2020 IEEE International Symposium on Information Theory Gaussian 1-2-1 Networks with Imperfect Beamforming Yahya H. Ezzeldin ‡ , Martina Cardone † , Christina Fragouli ‡ and Giuseppe Caire ★ ‡ University of California Los Angeles † University of Minnesota Twin Cities ★ Technische Universität Berlin Supported by NSF Awards 1514531, 1824568 and UC-NL grant LFR-18-548554
mmWave Communication [ www.rcrwireless.com ] + Abundant spectrum resource - Severe propagation loss and blockage at high frequencies (using omnidirectional communication) 1
mmWave Communication Receiver Antenna Array Transmitter Antenna Array Steerable high-gain Multi-hop communication directional antenna arrays 2
mmWave multi-hop network S D Goal: What is the maximum unicast traffic rate that we can send between any two nodes in the network ? 3
mmWave studies Rate coverage and interference-noise ratio ▪ Andrew Thornburg et al., "Performance analysis of outdoor mmWave ad hoc networks." IEEE Transactions on Signal Processing (2016) ▪ James C. Martin, et al., "Receiver Adaptive Beamforming and Interference of Indoor Environments in mmWave." PIMRC (2018) Potential connectivity through multi-hop ▪ Xingqin Lin et al., "Connectivity of Millimeter Wave Networks With Multi- Hop Relaying“, IEEE Wireless Communications Letters (2015) What is the potential unicast capacity if all intermediate network nodes are used to relay information ? (with mmWave transmission constraints) 4
Gaussian 1-2-1 network model [Ezzeldin et al. ISIT 2018] To model abstract aspects enabling mmWave communication: ➢ mmWave radios to use phased antenna arrays to focus/receive power along very narrow beams. ➢ Efficient communication possible when beams are aligned between two nodes. 5
Gaussian 1-2-1 network model [Ezzeldin et al. ISIT 2018] To model abstract aspects enabling mmWave communication: ➢ mmWave radios to use phased antenna arrays to focus/receive power along very narrow beams. ➢ Efficient communication possible when beams are aligned between two nodes. ➢ Beam steering/alignment need to be optimized for maximizing data rate. 5
Ideal beamforming [Ezzeldin et al. ISIT 2018] 6
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model 6
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model Imperfect beamforming (this work) 6
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model Imperfect beamforming (this work) ? 6 Imperfect 1-2-1 network model
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model Main Question How can we properly incorporate side-lobe leakage in our abstract modeling of the network ? Imperfect beamforming (this work) ? 6 Imperfect 1-2-1 network model
Gaussian full-duplex 1-2-1 network model [Ezzeldin et al. ISIT 2018] Nodes At any time: ● Each node can point its transmitting beam to at most one node. ● Each node can point its receiving beam to at most one node. ● In full-duplex, both beams can be simultaneously active. A link a → b is active only if node a points its Tx beam towards ● node b and node b points its Rx beam towards node a . 7
Gaussian full-duplex 1-2-1 network model [Ezzeldin et al. ISIT 2018] Nodes At any time: ● Each node can point its transmitting beam to at most one node. ● Each node can point its receiving beam to at most one node. ● In full-duplex, both beams can be simultaneously active. A link a → b is active only if node a points its Tx beam towards ● node b and node b points its Rx beam towards node a . 7
Gaussian full-duplex 1-2-1 network model [Ezzeldin et al. ISIT 2018] Nodes At any time: ● Each node can point its transmitting beam to at most one node. ● Each node can point its receiving beam to at most one node. ● In full-duplex, both beams can be simultaneously active. A link a → b is active only if node a points its Tx beam towards ● node b and node b points its Rx beam towards node a . Topology An edge exists between nodes a and b only if the link can be established by beam alignment (no blockage) 7
Gaussian full-duplex 1-2-1 network model [Ezzeldin et al. ISIT 2018] Network states At any time, the network has a particular state based on beam orientations of the N nodes. S D S D Full-Duplex wireless network Full-Duplex 1-2-1 network a single state states 8
Gaussian full-duplex 1-2-1 network model [Ezzeldin et al. ISIT 2018] Network schedule Fraction of time each state is active S D S D S D state s = 1 state s = 2 state s = 3 9
