Coordinated Multiantenna Interference Management in 5G Networks

Transcription

1 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 1 Coordinated Multiantenna Interference Management in 5G Networks Antti Tölli atolli@ee.oulu.fi Department of Communications Engineering (DCE) University of Oulu, Finland 8 September, 2015

2 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 2 Outline Evolution of multiantenna systems MIMO with large antenna arrays Linear transceiver design and resource allocation Introduction to convex optimisation Resource allocation and linear transceiver design Coordinated transceiver optimisation Coherent vs. coordinated beamforming Minimum power multicell beamforming with QoS constraints Centralised solution Decentralised solution via optimisation decomposition Large system approximation Throughput optimal linear TX-RX design Weighted sum rate maximisation (WSRM) via MSE minimisation WSRM with rate constraints Decentralised solution via precoded UL pilot Bidirectional signalling strategies for dynamic TDD Mode selection and transceiver design in underlay D2D MIMO systems

3 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 3 Motivation Conventional cellular systems are interference limited In-cell users are processed independently by each base station (BS) Other users are treated as inter-cell interference Interference mitigated by sharing and reusing available resources Coordinated multi-node transmission with multi-user precoding Increased spatial degrees of freedom in a multi-user MIMO channel A system with N distributed antennas can ideally accommodate up to N streams Inter-stream interference can be controlled or eliminated by a proper beamformer design. Coherent multi-cell MIMO: user data transmitted over a large virtual MIMO channel

4 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 4 General Objective Goal: Design dynamic multi-dimensional radio resource management across time, frequency, and space (location) Assumption: Heterogeneous network composed of Large macro cells with massive MIMO antenna arrays, Small cells and relays with small or distributed MIMO arrays, and D2D communication with macro cell coordination Backhaul / control Data

5 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 5 Evolution of Multiantenna Systems )!)*( +!)*,)!+*( +!+*(!"#$%&$%$"'$( +-.+!+*( +-.+!+*(/(0"#$%.( '$11(0"#$%&$%$"'$( 233%40"5#$4(6718'$11( +-.+!+*(

6 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 6 Coordinated Multi-cell Transmission/Reception Coherent (joint) multi-cell transmission Each data stream may be transmitted from multiple nodes Tight synchronisation across the transmitting nodes (common carrier phase reference) A high-speed backbone network, e.g. Radio over Fibre Controller

7 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 7 Coordinated Multi-cell Transmission/Reception Coordinated beamforming Dynamic multi-cell scheduling and inter-cell interference avoidance Coordinated precoder design and beam allocation Each data stream is transmitted from a single BS node No carrier phase coherence requirement Looser requirement on the coordination and the backhaul Decentralized processing Controller

8 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 8 Interference Alignment Consider a symmetric constant MIMO interference channel with K TX-RX pairs each node equipped with M antennas TX1 RX1 TX2 RX2 TX3 RX3

9 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 9 Interference Alignment Exact capacity characterization of the K-user interference channel is unknown Degrees of freedom (or multiplexing gain) DoF = lim SNR sum rate log 2 SNR Achievable via interference alignment (IA) 1 Feasibility conditions for IA (for constant MIMO channel, K 3) 234 (K + 1)d 2M = Total DoF 2M K 2M (1) K V.R. Cadambe and S.A. Jafar. Interference Alignment and Degrees of Freedom of the K-User Interference Channel. IEEE Trans. Inform. Theory, August C. Yetis, T. Gou, S. Jafar, and A. Kayran, On feasibility of interference alignment in MIMO interference networks, IEEE Trans. Signal Process., M. Razaviyayn, G. Lyubeznik, and Z.Q. Luo, On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel, IEEE Trans. Signal Process., G. Bresler, D. Cartwright, and D. Tse, Feasibility of Interference Alignment for the MIMO Interference Channel, in IEEE Trans. Info. Theory, 2014

10 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 10 Outline Evolution of multiantenna systems MIMO with large antenna arrays Linear transceiver design and resource allocation Introduction to convex optimisation Resource allocation and linear transceiver design Coordinated transceiver optimisation Coherent vs. coordinated beamforming Minimum power multicell beamforming with QoS constraints Centralised solution Decentralised solution via optimisation decomposition Large system approximation Throughput optimal linear TX-RX design Weighted sum rate maximisation (WSRM) via MSE minimisation WSRM with rate constraints Decentralised solution via precoded UL pilot Bidirectional signalling strategies for dynamic TDD Mode selection and transceiver design in underlay D2D MIMO systems

11 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 11 MIMO with Large Antenna Arrays D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge, England: Cambridge University Press, A. M. Tulino and Sergio Verd, Random Matrix Theory and Wireless Communications, Foundations and Trends in Communications and Information Theory, vol. 1, no. 1, pp Rusek, F.; Persson, D.; Buon Kiong Lau; Larsson, E.G.; Marzetta, T.L.; Edfors, O.; Tufvesson, F., Scaling Up MIMO: Opportunities and Challenges with Very Large Arrays, Signal Processing Magazine, IEEE, vol.30, no.1, pp.40 60, Jan Foundations and Trends in Communications and Information Theory, Vol. 1, Issue 1, Random Matrix Theory and Wireless Communications by A. Tulino and S Verdu R. Couillet and M. Debbah, Random Matrix Methods for Wireless Communications, 1st ed. Cambridge University Press, 2011.

12 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 12 Introduction Point-to-point MIMO channel capacity with large antenna arrays Capacity formulation Approximate capacity from deterministic eigenvalue distribution (n r, n t ) Asymptotic capacity when nr (n t ) is fixed while n t (n r ) Multiuser MIMO sum rate in UL/DL with large antenna arrays Capacity formulation Asymptotic capacity when number of users K is fixed while nt (n r ) Multi-user (Multi-cell) MIMO Uplink with linear MMSE receivers Large System Approximation MMSE receiver derivation MMSE SINR large system approximation

13 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 13 Point-to-point MIMO Architecture P 1 P nt AWGN coder rate R 1 AWGN coder rate R nt Q x[m] H[m] w[m] y[m] + Joint decoder [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005.] Generalized architecture to multiplex n t independent data streams The choice of Q depends on the CSIT Q = V requires full CSIT capacity achieving scheme with WF power allocation Q = I requires no CSIT independent streams sent on each TX antenna

14 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 14 Capacity in Fast Fading MIMO Channel Capacity of fast fading channel H C nr nt C = with CSIR max I(x; y, H) = max I(x; y H) (2) E[ x 2 ] P E[ x 2 ] P For fixed MIMO channel realization H = H I(x; y H = H) = h(y) h(y x) = h(y) h(n) = h(y) log(πen 0 ) nr log((πe) nr det(n 0 I nr + HK x H H )) log(πen 0 ) nr ) = log det (I nr + 1N0 HK x H H where K x = QPQ H is the covariance matrix of x, x CN (0, K x ), and P = diag (p 1,..., p nt )

15 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 15 Capacity in Fast Fading MIMO Channel CSI at receiver only In general, K x depends on the stationary distribution of the fading process {H[m]} When the elements of H are i.i.d. CN (0, 1), the optimal K x is K x = P n t I nt (3) The ergodic capacity of MIMO channel without CSIT is simplified to [ ( C = E log det I nr + P )] HH H n t N 0 )] = n min i=1 where n min = min(n t, n r ) [ ( E log 1 + P λ 2 i n t N 0 (4)

16 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 16 Large Antenna Array Regime Focus on the square channel n = n t = n r [ n ( ) ] C nn (SNR) = E log 1 + SNR λ2 i (5) n i=1 where λ i / n are the singular values of H/ n 4 n = n = When n, the distribution of λ i / n becomes deterministic { 1 f (x) = π 4 x 2 0 x 2, 0 else e n = Quarter circle law [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005]

17 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 17 Large Antenna Array Regime For increasing n 5 1 n n i=1 ( ) log 1 + SNR λ2 i n and the closed form solution to the integral is Furthermore 4 log(1 + SNRx)f (x)dx = c (SNR) (6) 0 ( ) 1 + 4SNR + 1 c (SNR) = 2 log log e ( 4SNR ) (7) 2 4SNR C nn (SNR) lim = c (SNR) C nn (SNR) nc (SNR) (8) n n Capacity grows linearly in n at any SNR 5 More in: Foundations and Trends in Communications and Information Theory, Vol. 1, Issue 1, Random Matrix Theory and Wireless Communications by A. Tulino and S Verdu

18 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 18 Example: Approximate vs. Exact Capacity Rate (bits /s / Hz) Approximate capacity c 2 Exact capacity 2 1 C 22 1 Exact capacity 4 1 C SNR (db) Figure: Comparison between the large-n approximation and the actual capacity for n = 2, 4. [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005]

19 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 19 Large Antenna Array Regime, n r >> n t Assume n r >> n t, and the elements of H are i.i.d. CN (0, 1) then H H H n r I nt (9) log I n r + P HH H n t N 0 = log I nt + P H H H n t N 0 Match filter receiver is asymptotically optimal n t log(1 + P n r n t N 0 ) (10)

20 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 20 Large Antenna Array Regime, n t >> n r Assume n t >> n r, and the elements of H are i.i.d. CN (0, 1) HH H I nr (11) n t then the rate expression without CSIT is simplified to log I n r + P HH H n t N 0 n r log(1 + P ) (12) N 0 The rate expression with full CSIT (at high SNR) is simplified to log I n r + 1 HK x H H n r log(1 + n t P ) (13) N 0 n r N 0 The rows of H are asymptotically orthogonal: K x = VPV H P n rn t H H H

