On the Capacity Regions of Single-Channel and Multi-Channel Full-Duplex Links. Jelena Marašević and Gil Zussman EE department, Columbia University

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1 On the Capacity Regions of Single-Channel and Multi-Channel Full-Duplex Links Jelena Marašević and Gil Zussman EE department, Columbia University MobiHoc 16, July 216

2 Full-Duplex Wireless (Same channel) Full-duplex communication = simultaneous transmission and reception on the same frequency channel Viability is limited by self-interference Transmitted signal is billions of times stronger than the received signal! Legacy wireless systems separate transmission and reception in either: Time Time Division Duplex (TDD) Frequency Frequency Division Duplex (FDD)

3 Full-Duplex Wireless Benefits of full-duplex: Increased system throughput More flexible use of the wireless spectrum Self-Interference Cancellation (SIC):

4 Imperfect Self-Interference Cancellation Columbia Stanford TX/RX Isolation (db) TX/RX Isolation (db) Frequency (GHz) Frequency (GHz) Jin Zhou, Peter R. Kinget and Harish Krishnaswamy, A Blocker-Resilient Wideband Receiver with Low-Noise Active Two-Point Cancellation of >dbm TX Leakage and TX Noise in RX Band for FDD/Co-Existence, in 214 IEEE International Solid-State Circuits Conference Digest of Technical Papers, pp , Feb Jin Zhou, Tsung-Hao Chuang, Tolga Dinc and Harish Krishnaswamy, Reconfigurable receiver with >>2MHz bandwidth self-interference cancellation suitable for FDD, co-existence and full-duplex applications, In Proc. IEEE ISSCC 15, 215. D. Bharadia, E. McMilin, and S. Katti. Full duplex radios. In Proc. ACM SIGCOMM 13, 213.

5 Related Work System design and Wi-Fi heuristics: [Choi et al. 21], [Duarte and Sabharwal 21], [Jain et al. 211], [Singh et al. 211], [Aryafar et al. 212], [Bharadia et al. 213], [Zhou et al. 213], [Bharadia and Katti 214], [Duarte et al. 214] Integrated (small form-factor) receiver design [Zhou et al. 214], [Zhou et al. 215], [van den Broek et al. 215] Cellular scheduling heuristics: [Goyal et al. 213], [Goyal et al. 214] Throughput gains from full-duplex: [Sahai et al. 213], [Xie and Zhang 214], [Li et al. 214], [Nguyen et al. 214], [Korpi et al. 215]

6 Full Duplex wireless from Integrated Circuits to Networks Testbed Evaluation Channel Allocation Scheduling Cellular MAC Power Control Modeling RF/analog SelfInterference Cancellation Digital Self-Interference Cancellation... Adaptive Self-Interference Cancellation Antenna Interface Cross-Layer Interference Management Fully Integrated RFIC PHY layer MAC layer Wi-Fi MAC Ongoing Research Obtained Results

7 This Talk How much can we gain from full-duplex and under what conditions?

8 Outline Motivation and Problem Statement Single Channel FD Structural Results Determining FD + TDD Capacity Region Multi-Channel FD Fixed Power Allocation General Power Allocation

9 FD and TDFD Capacity Region Maximization of the sum of the rates* gives us only one pair of uplink and downlink rates But, in many cases we want to prioritize one of the rates rm/rm rm/rm Using only full-duplex and varying the power allocation will give us one set of achievable rates, which may be non-convex power r b /r b uplink r b /r b power uplink Combining FD and TDD convexifies the capacity region time division FD (TDFD) Having convex capacity region is important for scheduling (and in our case gives higher rates) power downlink frequency frequency power downlink t frequency frequency *J. Marašević, J. Zhou, H. Krishnaswamy, Y. Zhong, G. Zussman, Resource Allocation and Rate Gains in Practical Full-Duplex Systems, to appear in IEEE/ACM Transactions on Networking, 216

10 Model and Problem Statement (I) k: channel index; K: # of channels Self-interference on channel k: constant fraction of the transmission power on channel k TX power of i on ch K i,k =,i2{m, b} max total TX power of i Signal-to-noise-ratio (SNR): mb,k = m,k mb,k bm,k = b,k bm,k Self-interference-to-noise-ratio (XINR): m b bb,k = b,k bb,k mm,k = m,k mm,k Shannon s capacity formula: = log 1+ SNR 1 + XINR

11 Model and Problem Statement (II) The UL and DL rates: r m = r b = KX log k=1 KX log k=1 1+ m,k mb,k 1+ b,k bb,k 1+ b,k m bm,k 1+ m,k mm,k b The problem: max s.t. r m r b = rb KX KX b,k apple 1, m,k apple 1 k=1 k=1 b,k, m,k, 8k

