Message Passing in Ultra Dense Wireless Networks: Scalability and - PowerPoint PPT Presentation

Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality Angela Yingjun Zhang Joint work with Xiaojun Yuan and Congmin Fan Department of Information Engineering The Chinese University of Hong Kong May 2017 Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 1 / 45

Ultra Dense Wireless Networks Limited bandwidth resource ◮ Radio resource management ◮ Interference mitigation Cloud Data Center ◮ Innovative frequency reuse Processing Unit ◮ Multi-RAT Storage Unit Ultra-dense cells and devices RRH ◮ Mobility management ◮ Small cell discovery Fronthaul Backhaul ◮ User association Fog-RAN Cloud-RAN Limited backhaul/fronthaul ca- pacity Macrocell Energy efficiency and green net- Macrocell works Femtocell Picocell ◮ BS idling and selection ◮ Massive MIMO and CoMP ◮ Energy-efficient wireless and wired backhaul Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 2 / 45

Ultra Dense Wireless Networks: Goals and Challenges Network-wide optimization Cloud Data Center Horizontal and vertical coordina- Processing Unit tion Storage Unit RRH Backhaul Fronthaul Fog-RAN Cloud-RAN Macrocell Macrocell Femtocell Picocell Distribution Localization Coordination Y. J. Zhang, L. Qian, and J. Huang, “Monotonic Optimization in Communication and Networking Systems,” Foundations and Trends in Networking, vol. 7, no. 1, Oct. 2013. Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 3 / 45

Ultra Dense Wireless Networks: Goals and Challenges Network-wide optimization Cloud Data Center Horizontal and vertical coordina- Processing Unit tion Storage Unit RRH Low complexity and cost Fronthaul Backhaul Distribution and parallelization Fog-RAN Cloud-RAN Local vs. global information Macrocell Macrocell scalable system capacity Femtocell Picocell scalable system complexity Coordination Distribution Localization Scalability is what makes a large system worth investing in! Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 4 / 45

Dense Wireless Networks Modelled as Graphs R6 U4 R7 U3 Observed node R1 (RRH) R4 U6 U1 Unobserved node U2 (User) R2 R5 R3 U5 Learning on graphs for Graphs can model ◮ Statistical inference ◮ Coverage ◮ Estimation and detection ◮ Interference and conflicts ◮ Resource allocation ◮ Physical and logical topology ◮ Optimization ◮ ... ◮ ... Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 5 / 45

Factor Graph A factor graph is a bipartite graph that expresses the structure of factorization p ( x ) = Π s f ( x s ) where x s ’s are subsets of x . Example: p ( x ) = f A ( x 1 ) f B ( x 2 ) f C ( x 1 , x 2 , x 3 ) f D ( x 3 , x 4 ) f E ( x 3 , x 5 ) p k ( x k ) = � Marginalization: ¯ x \ x k p ( x ) . Maximization: ˆ p k ( x k ) = max x \ x k p ( x ) . Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 6 / 45

Message Passing, Belief Propagation Messages are exchanged between variable nodes and factor nodes ω k → a ( x k ) µ a → k ( x k ) x k f a f a x k Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 7 / 45

Message Passing, Belief Propagation Messages are exchanged between variable nodes and factor nodes ω k → a ( x k ) µ a → k ( x k ) x k f a f a x k Sum-Product rule � � � ω k → a ( x k ) = µ c → k ( x k ) µ a → k ( x k ) = f a ( x a ) ω j → a ( x j ) c ∈ N ( k ) \ a x a \ x k j ∈ N ( a ) \ k ω k → a ( x k ) µ a → k ( x k ) f a x k x k f a Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 7 / 45

Message Passing Compute the marginal of x k � p k ( x k ) = ¯ µ a → k ( x k ) a ∈ N ( k ) x k Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 8 / 45

Outline Full-scale collaborative signal detection in C-RANs ◮ Randomized Gaussian message passing for scalable signal detection Blind signal detection in sparse massive MIMO channels ◮ Achievable degree of freedom (DoF) ◮ Belief propagation algorithm for blind detection Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 9 / 45

Collaborative Signal Detection Received signal y = Hx + n MMSE detection V = ( HH H + N 0 I ) − 1 H x = V H y = V H Hx + V H n ˜ Challenges ◮ High computational complexity (e.g., O ( N 3 ) for MMSE detection). Complexity/Cost Network Size Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 10 / 45

