Trust Degree Based Beamforming for Multi-Antenna Cooperative Communication Systems

Transcription

1 Introduction Main Results Simulation Conclusions Trust Degree Based Beamforming for Multi-Antenna Cooperative Communication Systems Mojtaba Vaezi joint work with H. Inaltekin, W. Shin, H. V. Poor, and J. Zhang Department of Electrical Engineering Princeton University Globecom 17, Singapore December 5, 2017 December 11, 2017 M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 1

2 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Mobile/Social Networks - Motivation A salient characteristic of mobile data networks: person behind each device Mobile Data Networks Physical coupling between mobile devices Virtual coupling among the users behind these devices Virtual ties, in many ways, shape the data traffic flows and quality-of-service (QoS) requirements in the physical domain. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 2

3 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Mobile/Social Networks - Motivation A salient characteristic of mobile data networks: person behind each device Mobile Data Networks Physical coupling between mobile devices Virtual coupling among the users behind these devices Virtual ties, in many ways, shape the data traffic flows and quality-of-service (QoS) requirements in the physical domain. Key questions How can we model/quantify social-physical interactions in communication networks? - Trust degrees How can we exploit social connections to improve physical communication performance? - cooperation among nodes to increase rate, security, access, etc. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 3

4 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation System Model T X H.. RN. h physical connections g R X M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 4

5 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation System Model T X H.. RN. h physical connections Node g R X # antenna source (S) relay (R) destination (D) 1 N s N r - channel state information (CSI) is known at the transmitters T X (α 1, β 1 )... RN. (α 0, β 0 ) (α 2, β 2 ) R X virtual (social) connections M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 5

6 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation System Model T X H.. RN. h physical connections Node g R X # antenna source (S) relay (R) destination (D) 1 N s N r - channel state information (CSI) is known at the transmitters T X (α 1, β 1 )... RN. (α 0, β 0 ) (α 2, β 2 ) R X virtual (social) connections social system is modeled by trust degree trust degree is a level of belief that one node can help the other node for relaying M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 6

7 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation System Model w s T X H. w r. RN. h g R X Why beamforming? To improve signal-to-noise ratio (SNR) signal-to-interference-plus-noise ratio (SINR) An optimal beamformer aims to balance between the direct link and the cooperating link as well as respecting the trust degree. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 7

8 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Physical Channel T X H.. RN. h physical connections (a two-hop relay) R X symbol x s is first multiplied by a beamforming vector w s before being transmitted at S Source Transmission: received signal at D and R y SD = h t w s x s + n SD, y SR = H t w s x s + n SR, -n SD CN (0, 1), n SR CN (0, I) are complex Gaussian noise -w s is beamforming vector received SNRs at D and R γ SD = h t w s 2 P s, γ SR = H t w s 2 P s, and C SD = log 2 (1 + γ SD ), C SR = log 2 (1 + γ SR ). M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 8

9 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Physical Channel T X.. RN. physical connections (a two-hop relay) decode-and-forward (DF) relaying g R X Relay Transmission: y RD = g t w r x r + n RD, where n RD CN (0, 1). - received SNR at D γ RD = g t w r 2 P r. -D can combine the signal received from S and R C D = log 2 (1 + γ SD + γ RD ). M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 9

10 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Physical Channel T X H.. RN. h g R X Relay may work in the full-duplex of half-duplex mod Half-duplex case is more practical but more involved (see [Vaezi et al. 17]) DF Achievable Rate: An achievable rate for full-duplex DF relay system is given by [Host-Madsen-Zhang 05] C DF = min{c SR, C D } { } = min log 2 (1 + γ SR ), log 2 (1 + γ SD + γ RD ). Beamforming design: is extensively studied [Tang-Hua 07],[Ryu-Choi 08],[ Xiong et al. 14] M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 10

11 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation Social-Physical Cooperation T X H (α 1, β 1 ).. RN. h (α 0, β 0 ) (α 2, β 2 ) g R X For each link i, (α i, β i ) represents a virtual (social) tie [Ryu-Lee-Quek 15] α i : the probability of cooperation β i : the fraction of power a node uses for relaying Physical-Virtual Cooperation Achievable Rate: the expected trust degree based rate R T = α 1 C DF + (1 α 1 )C SD { } = α 1 min log 2 (1 + γ SR ), log 2 (1 + γ SD + γ RD ) + ᾱ 1 log 2 (1 + γ SD ) (1) Optimal beamforming is open in general M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 11

12 Introduction Main Results Simulation Conclusions Motivation System Model Problem Formulation A New Problem Formulation Our goal is to jointly optimize the beamforming vectors w s and w r as well as α to maximize R T, i.e., where R T is defined in (1). max w s,w r,α R T s.t. w s 2 1, (2) w r 2 1, 0 α α 1, This optimization problem is non-convex α = 1 = MIMO DF realy MISO case (N r = 1) with α = α 1 [Ryu-Lee-Quek 15] M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 12

13 Introduction Main Results Simulation Conclusions Observations Solution Special Cases This Talk H w s T X. w r. RN. h g R X Our observations and contribution Question find optimal w s, w s, and α α = α 1 is not necessarily optimal; we find optimal α Maximal ratio transmission (MRT) beamformer is optimal at relay, i.e., w r = g g Optimal w s is found either in closed-form or heuristically The same approach is applicable to the half-duplex case M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 13

