On Optimal Multi-user Beam Alignment in Millimeter Wave Wireless Systems Abbas Khalili † , Shahram Shahsavari ◇ , Mohammad A. (Amir) Khojastepour ☆ , Elza Erkip † † New York University, ◇ University of Waterloo, ☆ NEC Laboratories America ISIT 2020 1/20 Khalili, Shahsavari, Khojastepour, Erkip
Motivation MmWave Pros : { Large bandwidth Multi-Gbps data rate 2/20 Khalili, Shahsavari, Khojastepour, Erkip
Motivation MmWave Pros : Cons : { Large bandwidth { High pathloss Multi-Gbps data rate Intense shadowing 2/20 Khalili, Shahsavari, Khojastepour, Erkip
Motivation MmWave Pros : Cons : { Large bandwidth { High pathloss Multi-Gbps data rate Intense shadowing ⇒ Beamforming: Use narrow beams for communication 2/20 Khalili, Shahsavari, Khojastepour, Erkip
Motivation MmWave channel is sparse with few spatial clusters 2/20 Khalili, Shahsavari, Khojastepour, Erkip
Motivation MmWave channel is sparse with few spatial clusters Beamforming Match the Tx pattern to the clusters’ angle of departure (AoD) Match the Rx pattern to the clusters’ angle of arrival (AoA) 2/20 Khalili, Shahsavari, Khojastepour, Erkip
Beam Alignment Beam Alignment The AoD and AoA do not change rapidly 3/20 Khalili, Shahsavari, Khojastepour, Erkip
Beam Alignment Beam Alignment The AoD and AoA do not change rapidly Use beams at the Tx and Rx to estimate the AoD and AoA 3/20 Khalili, Shahsavari, Khojastepour, Erkip
Beam Alignment Beam Alignment The AoD and AoA do not change rapidly Use beams at the Tx and Rx to estimate the AoD and AoA Interactive beam alignment Wait for feedback after each transmission Non-interactive beam alignment Sends all the packets without waiting for feedback 3/20 Khalili, Shahsavari, Khojastepour, Erkip
Beam Alignment Beam Alignment The AoD and AoA do not change rapidly Use beams at the Tx and Rx to estimate the AoD and AoA Interactive beam alignment Wait for feedback after each transmission Non-interactive beam alignment Sends all the packets without waiting for feedback Analog beam alignment use one RF-chain to perform beam alignment 3/20 Khalili, Shahsavari, Khojastepour, Erkip
Problem and Objective This talk: Non-interactive analog beam alignment at base station when there are multiple users: 4/20
Problem and Objective This talk: Non-interactive analog beam alignment at base station when there are multiple users: Objective : Minimize the average expected beamwidth of the users. 4/20
Problem and Objective This talk: Non-interactive analog beam alignment at base station when there are multiple users: Objective : Minimize the average expected beamwidth of the users. 1 What is the fundamental limit? 4/20
Problem and Objective This talk: Non-interactive analog beam alignment at base station when there are multiple users: Objective : Minimize the average expected beamwidth of the users. 1 What is the fundamental limit? 2 How to achieve this fundamental limit? 4/20 Khalili, Shahsavari, Khojastepour, Erkip
Preview of the Results Non-interactive analog beam alignment at the base station for two scenarios Base station can use beams of any shapes Base station is constrained to use only contiguous beams 5/20 Khalili, Shahsavari, Khojastepour, Erkip
Preview of the Results Non-interactive analog beam alignment at the base station for two scenarios Base station can use beams of any shapes Base station is constrained to use only contiguous beams Upper- and lower-bounds the minimum average expected beamwidth Upper- and Lower-bounds meet for uniform priors 5/20 Khalili, Shahsavari, Khojastepour, Erkip
Preview of the Results Non-interactive analog beam alignment at the base station for two scenarios Base station can use beams of any shapes Base station is constrained to use only contiguous beams Upper- and lower-bounds the minimum average expected beamwidth Upper- and Lower-bounds meet for uniform priors Schemes that achieve the upper-bounds and optimal performance 5/20 Khalili, Shahsavari, Khojastepour, Erkip
Preview of the Results Non-interactive analog beam alignment at the base station for two scenarios Base station can use beams of any shapes Base station is constrained to use only contiguous beams Upper- and lower-bounds the minimum average expected beamwidth Upper- and Lower-bounds meet for uniform priors Schemes that achieve the upper-bounds and optimal performance 2 × reduction of average expected beamwidth compared to exhaustive search used in the standards 5/20 Khalili, Shahsavari, Khojastepour, Erkip