Previous Results [Ezzeldin et al. ISIT 2018] Capacity approximation The capacity of a Gaussian 1-2-1 network with N nodes can be approximated to within a constant gap that depends only on the network size N . Efficient Scheduling For the full-duplex 1-2-1 network, the approximate capacity and an optimal schedule that achieves it can be computed in time. potential states ! Guarantees on simplified operation An optimal schedule activates at most 𝑂 2 + 1 states in full-duplex. ● ● At most 2N+2 paths need to be active for approximate capacity in Gaussian full-duplex 1-2-1 networks (out of potentially exponential). 10
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model Imperfect beamforming (this work) ? 11 Imperfect 1-2-1 network model
Gaussian Imperfect 1-2-1 network model Topology An edge exists between nodes a and b only if the communication can be established by beamforming (no blockage) Nodes At any time: ● Each node can point its main TX lobe to at most one node. ● Each node can point its main RX lobe to at most one node. ● In full-duplex, both beams can be simultaneously active. ● If Tx lobe an Rx lobe are aligned then channel coefficient a → b is enhanced by a gain of . Otherwise, channel coefficient a → b is attenuated by a factor ● of . 12
Gaussian Imperfect 1-2-1 network model Topology An edge exists between nodes a and b only if the communication can be established by beamforming (no blockage) Nodes At any time: ● Each node can point its main TX lobe to at most one node. ● Each node can point its main RX lobe to at most one node. ● In full-duplex, both beams can be simultaneously active. ● If Tx lobe an Rx lobe are aligned then channel coefficient a → b is enhanced by a gain of . Otherwise, channel coefficient a → b is attenuated by a factor ● of . 12
Ideal beamforming [Ezzeldin et al. ISIT 2018] Ideal 1-2-1 network model Imperfect beamforming (this work) 13 Imperfect 1-2-1 network model
Ideal vs Imperfect 1-2-1 network model Constant gap capacity approximation (ISIT 2018) 14
Ideal vs Imperfect 1-2-1 network model Constant gap capacity approximation Constant gap capacity approximation (ISIT 2018) (this work) 14
Ideal vs Imperfect 1-2-1 network model Constant gap capacity approximation Constant gap capacity approximation (ISIT 2018) (this work) Efficient polynomial-time ? scheduling 14
Ideal vs Imperfect 1-2-1 network model Constant gap capacity approximation Constant gap capacity approximation (ISIT 2018) (this work) Efficient polynomial-time ? scheduling Guarantees on operating only a ? fraction of the network paths 14
Ideal vs Imperfect 1-2-1 network model ? Constant gap capacity approximation Constant gap capacity approximation (ISIT 2018) (this work) Efficient polynomial-time ? scheduling Guarantees on operating only a ? fraction of the network paths 14
Ideal beamforming Question Ideal 1-2-1 network model For what values of the tuple ( , ) is the ideal 1-2-1 network model a good approximation of the imperfect 1-2-1 network model ? Imperfect beamforming 15 Imperfect 1-2-1 network model
Ideal beamforming Question Ideal 1-2-1 network model For what values of the tuple ( , ) is the ideal 1-2-1 network model a good approximation of the imperfect 1-2-1 network model ? Imperfect beamforming (sufficient conditions) 15 Imperfect 1-2-1 network model
Main Result : From imperfect to ideal 1-2-1 networks Theorem: Consider an N-relay Gaussian Imperfect 1-2-1 network with channel coefficients given . 16
Main Result : From imperfect to ideal 1-2-1 networks Theorem: Consider an N-relay Gaussian Imperfect 1-2-1 network with channel coefficients given . Let approximate capacity of the network for beamforming parameters , 16
Main Result : From imperfect to ideal 1-2-1 networks Theorem: Consider an N-relay Gaussian Imperfect 1-2-1 network with channel coefficients given . Let approximate capacity of the network for beamforming parameters , and be the maximum degree of the graph representing the network topology. 16
Main Result : From imperfect to ideal 1-2-1 networks Theorem: Consider an N-relay Gaussian Imperfect 1-2-1 network with channel coefficients given . Let approximate capacity of the network for beamforming parameters , and be the maximum degree of the graph representing the network topology. If the beamforming parameters satisfy that 16
Recommend
More recommend
