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

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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

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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)

:

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Contents

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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 :

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Motivation

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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 :

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Motivation

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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 :

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Motivation

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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 :

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Motivation

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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 :

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Single-group Multicasting

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Figure: K-user Multicasting

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Hybrid Precoder

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s m NRF

tx

F Ntx s m NRF

tx

= Ntx Ntx

Figure: Hybrid and fully-digital precoders

m ∈ CNRF

tx ×1: digital precoder

F ∈ FNtx×NRF

tx : analog precoder

F = √δtx, . . . , √δtxe

2π(Ltx−1) Ltx

  • :

set of phase shifts Ntx: number of transmit antennas NRF

tx : number of RF chains

Ltx: number of phase shifts

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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System Model

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The downlink signal is x = Fms (1) The received signal by user k ∈ K is yk = wH

k Hkx

  • multicast signal

+ wH

k nk noise

, (2)

wk: combiner of the k-th user F: analog precoder m: digital precoder Hk: 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 :

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System Model

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The received signal by user k ∈ K is yk = wH

k HkFms

  • multicast signal

+ wH

k nk noise

, (3) The SNR at user k is γk =

  • wH

k HkFm

  • 2

σ2 wk2

2

, (4)

wk: combiner of the k-th user F: analog precoder m: digital precoder Hk: 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 :

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Problem Formulation

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Phyb : max

F,m,{wk}K

k=1

min

k∈K

  • wH

k HkFm

  • 2

σ2 wk2

2

(5a) s.t. Fm2

2 = P max tx

, (5b) [F]q,r ∈ F, q ∈ Q, r ∈ R, (5c) wk2

2 = P max rx

, k ∈ K, (5d) [wk]l ∈ W, l ∈ L, ∀k ∈ K, (5e)

F = √δtx, . . . , √δtxej 2π(Ltx−1)

Ltx

  • : allowed phase shifts at the precoder

W = √δrx, . . . , √δrxej 2π(Lrx−1)

Lrx

  • : allowed phase shifts at the combiners

Ltx: number of phase shifts at the precoder Lrx: 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 :

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Proposed Solution

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1

: max

F

min

k∈K

  • wH

k HkFm

  • 2

σ2P max

rx

(6a) s.t. Fm2

2 = P max tx

, (6b) [F]q,r ∈ F, q ∈ Q, r ∈ R. (6c) Phyb

2

: max

m

min

k∈K

  • wH

k HkFm

  • 2

(7a) s.t. Fm2

2 = P max tx

. (7b) Phyb

3

: max

{wk}K

k=1

min

k∈K

  • wH

k HkFm

  • 2

σ2 wk2

2

(8a) s.t. [wk]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 :

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Optimization of the Analog Precoder F

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Phyb

1

: max

F

min

k∈K

  • wH

k HkFm

  • 2

σ2P max

rx

(9a) s.t. Fm2

2 = P max tx

, (9b) [F]q,r ∈ F, q ∈ Q, r ∈ R. (9c) We equivalently recast Phyb

1

as P

hyb 1

P

hyb 1

: max

F

min

k∈K

mHFHHH

k wkwH k HkFm

mHFHFm (10a) 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 :

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Optimization of the Analog Precoder F

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Instead of approaching (10), we propose to solve the surrogate problem (11), which consists of a weighted sum of all τ F

k = mHFHHH

k wkwH k HkFm

mHFHFm

, as shown in (11)

  • Phyb

1

: max

F K

  • k=1

ck mHFHHH

k wkwH k HkFm

mHFHFm (11a) s.t. [F]q,r ∈ F, q ∈ Q, r ∈ R, (11b) where ck ≥ 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 :

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Optimization of the Analog Precoder F

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Notice that τ F

k ≤ λmax

  • FHF

−1 FHHH

k wkwH k HkF

  • = wH

k HkF

  • FHF

−1 FHHH

k wk

  • JF

k

, (12) where λmax(·) extracts the maximum eigenvalue. Upon replacing τ F

k in (11) by its upper bound JF k , the problem collapses to

  • Phyb

1

: max

F K

  • k=1

ckwH

k HkF

  • FHF

−1 FHHH

k wk,

(13a) 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 :

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Optimization of the Analog Precoder F

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Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Optimization of the Digital Precoder m

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Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Optimization of the Analog Combiner wk

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Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Optimization Algorithm

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Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario I

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Goal: Evaluate the impact of exploration (Nxpr) and exploitation (Nxpt)

Table: Simulation parameters

Description Symbol Value Units Transmit power P max

tx

30 dBm Receive power P max

rx

10 dBm Noise power σ2 30 dBm Number of users K 30

  • Number of transmit antennas

Ntx 15

  • Number of receive antennas

Nrx 2

  • Number of RF chains (at the hybrid precoder)

NRF

tx

6

  • Number of phase shifts at the precoder

Ltx 8

  • Number of phase shifts at the combiner

Lrx 4

  • Number of exploration instances

Nxpr 100

  • Number of exploitation instances

Lxpt 100

  • Momentum factor

ρF = ρM = ρW 0.90

  • Diminishing learning factor

αF = αM = αW 0.98

  • Luis F. Abanto-Leon

Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario I

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20 40 60 80 100 20 40 60 80 100 0.0 0.3 0.6 0.9 1.2 1.5 1.8

Nxpt Nxpr Minimum SNR

Hybrid Fully- digital

20 40 60 80 100 20 40 60 80 100 30 40 50 60 70 80

Nxpt Nxpr Spectral Efficiency [bps/Hz]

Hybrid Fully- digital

Figure: Impact of exploration (Nxpr) and exploitation (Nxpt).