21 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 21 Uplink System Model Assume time-invariant uplink channel with K single-antenna users and a single BS with n r receive antennas. [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005] The received signal vector at symbol time m is described by K y[m] = h k x k [m] + n[m] k=1 (14) = Hx[m] + n[m] where x k is the TX symbol of user k, subject to E[ x 2 ] P k, y C n r is the RX signal, n CN (0, N0 I nr ) complex white Gaussian noise, hk = a k hk C nr is the channel vector of user k, where a k is the large scale fading factor and h k is the normalized channel

22 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 22 Sum Capacity for Multiuser Uplink Sum capacity expression for SDMA is equal to SU-MIMO without CSIT K log I P k n r + h k h H k N 0 = log I n r + 1 HK x H H N 0 = K i=1 k=1 log(1 + γ mmse sic k ) (15) where H = [h 1,..., h K ], K x = diag(p 1,..., P K ) y[m] MMSE Receiver 1 Decode User 1 User 1 Subtract User 1 MMSE Receiver 2 Decode User 2 User 2 [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005]

23 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 23 Large Antenna Array Regime, n r >> K Assume n r >> K, and the elements of h k are i.i.d. CN (0, 1) H H H n r A K (16) where A K = diag(a 1,..., a K ). Then, I n r + 1 HK x H H = log N 0 I K + 1 K x H H H N 0 K k=1 Match filter receiver is asymptotically optimal log(1 + n rp k a k N 0 ) (17)

24 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 24 Downlink System Model Assume time-invariant downlink channel with K single-antenna users and a single BS with n t transmit antennas. [D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005] The received signal vector at symbol time m is y k [m] = h H k x[m] + w k[m] K = h H k u k pk d k [m] + h H k u i pi d i [m] + w k [m] i=1,i k x C n t is the TX signal vector, subject to power constraint E[Tr(xx H )] = K k=1 p k P, uk C nt is the normalised beamformer, u k = 1 d k C is the normalised data symbol, E [ d k 2] = 1 y k C is the RX signal, w k CN (0, N 0 ) complex white Gaussian noise, hk = a k hk C nt is the channel vector of user k assumed to be ideally known at the transmitter (18)

25 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 25 Sum Capacity for the Multiuser Downlink Maximisation of the DL sum rate via dual uplink reformulation Optimal solution from constrained optimisation problem max log q 2 k I n t + 1 K q k h k h H k N 0 subject to k=1 K q k P, q k 0, k = 1,..., K (19) k=1 where q k is the dual UL power such that K k=1 q k = K k=1 p k = P When n t >> K, the objective of (19) is simplified to max log q k I K + 1 K x H H K H N 0 max log(1 + q kn t a k ) (20) q k N 0 k=1 where K x = diag(q 1,..., q K ) and HH H n t diag(a 1,..., a K )

26 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 26 Linear MMSE Receiver Derivation Consider the uplink system model y[m] = Hx[m] + n[m] (41), where the decision variables are generated as ˆx = W H y Assume n CN (0, K n ) and x CN (0, K x ) are independent, the optimal linear MMSE receiver is found by minimizing W = arg min E [ x W H y 2] (21) W }{{} MSE After differentiation with respect to W and setting the gradient to zero, the optimal MMSE filter is W = ( HK x H H + K n ) 1 HKx (22) If n CN (0, N 0 I nr ) and x CN (0, P n t I nt ) ( ) P 1 W = HH H + N 0 I H P (23) n t n t

27 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 27 Linear MMSE Receiver SINR Derivation Low SNR: P << N 0 W H P n t = Matched filter High SNR: P >> N 0 W ( HH H) 1 H = ZF receiver Output SINR for the kth stream with input power p k (P/n t ) is γ mmse k = E [ wk Hh kx k 2] [ ] = pkwh k h k hh k w k E wk H( i k h ix i + n k ) 2 wk HR kw k =... = p k h H k R 1 k h k (24) where R k = i k p ih i h H i + N 0 I nr and w k is kth column of W Achievable rate: [ nt ] R mmse = E log(1 + γk mmse ) (25) k=1

28 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 28 Large System Approximation of γ mmse k Some important lemmas Lemma 1: Assume a vector x C N with i.i.d elements which have zero mean and variance equal to 1 N. Also consider a Hermitian matrix A C N N with elements independent of x, then x H Ax 1 N tr(a) 0 (26) N Lemma 2:Let A N be a complex N N matrix with uniformly bounded spectral norm. Also, consider random Hermitian matrix C N such that for smallest eigenvalue of C N there exist an ɛ with probability one such that λ min > ɛ for all large N, then 1 N tr[a NC 1 N ] 1 N tr[a N(C N + uu H ) 1 ] N 0 (27) where u is a complex vector.

29 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 29 Large System Approximation of γ mmse k Theorem 3: Stieltjes transform of Gram matrix YY H. Consider a N n random matrix denoted by Y, such that elements of Y are independent and zero mean. The variance of entries is given by E[ y i,j 2 ] = α 2 i,j m YY H(z) = 1 N tr(yyh zi N ) 1 1 N tr(θ(z)) n, N n 0 (28) where Θ(z) = diag(θ 1 (z),..., θ N (z)). The entries θ i can be found by fixed point iteration c 1 θ i (z) = 1 i N (29) n z(1 + 1 α n 2 ˆθ i,j j (z)) j=1 1 ˆθ j (z) = 1 j n (30) N z(1 + 1 α n 2 i,j θ i(z)) i=1

30 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 30 Large System Approximation of γ mmse k The instantaneous random variable γk mmse (p) can be approximated by a deterministic quantity γk det (p) such that γ mmse k (p) γ det k nr, nr K (p) c 0 (31) Sketch of proof Define Σk = i k p ih i h H i and Σ = Hdiag(p 1,..., p K )H H Applying Lemma 1, γ mmse k can be approximated as p k a k hh k (Σ k + N 0 I nr ) 1 hk p ka k Tr n r Applying Lemma 2, we have p k a k Tr n r ( (Σ k + N 0 I nr ) 1) p ka k n r ( (Σ k + N 0 I nr ) 1) (32) Tr ((Σ + N 0 I nr ) 1) = p k a k m Σ ( N 0 ) (33) where m Σ ( N 0 ) is the Stieltjes transform of Σ and it only depends on p and a 1,..., a k

31 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 31 Large System Approximation of γ mmse k Uplink with K single-antenna users and a single BS with n r receive antennas Var(γ mmse - γ det ) Number of users Figure: Variance of γ mmse k γ det k, K = n r and p k a k /N 0 = 10

32 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 32 Outline Evolution of multiantenna systems MIMO with large antenna arrays Linear transceiver design and resource allocation Introduction to convex optimisation Resource allocation and linear transceiver design Coordinated transceiver optimisation Coherent vs. coordinated beamforming Minimum power multicell beamforming with QoS constraints Centralised solution Decentralised solution via optimisation decomposition Large system approximation Throughput optimal linear TX-RX design Weighted sum rate maximisation (WSRM) via MSE minimisation WSRM with rate constraints Decentralised solution via precoded UL pilot Bidirectional signalling strategies for dynamic TDD Mode selection and transceiver design in underlay D2D MIMO systems

33 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 33 Constrained Optimisation Problem Engineering designs are often posed as constrained optimisation problems: minimise f 0 (x) subject to f i (x) 0, i = 1,..., m h i (x) = 0, i = 1,..., p (34) where x is a vector of decision variables f0 is the objective function fi (x), i = 1,..., m are the inequality constraint functions h i (x), i = 1,..., p are the equality constraint functions Hard to solve in general especially when the number of variables in x is large the problem might have multiple local minima difficult to find a feasible solution possibly poor convergence rate

34 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 34 Convex Optimisation Problem aint, since ion (Ax + in R k+1 If. f 0, f 1,..., f m in III. CONVEX FUNCTIONS set of the In this minimise section, we introduce f 0 (x) the reader to some important convex subject functions to f i (x) and techniques 0, i = 1, for..., verifying m (35) 0 convexity. The objective his i (x) to sharpen = 0, i the = 1, reader s..., pability are convex to recognize and hconvexity. under an i, i = 1,..., p are affine (h i (x) = a T i x b i), then any A. Convex locally optimal functions point is globally optimal f : R m feasibility can be determined unambiguously can A be function solved efficiently f : R n using, R is convex e.g. interior if its domain point methods dom f incorporated is convex and in generic for all x, convex y dom optimisation f, θ [0, tools 1] A function ff(θx is convex + (1 ifθ)y) its domain θf(x) dom(f) + (1 θ)f(y); is convex and 0}. If f(θx C + f is (1 concave θ)y) if θf(x) f is + convex. (1 θ)f(y) x, y dom(f), θ [0, 1] sformation frag replacements fractional, y H, x x x convex c Antti concave Tölli, Department of Comm. Engineering neither S

35 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 35 infeasible). A point x C is an optimal point if f(x) = f and the optimal A set Simple is X Example opt = {x C f(x) = f } As an example consider the problem 5 minimize x 1 + x 2 subject to x 1 0 PSfrag x replacements x 1 x 2 0 x C 4 x The objective function is f 0 (x) = [1 1] T [A. Hindi, A Tutorial on Convex Optimization, Proc. of the 2004 American Control Conference Boston, x; the Massachusetts, feasible June, 2004] set C is half-hyperboloid; the optimal value is f = 2 and the only optimal point is x = (1, 1). In the standard problem c Antti Tölli, above, Department of Comm. theengineering explicit constraint

36 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 36 Resource Allocation with MIMO Multiuser MIMO: base station and users are equipped with multiple antennas The fundamental idea: inter-user interference is minimised Requires channel knowledge of all same cell users Multiple users only a subset of users selected at a time Scheduling/resource allocation In general, a difficult non-convex combinatorial problem 1. Select a set of users for each orthogonal dimension (frequency/sub-carrier, time) 2. Optimise transceivers for the selected set of users per dimension. Greedy allocation: Select a set of users with best channel conditions such that their spatial signatures overlap as little as possible Often unfair, users with weak channel conditions suffer

