0 BS 0 cluster 0 cluster 2 BS 1 BS 2 BS 3 BS 4... x -x x -x x f = 1 BS 0 BS 1 cluster 1 cluster 3 BS 2 BS 3 BS x x -x x -x 1-dimensional layout with C = 2 and F = 2. 23

25 Pilot reuse Q = 2 q = 0 q = 1 q = 0 cluster 0 cluster 1 cluster x x x Pilot reuse and contamination for C = 2, F = 1, and Q = 2. The dashed lines show the pilot contamination at cluster 0 from a user in cluster 2, sharing the same pilot signal. 24

26 x x x Fig. 4. Zero-Forcing and interference mitigation Pilot reuse and contamination for C =2, F =1, and Q =2. The dashed lines show the pilot contamination at cluster 0 from a user in cluster 2, sharing the same pilot signal. cluster B-1 cluster 0 cluster 1 BS 0 BS 1 BS 2... x -x x -x x -x (a) J = Q cluster B-1 cluster 0 cluster 1 BS 0 BS 1 BS 2... x -x x -x x -x (b) J = C(Q 1) + 1 Fig. 5. Two cases of a precoding scheme for C =2, F =1, and Q =2, with J = Q (a) and J = C(Q 1) + 1 (b). The dashed blue lines indicate the channel vectors of out-of-cluster user locations imposing a ZF constraint. In Figure (b), the light-shaded grey dashed lines indicate the channel vectors assumed zero in the beamforming calculation. 25

27 Multi-Mode MU-MIMO downlink scheduling Consider a system with K bins, {v(x 0 ),..., v(x K 1 )}, chosen to sample uniformly the coverage area V. The net bin spectral efficiency (in bit/s/hz) max{1 QS/T, 0} R Xk,C(F, C, J), Let R (X k ) denote the maximum of the above for given X k, optimized over the the parameters S, C, J, Q, F. A scheduler gives fraction ρ k of the total time-frequency transmission resource to bin v(x k ) in order to maximize a desired Network Utility Function. 26

28 The scheduler determines the transmission resource allocation {ρ k } by solving the following convex problem: maximize G(R 0,..., R K 1 ) subject to R k ρ k R (X k ), K 1 k=0 ρ k 1, ρ k 0. We obtain a multi-modal network MIMO architecture. Optimization can be done easily based on large-system limit closed form results. 27

29 Example: Proportional Fairness (PF) criterion corresponds to the choice G(R 0,..., R K 1 ) = K 1 k=0 log R k, and yields ρ k = 1/K (each bin is given an equal amount of slots). Example: Max-Min fairness criterion corresponds to the choice G(R 0,..., R K 1 ) = min R k, k=0,...,k 1 and yields ρ k = P K 1 j=0 1 R (X k ) 1 R (X j ). 28

30 Results Bin spectral efficiency (bits/s/hz) (1,1,0), Q=1 (1,1,1), Q=1 (1,1,2), Q=2 (1,2,3), Q= Bin location, x (km) Bin spectral efficiency vs. location within a cell obtained from the large system analysis (solid) and the finite dimension (N = 1) simulation (dotted) for various (F, C, J). M = 30 and L =

31 y coordinate (km) (1,1,1), Q=1 (3,3,1), Q=1, cluster pattern 1 (3,3,1), Q=1, cluster pattern 2 y coordinate (km) (1,1,1), Q=1 (3,1,1), Q=1 (3,3,1), Q=1, cluster pattern 1 (3,3,1), Q=1, cluster pattern x coordinate (km) x coordinate (km) Optimal scheme at each user locations. M = 20 and 100, K = 16, and L =

32 Bin-optimized spectral efficiencies normalized by the (1,1,0) (Marzetta) spectral efficiencies, for M = 50, K = 48,and L =

33 Performance under PFS Cell/cluster throughput (Mbps) (1,1,0), Q=1 (1,1,1), Q=1 (1,1,3), Q=3 (3,3,1), Q=1, w/o cluster switching (3,3,1), Q=1, w/ cluster switching Bin optimized Factor of the number of BS antennas, M 32

34 Performance under Max-Min Fairness Cell/cluster throughput (Mbps) (1,1,0), Q=1 (1,1,1), Q=1 (1,1,3), Q=3 (3,3,1), Q=1, w/o cluster switching (3,3,1), Q=1, w/ cluster switching Bin optimized Factor of the number of BS antennas, M 33

