How to Split UL/DL Antennas in Full-Duplex Cellular Networks

School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Ericsson Research Stockholm, Sweden https://people.kth.se/~jmbdsj/index.html jmbdsj@kth.se How to Split UL/DL Antennas in Full-Duplex Cellular Networks José Mairton B. da Silva Jr, Hadi Gauch, G. Fodor, C. Fischione IEEE ICC 18 - Workshop on Full-Duplex Communications for Future Wireless Networks May 20, 2018

Architectures in full-duplex cellular networks Tx Chain Tx Chain Circulator Rx Chain Rx Chain Split Antenna Shared Antenna Split architecture current radios + select UL/DL antennas Shared architecture circulator + bad with # of antennas Why select UL/DL antennas? Severe self-interference (SI) reduce # DL antennas Severe UE-to-UE interference reduce # UL antennas Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Motivation 1/15

Outline 1. Introduction 2. System Model & Problem Formulation 3. Solution Approach: Parallel Successive Convex Approximation 4. Numerical Results 5. Conclusion Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Introduction 1/15

FD characteristics in cellular networks SI UE d 2 UE u 1 BS UE d 1 Uplink Downlink UE-to-UE Interf. Self-Interf. (SI) UE u 2 Benefits Spectral efficiency: 2 Medium access layer: mitigate hidden terminal, collision avoidance, low latency... Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Introduction 2/15

FD characteristics in cellular networks SI UE d 2 UE u 1 BS Challenges Severe SI UE d 1 UE-to-UE interference Uplink Downlink UE-to-UE Interf. Self-Interf. (SI) Mitigate both interferences user-frequency assignment, power allocation and antenna splitting UE u 2 Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Introduction 2/15

Research gap in FD cellular networks Understand impact of split antennas How to split the antennas? Everett2016 fixed splitting based on array geometry Gowda2018 split to minimize gap between demand and achievable rates Lack of efficient splitting algorithms Initial assumption on the # split antennas If SI high reduce # DL antennas If UE-to-UE interference high reduce # UL antennas If UL/DL asymmetry increase # antennas with higher demand [Everett2016] E. Everett et al., SoftNull: Many-Antenna Full-Duplex Wireless via Digital Beamforming, IEEE TWC, Dec. 2016. [Gowda2018] N. M. Gowda et al., JointNull: Combining Partial Analog Cancellation With Transmit Beamforming for Large-Antenna Full-Duplex Wireless Systems, IEEE TWC, Mar. 2018. Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Introduction 3/15

Contributions Antenna splitting with UE-to-UE interference + distortions Sum MSE minimization maximize sum spectral efficiency Combinatorial problem for UL/DL antenna splitting Equivalent problem reformulation quadratic and biquadratic terms + first-order Taylor approximation NP-hard binary quadratic problem Binary relaxation to hypercube [0, 1] M 1 solve with Parallel Successive Convex Approximation (PSCA) Show spectral efficiency gains over simple splitting Realistic system simulations Yes, 23% with high SI cancellation! How and when to split Yes, # antennas is the key! Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Introduction 4/15

Definitions (1/2) g 12 h u 1 H SI h d 2 UE d 2 UE u 1 g 22 g 11 h d 1 BS h u 2 g 21 UE d 1 Uplink Downlink UE-to-UE Interf. Self-Interf. (SI) UE u 2 Single-cell cellular system only BS is FD-capable # M/1 antennas at BS/UE; # UL users I ; # DL users J Channel for flat fading h u i, h d j, g ij SI cancellation matrix H SI C M M Tx and Rx distortion signals are present c u j, c d i, e u i, e d j Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) System Model & Problem Formulation 5/15

Definitions (2/2) Tx beamforming and UL power fixed wj d, qi u UL and DL antenna assignment vector x u, x d {0, 1} M 1 { 1, if antenna k is Rx (Tx) in the UL (DL), x u(d) k = 0, otherwise. UL and DL received signals ( q y u u = i su i + ci u I hi u i=1 y d j =h dh j ( J m=1 w d ms d m +c d )+ ) ( J +H SI wj d sj d +c )+η d u +e u, j=1 I i=1 Effective channels and received signals g ij ( q u i s u i +c u i ) +η d j +e d j, h i u =X u hi u, hd j =X d hj d, HSI =X u H SI X d, η u =X u η u, ( J ) ẽ u =X u e u, X d wms d m d +c d, ỹ u =X u y u. m=1 }{{} DL Tx signal Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) System Model & Problem Formulation 6/15