37 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 37 Resource Allocation with MIMO Time instant t Time instant t+1 User 1 User 1 MIMO BS User 2 MIMO BS User 2 User 3 User 3 User 4 User 4

38 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 38 Multi-cell MIMO System Model B BSs, N T TX antennas per BS and N Rk RX antennas per user k A user k is served by M k = B k BSs from the joint processing set B k, B k B = {1,..., B} 6 where y k = b B a b,k H b,k x b + n k (36) = a b,k H b,k x b,k + a b,k H b,k b B k b B k i k + a b,k H b,k x b + n k b B\B k ab,k H b,k C N R k N T channel from BS b to user k x b C NT total TX signal from BS b, and x b,i xb,k is the transmitted data vector from BS b to user k 6 Extension to multicarrier systems is straightforward add sub-carrier index c to every variable

39 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 39 System Model x b,k = M b,k d k C N T is the transmitted data vector from BS b to user k, where M b,k C NT m k pre-coding matrix, dk = [d 1,k,..., d mk,k] T vector of normalised data symbols, mk min(n T M k, N Rk ) number of active data streams. The optimal linear receiver is equipped with a LMMSE filter, d k = U H k y k: U k = ( K ) 1 a 2 b,kh b,k M b,i M H b,ih H b,k + N 0 I NRk i=1 b B i a b,k H b,k M b,k (37) b B k

40 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 40 Linear Transceiver Design Entire capacity region of multiuser MIMO DL has been recently discovered Also with individual peak power constraint per BS antenna 78 Require complex nonlinear precoding based on dirty paper coding Sub-optimal but less complex transmission methods are needed Linear beamforming is usually remarkably simpler in practice Dimensionality contraint per BS: 0 k U b m k N T, 0 m k N Rk. (38) Dimensionality constraint in the multi-cell network: Upper bound k U m k BN T Very difficult in general (feasibility conditions for interference alignment in high SNR) 7 W. Yu and T. Lan, Transmitter optimization for the multi-antenna downlink with per-antenna power constraints, IEEE Transactions on Signal Processing, vol. 55, no. 6, part 1, pp , Jun H. Weingarten, Y. Steinberg, and S. Shamai, The capacity region of the Gaussian multiple-input multiple-output broadcast channel, IEEE Transactions on Information Theory, vol. 52, no. 9, pp , Sep

41 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 41 Linear Transceiver Design A generalised method for joint design of linear transceivers with Coordinated multi-cell processing Per-BS or per-antenna power constraints Subject to various optimisation criteria and Quality of Service (QoS) constraints The proposed method can accommodate any scenario between Coherent multi-cell beamforming across virtual MIMO channel Single-cell beamforming with inter-cell interference coordination and beam allocation The presented methods require a complete CSI between all pairs of users and BSs The solution represent an upper bound for the less ideal solutions with an incomplete CSI. Centralised and decentralised mechanisms to perform scheduling and precoding

42 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 42 Linear Transceiver Design Per data stream processing: B BSs send S independent streams, S min(bn T, k U N R k ) For each data stream s, scheduler associates a user k s, with the channel matrices H b,ks, b B s. In some special cases Bs B ks. For example, a user may receive data from several BSs, while B s = 1 s. Let m b,s C N T and u s C N R ks be arbitrary TX and RX beamformers for the stream s SINR per stream: γ s = a b,ks u H s H b,ks m b,s e jφ b b B s N 0 u s S i=1,i s 2 (39) a b,ks u H s H b,ks m b,i e jφ b 2 b B i φ b represents the possible carrier phase uncertainty of BS b

43 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 43 Coordinated Transceiver Optimisation The SINR expression can accommodate several special cases for multicell coordination: 1. Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints 2. Coordinated single-cell beamforming ( B s = 1 s): the other-cell transmissions considered as inter-cell interference 3. Any combination of above two, where B k and B s may be different for each user k and/or stream s. γ s = a b,ks u H s H b,ks m b,s e jφ b b B s N 0 u s S i=1,i s 2 a b,ks u H s H b,ks m b,i e jφ b b B i 2

44 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 44 Coordinated Transceiver Optimisation The general system optimisation objective is to maximise a function f(γ 1,..., γ S ) that depends on the individual SINR values maximise f(γ 1,..., γ S ) subject to N 0 us S b B s a b,ks u H s H b,ks m b,s 2 a b,ks u H s H b,ks m b,i 2 i=1,i s b B i s = 1,..., S m b,s 2 2 P b, b = 1,..., B s S b γ s, (40) Additional Quality of Service constraints (QoS) can be also incorporated in (40), e.g., minimum/maximum SINR or rate constraints per stream or per user

45 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 45 Coordinated Transceiver Optimisation Optimisation criteria, e.g., 1. Sum power minimisation with fixed per stream SINR constraints: f(γ 1,..., γ S ) = B b=1 P b 2. Weighted sum MSE minimisation: f(γ 1,..., γ S ) = S s=1 β smse s = S s=1 β s (1+γ s) 3. Weighted sum rate maximisation: f(γ 1,..., γ S ) = S s=1 β s log 2 (1 + γ s ) = log 2 S s=1 (1 + γ s) βs 4. Max min weighted SINR per data stream, i.e., SINR balancing : f(γ 1,..., γ S ) = max min s=1,...,s βs 1 γ s 5. Maximisation of weighted common user rate: f(γ 1,..., γ S ) = r o = min k A β 1 k s P k log 2 (1 + γ s ), P k is a subset of data streams that correspond to user k

46 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 46 Coordinated Transceiver Optimisation Linear MIMO transceiver optimisation problems cannot be solved directly, in general iterative procedures are required No cooperation between users Transmitter and receivers optimised separately in an iterative manner Some controlled inter-user interference allowed Iteration t+1 Transmit beamformers optimised Receive beamformers fixed Controller

47 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 47 Coherent Multi-cell versus Coordinated Single-cell Beamforming A. Tölli, H. Pennanen and P. Komulainen, On the Value of Coherent and Coordinated Multi-cell Transmission, The International Workshop on LTE Evolution in conjunction with the International Conference on Communications (ICC 09), Dresden, Germany, June 2009 A. Tölli, M. Codreanu, and M. Juntti, Linear multiuser MIMO transceiver design with quality of service and per antenna power constraints, IEEE Transactions on Signal Processing, vol. 56, no. 7, pp , Jul A. Tölli, M. Codreanu, and M. Juntti, Cooperative MIMO-OFDM cellular system with soft handover between distributed base station antennas, IEEE Transactions on Wireless Communications, vol. 7, no. 4, pp , Apr

48 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 48 Coordinated single-cell beamforming Each stream is transmitted from a single BS, B s = 1 s A user k s is typically allocated to arg max b B a b,ks Near the cell edge, the optimal beam allocation strategy depends on the the channel H b,k. Large gains from fast beam allocation (cell selection) available A difficult combinatorial problem exhaustive search Sub-optimal allocation algorithms Allocation objectives Generate the least inter-stream interference Provide large beamforming gains Controller

49 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 49 Heuristic Beam Allocation Algorithms 1. Greedy selection: Beams with the largest component orthogonal to the previously selected set of beams are chosen. 2. Maximum eigenvalue selection: The eigenvalues of channel vectors are simply sorted and at most N T streams are allocated per cell. 3. Eigenbeam selection using maxmin SINR criterion: A simplified exhaustive search over all possible combinations of user-to-cell and stream/beam-to-user allocations Beamformers matched to the channel, i.e., m b,s = v b,ks,l s PT / S b For each allocation, the receivers u s and the corresponding SINR values γ s are recalculated The selection of the allocation is based on the maxmin SINR criterion, i.e., arg max min γ s. b,k,l s=1,...,s

50 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 50 Simulation Cases 1. Coherent multi-cell MIMO transmission (B s = B s) with per BS power constraints 2. Coordinated single-cell transmission ( B s = 1 s) Exhaustive search over all possible combinations of beam allocations. The SINR balancing algorithm is recomputed for each allocation. Fixed allocation, i.e., user k s is always allocated to a cell b with the smallest path loss, arg max a b,ks. b B Heuristic allocation methods 3. Non-coordinated single-cell transmission ( B s = 1 s), where the inter-cell interference is neglected at the transmitters 4. Single-cell transmission with time-division multiple access (TDMA), i.e., without inter-cell interference

51 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 51 Simulation Scenario A flat fading multiuser MIMO system K = 2 4 users served simultaneously by 2 BSs {N T, N Rk } = {2-4, 1} Equal maximum power limit P T for each BS, i.e. P b = P T b SNR k = P T max b B a2 b,k /N 0 2 k = 2 a1,1 k = 4 α = a = a a = 1,1 a1,2 1,3 2,3 a2,4 k = 1 k = 3 2 a 1,3 b = 1 b = 2

52 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 52 SINR Balancing - Full Spatial Load Coherent multi cell TX Coord. single cell TX (ex. search) Coord. single cell TX (fixed) Coord. single cell TX (MaxMinSINR) Coord. single cell TX (MaxNorm) Non Coord. single cell TX (ex. search) Non Coord. single cell TX (fixed) TDMA (ex. search) TDMA (fixed) Ergodic sum rate [bits/s/hz] Inf Distance α between different user sets [db] Figure: Ergodic sum of user rates of {K, B, N T, N Rk } = {4, 2, 2, 1} system, 0 db single link SNR. [A. Tölli, H. Pennanen and P. Komulainen, On the Value of Coherent and Coordinated Multi-cell Transmission, IEEE ICC 09, Dresden, Germany, June 2009]

