Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting - PowerPoint PPT Presentation

Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Luis F. Abanto-Leon Co-author: Gek Hong (Allyson) Sim Department of Computer Science Technical University of Darmstadt IEEE International Conference on Communications (ICC 2020) WC5: Machine Learning I (3rd Paper) Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Contents 2/ 25 1 Motivation 2 System Model 3 Problem Formulation 4 Proposed Solution 5 Simulation Results 6 Conclusions Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Motivation 3/ 25 Multicast beamforming with fully-digital precoders has been widely studied in the literature. Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Motivation 3/ 25 Multicast beamforming with fully-digital precoders has been widely studied in the literature. However, the benefits and challenges with hybrid precoders require additional study. Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Motivation 3/ 25 Multicast beamforming with fully-digital precoders has been widely studied in the literature. However, the benefits and challenges with hybrid precoders require additional study. We investigate the joint design of hybrid precoding and analog combining for max-min fairness single-group multicasting in millimeter-wave systems. We propose LB-GDM , a learning-based approach that leverages (i) gradient descent with momentum and (ii) alternating optimization. Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Motivation 4/ 25 Features of the proposed scheme LB-GDM – Has low complexity [compared to SDR] – Leverages alternating optimization [several parameters] – Is based on learning with gradient descent with momentum Our proposed design does not require: – Code-books – Solution with a fully-digital precoder. Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Single-group Multicasting 5/ 25 Figure: K -user Multicasting Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Hybrid Precoder 6/ 25 N tx s m ∈ C N RF tx × 1 : digital precoder F ∈ F N tx × N RF tx : analog precoder m N RF � √ δ tx , . . . , √ δ tx e 2 π ( L tx − 1) � tx F F = L tx : set of phase shifts N tx : number of transmit antennas N tx s N RF tx : number of RF chains L tx : number of phase shifts m N RF = N tx tx Figure: Hybrid and fully-digital precoders Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions System Model 7/ 25 The downlink signal is x = Fm s (1) The received signal by user k ∈ K is w H + w H y k = (2) k H k x k n k , � �� � � �� � multicast signal noise w k : combiner of the k -th user F : analog precoder m : digital precoder H k : channel between the gNodeB and the k -th user K : number of users K = { 1 , . . . , K } : set of users s : multicast symbol Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions System Model 8/ 25 The received signal by user k ∈ K is y k = w H + w H k H k Fm s k n k , (3) � �� � � �� � multicast signal noise The SNR at user k is � � � 2 � w H k H k Fm γ k = , (4) σ 2 � w k � 2 2 w k : combiner of the k -th user F : analog precoder m : digital precoder H k : channel between the gNodeB and the k -th user K : number of users K = { 1 , . . . , K } : set of users s : multicast symbol Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Problem Formulation 9/ 25 � � � 2 � w H k H k Fm P hyb : max min (5a) σ 2 � w k � 2 0 k ∈K F , m , { w k } K 2 k =1 � Fm � 2 2 = P max s . t . , (5b) tx [ F ] q,r ∈ F , q ∈ Q , r ∈ R , (5c) � w k � 2 2 = P max , k ∈ K , (5d) rx [ w k ] l ∈ W , l ∈ L , ∀ k ∈ K , (5e) � √ δ tx , . . . , √ δ tx e j 2 π ( L tx − 1) � F = L tx : allowed phase shifts at the precoder � √ δ rx , . . . , √ δ rx e j 2 π ( L rx − 1) � W = : allowed phase shifts at the combiners L rx L tx : number of phase shifts at the precoder L rx : number of phase shifts at the combiners Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Proposed Solution 10/ 25 � 2 � � w H � k H k Fm P hyb : max min (6a) 1 σ 2 P max k ∈K F rx � Fm � 2 2 = P max s . t . , (6b) tx [ F ] q,r ∈ F , q ∈ Q , r ∈ R . (6c) 2 � � P hyb � w H : max min (7a) k H k Fm � � 2 � m k ∈K � Fm � 2 2 = P max s . t . (7b) . tx � 2 � w H � � k H k Fm P hyb : max min (8a) 3 σ 2 � w k � 2 k ∈K { w k } K k =1 2 s . t . [ w k ] l ∈ W , l ∈ L , ∀ k ∈ K . (8b) Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Analog Precoder F 11/ 25 � � � 2 � w H k H k Fm P hyb : max min (9a) 1 σ 2 P max k ∈K F rx � Fm � 2 2 = P max s . t . (9b) , tx [ F ] q,r ∈ F , q ∈ Q , r ∈ R . (9c) hyb We equivalently recast P hyb as P 1 1 m H F H H H k w k w H k H k Fm hyb P : max min (10a) 1 m H F H Fm F k ∈K s . t . [ F ] q,r ∈ F , q ∈ Q , r ∈ R . (10b) Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Analog Precoder F 12/ 25 Instead of approaching (10), we propose to solve the surrogate problem (11), which consists of a weighted sum of all k = m H F H H H k w k w H k H k Fm τ F , as shown in (11) m H F H Fm K � m H F H H H k w k w H k H k Fm P hyb � : max (11a) c k 1 m H F H Fm F k =1 s . t . [ F ] q,r ∈ F , q ∈ Q , r ∈ R , (11b) where c k ≥ 0 denotes the k -th weighting factor Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Analog Precoder F 13/ 25 Notice that �� � � − 1 F H H H τ F F H F k w k w H k ≤ λ max k H k F � � − 1 F H H H (12) = w H F H F k H k F k w k , � �� � J F k where λ max ( · ) extracts the maximum eigenvalue. Upon replacing τ F k in (11) by its upper bound J F k , the problem collapses to K � � � − 1 F H H H P hyb � c k w H F H F : max (13a) k H k F k w k , 1 F k =1 s . t . [ F ] q,r ∈ F , q ∈ Q , r ∈ R . (13b) Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Analog Precoder F 14/ 25 Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Digital Precoder m 15/ 25 Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :

Motivation System Model Problem Formulation Proposed Solution Simulation Results Conclusions Optimization of the Analog Combiner w k 16/ 25 Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting Elapsed time: :