Channel Sparsity = Scalability ? Antenna Selection [Mehanna’2013], [Hoy- dis’2013], [Wang’2015], [Liu’2014] Clustering [Papadogiannis’2008], [Zhang’ 2009], [Lee’2014] By converting HH H + N 0 I into a doubly bordered block diagonal matrix, the optimal computationally time is O ( N 2 ) by parallel computing. C. Fan, Y. J. Zhang , and X. Yuan, “Dynamic nested clustering for parallel PHY-layer pro- cessing in cloud-RANs,” IEEE Transactions on Wireless Commununications, vol. 15, no. 3, pp. 1881-1894, Mar. 2016. Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 11 / 45

Bipartite Graph Representation R6 U4 R7 U3 Observed node R1 (RRH) d 0 R4 U6 U1 Unobserved node RRH U2 (User) R2 R5 User R3 U5 d 0 Distance threshold The graph is random due to random locations of users. The graph is sparse but locally dense. Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 12 / 45

Inference Over a Bipartite Graph MMSE is equivalent to MAP in a Gaussian channel with Gaussian signals � x = arg max p ( x | y , H ) x = arg max p ( y 1 | x I 1 ) · · · p ( y n | x I n ) · · · p ( y N | x I N ) x × p ( x 1 ) · · · p ( x k ) · · · p ( x K ) , . . . . . . ( | x ) ( | ) p y p y ( | x ) p y x 1 I 4 I 7 I 1 7 4 Factor node Variable node x 1 x 2 x 3 x 4 x 5 x 6 Factor node p x ( ) p x ( ) p x ( ) p x ( ) p x ( ) p x ( ) 1 2 3 4 5 6 Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 13 / 45

Gaussian Message Passing Assumption: n ∼ CN ( 0 , N 0 I ) , x ∼ CN ( 0 , I ) Iteration: For all n, k such that H n,k � = 0 , compute   1 v ( t ) � | H n,j | 2 v ( t − 1) y n → x k =  N 0 + P x j → y n  P | H n,k | 2 j � = k   1 1 m ( t ) 2 � H n,j m ( t − 1) y n → x k =  y n − P x j → y n  1 2 H n,k P j � = k − 1   1 v ( t ) � x k → y n = + 1   v ( t ) y j → x k H j,k � =0 ,j � = n   m ( t ) y j → x k � m ( t ) x k → y n = v ( t ) x k → y n   v ( t ) y j → x k H j,k � =0 ,j � = n m ( t +1) = Ωm ( t ) + z , where Ω is a function of the limit point of variances. Y. Weiss and W. T. Freeman, ”Correctness of belief propagation in Gaussian graphical models for arbitrary topology,” Neural Computation , vol. 13, no. 10, pp. 2173-2200, 2001. Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 14 / 45

Message Passing for C-RAN: Scalability Complexity per iteration: linear with the network size ✓ Convergence ? Convergence speed ? Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 15 / 45

Convergence Convergence is guaranteed only The factor graph of C-RAN is loopy when the factor graph is a tree Likely to converge when the factor The factor graph of C-RAN is graph is ◮ locally dense ◮ locally sparse ◮ globally sparse with distance- ◮ with i.i.d. edge weights dependent edge weights Gaussian Message Passing converges In C-RAN when ◮ A is not always diagonally domi- ◮ A = HH H + N 0 I is strictly diag- nant onally dominant ◮ ρ ( Ω ) > 1 sometimes ◮ ρ ( Ω ) < 1 1 Empirical probability of convergence 0.995 0.99 0.985 0.98 0.975 0.97 100 200 300 400 500 600 700 800 Number of RRHs m ( t +1) = Ωm ( t ) + z Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 16 / 45

Asynchronous Gaussian Message Passing Synchronous vs. Asynchronous ⇒ Jacobi vs. Gauss-Seidel Example: update order { 1 , 3 , 2 , 4 } p y ( | x ) p y ( | x ) p y ( | x ) p y ( | x ) 1 I 2 I 3 I 4 I 1 2 3 4 Factor node Variable node x 1 x 2 x 3 x 4 Factor node p x ( ) p x ( ) p x ( ) p x ( ) 1 2 3 4 Angela Yingjun Zhang (IE, CUHK) Message Passing in Ultra Dense Wireless Networks: Scalability and Optimality May 2017 17 / 45