53 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 53 SINR Balancing - Full Spatial Load Ergodic sum rate [bits/s/hz] Coherent multi cell TX Coord. single cell TX (ex. search) Coord. single cell TX (fixed) Coord. single cell TX (MaxMinSINR) Coord. single cell TX (MaxNorm) Non Coord. single cell TX (ex. search) Non Coord. single cell TX (fixed) TDMA (ex. search) TDMA (fixed) Inf Distance α between different user sets [db] Figure: Ergodic sum of user rates of {K, B, N T, N Rk } = {4, 2, 2, 1} system, 20 db single link SNR. [A. Tölli, H. Pennanen and P. Komulainen, On the Value of Coherent and Coordinated Multi-cell Transmission, IEEE ICC 09, Dresden, Germany, June 2009]

54 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 54 SINR Balancing - Partial Spatial Load Ergodic sum rate [bits/s/hz] Coherent multi cell TX Coord. single cell TX (ex. search) Coord. single cell TX (fixed) Coord. single cell TX (MaxMinSINR) Coord. single cell TX (MaxNorm) Coordinated single cell TX (Greedy) Non Coord. single cell TX (ex. search) Non Coord. single cell TX (fixed) TDMA (ex. search) TDMA (fixed) Inf Distance α between different user sets [db] Figure: Ergodic sum rate of {K, B, N T, N Rk } = {2, 2, 2, 1} system at 20 db single link SNR. [A. Tölli, H. Pennanen and P. Komulainen, On the Value of Coherent and Coordinated Multi-cell Transmission, IEEE ICC 09, Dresden, Germany, June 2009]

55 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 55 SINR Balancing vs. Rate Maximisation Max rate Max min SINR Ergodic sum rate [bits/s/hz] Coherent multi cell TX Coord. single cell TX (ex. search) 5 Coord. single cell TX (fixed) Non Coord. single cell TX (ex. search) Non Coord. single cell TX (fixed) TDMA (ex. search) TDMA (fixed) Inf Distance α between different user sets [db] Figure: Ergodic sum rate of {K, B, N T, N Rk } = {4, 2, 2, 1} system at 20 db single link SNR. [A. Tölli, H. Pennanen and P. Komulainen, On the Value of Coherent and Coordinated Multi-cell Transmission, IEEE ICC 09, Dresden, Germany, June 2009]

56 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 56 Outline Evolution of multiantenna systems MIMO with large antenna arrays Linear transceiver design and resource allocation Introduction to convex optimisation Resource allocation and linear transceiver design Coordinated transceiver optimisation Coherent vs. coordinated beamforming Minimum power multicell beamforming with QoS constraints Centralised solution Decentralised solution via optimisation decomposition Large system approximation Throughput optimal linear TX-RX design Weighted sum rate maximisation (WSRM) via MSE minimisation WSRM with rate constraints Decentralised solution via precoded UL pilot Bidirectional signalling strategies for dynamic TDD Mode selection and transceiver design in underlay D2D MIMO systems

57 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 57 Minimum Power Multi-cell Beamforming with User Specific QoS Constraints D. N. C. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge University Press, 2005, Chapter 10 H. Dahrouj and W. Yu, Coordinated beamforming for the multicell multi-antenna wireless system, IEEE Transactions on Wireless Communications, vol. 9, no. 5, pp , A. Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February 2011 H. Pennanen, A. Tölli and M. Latva-aho, Decentralized Coordinated Downlink Beamforming via Primal Decomposition, IEEE Signal Processing Letters, vol. 8, no.11, pp , November 2011 H. Pennanen, A. Tölli and M. Latva-aho, Multi-Cell Beamforming with Decentralized Coordination in Cognitive and Cellular Networks, IEEE Transactions on Signal Processing, vol. 62, no. 2, pp , January 2014

58 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 58 Simplified Downlink System Model Assume now downlink channel with B BSs each with N T transmit antennas serving in total K single-antenna users Focus on the coordinated beamforming case B k = 1, B k = b k k. The system model from (36) is simplified to where y k = h bk,km k d k + K i=1,i k h bi,km i d i + n k (41) bk is the index of the BS serving user k m k = p k u k where u k C nt, u k = 1 is the normalised beamformer, and p k the corresponding power allocation dk C is the normalised data symbol, E [ d k 2] = 1 hb,k C 1 NT is the channel row vector from BS b to user k including the pathloss a b,k, assumed to be ideally known at the transmitter

59 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 59 Coordinated Minimum Power Beamforming Minimise the transmitted power Subject to user specific SINR targets Centralised optimisation problem: min. s. t. N B b=1 N 0 + m k 2 2 k U b hbk,km k 2 K i=1,i k h bi,km i 2 γ target k, k = 1,... K where the variables are m k C N T, k = 1,..., K. Controller (42)

60 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 60 Solution via Uplink-Downlink Duality Downlink SINR γ k for user k: γ k = p k h bk,ku k 2 N 0 + i k p 2, k = 1,... K (43) i h bi,ku i Denote a = [a 1,..., a K ] T where Rewrite (43) as a k = γ k (1 + γ k ) h bk,ku k 2 (44) (I K D a G) p = N 0 a (45) where p = [p 1,..., p K ] T, (k, i) th entry of G IR K K is equal to G k,i = h bi,ku i 2 and D a = diag{a 1,..., a K }

61 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 61 Uplink-Downlink Duality The RX signal for user k in the dual UL is ˆd k [m] = u H k hh b k,k qk d k + u H k hh b k,i qi d i + u H k n b k i k where q k is the TX power of user k The dual uplink SINR γk ul for user k ( u H k hh b k,i = hbk,iu k ): γk ul = q k h bk,ku k 2 N 0 + i k q 2, k = 1,... K (46) i h bk,iu k

62 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 62 Uplink-Downlink Duality Denote b = [b 1,..., b K ] T where Rewrite (46) as b k = γ ul k (1 + γ ul k ) h b k,ku k 2 (47) ( I K D b G T) q = N 0 b (48) where q = [q 1,..., q K ] T and D b = diag{b 1,..., b K } Solve p from (45) and q from (48) p = N 0 (I K D a G) 1 ( a = N 0 D 1 a G ) 1 1 ( q = N 0 I K D b G T) 1 ( b = N0 D 1 b G T) 1 1 (49) (50)

63 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 63 Uplink-Downlink Duality To achieve the same SINR s in both DL and dual UL γ k = γ ul k k, set a = b (D a = D b ) K k=1 p k = 1 T p = N 0 1 T ( D 1 a G ) 1 1 = N 0 1 T ( D 1 a G T) 1 K 1 = q k (51) k=1 The total transmit power is the same in both DL and dual UL

64 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 64 Solution for Fixed Beamformers Find power allocation p (similarly for q) that satisfies γ target = [γ target 1,..., γ target K ] minimise subject to k p k γ k (p) γ target k where the variables are p and (G k,i = h bi,ku i ) γ k (p) = Equivalent to a linear program (LP), k (52) G k,k p k i k G k,ip i + w k (53) minimise subject to 1 ( T p I K D target a ) G p N 0 a (54) For a feasible γ target, the closed form solution is given by (49)-(50).

65 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 65 Iterative Solution Transmit beamforming and power loading can be solved optimally via dual uplink formulation 9 k q k min. q k,u k k subject to γ k (q) γ target k, k (55) Iterative solution alternate until convergence 1. MMSE filter u k = ũ k / ũ k, ũ k = ( i q ih H b k,i h b k,i + N 0 I) 1 h bk,k is the optimal power minimizing receiver for fixed powers q 2. Eq. (50) is optimal for fixed receivers u k k Joint update method q [t+1] k = h H k γ target k ( i k q[t] i hh b k,i hh b k,i + N 0I) 1 hbk,k = γtarget k γ k [t] q[t] k (56) 9 More details in: M. Chiang, P. Hande, T. Lan, C.W. Tan, Power control in Wireless Cellular Networks, 2006

66 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 66 t SOCP Reformulation 2.2 Some important examples 1 Second order cone is associated with the Euclidian norm x 2 Important constraint in many precoding design applications x2 1 1 x1 0 1 Canonical form of SOCP minimise subject to Figure 2.10 Boundary of second-order cone in R 3, {(x1,x2,t) (x 2 1+x 2 2) 1/2 t}. Boundary of second-order cone in IR 3, {(x 1, x 2, t) (x x2 2 ) t} It is (as the name suggests) a convex cone. c T x A i x + b i 2 c T i x + d i, i = 1,..., m Fx = g, Example 2.3 The second-order cone is the norm cone for the Euclidean norm (57) C = {(x, t) R n+1 x 2 t} { [ ] [ ] T [ ][ ] } x x I 0 x = 0, t 0. t t 0 1 t The second-order cone is also known by several other names. It is called the qu cone, since it is defined by a quadratic inequality. It is also called the Loren or ice-cream cone. Figure 2.10 shows the second-order cone in R 3. where x IR n is the opt. variable, A i IR n i n and F IR p n c Antti Tölli, 2.2.4Department Polyhedra of Comm. Engineering

67 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 67 SOCP Reformulation By rearranging the constraint in (42) as N 0 + K h bi,km i 2 (1 + 1 i=1 γ target k Eq. (42) can be reformulated into epigraph form min. s. t. p h b1,km 1. h bk,km K N0 vec(m) 2 p ) h bk,km k 2, k = 1,... K γ target k h H b k,k m k, k = 1,... K where the variables are m k C N T, k = 1,..., K, and where M = [m 1,..., m K ]. (58) Standard form SOCP