35 What about FDD systems? Exploiting Tx antenna correlation Users separated by a few meters (say 10 λ) are practically uncorrelated. In contrast, the base station sees user groups at different AoAs under narrow Angular Spread arctan(r/s). r s scattering ring region containing the BS antennas 34

36 Tx antenna correlation: h = UΛ 1/2 w, R = UΛU H with [R] m,p = 1 2 e jkt (α+θ)(u m u p ) dα. The downlink channel model is given by y = H H x + z = H H Vd + z where H is the M K system channel matrix (channel vectors by columns). 35

37 Joint Space Division and Multiplexing (JSDM) K users selected to form G groups, with same channel correlation. H = [H 1,..., H G ], with H g = U g Λ 1/2 g W g. Two-stage precoding: V = BP. B C M b is a pre-beamforming matrix function of {U g, Λ g } only. P C b s is a precoding matrix that depends on the effective channel. The effective channel matrix is given by H H 1B 1 H H 1B 2 H H 1B G H H = H H 2B 1 H H 2B 2 H H 2B G H H G B 1 H H G B 2 H H G B G 36

38 Joint Group Processing: If the estimation and feedback of the transformed channel H can be afforded, the precoding matrix P is determined as a function of H. Per-Group Processing: If estimation and feedback of the whole H is still too costly, then each group estimates its own diagonal block H g = B H g H g, and P = diag(p 1,, P G ). This results in y g = H H g B g P g d g + g g H H g B g P g d g + z g 37

39 Achieving capacity with reduced CSI Assume that the G groups are such that U = [U 1,, U G ] is M rg tall unitary (i.e., rg M and U H U = I). We choose b = r and B g = U g and obtain exact Block Diagonalization (BD): y g = H H g B g P g d g + z g = W H g Λ 1/2 g P g d g + z g (1) Theorem 3. For U tall unitary, the sum capacity of the original Gaussian vector broadcast channel with full CSI is equal to the sum capacity of the set of decoupled channels (1). 38

40 Analysis and results Analysis possible using the deterministic equivalent method (see [Couillet, Debbah, CUP 2011]). Example: M = 100, G = 6 user groups, Rank(R g ) = 21, we serve 5 users per group with b = 10. Sum throughput (bit/s/hz) vs. SNR (db), approximated BD and regularized ZF, r = 6 and r = Capacity ZFBF, JGP RZFBF, JGP ZFBF, PGP RZFBF, PGP Capacity ZFBF, JGP RZFBF, JGP ZFBF, PGP RZFBF, PGP Sum Rate Sum Rate SNR (in dbs) SNR (in dbs) 39

41 Remarks Full CSI: channel matrix 3000 complex channel coefficients per coherence block (CSI feedback), with unitary common pilot matrix for downlink channel estimation. JSDM with PGP: diagonal blocks 300 complex channel coefficients per coherence block (CSI feedback), with unitary dedicated pilot matrices for downlink channel estimation, sent in parallel to each group through the pre-beamforming matrix. One order of magnitude saving in both downlink training and CSI feedback. 150 bit/s/hz at SNR = 18 db: 5 bit/s/hz per user, for 30 users served simultaneously on the same time-frequency slot. 40

42 Is the tall unitary realistic? For a Uniform Linear Array (ULA), R is Toeplitz, with elements [R] m,p = 1 2 e j2πd(m p) sin(α+θ) dα, m, p {0, 1,..., M 1} We use Szego s asymptotic theory of Toeplitz matrices. 41

43 Theorem 4. by where The empirical eigenvalue distribution of R can be approximated lim F R(λ) = µ{s(ξ) λ} M S(ξ) = m= [R] m,0 = 1 2 m [D sin( +θ)+ξ,d sin( +θ)+ξ] 1 D2 (m ξ) 2. Theorem 5. The asymptotic normalized rank of the channel covariance matrix R with antenna separation λd, AoA θ and AS, is given by ρ = lim M 1 Rank(R) = min{1, B(D, θ, )}, M where B(D, θ, ) = D sin( + θ) D sin( + θ). 42

44 Theorem 6. Let S denote the support of S(ξ), let J S = {m : [m/m] S, m = 0,..., M 1} be the set of indices for which the corresponding angular frequency ξ m = [m/m] belongs to S, let f m denote the m-th column of the unitary DFT matrix F, and let F S = (f m : m J S ) be the DFT submatrix containing the columns with indices in J S. Then, lim M 1 M UU H F S F H 2 S = 0, F where U is the M r tall unitary matrix of the non-zero eigenvectors of R. 43