Literature Chiu, Ronquillo, Javidi JSAC 2019 . Single-user analog interactive beam alignment Adaptive and sequential alignment algorithm Search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection 6/20 Khalili, Shahsavari, Khojastepour, Erkip
Literature Chiu, Ronquillo, Javidi JSAC 2019 . Single-user analog interactive beam alignment Adaptive and sequential alignment algorithm Search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection Hassan, Michelusi ITA 2018 . Two user analog interactive beam alignment Minimize the power consumption during data transmission Bisection search algorithm is optimal 6/20 Khalili, Shahsavari, Khojastepour, Erkip
Literature Chiu, Ronquillo, Javidi JSAC 2019 . Single-user analog interactive beam alignment Adaptive and sequential alignment algorithm Search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection Hassan, Michelusi ITA 2018 . Two user analog interactive beam alignment Minimize the power consumption during data transmission Bisection search algorithm is optimal Shahsavari, Khojastepour, Erkip PIMRC 2019 . Single-user analog interactive beam alignment Dynamic programming scheme that maximizes system throughput given the total number of time-slots 6/20 Khalili, Shahsavari, Khojastepour, Erkip
Literature Chiu, Ronquillo, Javidi JSAC 2019 . Single-user analog interactive beam alignment Adaptive and sequential alignment algorithm Search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection Hassan, Michelusi ITA 2018 . Two user analog interactive beam alignment Minimize the power consumption during data transmission Bisection search algorithm is optimal Shahsavari, Khojastepour, Erkip PIMRC 2019 . Single-user analog interactive beam alignment Dynamic programming scheme that maximizes system throughput given the total number of time-slots This work: Multi-user non-interactive analog beam alignment Bounds on the minimum average expected beamwidth Achievablity schemes 6/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions N -user downlink each with a single link 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions N -user downlink each with a single link Omnidirectional reception at users 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions N -user downlink each with a single link Omnidirectional reception at users Analog beamforming at base station 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions θ 2 θ 3 θ 4 N -user downlink each with a single link θ 1 Omnidirectional reception at users Analog beamforming at base station Ideal beams ACR = ( θ 1 , θ 2 ] ∪ ( θ 3 , θ 4 ] ACR stands for angular coverage region 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions θ 2 θ 3 θ 4 N -user downlink each with a single link θ 1 Omnidirectional reception at users Analog beamforming at base station Ideal beams ACR = ( θ 1 , θ 2 ] ∪ ( θ 3 , θ 4 ] ACR stands for angular coverage region Base station transmits beam alignment packets through b scanning beams 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions θ 2 θ 3 θ 4 N -user downlink each with a single link θ 1 Omnidirectional reception at users Analog beamforming at base station Ideal beams ACR = ( θ 1 , θ 2 ] ∪ ( θ 3 , θ 4 ] ACR stands for angular coverage region Base station transmits beam alignment packets through b scanning beams Users’ feedback determines the indices of received beam alignment packets 7/20 Khalili, Shahsavari, Khojastepour, Erkip
System Assumptions θ 2 θ 3 θ 4 N -user downlink each with a single link θ 1 Omnidirectional reception at users Analog beamforming at base station Ideal beams ACR = ( θ 1 , θ 2 ] ∪ ( θ 3 , θ 4 ] ACR stands for angular coverage region Base station transmits beam alignment packets through b scanning beams Users’ feedback determines the indices of received beam alignment packets No noise at the users’ side and no noise on the feedback 7/20 Khalili, Shahsavari, Khojastepour, Erkip
Objective Objective: N { Φ ∗ j } b j = 1 = arg min ∑ w i E [∣ Beam ( Ψ i )∣] { Φ j } b i = 1 j = 1 i = 1 w i = 1 ∶ Importance or quality of service w i , ∑ N Φ j ∶ Scanning beam used at the j th time slot Ψ i ∼ f Ψ i ( ψ ) ∶ Angle of departure of the i th user ∣ Beam ( Ψ i )∣ ∶ Width of the beam allocated to the i th user that includes its AoD 8/20 Khalili, Shahsavari, Khojastepour, Erkip
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