Problem formulation MSE for UL and DL users with optimal MSE receivers r u i, rj d Ei u = qi uruh i hu i 1 2 +r uh i Ψ u i r u i, Ej d = rj dh h j dh wj d 1 2 + r d j 2 Ψ d j. MSE minimization with UL/DL antenna assignment minimize x u,x d I i=1 E u i + J j=1 E d j (Objective) subject to x u + x d = 1, (UL/DL orthogonality) x u, x d {0, 1} M 1. (Binary association) Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) System Model & Problem Formulation 7/15

General solution approach NP-Hard MSE Minimization Problem Equivalent Problem Reformulation MSE Approximated Problem Binary Relaxation Equivalent problem reformulation Sum MSE as two quadratic and one biquadratic terms of X u, X d One quadratic and one quartic in terms of x u Quartic term complicated First-order Taylor approximation quartic becomes linear in x u NP-Hard binary quadratic problem Relaxation into unit hypercube [0, 1] M 1 Successive convex approximation Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) System Model & Problem Formulation 8/15

Problem reformulation MSE minimization Equivalent problem minimize x u,x d I Ei u + i=1 J j=1 s. t. x u + x d = 1, E d j x u, x d {0, 1} M 1. minimize x u,x d f u (x u ) + f u,d (x u, x d ) + f d (x d ) s. t. x u + x d = 1, x u, x d {0, 1} M 1. Biquadratic f u,d (x u, x d ) quartic f u,d (x u ) First-order approximation of f u,d ( X u ) ( g u (x u ) = f u,d ( x u ) + Diag f u,d ( X T )) u x u. Binary quadratic problem NP-Hard minimize x ut Λx u 2b T x u x u subject to x u {0, 1} M 1. Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Solution Approach: PSCA 9/15

Iterative solution approach Relaxation into unit hypercube x u [0, 1] M 1 Iterative convex approximation required Taylor approx. for neighbourhood of x u PSCA includes proximal operator α 2 x u x u(n) 2 2 minimize objective and stay close to previous iteration Relaxed MSE minimization problem (RLX-PROX) minimize x ut Λx u b T x u + α x u x u(n) 2 x u 2 2 subject to x u [0, 1] M. Centralized solution with low computational complexity Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Solution Approach: PSCA 10/15

Simulation Parameters Small cell with I = J = 4 and M = 8,..., 128 SI cancellation β = [ 50,..., 100]dB BS/UL user maximum power 30/23 dbm Proposed algorithm RLX-PROX: Relaxed solution to MSE minimization problem compared to EXH: exhaustive search SPLIT: equal splitting between UL and DL antennas 600 Monte Carlo iterations Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Numerical Results 11/15

Optimality gap - M = 8, SI= 100 db 1 0.9 0.8 0.7 CDF 0.6 0.5 0.4 0.3 0.2 0.1 23% of gain RLX-PROX EXH SPLIT 0 10 20 30 40 50 60 70 80 Sum Spectral Efficiency [bps/hz] UL/DL antenna splitting substantial gains of 23% to 32% RLX-PROX close to optimal solution 9% difference Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Numerical Results 12/15

Average sum spectral efficiency SI cancellation 60 Average Sum Spectral Efficiency [bps/hz] 50 40 30 20 10 RLX-PROX EXH SPLIT 0-100 -90-80 -70-60 -50 SI Cancellation [-db] Naive splitting performance decreases quickly with SI UL/DL antenna splitting Maintains performance across SI Crucial for low SI cancellation Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Numerical Results 13/15

Average sum spectral efficiency # antennas 85 Average Sum Spectral Efficiency [bps/hz] 80 75 70 65 60 55 50 45 40 RLX-PROX SPLIT 35 8 16 32 64 128 Number of Antennas at BS RLX-PROX and naive splitting gap decreases with # antennas Role of antenna splitting small for large # antennas Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Numerical Results 14/15

Some takeaways Conclusions Combinatorial problem to split UL/DL antennas MSE minimization sum spectral efficiency maximization NP-hard problem solved with successive convex approximation Gains with UL/DL antenna splitting Gains for spectral efficiency Reduced role for large number of antennas Low and high SI cancellation maintains spectral efficiency Future works Impact of DL/UL beamforming in the splitting joint beamforming and antenna splitting Mairton Barros (jmbdsj@kth.se) ICC 18 (W10-S4 FDCOMM) Conclusion 15/15