45 Corollary 1. Groups g and g with angle of arrival θ g and θ g and common angular spread have spectra with disjoint support if their AoA intervals [θ g, θ g + ] and [θ g, θ g + ] are disjoint. 8 7 θ = 45 θ = 0 θ = RZFBF, Full ZFBF, Full RZFBF, DFT ZFBF, DFT 6 Eigen Values Sum Rate ξ SNR ULA with M = 400, G = 3, θ 1 = π 4, θ 2 = 0, θ 3 = π 4, D = 1/2 and = 15 deg. 44

46 Super-Massive MIMO 45

47 Idea: produce a 3D pre-beamforming by Kronecker product of a vertical beamforming, separating the sector into L concentric regions, and a horizontal beamforming, separating each l-th region into G l groups. Horizontal beam forming is as before. For vertical beam forming we just need to find one dominating eigenmode per region, and use the BD approach. A set of simultaneously served groups forms a pattern. Patterns need not cover the whole sector. Different intertwined patterns can be multiplexed in the time-frequency domain in order to guarantee a fair coverage. 46

48 An example Cell radius 600m, group ring radius 30m, array height 50m, M = 200 columns, N = 300 rows. Pathloss g(x) = 1 1+( x d 0 ) δ with δ = 3.8 and d 0 = 30m. Same color regions are served simultaneously. power. 0 Each ring is given equal 120 degree sector BD, RZFBF BD, ZFBF DFT, RZFBF DFT, ZFBF 1 km 50 m Sum rate of annular regions Annular Region Index l 47

49 Sum throughput (bit/s/hz) under PFS and Max-min Fairness Scheme Approximate BD DFT based PFS, RZFBF PFS, ZFBF MAXMIN, RZFBF MAXMIN, ZFBF bit/s/hz 40 MHz of bandwidth = 40 Gb/s per sector. 48

50 Heterogeneous/D2D Wireless Networks Scaling laws of D2D wireless networks: C = O( K) bit meter/second. If source-destination are at distance O(1), then the per-connection throughput vanishes as O( 1 K ). If source-destination are at distance O(1/ K), then the per-connection throughput is constant O(1). Source-destination pairs at 1 hop = Small Cells or D2D with Caching. 49

51 User-deployed small cells tier: In-Band or Out-of-Band? R femto R femto R macro a) b) R macro In case a), time-sharing or bandwidth splitting is optimal (tier 1 and tier 2 on orthogonal dimensions). In case b), orthogonalization is not optimal, and tier 1 and tier2 should interfere. 50

52 Smart Spectrum Reuse via Cognition Small Cells operate in TDD, macrocell operates either in TDD or in FDD (in this talk we focus on TDD macrocell). Small Cells overhear the macrocell control channel (similar to relays in WiMax j). Small Cells are aware of their location, and of the location of the macrocell users being scheduled. Open-access: any macrocell user inside the range of a small cell is absorbed. Closed-access: macrocell users can be anywhere, even inside a small cell. 51

53 Preamble BS UL-MAP Frame Structure for Cognition DL-MAP FCH Macro-DL Macro-UL Femto listening Femto transmitting (both directions) 52

54 Reverse TDD Macro User Macro BS Macro User Femto BS Femto User Femto BS Femto User We align the Macro DL with the Femto UL, and Vice-Versa. 53

55 MISO/SIMO Interference Channel and UL/DL Duality In the macro-dl/femto-ul, we use interference temperature PC as in the baseline scheme. Femto APs use linear MMSE (optimal linear receivers). In the macro-ul/femto-dl, we use the MMSE receiving vectors as transmit beamforming vectors. By UL/DL duality, there exist a power assignment of the Femto APs and of the Macro user powers such that: 1. The sum-power is the same. 2. The SINR are the same. 54

56 Femto-UL/Macro-DL with co-located macro UTs Aggregate Femto Cell rate (in bits/sec/hz) Macro User 2 Macro User 3 Macro User 4 Macro User 5 Macro User 6 Macro User 7 Macro User 8 Macro User Macro User Rate (in bits/sec/hz) 55

57 Femto-UL/Macro-DL with non co-located macro UTs Aggregate Femto Cell rate (in bits/sec/hz) Macro User 2 Macro User 3 Macro User 4 Macro User 5 Macro User 6 Macro User 7 Macro User 8 Macro User Macro User Rate (in bits/sec/hz) 56

58 Co-located vs. non co-located: comparison 1500 Colocated Non colocated Aggregate Femto Cell rate (in bits/sec/hz) Macro User Rate (in bits/sec/hz) 57

