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Introduction System Model Proposed BF Scheme Simulations Conclusion Robust Hybrid Beamforming for Satellite-Terrestrial Integrated Networks Zhi Lin 1 , 2 , Min Lin 3 , Benoit Champagne 2 , Wei-Ping Zhu 3 , 4 , Naofal Al-Dhahir 5 1 . Army

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Introduction System Model Proposed BF Scheme Simulations Conclusion

Robust Hybrid Beamforming for Satellite-Terrestrial Integrated Networks

Zhi Lin1,2, Min Lin3, Benoit Champagne2, Wei-Ping Zhu3,4, Naofal Al-Dhahir5

  • 1. Army Engineering University of PLA, Nanjing, China
  • 2. McGill University, Montreal, Canada
  • 3. Nanjing University of Posts and Telecommunications, Nanjing, China
  • 4. Concordia University, Montreal, Canada
  • 5. The University of Texas at Dallas, Dallas, USA

April 13, 2020

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Outline

1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion

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Introduction

SATCOM Superiority

1 Inherent large coverage 2 High-speed broadband access 3 Services in areas where terrestrial communication systems are

infeasible

The goal of next generation communication system:

1 Seamless Connectivity 2 Increasing demand for broadband satellite services

Problems:

1 Scarce spectrum resources 2 Increasing data rate demands

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Introduction

The deployment of high frequency band: Ka or mmWave

1 Huge available bandwidth. 2 Antenna arrays with directional beam compensating

propagation losses.

Promising Infrastructure: Satellite-Terrestrial Integrated Networks (STIN)

1 An supplement for drawbacks experienced by

terrestrial/satellite systems.

2 Use dynamic spectrum access technology to enhance the

utilization of limited spectrum significantly.

3 Design an integrated network to satisfy the demand for

anytime, anywhere, and anyway service.

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Introduction

Energy Efficiency and Security Requirements

1 Huge energy consumption of base stations and especially the

radio access subsystems

2 Important factor from both economic and ecological

perspectives

3 Security requirement brings new challenage 4 By defining the ratio between the secrecy rate and the

consumed power, the concept of secrecy energy efficiency (SEE) is introduced to balance the security and EE

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Introduction

Our contributions: We formulate a constrained optimization problem to maximize the SEE of the considered system while satisfying the SINR requirements of both the earth station and cellular user. Robustness is incorporated in the design by considering imperfect knowledge of the angles of departure for the downlink wiretap channels. We then propose a new iterative search algorithm based on the Charnes-Cooper approach to solve the optimization problem and obtain the desired hybrid BF weight vectors.

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Outline

1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion

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System Model

System Model of the considered STIN: The GEO satellite serves an earth station (ES) in the presence

  • f K eavesdroppers (Eves), while the BS serves a cellular user

(CU). It is assumed that the Eves, but not the ES, are under coverage of the cellular sub-network, and therefore receive interference from the BS.

SAT Terrestrial Core Network ES BS Gateway CU K Eves Signal link Wiretap link Control link Green Interference link

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System Model

Channel Model

Satellite downlink channel Considering the effects of path loss, atmospheric attenuation and satellite antenna gain in satellite downlink channel, it can be written as

f =

  • CLGrr ⊙ b

1 2

(1)

Terrestrial downlink channel A typical mmWave channel with a predominant LoS propagation component and a sparse set of single-bounce NLoS components can be described as

h =

  • g (θ0, ϕ0)ρ0ah (θ0, ϕ0) ⊗ av (θ0)

+

  • 1

J J

  • j=1
  • g (θj, ϕj)ρjah (θj, ϕj) ⊗ av (θj).

(2)

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System Model

Channel Model

Steering vector ah (θ, ϕ) and av (θ) denote the horizontal and vertical array steering vectors (SVs) of the UPA, which are, respectively, given by ah (θ, ϕ) =

  • e−iβ((N1−1)/2)d1 sin θ cos ϕ, · · ·

, e+iβ((N1−1)/2)d1 sin θ cos ϕT , (3a) av (θ)=

  • e−iβ((N2−1)/2)d2 cos θ, · · · , e+iβ((N2−1)/2)d2 cos θT .

(3b)

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System Model

Signal Models

The received signals at the CU, ES, and k-th Eve are, respectively, expressed as yc (t) = hH

c Pvx (t) + f H c ws (t) + nc (t) ,

ys (t) = f H

s ws (t) + ns (t) ,

yk (t) = f H

k ws (t) + hH k Pvx (t) + nk (t)

(4) Then, the SINR at the CU, ES, and k-th Eve are given by

γc =

  • hH

c Pv

  • 2

|f H

c w|2 + σ2 c

, γs =

  • f H

s w

  • 2

σ2

s

, γk =

  • f H

k w

  • 2

|hH

k Pv|2 + σ2 k

. (5)

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System Model

The achievable secrecy rate of the ES is given by Rs =

  • log2 (1 + γs) −

max

k∈{1,··· ,K} log2 (1 + γk)

+

(6) The total power consumption of the considered system is modeled as Ptot = η1w2 + η2v2 + PS + PB (7)

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System Model

Problem formulation

By assuming that the available cellular wiretap channel of the k-th Eves belongs to a given AoD uncertainty set ∆k defined by θk ∈

