On the Value of Coherent and Coordinated Multi-point Transmission

Transcription

1 On the Value of Coherent and Coordinated Multi-point Transmission Antti Tölli, Harri Pennanen and Petri Komulainen Centre for Wireless Communications University of Oulu December 4, 2008

2 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-point transmission (CoMP) 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

3 Coordinated Multi-point Transmission Distributed antenna system based on, e.g. Radio over Fibre (RoF) Capability of joint control of the signals at multiple cells BS BS BS Fibre Fibre BS Distributed BS antennas Backbone network Fibre BS Fibre Fibre BS BS Fibre

4 Coordinated Multi-point Transmission Complete channel state information (CSI) of all jointly processed links (ideally) needed Centralised RRM mechanisms to perform scheduling and precoding Coherent multi-cell transmission Each data stream may be transmitted from multiple nodes Tight synchronisation across the transmitting nodes (common phase reference) A high-speed backbone network, e.g. Radio over Fibre Non-coherent multi-cell processing 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

5 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 The proposed method [1] 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.

6 System Model Coordinated multi-cell MIMO system: NB BSs, N T TX antennas per BS and N Rk RX antennas per user k A user k is served by Mk BSs from the joint processing set B k, B k B = {1,..., N B } y k = X b B a b,k H b,k x b + n k (1) = X X X a b,k H b,k x b,k + a b,k H b,k b B k b B k i k X + 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 N T total TX signal from BS b, and x b,k = M b,k d k C N T transmitted data vector from BS b to user k, where M b,k C N T m k pre-coding matrix, d k = [d 1,k,..., d mk,k] T vector of normalised data symbols, m k min(n TM k, N Rk ) number of active data streams. x b,i

7 Linear Transceiver Design Per data stream processing: N B BS transmitters send S independent streams, S min(n B N 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 B s B ks. For example, a user may receive data from several BSs, while B s = 1 s.

8 Linear Transceiver Design Per data stream processing: N B BS transmitters send S independent streams, S min(n B N 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 B s 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 w s C N R ks be arbitrary TX and RX beamformers for the stream s SINR per stream: γ s = a b,ks ws H H b,ks m b,s e jφ b b B s N 0 ws S i=1,i s 2 (2) a b,ks ws H H b,ks m b,i e jφ b 2 b B i φ b represents the possible carrier phase uncertainty of BS b

9 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3]

10 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4]

11 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4] 3 Any combination of above two, where B k and B s may be different for each user k and/or stream s.

12 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4] 3 Any combination of above two, where B k and B s may be different for each user k and/or stream s.

13 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4] 3 Any combination of above two, where B k and B s may be different for each user k and/or stream s. Optimization criteria, e.g., 1 Weighted sum rate maximisation [3]: S β s r s = s=1 S β s log 2 (1 + γ s ) s=1

14 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4] 3 Any combination of above two, where B k and B s may be different for each user k and/or stream s. Optimization criteria, e.g., 1 Weighted sum rate maximisation [3]: S β s r s = s=1 2 Max min weighted SINR per data stream [6]: max min S β s log 2 (1 + γ s ) s=1 s=1,...,s β 1 s γ s

15 Transceiver Optimisation with CoMP General method for linear transceiver optimisation with CoMP: 1 Coherent multi-cell beamforming (B s = B k = B s, k) with per BS and/or per-antenna power constraints [2, 3] 2 Coordinated single-cell beamforming ( B s = 1 s): all transceivers are jointly optimised while considering the other-cell transmissions as inter-cell interference [4] 3 Any combination of above two, where B k and B s may be different for each user k and/or stream s. Optimization criteria, e.g., 1 Weighted sum rate maximisation [3]: S β s r s = s=1 2 Max min weighted SINR per data stream [6]: max min 3 Maximisation of weighted common user rate [6]: r o = min k A β 1 k log 2 (1 + γ s ), s P k P k is a subset of data streams that correspond to user k S β s log 2 (1 + γ s ) s=1 s=1,...,s β 1 s γ s

16 BS Coordination with Linear Processing 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 Guaranteed bit rate users Best effort users Controller

17 BS Coordination with Linear Processing Iteration t Transmit beamformers fixed Guaranteed bit rate users Receive beamformers optimised Best effort users Controller