68 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 68 Decentralised Solution via Optimisation Decomposition TDD assumption: each BS is able to measure at least the channels of all cell edge users 1 B K-1 K 1 2 Implementation alternatives 1. Simple ZF solution: inter-cell interference nulled while optimising the served users 2. Interference balancing: allow some controlled inter-cell interference, and design the precoders in the adjacent BSs accordingly

69 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 69 Decentralised Solution via Optimisation Decomposition Proposed distributed solution Beamformers are designed locally relying on limited information exchanged between adjacent BSs The coupled terms are decoupled by a dual decomposition 10, Alternating direction method of multipliers (ADMM) 11, or primal decomposition 12 approach Decentralized algorithm The approach is able to guarantee always feasible solutions even with low feedback rate Allows for a number of special cases with reduced backhaul information exchange 10 A. Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February C. Shen, T. H. Chang, K. Y. Wang, Z. Qiu, and C. Y. Chi, Distributed robust multi-cell coordinated beamforming with imperfect CSI: An ADMM approach, IEEE Trans. Signal Processing, vol. 60, no. 6, pp , Jun H. Pennanen, A. Tölli and M. Latva-aho, Decentralized Coordinated Downlink Beamforming via Primal Decomposition, IEEE Signal Processing Letters, vol. 8, no.11, pp , November 2011

70 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 70 Decentralised Solution via Optimisation Decomposition For the coordinated single-cell beamforming case ( B k = 1 k), SINR formula can be written Γ k = = N 0 + h bk,km k 2 K i=1,i k h bi,km i 2 hbk,km k 2 N 0 + ζb,k 2 + b b k i U bk \k where the inter-cell interference term is hbk,km i 2 (59) ζ 2 b,k = i U b h b,k m i 2 (60)

71 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 71 Decentralised Solution via Optimisation Decomposition Now, (42) can be reformulated for the special case B k = 1 k as: B min. m k 2 2 b=1 k U b s. t. Γ k γ k, k h b,k m i 2 ζ 2 b,k, k U b, b i U b (61) where the variables are m k and ζ b,k. Inter-cell interference generated from a given base station b cannot exceed the user specific thresholds ζ b,k k U b BSs are coupled by the interference terms ζ b,k. For fixed ζ b,k, the problem would be decoupled between BSs

72 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 72 Decentralised Solution via Dual Decomposition 13 Introduce local copies ζ (b) b,k of the interference terms ζ b,k Introduce additional equality constraints Each ζb,k couples exactly two (adjacent) base stations, i.e., the serving BS b k and the interfering BS b. (b) Enforce the two local copies to be equal ζ b,k = ζ(b k) b,k k, b B k, where B k = B \ b k. B min. m k 2 2 b=1 k U b s. t. Γ (b) k γ k, k U b b (62) h b,k m i 2 (b)2 ζ b,k, k U b b i U b ζ (b) b,k = ζ(b k) b,k, k, b B k where the variables m k, and ζ (b) b,k k, b B k are local for each BS b 13 S. Boyd, L. Xiao, A. Mutapcic, and J. Mattingley, Notes on decomposition methods: course reader for convex optimization II, Stanford, Available online:

73 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 73 Decentralised Solution via Dual Decomposition Dual decomposition approach: the consistency constraints in (62) are relaxed by forming the partial Lagrangian as ) L (M 1,..., M B, ζ (1),..., ζ (B), ν 1,..., ν B = B b=1 k U b m k K ν b,k (ζ (b) b,k ζ(b k) b,k ) = B k=1 b B k b=1 k U b mk 2 (63) B 2 + ν T b ζ(b) b=1 where ν b,k k, b B k are real valued Lagrange multipliers associated with the consistency constraints The dual function can now be written as g(ν 1,..., ν B ) = B b=1 g b(ν b ) (64) where g b (ν b ) is the minimum value of the partial Lagrangian solved for a given ν b g b (ν b ) = inf mk νt b ζ (b). (65) m k,ζ (b) k U b

74 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 74 Decentralised Solution via Dual Decomposition Finally, the local problem of BS b can be formulated as min. mk νt b ζ(b) k U b s. t. Γ (b) k γ k, k U b h b,k m i 2 (b)2 ζ b,k, k U b i U b where the variables are m k k U b, and ζ (b) Locally solved as SOCPs in each BS b with knowledge of νb (66) The master problem: max. g(ν 1,..., ν B ) with variables ν b b Solved iteratively with the following updates: ( ) ν b,k (t + 1) = ν b,k (t) + µ ζ (b) b,k (t) ζ(b k) b,k (t), b, k (67) t is the iteration/time index, µ is a positive step-size Feasible solution by using ζ b,k (t) = 1 2 (ζ(b k) b,k (t) + ζ(b) b,k (t)) in (61)

75 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 75 x xx x xx x x b=1 Distributed Algorithm interference 2 2, 1 k=1 b= 2 k=2 interference 2 2, 2 interference 2 1, 3 k=3 interference 2 1, 4 k=4 ( 1) ( 1 ) ( 1 ) ( 1 ) ( 2) ( 2) 1, 3 1, 4 2, 1 2, 2 2, 2 2, 1 ( 2 ) 1, 4 ( 2) 1, 3 Information exchange between adjacent BSs Real-valued inter-cell interference terms

76 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 76 Distributed Algorithm Always feasible solution: use the average vector ζ(t) in (66) Feasible γ k, k can be guaranteed even if the update rate of ζ (b) (t) between BSs is slower than the channel coherence time Special cases with reduced backhaul information exchange 1. Group-specific inter-cell interference constraint, ζ b,k = ζ b,i k, i C, k, i U b 2. BS-specific inter-cell interference constraint, ζ b,k = ζ b k U b. 3. One common constraint for all BSs (within a given joint processing area), ζ b,k = ζ k, b. Cases that do not require exchange of ζ b,k 1. The constraints ζ b,k can be fixed to some values that may depend for example on the BS- and user-specific operating environment. 2. Zero-forcing for the inter-cell interference, ζ b,k = 0 k, b.

77 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 77 Simulation Scenario A flat fading multiuser MIMO system K = 4 users served simultaneously by 2 BSs {N T, N Rk } = {4, 1} a 1,1 = a 1,2 = a 2,3 = a 2,4 = a Path gain to noise ratio is normalized to a 2 /N 0 = 1 2 k = 2 a1,1 k = 4 α = a = a a = 1,1 a1,2 1,3 2 2,3 a2,4 k = 1 k = 3 2 a 1,3 b = 1 b = 2

78 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 78 Numerical Results Convergence Behaviour db SINR target 10 db SINR target 10 0 P decomp (t) P opt Iterations [t] Figure: Suboptimality of the distributed algorithm versus the iteration number t for 0 db and 10 db SINR targets. [Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February 2011]

79 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 79 Numerical Results Block Fading 16 Transmit power [db] ZF for all interference ZF for inter cell interference coordinated, one constr. coordinated, per BS constr. coordinated, per user constr. coherent Distance α between different user sets [db] Figure: Sum power of {K, B, N T } = {4, 2, 4} system with 0 db SINR target. [Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February 2011]

80 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 80 Numerical Results Block Fading Transmit power [db] ZF for all interference ZF for inter cell interference coordinated, one constr. coordinated, per BS constr. coordinated, per user constr. coherent Distance α between different user sets [db] Figure: Sum power of {K, B, N T } = {4, 2, 4} system with 20 db SINR target. [Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February 2011]

81 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 81 Time correlated fading - Example 10 2 coordinated, per user constr. coordinated (ideal), per user constr. ZF for inter cell interference Transmit power time x 10 4 Figure: Time evolution of the distributed algorithm with 0 db SINR target, T S f d = 0.1 (e.g., 30 km/h with 2 ms reporting period). [Tölli, H. Pennanen, and P. Komulainen, Decentralized Minimum Power Multi-cell Beamforming with Limited Backhaul Signalling, IEEE Trans. on Wireless Comm., vol. 10, no. 2, pp , February 2011] T S is the signalling period and f d is the maximum Doppler shift.

82 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 82 Extensions Cognitive underlay cellular network 14 - a sum interference constraint is imposed to every primary user k U P from the secondary BSs B S hb,k m i 2 φb,k, b B S, k U P (68) i Ub S φ b B S b,k Φ k, k U P (69) Worst case beamformer design with ellipsoid CSIT uncertainty 15,16 h b,k = h b,k + u b,k b B, k U (70) E b,k = {u b,k : u b,k E b,k u H b,k 1} b B, k U (71) where h b,k and u b,k are the estimated channel at the BS and the CSI error, respectively, and PSD matrix E b,k defines the CSI accuracy. 14 H. Pennanen, A. Tölli and M. Latva-aho, Multi-Cell Beamforming with Decentralized Coordination in Cognitive and Cellular Networks, IEEE Transactions on Signal Processing, vol. 62, no. 2, pp , January C. Shen, T. H. Chang, K. Y. Wang, Z. Qiu, and C. Y. Chi, Distributed robust multi-cell coordinated beamforming with imperfect CSI: An ADMM approach, IEEE Trans. Signal Processing, vol. 60, no. 6, pp , Jun H. Pennanen, A. Tölli and M. Latva-aho, Decentralized Robust Beamforming for Coordinated Multi-Cell MISO Networks, IEEE Signal Processing letters, vol. 21, no. 3, pp , March 2014

83 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 83 Decentralising the Optimal Multi-cell Beamforming via Large System Analysis H. Asgharimoghaddam, A. Tölli & N. Rajatheva, Decentralizing the Optimal Multi-cell Beamforming via Large System Analysis, in Proc. IEEE ICC 2014, Sydney, Australia, June, 2014 H. Asgharimoghaddam, A. Tölli & N. Rajatheva, Decentralized Multi-cell Beamforming Via Large System Analysis in Correlated Channels, in Proc. EUSIPCO 2014, Lisbon, Portugal, September, 2014 H. Asgharimoghaddam, A. Tölli & N. Rajatheva, Decentralizing the Optimal Multi-cell Beamforming in Correlated Channels via Large System Analysis, submitted to IEEE Trans on Signal Prog., July 2015

