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 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 Z. Lin, et al . - AEU 1/25
Introduction System Model Proposed BF Scheme Simulations Conclusion Outline 1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion Z. Lin, et al . - AEU 2/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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 Z. Lin, et al . - AEU 3/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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. Z. Lin, et al . - AEU 4/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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 Z. Lin, et al . - AEU 5/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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. Z. Lin, et al . - AEU 6/25
Introduction System Model Proposed BF Scheme Simulations Conclusion Outline 1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion Z. Lin, et al . - AEU 7/25
Introduction System Model Proposed BF Scheme Simulations Conclusion System Model System Model of the considered STIN: The GEO satellite serves an earth station (ES) in the presence of 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. Signal link SAT Green Interference link Wiretap link Control link BS ES Gateway K Eves CU Terrestrial Core Network Z. Lin, et al . - AEU 8/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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 � 1 f = C L G r r ⊙ b (1) 2 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 ( θ 0 , ϕ 0 ) ρ 0 a h ( θ 0 , ϕ 0 ) ⊗ a v ( θ 0 ) J (2) � 1 � � + g ( θ j , ϕ j ) ρ j a h ( θ j , ϕ j ) ⊗ a v ( θ j ) . J j =1 Z. Lin, et al . - AEU 9/25
Introduction System Model Proposed BF Scheme Simulations Conclusion System Model Channel Model Steering vector a h ( θ, ϕ ) and a v ( θ ) denote the horizontal and vertical array steering vectors (SVs) of the UPA, which are, respectively, given by � e − iβ (( N 1 − 1)/2) d 1 sin θ cos ϕ , · · · a h ( θ, ϕ ) = (3a) , e + iβ (( N 1 − 1)/2) d 1 sin θ cos ϕ � T , e − iβ (( N 2 − 1)/2) d 2 cos θ , · · · , e + iβ (( N 2 − 1)/2) d 2 cos θ � T . � a v ( θ )= (3b) Z. Lin, et al . - AEU 10/25
Introduction System Model Proposed BF Scheme Simulations Conclusion System Model Signal Models The received signals at the CU, ES, and k -th Eve are, respectively, expressed as y c ( t ) = h H c Pv x ( t ) + f H c w s ( t ) + n c ( t ) , y s ( t ) = f H s w s ( t ) + n s ( t ) , (4) y k ( t ) = f H k w s ( t ) + h H k Pv x ( t ) + n k ( t ) Then, the SINR at the CU, ES, and k -th Eve are given by � 2 � 2 � 2 � � � � � � � h H � f H � f H c Pv s w k w γ c = , γ s = , γ k = . (5) c w | 2 + σ 2 k Pv | 2 + σ 2 σ 2 | f H | h H s c k Z. Lin, et al . - AEU 11/25
Introduction System Model Proposed BF Scheme Simulations Conclusion System Model The achievable secrecy rate of the ES is given by � + � R s = log 2 (1 + γ s ) − k ∈{ 1 , ··· ,K } log 2 (1 + γ k ) max (6) The total power consumption of the considered system is modeled as P tot = η 1 � w � 2 + η 2 � v � 2 + P S + P B (7) Z. Lin, et al . - AEU 12/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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 � � � � θ L k , θ U ϕ L k , ϕ U by θ k ∈ and ϕ k ∈ , the optimization k k problem can be formulated as w , v , P min max R s /P tot (8a) ∆ k s . t . γ c ≥ Γ c , (8b) γ s ≥ Γ s , (8c) 2 = 1 /N b , i = 1 , · · · , N b , j = 1 , · · · , N r , � � � [ P ] i,j (8d) � � � � v � 2 F ≤ P b , � w � 2 F ≤ P s (8e) Z. Lin, et al . - AEU 13/25
Introduction System Model Proposed BF Scheme Simulations Conclusion Outline 1 Introduction 2 System Model 3 Proposed BF Scheme 4 Simulations 5 Conclusion Z. Lin, et al . - AEU 14/25
Introduction System Model Proposed BF Scheme Simulations Conclusion 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 � � θ L k , θ U spaced values within their respective range θ k ∈ and k � � ϕ L k , ϕ U ϕ k ∈ , as given by k θ ( i ) = θ L k + i ∆ θ, i = 0 , · · · , M 1 , k (9) ϕ ( j ) = ϕ L k + j ∆ ϕ, j = 0 , · · · , M 2 k where ∆ θ = ( θ U k − θ L k ) /M 1 and ∆ ϕ = ( ϕ U k − ϕ L k ) /M 2 . j =0 µ i,j H ( i,j ) and Then, we define ˜ H = � M 1 � M 2 i =0 h ( i,j ) � H , j =0 µ i,j F ( i,j ) , where H ( i,j ) = h ( i,j ) � ˜ F = � M 1 � M 2 i =0 f ( i,j ) � H , µ i,j = F ( i,j ) = f ( i,j ) � 1 ( M 1 +1)( M 2 +1) . By using these averaged channel matrices in problem (8) instead of the imperfect ones, the minimization over ∆ k can be removed. Z. Lin, et al . - AEU 15/25
Introduction System Model Proposed BF Scheme Simulations Conclusion Robust BF Scheme By invoking the Charnes-Cooper approach and introducing auxiliary variables α and τ , (8) can be further transformed as σ 2 + Tr ( F s W ) � � W , V , P τ − 1 log 2 max (10a) α s . t . η 1 Tr ( W ) + η 2 Tr ( V ) + P S + P B = τ, (10b) Tr � ˜ F k W � + σ 2 ≤ α, ∀ k, (10c) P H ˜ Tr � H k PV � P H H c PV � Tr � � Tr ( F c W ) + σ 2 � − Γ c ≥ 0 , (10d) Tr ( F s W ) − Γ s σ 2 ≥ 0 , (10e) � 2 = 1 /N b , i = 1 , · · · , N b , j = 1 , · · · , N r , � � � [ P ] i,j (10f) Tr ( W ) ≤ P s , Tr ( V ) ≤ P b , (10g) rank ( W ) = 1 , rank ( V ) = 1 (10h) Tr ( H ir,k W k, 1 ) where a k = . σ 2 ir,k Z. Lin, et al . - AEU 16/25
Introduction System Model Proposed BF Scheme Simulations Conclusion Robust BF Scheme Iteratively Solving W The optimization problem for the digital beamforming weight vector can be expressed as � σ 2 + Tr ( F s W ) � τ − 1 W , V ,τ,α log 2 max (11a) α s . t . η 1 Tr ( W ) + η 2 Tr ( V ) + P S + P B = τ, (11b) � ˜ � Tr F k W + σ 2 ≤ α, ∀ k, (11c) P ( n ) H ˜ � � Tr H k P ( n ) V � � P ( n ) H H c P ( n ) V Tr ( F c W ) + σ 2 � � Tr − Γ c ≥ 0 , (11d) Tr ( F s W ) − Γ s σ 2 ≥ 0 , (11e) Tr ( W ) ≤ P s , Tr ( V ) ≤ P b , (11f) rank ( W ) = 1 , rank ( V ) = 1 (11g) Z. Lin, et al . - AEU 17/25
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