18 BS Coordination with Linear Processing Iteration t+1 Transmit beamformers optimised Guaranteed bit rate users Receive beamformers fixed Best effort users Controller

19 BS Coordination with Linear Processing The general system optimisation objective is to maximise a function f(γ 1,..., γ K ) that depends on the individual SINR values max f(γ 1,..., γ S ) s. t. N 0 w s S b B s a b,ks w H s H b,ks m b,s 2 a b,ks ws H 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,..., N B s S b γ s, (3) Objective in this presentation: max. of min weighted SINR f(γ 1,..., γ S ) = min s=1,...,s βs 1 γ s Quasiconvex in m b,s [5, 6], and it can be solved optimally for fixed w s [1]

20 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 a b,ks b B 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 BS 1 BS 2 Optical fibre 1 N T 1 N T Central Controller 1 NR1 user 1 1 NRk user k 1 N T BS M

21 Heuristic Beam Allocation Algorithms 1 Greedy selection: Beams with the largest component orthogonal to the previously selected set of beams are chosen.

22 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.

23 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:

24 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

25 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

26 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 w s and the corresponding SINR values γ s are recalculated

27 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 w s and the corresponding SINR values γ s are recalculated The selection of the allocation is based on the maximum rate criterion, i.e., arg max min γ s. b,k,l s=1,...,s

28 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 other-cell interference is assumed to be white Gaussian distributed 4 Single-cell transmission with time-division multiple access (TDMA), i.e., without inter-cell interference

29 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 ,1 a1,2 a = 2 k = 2 a1,1 k = 4 α = 2 a1, ,3 a2,4 a = k = 1 k = 3 2 a 1,3 b = 1 b = 2

30 Numerical Results - 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 (MaxRate) Coord. single cell TX (MaxEigenValue) 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] (a) 0 db single link SNR 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 (MaxRate) Coord. single cell TX (MaxEigenValue) 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] (b) 20 db single link SNR Figure: Ergodic sum of user rates of {K, N B, N T, N Rk } = {4, 2, 2, 1} system with per BS power constraint.

31 Numerical Results - 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 (MaxRate) Coord. single cell TX (MaxEigenValue) Coordinated single cell TX (Greedy) Non Coord. single cell TX (ex. search) Non Coord. single cell TX (fixed) TDMA (ex. search) TDMA (fixed) 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 (MaxRate) Coord. single cell TX (MaxEigenValue) 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] Inf Distance α between different user sets [db] Figure: Ergodic sum rate of {K, N B, N T, N Rk } = {2, 2, 2, 1} system at 20 db single link SNR. Figure: Ergodic sum rate of {K, N B, N T, N Rk } = {4, 2, 4, 1} system at 20 db single link SNR.

32 Conclusions A generalised method for joint design of linear transceivers with Coordinated multi-cell processing Per-BS or per-antenna power constraints Optimisation objective: weighted SINR blancing 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 Upper bound for the less ideal solutions with an incomplete CSI. The coherent multi-cell beamforming greatly outperforms the non-coherent cases, Especially at the cell edge and with a full spatial load. However, the coordinated single-cell transmission with interference avoidance and dynamic beam allocation performs considerably well with a partial spatial loading.

33 References [1] A. Tölli, H. Pennanen, and P. Komulainen, SINR balancing with coordinated multi-cell transmission, in Proc. IEEE Wireless Commun. and Networking Conf., Budapest, Hungary, Apr (to appear). [2] M. K. Karakayali, G. J. Foschini, and R. A. Valenzuela, Network coordination for spectrally efficient communications in cellular systems, IEEE Wireless Communications Magazine, vol. 3, no. 14, pp , Aug [3] 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 [4] M. Bengtsson and B. Ottersten, Optimal and suboptimal transmit beamforming, in Handbook of Antennas in Wireless Communications, L. C. Godara, Ed. Boca Raton, FL: CRC Press, [5] A. Wiesel, Y. C. Eldar, and S. Shamai, Linear precoding via conic optimization for fixed MIMO receivers, IEEE Transactions on Signal Processing, vol. 54, no. 1, pp , Jan [6] 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