14 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Optimal Trust Degree and w r Lemma 1: Maximal ratio transmission (MRT) beamformer is optimal at the relay, i.e., w r = g g. Proof: w r merely affects γ RD (γ SD and γ SR are independent of w r ) M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 14

15 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Optimal Trust Degree and w r Lemma 1: Maximal ratio transmission (MRT) beamformer is optimal at the relay, i.e., w r = g g. Proof: w r merely affects γ RD (γ SD and γ SR are independent of w r ) M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 15

16 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Optimal Trust Degree and w r Lemma 1: Maximal ratio transmission (MRT) beamformer is optimal at the relay, i.e., w r = g g. Proof: w r merely affects γ RD (γ SD and γ SR are independent of w r ) Lemma 2: The optimal value of α is either zero or α 1. Proof: R T is linear with α. Thus, its maximum happens in either of the ends. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 16

17 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Optimal Trust Degree and w r Lemma 1: Maximal ratio transmission (MRT) beamformer is optimal at the relay, i.e., w r = g g. Proof: w r merely affects γ RD (γ SD and γ SR are independent of w r ) Lemma 2: The optimal value of α is either zero or α 1. Proof: R T is linear with α. Thus, its maximum happens in either of the ends. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 17

18 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Optimal Trust Degree and w r Lemma 1: Maximal ratio transmission (MRT) beamformer is optimal at the relay, i.e., w r = g g. Proof: w r merely affects γ RD (γ SD and γ SR are independent of w r ) Lemma 2: The optimal value of α is either zero or α 1. Proof: R T is linear with α. Thus, its maximum happens in either of the ends. Lemma 3: For α = 0, MRT is optimal at the source (w s = h h ). Proof: For α = 0 direct transmission is optimal and R T is linear with α. Thus, its maximum happens in either of the ends M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 18

19 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Solving the New Problem where The only case left is to find w s for α = 1. Thus, the optimization problem is reduced to max w s R T s.t. w s 2 1 { } R T = α 1 min log 2 (1 + γ SR ), log 2 (1 + γ SD + γrd) + ᾱ 1 log 2 (1 + γ SD ) An optimal beamformer must balance between the direct link (γ SD ) and the cooperating link (γ SR ). M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 19

20 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Precoding and Power Allocation w s depends on γ SD and γ SR which are functions of h and H Let w s = ch + N r i=1 c ih i, where h i is the ith column of H Intractable! as h and the h i s are not orthogonal We compute the following orthogonal vectors w h h w i h i h i, i {1,..., N r}. By definition, we have w w i, i.e., w.w i = 0 i {1,..., N r }. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 20

21 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Special Cases Theorem The transmit beamformer that maximizes the achievable rate can be represented as w s = N r γ 0 w + γi w i in which w and the w i s are orthonormal bases spanning the column space of h and H, and γ 0 + γ γ Nr = 1. i=1 Proof. We prove this Theorem by contradiction. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 21

22 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Special Cases Remark 1: We only need to find N r real numbers whereas in the original problem we needed to find N s complex numbers. Usually N s N r and N r as relay nodes are assumed to be network users. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 22

23 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Special Cases Remark 1: We only need to find N r real numbers whereas in the original problem we needed to find N s complex numbers. Usually N s N r and N r as relay nodes are assumed to be network users. Remark 2: For the MISO case (N r = 1), w = w 1. Then, to find w s, we only need to find. γ 0. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 23

24 Introduction Main Results Simulation Conclusions Observations Solution Special Cases Special Cases Remark 1: We only need to find N r real numbers whereas in the original problem we needed to find N s complex numbers. Usually N s N r and N r as relay nodes are assumed to be network users. Remark 2: For the MISO case (N r = 1), w = w 1. Then, to find w s, we only need to find. γ 0. Remark 3: Ignoring social connection (α 1 = 0), the system and solution reduces to those of DF relay. M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 24

25 Introduction Main Results Simulation Conclusions Simulation Results Achievable Rate (bps/hz) Optimized α Ryu et al. BF [7] Direct transmission Transmission SNR (db) Achievable Rate (bps/hz) Proposed BF (Nr =4) Proposed BF (Nr =2) Proposed BF (Nr =1) Direct transmission Transmission SNR (db) N s = 4, N r = 1, α 1 = 0.7 N s = 4, α 1 = 0.7 (σ 2 h, σ 2 H, σ 2 g) = ( 5, 4, 10)dB (σ 2 h, σ 2 H, σ 2 g) = ( 5, 0, 10)dB M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 25

26 Introduction Main Results Simulation Conclusions Conclusions Summary Design communication systems with consideration of social links beside physical connection Cooperative communication can largely benefit from social connections modeled by trust degree The underlying problem in non-convex and hard to solve Linear beamforming is designed to maximize achievable rate Future Work This kind of approaches does not scale with network nodes Can we use machine learning for this purpose? M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 26

27 Introduction Main Results Simulation Conclusions Thank you! M. Vaezi (Princeton) Trust Degree Based Beamforming Globecom 17 27