84 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 84 Very Large Antenna Array Assume a large antenna array scenario where 1. the number of antennas N T at the serving node is large while the number of users U b in the cell b is fixed, N T >> U b 2. both N T and U b are large, N T, U b while N T / U b > 1 The main research problem is to study how the increased degrees of freedom can be utilised both to simplify the transmitter/receiver processing and to reduce the backhaul signalling. The impact of non-idealities is assessed Non-zero antenna correlation Tools from random matrix theory can be utilised

85 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 85 System assumptions and research problem Assumptions: Local CSI available at each BS Linear TX-RX processing TDD mode channel reciprocity N T > K b 1 B K-1 K 1 2 Problem: Minimum power beamforming Sum power minimization over BSs with user specific minimum rate/sinr targets

86 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 86 Simplified solutions Matched filter: m k = c bk,kh H b k,k / h b k,k 2, where c bk,k is scaled such that γ k = h bk,km k 2 /N 0 Channel inversion (ZF): the required sum power for a given user allocation U b is obtained from B b=1 k U b γ k z b,k 2 2 N 0 (72) where the ZF precoders are Z b = [z b,1,..., z b,k ] = H H b (H bh H b ) 1 and where H b = [h T b,1,..., ht b,k ]T, b. Fixed ICI thresholds {ζ b,k }, with independent optimisation per BS min. {m k } k U b m k 2 2 s. t. Γ k γ k, k U b i U b h b,k m i 2 ζ 2 b,k, k U b (73)

87 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 87 UL-DL Duality Revisited Recall the dual uplink presentation of (42) and (61) minimize u k,q k subject to q k b B k U b q k u H k hh b k,k 2 l k q l u H k hh b k,l 2 + N 0 u k 2 γ k k U (74) The dual uplink power of each user is found by fixed point iteration 17 1 q k = (1 + 1 γ k )h bk,k( l U q lh H b k,l h b k,l + I) 1 h H b k,k (75) The dual uplink detection vector u b,k is given by the MMSE receiver u k = ( l U q l h H b k,l h b k,l + N 0 I) 1 h H b k,k (76) 17 Note that (75) is equivalent to (56)

88 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 88 UL-DL Duality Revisited A link between the DL and UL beamformers is provided by where δ k can be found by m k = δ k u k (77) δ = Ĝ 1 1 K (78) and where δ is a vector that contains all δ k values 18. The elements of Ĝ are given as: Ĝ i,j = { 1 γ i h bi,iu i 2 i = j h bj,iu j 2 i j. (79) 18 δk = p k and Ĝ = D 1 a G in (49) if u k 2 = 1

89 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 89 Large Dimension Approximation of (75) As N, K with K/N (0, B) q k q k 0 (80) almost surely, where the approximated power q k is given as the result of the convergence of the following iterative formula q (t+1) k = q (t) k γ k e (t) b k,k. (81) e (t) b k,k is the large system approximation of kth user s SINR at iteration t. The functions e bk,1,..., e bk,n are given as the unique nonnegative solution of the following system of equation, e (t+1) b k,i = 1 N T r{ q(t) i θ bk,i( 1 q (t) l θ bk,l N l U 1 + e (t) + µ bk I N ) 1 } i. (82) b k,l where θ bk,k is the correlation matrix from user k to BS b k,

90 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 90 Large Dimension Approximation of (75) Similarly, the entries of matrix G can be approximated by, 19 G l,k = γ k ( λ k ) 2 1 e b k,l N λ k (1+e b k,l )2 l = k l k (83) where, e b k,l ( 1) is the differential of e b k,l(z) with respect to z at point z = 1 19 H. Asgharimoghaddam, A. Tölli & N. Rajatheva, Decentralizing the Optimal Multi-cell Beamforming in Correlated Channels via Large System Analysis, submitted to IEEE Trans on Signal Processing, July 2015

91 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 91 Approximation of Intercell Interference Terms From (61) and (59), the total ICI from all BSs towards user k is ζb,k 2 = h b,k m l 2 (84) b b k l U b b b k Considering (77), the ICI term ζb,k 2 in (84) can be written as follows, ζb,k 2 = δl h b,k u l 2 δl Ĝ l,k (85) l U b l U b where δ b,l is found from (78) and h b,k u b,l 2 G l,k is from (83), In i.i.d case the ICI can be expressed in a simple form as follows, ζ 2 b,i αb,i 2 N(1 + e b,i )2 j U b p b,j. (86) Approximately optimal ICI based on only large scale characteristics of the user channels.

92 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 92 Numerical Examples Multi-cell case 7 cell wrap-around, K = 28 users dropped randomly Number of TX antennas per BS, N T = Frequency flat Rayleigh fading Correlation between adjacent antennas, Algorithm 1: Approximation of uplink/downlink powers and detection/beamformering vectors. Algorithm 2: Decentralized beamforming with approximated ICI values.

93 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 93 Numerical Examples Transmit SNR [db] Resulted SINR [db] Transmit SNR Alg 1 Transmit SNR Alg Trial index Resulted SINR Alg 1 Resulted SINR Alg Trial index Figure: Transmit powers and SINR variation of Algorithms 1 and 2, N = K = 56, ρ = 0.

94 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 94 Numerical Examples Transmit SNR[dB] MRT SINR MRT ZF Centralized Algorithm MRT SINR(dB) Transmit SNR[dB] MRT SINR MRT ZF Centralized Algorithm MRT SINR(dB) Number of antennas Number of antennas (a) 0 db SINR target (b) 10 db SINR target Figure: Transmit SNR versus the number of antennas, K = N/2, ρ = 0.8.

95 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 95 Numerical Examples Transmit SNR[dB] MRT SINR MRT ZF Centralized Algorithm MRT SINR(dB) Number of antennas Figure: Transmit SNR vs. the number of antennas, γ k = 0 db, ρ = 0.8, K = 28.

96 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 96 Outline Evolution of multiantenna systems MIMO with large antenna arrays Linear transceiver design and resource allocation Introduction to convex optimisation Resource allocation and linear transceiver design Coordinated transceiver optimisation Coherent vs. coordinated beamforming Minimum power multicell beamforming with QoS constraints Centralised solution Decentralised solution via optimisation decomposition Large system approximation Throughput optimal linear TX-RX design Weighted sum rate maximisation (WSRM) via MSE minimisation WSRM with rate constraints Decentralised solution via precoded UL pilot Bidirectional signalling strategies for dynamic TDD Mode selection and transceiver design in underlay D2D MIMO systems

97 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 97 Throughput Optimal Linear Transmitter-Receiver Design S. S. Christensen, R. Agarwal, E. Carvalho, and J. Cioffi, Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design, IEEE Trans. Wireless Commun., vol. 7, no. 12, pp , Dec Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel, IEEE Trans. Signal Processing, vol. 59, no. 9, pp , Sep Kaleva, J.; Tölli, A.; Juntti, M.;, Weighted Sum Rate Maximization for Interfering Broadcast Channel via Successive Convex Approximation, Global Communications Conference, GLOBECOM IEEE, Dec P. Komulainen, A. Tölli & M. Juntti, Effective CSI Signaling and Decentralized Beam Coordination in TDD Multi-Cell MIMO Systems, IEEE Transactions on Signal Processing, vol. 61, no. 9, pp , May 2013 J. Kaleva, A. Tölli & M. Juntti, Primal Decomposition based Decentralized Weighted Sum Rate Maximization with QoS Constraints for Interfering Broadcast Channel, in Proc. IEEE SPAWC 2013, Darmstadt, Germany, June, 2013 J. Kaleva, A. Tölli & M. Juntti, Decentralized Beamforming for Weighted Sum Rate Maximization with Rate Constraints, in Proc. IEEE PIMRC Workshop on Cooperative and Heterogeneous Cellular Networks, London, UK, Sep J. Kaleva, A. Tölli & M. Juntti, Decentralized Sum Rate Maximization with QoS Constraints for Interfering Broadcast Channel via Successive Convex Approximation, IEEE Transactions on Signal Processing, submitted Feb 2014, major revision May 2015

98 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 98 Assumptions: System Assumptions and Research Problem Cellular multi-user MIMO system. Each user is associated to single BS (non-cooperative) TDD and perfect CSI quantization. BS1 User 1 User 3 User 2 User 4 BS2 Decentralised beamformer design Objective: WSRM problem (with user specific rate constraints) NP-hard problem Efficient relaxation methods are required for tractability Focus: low computational complexity and CSI acquisition (pilot/backhaul signalling)

99 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 99 WSRM Problem Formulation Maximise the WSRM over a set of transmit covariance matrices K xk = M k M H k max. K xk s. t. B µ k log det b=1 k U b ( ) 1 I + R k H b k,kk xk H H b k,k k U b Tr(K xk ) P b, b = 1,..., B, where the interference+noise covariance matrix for user k is R k = K i=1,i k (87) H bi,kk xi H H b i,k + N 0I (88) Difficult non-convex optimisation problem in general (except when B = 1 or B k = B k)

100 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 100 MSE Reformulation The MSE of the received data vector ˆd k = U H k y k for user k is E k E[(ˆd k d k )(ˆd k d k ) H ] = I U H k H b k,km k (U H k H b k,km k ) H + U H k R ku k, (89) where the received signal covariance R k for user k is K R k E[y k yk H ] = H bi,km i M H i H H b i,k + σ2 ki. (90) i=1 When the MMSE receiver (37) is employed in (89), the MSE matrix becomes Furthermore E MMSE k = I M H k HH b k,k R 1 k H b k,km k (91) ( ) 1 E MMSE k = I + M H k HH 1 b k,k R b,k H b k,km k (92)

101 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 101 MSE Reformulation Applying (92) to (87), we can reformulate the WSRMax objective as min K k=1 µ k log det ( E MMSE ) M k still non-convex k Local solution: introduce new variables and split the problem into solvable subproblems min. U k,m k,ẽk K k=1 ) µ k log det (Ẽk s. t. E k Ẽk, k = 1,..., K, M k P bk, k = 1,..., K, (93) where P b, b = 1,..., B are separable convex per-bs power constraints, and the relaxation E k Ẽk, k = 1,..., K bounds the achieved MSE The relaxation tightness follows from the matrix monotonicity of the determinant function [Boyd&Vandenbergh].