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario II

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Goal: Evaluate the impact of the number of antennas Ntx and Nrx

Table: Simulation parameters

Description Symbol Value Units Transmit power P max

tx

30 dBm Receive power P max

rx

10 dBm Noise power σ2 30 dBm Number of users K 50

  • Number of transmit antennas

Ntx {8, 12, 16}

  • Number of receive antennas

Nrx {1, 2, 3, 4, 5}

  • Number of RF chains (at the hybrid precoder)

NRF

tx

2

  • Number of phase shifts at the precoder

Ltx 8

  • Number of phase shifts at the combiner

Lrx 4

  • Number of exploration instances

Nxpr 100

  • Number of exploitation instances

Lxpt 100

  • Momentum factor

ρF = ρM = ρW 0.90

  • Diminishing learning factor

αF = αM = αW 0.98

  • Luis F. Abanto-Leon

Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario II

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Ntx = 8 Ntx = 12 Ntx = 16 1 2 3

0.29 0.38 0.46 0.58 0.73 0.85 0.95 1.16 1.39 1.4 1.64 1.86 1.76 2.04 2.46 0.37 0.51 0.64 0.65 0.82 0.99 1.09 1.31 1.53 1.51 1.81 2.02 1.9 2.17 2.51

Minimum SNR

H |Nrx = 1 H |Nrx = 2 H |Nrx = 3 H |Nrx = 4 H |Nrx = 5 D |Nrx = 1 D |Nrx = 2 D |Nrx = 3 D |Nrx = 4 D |Nrx = 5

Ntx = 8 Ntx = 12 Ntx = 16 50 100 150

72.56 82.02 89.28 96.42 106.42 116.43 116.56 126.34 136.16 131.06 141.91 151.48 143.99 154.86 164.69 81.46 91.81 101.24 102.26 113.46 123.63 123.08 134.17 144.33 137.78 149.48 159.31 150.9 161.41 171.53

SE [bps/Hz]

Figure: Performance evaluation of LB-GDM for varying Ntx and Nrx in fully-digital (D) and hybrid (H) precoders.

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario III

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Goal: Compare the performance with a SDR-based scheme

Table: Simulation parameters

Description Symbol Value Units Transmit power P max

tx

30 dBm Receive power P max

rx

10 dBm Noise power σ2 30 dBm Number of users K {25, 50, 75, 100}

  • Number of transmit antennas

Ntx 20

  • Number of receive antennas

Nrx 3

  • Number of RF chains (at the hybrid precoder)

NRF

tx

6

  • Number of phase shifts at the precoder

Ltx 8

  • Number of phase shifts at the combiner

Lrx 4

  • Number of exploration instances

Nxpr 120

  • Number of exploitation instances

Lxpt 120

  • Momentum factor

ρF = ρM = ρW 0.90

  • Diminishing learning factor

αF = αM = αW 0.98

  • Number of randomizations (SDR-C)

Nrand {1, 10, 50, 100, 500, 1000}

  • Luis F. Abanto-Leon

Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Simulation Results - Scenario III

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K = 25 K = 50 K = 75 K = 100 2 4

3.78 2.24 1.69 1.43 1.86 0.92 0.65 0.46 1.76 1.01 0.75 0.56 1.98 1.12 0.8 0.62 1.93 1.13 0.8 0.62 2.11 1.28 0.87 0.7 2.06 1.34 0.81 0.71

  • Min. SNR (H)

LB-GDM SDR-C | 1 SDR-C | 10 SDR-C | 50 SDR-C | 100 SDR-C | 500 SDR-C | 1000

K = 25 K = 50 K = 75 K = 100 2 4

4.24 2.6 1.8 1.46 1.85 0.62 0.37 0.24 3.01 1.25 0.71 0.45 3.12 1.36 0.82 0.56 3.18 1.45 0.81 0.68 3.18 1.39 0.85 0.66 3.3 1.43 0.88 0.71

  • Min. SNR (D)

Figure: Performance comparison between LB-GDM and SDR-C

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Conclusions

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We investigated the design of fully-digital and hybrid precoders for single-group multicasting using a learning-based scheme, LB-GDM. Our proposed low-complexity LB-GDM uses only matrix multiplications / additions and low-dimensional matrix inversion operations. We compare the performance of precoders based on SDR-C and LB-GDM. The results show that LB-GDM attains substantial additional gain for both digital and hybrid precoders. We corroborate the importance of incorporating more receive

  • antennas. We achieve 75.7% and 100% gains in terms of the

minimum SNR by increasing the number of receive antennas from one to two.

Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :

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Questions

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Email: l.f.abanto@ieee.org Website: www.luis-f-abanto-leon.com

This work has been funded by the Deutsche Forschungsgemeinschaft (DFG) within the B5G-Cell project as part of the SFB 1053 MAKI. Luis F. Abanto-Leon Technical University of Darmstadt Learning-based Max-Min Fair Hybrid Precoding for mmWave Multicasting :