12 Rate Improvement (r b,r m ) Normalized UL rate rm/rm rb p, r m p rate improvement r b /r b Normalized DL rate

13 Outline Motivation and Problem Statement Single Channel FD Structural Results Determining FD + TDD Capacity Region Multi-Channel FD Fixed Power Allocation General Power Allocation

14 Structural Results (I) FD Capacity Region: Proposition. At the boundary of the capacity region either the uplink or downlink power must be equal to its maximum rate. m =1 1.8 S b (s b,s m ) rm/rm.6.4 S m b = r b /r b

15 Structural Results (II) Lemma. S b can take only one of the following three shapes: Concave Convex Concave, then convex Proposition. S b S m 1. If both and are concave, FD capacity region is convex. 2. If (s b,s m ) maximizes the sum of the uplink and downlink rates, then (s b,s m ) is outside the convex hull of the FD capacity region. 3. If s b + s m apple r m, then S b is convex.

16 FD+TDD Capacity Region Proposition. Any point on the FD+TDD capacity region can be determined either in a closed form, or through a simple bisection. Symmetric UL/DL SNR 1.8 UL and DL SNRs grow, DL SNR = UL SNR 1.8 Asymmetric UL/DL SNR UL and DL SNRs grow, DL SNR > UL SNR rm/r m TDD rm/rm.6.4 rm/r m TDD rm/rm r b /r b r b /r b bb =1, mm = 1

17 Outline Motivation and Problem Statement Single Channel FD Structural Results Determining FD + TDD Capacity Region Multi-Channel FD Fixed Power Allocation General Power Allocation

18 Cancellation Profiles Base Station/Access Point 1 γbb,k/k[db] Mobile Station γmm,k/k[db] k γmm,k/k[db] k Conventional MS TX 1 Filter FDE MS TX 2 Filters FDE MS TX k γmm,k/k[db] k Jin Zhou, Peter R. Kinget and Harish Krishnaswamy, A Blocker-Resilient Wideband Receiver with Low-Noise Active Two- Point Cancellation of >dbm TX Leakage and TX Noise in RX Band for FDD/Co-Existence, in Proc. IEEE ISSCC, Feb Jin Zhou, Tsung-Hao Chuang, Tolga Dinc and Harish Krishnaswamy, Reconfigurable receiver with >>2MHz bandwidth selfinterference cancellation suitable for FDD, co-existence and full-duplex applications, In Proc. IEEE ISSCC 15, 215. D. Bharadia, E. McMilin, and S. Katti. Full duplex radios. In Proc. ACM SIGCOMM 13, 213.

19 Fixed Power Allocation The shape of the power allocation is fixed, but the sum TX power over channels can be varied power frequency Lemma: At the boundary of the capacity region, either uplink or downlink sum of the power levels must be equal to its maximum value Equivalent to the result for the single channel Every point on the boundary of FD capacity region can be found via bisection

20 Fixed Power Allocation (cont.) Do not have the same structural properties for the shape of the FD capacity region as in the single channel case However, the convex hull (TDFD capacity region) can still be determined in reasonable time 1 Residual Self-Interference γbb,k/k[db] γmm,k/k[db] k k rm=rm.5 1 UL SNR [db] r b =r b (avg DL SNR) - (avg UL SNR) = 2dB

21 General Power Allocation (I) Can assign any TX power to any channel, as long as P K k=1 P K b,k apple 1, k=1 m,k apple 1 A non-convex problem We show how to, under mild restrictions, solve this problem with an alternating minimization (maximization) method The algorithm converges to a stationary point that is a global max in practice We also design a simple heuristic that has similar performance Intuition for the heuristic: Half-duplex power allocation when one of the rates is close to zero High-SINR approximation power allocation around the point that maximizes the sum of the uplink and downlink rates over channels Turning some of the channels off may increase the rate max s.t. r m r b = r b

22 General Power Allocation (II) γbb,k/k[db] Heuristic Alt. Max. 1 γmm,k/k[db] k k rm=rm Low UL/DL SNR db and 1 db r b =r b rm=rm High UL/DL SNR 2 db to 5 db r b =r b avg DL SNR = avg UL SNR

23 Summary Characterized rate improvements and properties of the capacity regions for full-duplex links Used realistic models of the hardware The results are analytical and insightful Bottom line: simple policies and algorithms are enough Future work: Wi-Fi and cellular MAC: (fair) resource allocation and scheduling

24 Questions? wimnet.ee.columbia.edu flexicon.ee.columbia.edu