59 Femto-DL/Macro-UL: iterative power allocation Aggregate Femto Cell rate (in bits/sec/hz) Femto UL, Macro DL Femto DL, Macro UL, no iter Femto DL, Macro UL, 1 iter Femto DL, Macro UL, 2 iter Femto DL, Macro UL, 3 iter Femto DL, Macro UL, 6 iter Femto DL, Macro UL Macro User Rate (in bits/sec/hz) 58

60 Performance Let s focus on the point (15, 1000) and assume 40 MHz of system bandwidth. Macro users: 6 users per cell at 2.5 bit/s/hz yields 100 Mb/s per user. Femto users: femtocell. 625 femtocells per cell at 1.6 bit/s/hz yields 64 Mb/s per These rates are in line with today s target peak rates for LTE and WLANs (Wifi). The two systems can co-exist in the same system bandwidth. In terms of system special efficiency, we go well above the desired x100 increase, with relatively conventional technology. Key point to take home: multiuser MIMO and inter-tier interference management must be at the core of the system design, not added later as afterthoughts. 59

61 Even Denser Spatial Reuse: Distributed Caching in Wireless Devices Cache predictable Internet content (web-pages, coded video) into the user devices and auxiliary wireless helpers. 0%5)6!'%7/"#!6%("56)8/9% :5%"5%"(!"%),%':;!%0% 2"'!%'3"4)5%$"'%% #)*!("+!%"(!"%-.01%!"#$%&'!(%$"'%#)*!("+!%% "(!"%),%-./)+.011% 60

62 N nodes in an area of size N. The base station has total downlink capacity C base bit/s/hz. Short-range D2D links between the user terminals can support capacity C d2d. Following the current LTE-Advanced eicic the base station leaves a fraction β of the time-frequency slots free for D2D communication. Random placement of content in the caches. Probability that a given cache satisfies a random demand: 0 < p cache 1. Range of D2D communication such that the number of nodes reachable from any given node in one hop is c log N, for some c > 0. Probability of not finding the requested file in the neighboring caches is p = (1 p cache ) c log N. Let the fraction of users originating demands (active users) be α, and let the individual rate per user be r bit/s/hz. 61

63 The demands not found in the local caches are handled directly by the base station. Hence, we have the constraint rαn p (1 β)c base. (2) The demands found in the neighboring caches are handled by D2D communication. N Using simple interference avoidance, we can schedule c log N non-interfering links simultaneously on each time-frequency slot freed by the base station. The source rate constraint for the traffic handled by the caches is N rαn(1 p) β c log N C d2d. (3) 62

64 By solving for the optimum β and replacing it in (3), we find r 1 1 p + pn c log N C d2d C base C d2d αc log N. (4) Since p = N c log 1 1 p cache, for c log 1 1 p cache > 1, we have that N p 0 polynomially with N. As a consequence, r C d2d αc log N vanishes only logarithmically with N. The gain over a conventional cellular system, achieving system: r conv = C base αn, is unbounded!!! 63

65 Example Realistic LTE downlink capacity and a D2D link capacity inspired by Qualcomm FlashLinQ. C base = 5 bit/s/hz and C d2d = 2 bit/s/hz. Assume a cell bandwidth of 40 MHz and a target per-user rate of 10 Mb/s resulting in r = 0.25 bit/s/hz. Assuming a user activity factor α = 0.2, a conventional system would serve N = 100 users. With a modest cache hit probability p cache = 0.2, requiring c > 1 log(1.25) = , and letting c = 4.5, the proposed system serves N = users (we meet the target 100x capacity boost). 64

66 6 5 U se r lin k rate r (b it/s/h z ) Caching system Conventional cellular system 1 b) N u mb e r of u se rs N 65

67 Global Caching Gain Recent result [Maddah-Ali, Neesen, arxiv: ]... broadcast into multicast. caching turns (A 2 B 1,A 3 C 1,B 3 C 2 ) A 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 66

68 Conclusions Network MIMO (CoMP): appears to be fundamentally limited in conventional cellular systems. Large number of antennas at each BS: essentially no need for BS cooperation, beyond simple coordination of scheduling/frequency/pilots/beams. Large number of antennas naturally suited to TDD: but also possible with FDD, if Tx antenna correlation is properly exploited (JSDM). Further improvements: reduce the distance between source and destination. HetNets: cognitive multi-antenna small cells can share the same macro bandwidth. D2D: for throughput is meaningful if coupled with caching. Further caching gains from (index) coding. 67

69 Thank You 68