102 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 102 MSE Reformulation For fixed M k, the rate maximizing U k are solved from the roots of the Lagrangian of (93) as U k = R 1 k H b k,km k, k = 1,..., K For fixed receive beamformers U k, the concave objective function is iteratively linearised w.r.t Ẽk. 21 The linearised convex subproblem in i th iteration is given as K ( ) min. µ k Tr W M kẽi i k k,ẽi k k=1 (94) s. t. E k Ẽi k, k = 1,..., K, where W i k = Gi k and Gi k = Ẽ i 1 k M k P bk, k = 1,..., K, ( )) log det (Ẽi 1 k = [Ẽi 1 k ] 1 for all k = 1,..., K. Monotonic improvement of the objective of (93) on every iteration. 21 This method in the context of weighted sum rate maximisation was established in [Shi et al, TSP 11], where it was referred to as (iteratively) weighted MMSE minimization.

103 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 103 TX precoder adaptation step The relaxation E k Ẽi k is tight Replace Ẽi k with E k (89) in the objective of (94) Local convex problem for each BS b min k U b ( 2µ k Tr(W k U H k H b k,km k ) s. t. + K i=1 ) µ i Tr(M H k HH b k,i U iw i U H i H bk,im k ) k U b Tr(M k M H k ) P b (95) Iterative ( solution from the KKT conditions K ) 1 M k = H H b k,i U iw i U H i H bk,i + ν bk I H H b k,k U kw k (96) i=1 where the optimal ν bk 22 is found via bisection 22 dual variable related to the power constraint

104 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 104 Alternating Optimization, Global Algorithm WSRM via WSMSE Initialize TX beamformers M k, i = 1,..., K 2. Compute the optimal LMMSE receivers U k k, for given M i i 3. Compute the MSE weights W k, for given U k, M k b, k 4. Compute M k k, for given U i, W i i 5. Repeat steps 2-4 until convergence Every step can be calculated locally decentralised design Implementation challenges: Uk k needs to be conveyed to the BSs precoded UL pilot Wk k needs to be shared among BSs backhaul exchange 23 Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel, IEEE Trans. Signal Processing, vol. 59, no. 9, pp , Sep. 2011

105 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 105 Alternative WSRM Problem Formulation Data stream specific processing max. m k,l,u k,l s. t. B µ k b=1 k U b m k ( mk ) log 2 (1 + Γ k,l ) l=1 m k,l 2 P b, b = 1,..., B, k U b l=1 where SINR of data stream l of user k is (97) Γ k,l = K i=1 m i j=1 (i,j) (k,l) u H k,l H b k,km k,l 2 u H k,l H b i,km i,j 2 + σ 2 k u k,l 2.

106 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 106 Preliminaries Rate maximising receive beamformers for fixed precoders are 1 K m k u k,l = H bj,km j,l m H j,l HH b j,k + Iσ2 k H bk,lm k,l (k, l). j=1 l=1 Mean-squared error (MSE) for data stream l of user k is defined as ɛ k,l 1 u H k,l H b k,km k,l 2 + K m i u H k,l H b i,km j,i 2 + σk 2 u k,l 2. i=1 j=1 (i,j) (k,l) MSE and SINR have following relation (assuming MMSE receive beamformers) ɛ 1 k,l = Γ k,l + 1.

107 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 107 max. t k,l,m k,l MSE formulation B µ k b=1 k U b ( mk ) log 2 (g(t k,l )) l=1 s. t. ɛ k,l [g(t k,l )] 1 (k, l), m k m k,l 2 P b, b = 1,..., B. k U b l=1 (98) MSE constraint can be formulated as a difference of convex functions program (DCP), by introducing upper boundary g(t k,l ) for each MSE term ɛ k,l ɛ k,l [g(t k,l )] 1 ɛ k,l [g(t k,l )] 1 0. Note that the problem is still non-convex. g(tk,l ) is monotonic and log-concave. [g(t k,l )] 1 is convex.

108 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 108 Successive convex approximation At each point t (i) k,l (k, l), (98) is approximated as convex problem by taking first-order Taylor series approximation of the MSE upper boundary. f(x, x 0 ) f(x 0 ) + (x x 0 ) x f(x0 ). (99) Convex, i th, approximation of (98) at point t (i) k,l (k, l) is ) max. t k,l,m k,l B µ k b=1 k U b ( mk log 2 (g(t k,l )) l=1 s. t. ɛ k,l ḡ(t k,l, t (i) k,l ) (k, l) m k m k,l 2 P b, b = 1,..., B. k U b l=1 (100)

109 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 109 SCA algorithm outline [ ] 1: Initialize t (1) k,l (k, l) in such a away that g(t (1) 1 k,l ) = 1. 2: Initialize precoders m k,l (k, l) in such a way that sum power constraints are satisfied. 3: Set i = 1. 4: repeat 5: Generate MMSE receive beamformers u k,l (k, l). 6: repeat 7: Solve precoders m k,l (k, l) and t k,l (k, l) from (100). 8: i = i : t (i) k,l = t k,l (k, l). 10: until Desired level of convergence has been reached. 11: until Desired level of convergence has been reached.

110 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 110 Exponential MSE boundary functions An import class of functions for MSE boundary are exponential functions g(t k,l ) = α t k,l, where α > 0. Allow efficient iterative solution and distributed design. max. t k,l,m k,l B µ k b=1 k U b ( mk ) log 2 (α)t k,l l=1 s. t. ɛ k,l α t(i) k,l log(α)(t k,l t (i) k,l (k, l) m k m k,l 2 P b, b = 1,..., B. k U b l=1 k,l )α t(i) (101)

111 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 111 Solution via KKT Conditions Beamformers m k,l can be solved from the roots of the gradient of the Lagrangian as m k,l = λ i,j H H b k,i u i,ju H i,jh bk,i + ν bk I λ k,l H H b k,k u k,l. (102) (i,j) 1 The Lagrange multipliers are λ k,l = µ kα t (i) k,l log(α) and optimal ν b b are found by bisection. t (i+1) k,l can be found from the corresponding complementary slackness constraint to be t (i+1) k,l Here, term 1 log(α) = t (i) k,l + 1 log(α) (1 ɛ k,lα t (i) k,l) (k, l). can be seen as step size for an exact line search.

112 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 112 Improved Rate of Convergence To increase the rate of convergence it is beneficial to choose the next point of approximation further than indicated by the exact line search. Choose larger step sizes. Too large steps size causes oscillation in the objective. Simple adaptive update of the step size can be, for example, formulated as t (i+1) k,l = t (i) k,l + 1 log(α α e i β ) (1 ɛ k,lα t (i) k,l) (k, l). Use more aggressive search at first iterations. Converges to exact line search.

113 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 113 Numerical Results SCA (I max = 3) [4] (I max = 3) [3] (I max = 3) Sum rate (bits/hz/s) SCA (I max = 6) [4] (I = 6) max [3] (I = 6) max SCA (I = 10) max [4] (I = 10) max [3] (I = 10) max 6 Iterations 10 Iterations Iterations SNR (db) Figure: Impact of the limited number of iterations to the achievable sum rate with N T = 4, N R = 2, K = 8. [Kaleva, J.; Tölli, A.; Juntti, M.;, Weighted Sum Rate Maximization for Interfering Broadcast Channel via Successive Convex Approximation, Global Communications Conference, GLOBECOM IEEE, Dec. 2012] [3] Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel, IEEE Trans. Signal Processing, Sep [4] T. Bogale and L. Vandendorpe, Weighted sum rate optimization for downlink multiuser MIMO coordinated base station systems: Centralized and distributed algorithms, IEEE Trans. Signal Processing, Dec

114 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 114 WSRmax with QoS Constraints 24 Objective: WSRmax with per user QoS constraints ( B mk ) max. log m k,l,u 2 (1 + Γ k,l ) k,l s. t. µ k b=1 k U b m k l=1 log 2 (1 + Γ k,l ) R k k = 1,..., K, l=1 mk k U b l=1 m k,l 2 P b, b = 1,..., B, where SINR of data stream l of user k is Γ k,l = u H k,l H b k,km k,l 2 K mij=1, i=1 u H k,l H b i,km i,j 2 + σk 2 u k,l. 2 (i,j) (k,l) 24 J. Kaleva, A. Tölli & M. Juntti, Decentralized Beamforming for Weighted Sum Rate Maximization with Rate Constraints, in Proc. IEEE PIMRC Workshop on Cooperative and Heterogeneous Cellular Networks, London, UK, Sep. 2013

115 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 115 Introduce upper boundary 2 t k,l max t k,l,m k,l MSE Reformulation B µ k b=1 k U b for each MSE term ɛ k,l ( mk ) t k,l l=1 s. t. ɛ k,l 2 t k,l (k, l), m k l=1 t k,l R k, k = 1,..., K, m k m k,l 2 P b, b = 1,..., B, k U b l=1 Difference of convex functions program (DCP), ɛ k,l 2 t k,l 0 Successive convex (linear) approximation is used to approximate the MSE bounds 2 t k,l (k, l) iteratively.

