Bi-directional Signalling Strategies for Dynamic TDD Networks

Transcription

1 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 1 Bi-directional Signalling Strategies for Dynamic TDD Networks Antti Tölli Praneeth Jayasinghe, Jarkko Kaleva University of Oulu 12 October, 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, P. Jayasinghe, A. Tölli, J. Kaleva & M. Latva-aho, Bi-directional Signaling Strategies for Dynamic TDD Networks in Proc. IEEE SPAWC 2015, Stockholm, Sweden, July, 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),

2 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 2 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.

3 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 3 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

4 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 4 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

5 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 5 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 (1) R k = K i=1,i k H bi,kk xi H H b i,k + N 0I (2) Difficult non-convex optimisation problem in general (except when B = 1 or when all K users are jointly served by all B BSs.)

6 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 6 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, 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. (4) i=1 When the MMSE receiver is employed in (3), the MSE matrix becomes Furthermore (3) E MMSE k = I M H k HH b k,k R 1 k H b k,km k (5) ( ) 1 E MMSE k = I + M H k HH 1 b k,k R k H b k,km k (6)

7 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 7 MSE Reformulation Applying (6) to (1), 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, (7) 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 4. 4 The relaxation tightness follows from the matrix monotonicity of the determinant function [Boyd&Vandenbergh].

8 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 8 MSE Reformulation For fixed M k, the rate maximizing U k are solved from the roots of the Lagrangian of (7) 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. 5 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 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 (8) = [Ẽi 1 k ] 1 for all k = 1,..., K. Monotonic improvement of the objective of (7) on every iteration. 5 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.

9 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 9 TX precoder adaptation step The relaxation E k Ẽi k is tight Replace Ẽi k with E k (3) in the objective of (8) Local convex problem for each BS b min M k s. t. 2µ k Tr(W k U H k H b k,km k ) + K ) µ itr(m H i=1 k HH b k,i U iw i U H i H bk,im k ) Tr(M k M H k U k ) P b b k U b ( Iterative solution from the KKT conditions ( K ) 1 M k = i=1 HH b k,i U iw i U H i H bk,i + ν bk I H H b k,k U kw k (10) where the optimal ν bk 6 is found via bisection 6 dual variable related to the power constraint (9)

10 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 10 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 9 Implementation challenges: U k k needs to be conveyed to the BSs precoded UL pilot W k k needs to be shared among BSs backhaul exchange 7 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 Proc., vol. 59, no. 9, pp , Sep 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

11 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 11 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

12 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 12 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

13 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 13 Strategy B: Separate Channel Sounding (CS) and Busy Burst (BB) Pilots

14 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 14 Convergence with different signalling strategies 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. 10 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

15 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 15 Bi-directional training Bidirectional training 11 (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 11 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

16 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 16 Bi-directional training in Dynamic TDD Figure: TDD frame structure with two bi-directional beamformer signaling iterations.

17 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 17 Bi-directional signalling: Simulation setup 4-antenna BSs, 4 2-antenna UEs per BS The signaling overhead per one signaling iteration is γ and the total signaling overhead is ρ = BIT γ. The actual throughput is (1 ρ)r, where R is the achieved WSR from the iterative algorithm.

18 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 18 Synchronous 2-cell Downlink, Strategy A Actual Sum Rate (SNR = 10 db) Peak Rate α = 0 db & γ = 0.01 α = 0 db & γ = 0.02 α = 0 db, uncoordinated α = 12 db & γ = 0.01 α = 12 db & γ = 0.02 α = 12 db, uncoordinated Actual Sum Rate (SNR = 20 db) Peak Rate Overhead Overhead α = 0 db & γ = 0.01 α = 0 db & γ = 0.02 α = 0 db, uncoordinated α = 12 db & γ = 0.01 α = 12 db & γ = 0.02 α = 12 db, uncoordinated Figure: Actual Sum rate vs overhead with different SNR (10, 20 db) values.

19 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 19 Dynamic TDD 3-cell, Strategy A Actual Sum Rate Peak Rate α = 0dB,β = 3dB, δ = 6dB, γ = 0.01 α = 0dB,β = 3dB, δ = 6dB uncoordinated α = 0dB,β = 9dB, δ = 12dB, γ = 0.01 α = 0dB,β = 9dB, δ = 12dB uncoordinated α = 6dB,β = 3dB, δ = 6dB, γ = 0.01 α = 6dB,β = 3dB, δ = 6dB uncoordinated α = 6dB,β = 9dB, δ = 12dB, γ = 0.01 α = 6dB,β = 9dB, δ = 12dB uncoordinated Overhead Figure: Actual sum rate vs overhead at SNR = 20 db, with diferent α, β, δ.

20 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 20 Time-correlated Fading Scenario 26 Average Actual Sum Rate BIT =1, no reset BIT =3, reset = 10 BIT =5, reset = 10 BIT =10, reset = Channel Number Figure: Average sum rate over time-correlated channel at SNR = 20 db with γ = 0.01.

21 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 21 Comparison of different signalling strategies Actual Rate at SNR = 20 db Strategy A Strategy B Strategy C Uncoordinated method Overhead Figure: Actual sum rate at SNR = 20dB vs overhead for different bi-directional signaling strategies.

22 12 October, 2015 Bi-directional Signalling Strategies for Dynamic TDD Networks 22 Concluding Remarks Decentralized and iterative WSR maximization algorithm for multi-cell multi-user MIMO system was proposed A novel bi-directional signaling scheme was embedded into TDD frame to facilitate OTA signaling A significant gain compared to uncoordinated system over large signaling overhead region. Periodic re-initialization to improve the performance further Work in progress Realistic multi-cell evaluation Impact of limited pilot resources and channel acquisition pilot reuse (contamination)