  • θL

k , θU k

  • and ϕk ∈
  • ϕL

k , ϕU k

  • , the optimization

problem can be formulated as max

w,v,P min ∆k

Rs/Ptot (8a) s.t. γc ≥ Γc, (8b) γs ≥ Γs, (8c)

  • [P]i,j
  • 2 = 1/Nb, i = 1, · · · , Nb, j = 1, · · · , Nr,

(8d) v2

F ≤ Pb, w2 F ≤ Ps

(8e)

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Outline

1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion

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Robust BF Scheme

By assuming that the elevation and azimuth AoD angles for the wiretap channel of the k-th Eve can only take uniformly spaced values within their respective range θk ∈

  • θL

k , θU k

  • and

ϕk ∈

  • ϕL

k , ϕU k

  • , as given by

θ(i)

k

= θL

k + i∆θ,

i = 0, · · · , M1, ϕ(j)

k

= ϕL

k + j∆ϕ,

j = 0, · · · , M2 (9)

where ∆θ = (θU

k − θL k )/M1 and ∆ϕ = (ϕU k − ϕL k )/M2.

Then, we define ˜ H = M1

i=0

M2

j=0 µi,jH(i,j) and

˜ F = M1

i=0

M2

j=0 µi,jF(i,j), where H(i,j) = h(i,j)

h(i,j)H, F(i,j) = f (i,j) f (i,j)H, µi,j =

1 (M1+1)(M2+1). By using these

averaged channel matrices in problem (8) instead of the imperfect ones, the minimization over ∆k can be removed.

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Robust BF Scheme

By invoking the Charnes-Cooper approach and introducing auxiliary variables α and τ, (8) can be further transformed as

max

W,V,P τ −1log2

  • σ2 + Tr (FsW)

α

  • (10a)

s.t. η1Tr (W) + η2Tr (V) + PS + PB = τ, (10b) Tr ˜ FkW Tr PH ˜ HkPV + σ2 ≤ α, ∀k, (10c) Tr PHHcPV − Γc

  • Tr (FcW) + σ2

≥ 0, (10d) Tr (FsW) − Γsσ2 ≥ 0, (10e)

  • [P]i,j
  • 2 = 1/Nb, i = 1, · · · , Nb, j = 1, · · · , Nr,

(10f) Tr (W) ≤ Ps, Tr (V) ≤ Pb, (10g) rank (W) = 1, rank (V) = 1 (10h)

where ak =

Tr(Hir,kWk,1) σ2

ir,k

.

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Robust BF Scheme

Iteratively Solving W

The optimization problem for the digital beamforming weight vector can be expressed as

max

W,V,τ,α log2

σ2 + Tr (FsW) α

  • τ −1

(11a) s.t. η1Tr (W) + η2Tr (V) + PS + PB = τ, (11b) Tr ˜ FkW

  • Tr
  • P(n)H ˜

HkP(n)V

  • + σ2 ≤ α,

∀k, (11c) Tr

  • P(n)HHcP(n)V
  • − Γc
  • Tr (FcW) + σ2

≥ 0, (11d) Tr (FsW) − Γsσ2 ≥ 0, (11e) Tr (W) ≤ Ps, Tr (V) ≤ Pb, (11f) rank (W) = 1, rank (V) = 1 (11g)

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Robust BF Scheme

Iteratively Solving P

The optimization problem of the analog precoder can then be written as follows

max

ˆ P

t s.t. Tr

  • ˆ

V(n)H ˜ Hk ˆ V(n) ˆ P

  • + σ2 ≥ tTr

˜ FkW(n) , ∀k, Tr

  • ˆ

V(n)H ˜ Hc ˆ V(n) ˆ P

  • ≥ Γc
  • Tr
  • FcW(n)

+ σ2 , diag

  • ˆ

P

  • q =
  • qqH

q,

q = 1, · · · , NbNr, rank

  • ˆ

P

  • = 1

(12)

where ˆ P = ppH, q = vec (Φ), p=vec (P) ∈ CNbNr×1, ˆ V(n) =block − diag(v(n)T , · · · , v(n)T ) ∈ CNb×NbNr, Φ = 1Nb×Nr/Nb

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Outline

1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion

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Simulations

3D beampattern of Pv:

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Simulations

SEE versus Pb:

5 10 15 20 0.09 0.1 0.11 0.12 0.13 0.14 0.15

Pb (dBmW) SEE (bps/Hz/Joule)

Proposed hybrid BF scheme Digital BF scheme [18]

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Simulations

SEE versus ∆:

2 4 6 8 10 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16

Wiretap Channel Uncertainty Bound  SEE (bps/Hz/Joule)

Proposed hybrid BF scheme Digital BF scheme [18]

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Outline

1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion

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Conclusion

We have proposed a hybrid BF scheme to achieve SEE maximization in STIN. To solve the original non-convex problem, we first used a discretization method to transform the constraints on the imperfect channel AoD into solvable

  • nes.

Then, an iterative BF algorithm based on the Charnes-Cooper method was conceived to solve the problem and obtain the digital and analog BF weight vectors. Finally, numerical results were given to demonstrate the superiority and effectiveness of the proposed hybrid BF scheme in comparison with an existing method.

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Introduction System Model Proposed BF Scheme Simulations Conclusion

Thank You!

Zhi Lin

zhi.lin4@mail.mcgill.ca

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