116 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 116 Linear Approximation + Lagrangian Relaxation max t k,l,m k,l B µ k b=1 k U b ( mk ) t k,l l=1 B γ k b=1 k U b s. t. ɛ k,l a (i) k,l t k,l + b (i) k,l (k, l), m k m k,l 2 P b, b = 1,..., B. k U b l=1 Convex problem Partial Lagrangian relaxation of the rate constraints WSRmax with new weights µ k + γ k per user ( ) m k R k t k,l γ k represent demand of rate for user k = 1,..., K Still coupled by the MSE constraints ɛ k,l a (i) k,l t k,l + b (i) k,l (k, l) l=1

117 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 117 Iterative Solution Transmit beamformers are obtained directly from the KKT conditions as where K k,l = m k,l = K k,l HH b k,l u k,lλ k,l (k, l), K m i λ i,j H H b k,i u i,ju H i,jh bk,i + Iν b. i=1 j=1 MSE constraint related dual variables (MSE weights) can be written in closed form as λ k,l = (µ k + γ k )/a (i) k,l (k, l). Depends only on the point of approximation and rate demand dual variables γ k = 1,..., K. The rate demand weight factors γ k k = 1,..., K are updated according to the subgradients of the corresponding rate constraints γ (i+1) k = ( γ (i) k + β(i) k ( m k R k + l=1 t (i) k,l ))) +. All steps can be executed locally at each BS / terminal

118 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 118 Features & Issues Computational complexity Receive beamformers u k,l can be solved in a closed form (LMMSE) Transmit beamformers m k,l require simple bisection over ν b Dual variables λ k,l are solved in a closed form Feasibility Each step is not required to be feasible (rate constraints) Possibly strictly feasible only after convergence Initialization Does not require feasible initial point Simplifies distributed design

119 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 119 Algorithm Outline 1: Initialize precoders m k,l (k, l). 2: Initialize γ k,l = 0 (k, l). 3: repeat 4: Generate LMMSE receive beamformers u k,l (k, l). 5: repeat 6: Measure MSE ɛ k,l (k, l). 7: Update rate demand variables γ k k = 1,..., K. 8: Assign weights λ k,l (k, l). 9: Exchange weights λ k,l (k, l) between the adjacent BSs. 10: Solve transmit beamformers m k,l (k, l). 11: until Desired level of convergence has been reached or i > I max. 12: until Desired level of convergence has been reached or j > J max.

120 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 120 Numerical Results (1/2) Rate (bits/hz/s) 3 2 k = 1, b = 1, R = 4 bits/s/hz k = 2, b = 1 k = 1, b = 2, R = 4 bits/s/hz k = 2, b = 2 Average sum rate per BS Iteration Figure: Behaviour of the unconstrained users at SNR = 5dB with 3dB cell separation, N T = 4, N R = 2, K b = 2 and β = 10. [J. Kaleva, A. Tölli & M. Juntti, Decentralized Beamforming for Weighted Sum Rate Maximization with Rate Constraints, in Proc. IEEE PIMRC Workshop on Cooperative and Heterogeneous Cellular Networks, London, UK, Sep. 2013]

121 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 121 Numerical Results (2/2) Rate (bits/hz/s) k = 1, b = 1, R = 4 bits/s/hz k = 2, b = 1, R = 2 bits/s/hz k = 3, b = 1, R = 2 bits/s/hz k = 1, b = 2, R = 4 bits/s/hz k = 2, b = 2, R = 2 bits/s/hz k = 3, b = 2, R = 2 bits/s/hz Iteration Figure: Convergence at SNR = 15dB with 3dB cell separation, N T = 4, N R = 2, K b = 3 and β = 4. [J. Kaleva, A. Tölli & M. Juntti, Decentralized Beamforming for Weighted Sum Rate Maximization with Rate Constraints, in Proc. IEEE PIMRC Workshop on Cooperative and Heterogeneous Cellular Networks, London, UK, Sep. 2013]

122 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 122 Numerical Results - ADMM extension 5 Alternating Direction Method of Multipliers (ADMM) Rate (bits/hz/s) k = 1 1 k = Iteration k = 3 k = Dual Decomposition. Rate (bits/hz/s) Iteration Figure: Convergence of the ADMM and dual decomposition methods with B = 2, K b = 2, N T = 2, N R = 2, R k = 3bits/Hz/sec, β = 2, ρ = 1.5, χ = 3dB and SNR = 15dB. [J. Kaleva, A. Tölli and M. Juntti, Rate Constrained Decentralized Beamforming for MIMO Interfering Broadcast Channel, PIMRC 15, Hong Kong, June, 2015]

123 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 123 Decentralised Solution via Precoded UL Pilot Assumptions: Each user is associated to single BS (non-cooperative) TDD and perfect CSI Precoded UL pilot sequences 1 B K-1 K 1 2 Goal: Scheduling & TX RX design to control interference a CSI acquisition: Pilot & Backhaul signalling Decentralized, practical methods, based on locally available CSI Support for independent user scheduling by BSs a P. Komulainen, A. Tölli & M. Juntti, Effective CSI Signaling and Decentralized Beam Coordination in TDD Multi-Cell MIMO Systems, IEEE Transactions on Signal Processing, vol. 61, no. 9, pp , May 2013

124 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 124 Strategy A: Global Algorithm Each BS b calculates own weights W k k U b : distribute via backhaul Each BS calculates own precoders M k k U b : use for data transmission Each UE calculates own receiver U k : use for reception and UL sounding Slow convergence

125 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 125 Strategy B: Separate Channel Sounding (CS) and Busy Burst (BB) Pilots CS pilot Q k whitens the inter-cell interference at terminal k so that Q H k Q 1 k = R k, where R k = i U bk H bi,km i M H i HH b i,k + N 0I The MSE weights calculated by the terminals can be incorporated to the uplink BB signaling so that pilot precoder is W 1 2 k U k Allows local iterations no backhaul required

126 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 126 Strategy C: Cell-specific Iterations with CS Only Allows local iterations fast convergence

127 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 127 Numerical Results: Setup Two 4-antenna BSs, five 2-antenna UEs per BS Cell separation defined as a 1 /a 2 Uncorrelated Rayleigh (quasistatic) fading

128 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 128 Numerical Results: Convergence 18 M = 4, N = 2, K = 5, SNR = 25dB, cell sep. = 0dB 16 Sum rate per BS [bits/hz/s] Alg. 1 (matrix weighted) Strat. A: BB only Strat. B: BB+CS Strat. C: CS only Strat. A (AP constraints) Non cooperative Frame Figure: Average convergence of the sum rate at 0dB cell separation, at 25dB SNR. [P. Komulainen, A. Tölli & M. Juntti, Effective CSI Signaling and Decentralized Beam Coordination in TDD Multi-Cell MIMO Systems, IEEE Transactions on Signal Processing, vol. 61, no. 9, pp , May 2013]

129 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 129 Bidirectional Signalling Strategies for Dynamic TDD P. Jayasinghe, A. Tölli, J. Kaleva and M. Latva-aho, Bi-directional Signaling for Dynamic TDD with Decentralized Beamforming ICC Workshop on Small Cell and 5G Networks (SmallNets), London, UK, June, 2015 P. Jayasinghe, A. Tölli, and M. Latva-aho, Bi-directional Signaling Strategies for Dynamic TDD Networks IEEE SPAWC, Stockholm, Sweden, July, 2015 METIS Deliverable D3.3 on Final performance results and consolidated view on the most promising multi-node/multi-antenna transmission technologies (A. Tölli & P. Jayasinghe),

130 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 130 Background & Introduction Figure: Dynamic TDD system The load variation between adjacent small cells can be significant. Fixed UL/DL switching would be highly suboptimal. With the flexible UL/DL allocation provides large potential gains in spectral efficiency dynamic traffic aware TDD transmission Allowing such flexibility makes obviously the interference management considerably more challenging.

131 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 131 Interference scenarios Figure: Interference at DL terminal Figure: Interference at UL BS Additional interference associated with the dynamic TDD UL-to-DL interference. DL-to-UL interference. Interference mitigated by coordinated beamforming. More measurements and info exchange also at the terminal side

132 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 132 Synchronous TDD - System Model Assumptions: Multi-cell multiuser MIMO Each user served by one BS Linear TX-RX processing TDD and perfect CSI Coordination via pilot and backhaul signaling 1 B K-1 K 1 2 Problem: System utility maximization low computational complexity and CSI acquisition Impact of forward-backward training on the system performance

133 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 133 Bi-directional training Figure: Backward-Forward training structure [Changxin Shi; Berry, R.A.; Honig, M.L., Bi-Directional Training for Adaptive Beamforming and Power Control in Interference Networks, Signal Processing, IEEE Transactions on, vol.62, no.3, pp , Feb.1, 2014] Bidirectional training(bit) phase is used in the beginning of each TDD frame to speed up the convergence of the iterative algorithms A number of blocks of pilots are alternately transmitted in the downlink and the uplink

134 8 September, 2015 Coordinated Multiantenna Interference Management in 5G Networks 134 Bi-directional training in Dynamic TDD Figure: TDD frame structure with two bi-directional beamformer signaling iterations. [P. Jayasinghe, A. Tölli, and M. Latva-aho, Bi-directional Signaling Strategies for Dynamic TDD Networks IEEE SPAWC, Stockholm, Sweden, July, 2015]