Cooperative Base Station Coloring Achieving dynamic clustering gain from static partitions

Transcription

1 Cooperative Base Station Coloring Achieving dynamic clustering gain from static partitions Robert W. Heath Jr. Wireless Networking and Communications Group Department of Electrical and Computer Engineering The University of Texas at Austin Joint work with Jeonghun Park and Namyoon Lee Funded by Huawei and NSF-CCF

2 Out-of-cluster interference is a fundamental limit Spectral Efficiency Spectral efficiency ceiling at high SNR It is impossible to reap benefits from full coordination of all the base stations SNR There are some benefits to coordination at moderate SNRs A. Lozano, R. W. Heath, and J. Andrews, Fundamental Limits of Cooperation, IEEE Transactions on Information Theory, 013

3 Static clustering inspired by backhaul network Robert W. Heath Jr. (015) L user at the cluster edge J user at the cluster center u Predefined cooperation clusters, heavily investigated in prior work* u Value of clustering depends heavily on the locations of the users O. Simeone, O. Somekh, H. V. Poor, and S. Shamai, Local Base Station Cooperation Via Finite-Capacity Links for the Uplink of Linear Cellular Networks, IEEE Transactions on Information Theory, 009. J. Zhang, R. Chen, J. G. Andrews, A. Ghosh, and R. W. Heath, Networked MIMO with Clustered Linear Precoding, IEEE Transactions on Wireless Communications, 009 K. Huang and J. G. Andrews, An Analytical Framework for Multicell Cooperation via Stochastic Geometry and Large Deviations, IEEE Transactions on Information Theory, 013 3

4 Dynamic clustering centered around the user Robert W. Heath Jr. (015) J user also at the cluster center J user at the cluster center Base station is conflicted u Dynamic cooperation clusters, also investigated in prior work* u Creates a challenging scheduling problem A. Papadogiannis, D. Gesbert, and E. Hardouin, A Dynamic Clustering Approach in Wireless Networks with Multi-Cell Cooperative Processing, in Proc. of IEEE ICC, 008 N. Lee, R. W. Heath Jr., D. Morales, and A. Lozano, Base station cooperation with dynamic clustering in super-dense cloud-ran, in Proc. of IEEE Globecom Workshop, 013. N. Lee, D. Morales, A. Lozano, and R. W. Heath, Spectral Efficiency of Dynamic Coordinated Beamforming, IEEE Transactions on Wireless Communications, 015 4

5 Alternative is semi-static clustering Robert W. Heath Jr. (015) Dynamic clustering Static clustering Semi-static clustering multiple predefined cluster patterns Semi-static clustering gives the benefits of dynamic clustering with low complexity 5

6 Semi-static clustering uses cluster patterns base stations subscribers coordination clusters f 1 f f 3 f 4 Different carriers assigned to each cluster 6

7 How are cluster patterns formed in irregular topologies? u In practice, BS topology is irregular, patterns not obvious Base station u Needs framework to design and analyze cluster pattern in irregular network topologies Y coordinate X coordinate 7

8 Graph theoretic approach for interference models 1 st order Voronoi (frequency reuse) d 9 d 10 d 8 d 1 d 0 d d 4 nd order Voronoi (Delaunay triangulation graph) V (d 0, d 10 ) d 9 d 10 V (d 0, d 1 ) d 1 V (d 0, d 9 ) d 0 d 4 d 8 d V (d 0, d ) d 7 d6 d 5 d 7 V (d 0, d 8 ) d 6 d 5 Delaunay triangulation (Dual graph) Characterization of cooperation set by the graph 8

9 Avoid base station conflicts u Our approach is edge coloring ª E : set of edges, V : set of vertices, and v, w, u V ª Design a coloring function f C (E) : E! {1,..., } such that if v 6= w and (u, v), (u, w) E then c (u, v) 6= c (u, w) u Other work that uses graph coloring ª Training resource allocation for cooperative networks [Chen et al.] ª Resource allocation for dynamic clustering [Chang et al.] Z. Chen, X. Hou, and C. Yang, Training Resource Allocation for User-centric Base-station Cooperation Networks, IEEE Transactions on Vehicular Technology, 015. Y. Chang, Z. Tao, J. Zhang, and C. Kuo, A Graph-Based Approach to Multi-Cell OFDMA Downlink Resource Allocation, in Proc. IEEE Globecom, 008. Y. Chang, Z. Tao, J. Zhang, and C. Kuo, A Graph Approach to Dynamic Fractional Frequency Reuse (FFR) in Multi-Cell OFDMA Networks, in Proc. IEEE ICC, 009. Weisstein, Eric W. "Edge Coloring." From MathWorld--A Wolfram Web Resource. 9

10 Use coloring to build pair-wise cooperation sets 1/3 V (d 1, ) V (d, ) V (d 0, ) d 0 d 0 V (d 0, d 1 ) V (d 0, d ) d 1 d 1. Tessellate a network plane with nd order Voronoi cells d 1 d V (d 1, d ) J. Park, N. Lee, and R. W. Heath, Cooperative Base Station Coloring for Pair-wise Multicell Coordination, submitted to IEEE Transactions on Communications, available on ArXiv 10

11 Use coloring to build pair-wise cooperation sets /3 Delaunay triangulation V (d 1, ) V (d, ) V (d 0, ) BSs locations G =(V, E) d 0 V (d 0, d 1 ) V (d 0, d ). Draw a graph d 1 d V (d 1, d ) P P 3 P 1 3. Solve edge-coloring for the drawn graph (color = pattern) P 1 d 0 P P 3 d 1 d 11

12 Use coloring to build pair-wise cooperation sets 3/3 No conflict with edge-coloring! P 1 : P : P 3 : } Different time-frequency resources for different patterns V (d 1, ) V (d, ) V (d 0, ) d 0 V (d 0, d 1 ) V (d 0, d ) d 1 d d 0 4. Serve a user according to designed pattern V (d 1, d ) d 1 d 1

13 General network application Follow same procedure Y coordinate d 1 d 5 d 0!!!!:!Base!sta(on! station!!!!:!user! d 4 1. Tessellate a network plane with nd order Voronoi cell 5 4 Y coordinate Base station X coordinate. Draw a graph 0 1 d X coordinate Y coordinate Base station X coordinate Y coordinate d P 5 P 7 d 4 P d 8 P 1 P P X coordinate P 6 d 0 P 3 P 5 P 4 d 5 P 5 d 6 P 1 P P 1 3. Solve edge-coloring for the drawn graph (color = pattern) d 7 P 1 P 13

14 How many resources are required in the network? u Related to number of colors for edge-coloring (chromatic index) u Vizing s theorem ª A simple planar graph of maximum degree Δ has chromatic index Δ or Δ+1 in general ª Δ means the maximum number of connected edges to a vertex ª The required resources are dominated by Δ Need Δ+1 time-frequency resources to cover all the clusters 14

15 Example for Vizing s theorem Number of colors =5 Maximum degree =5 Edge Coloring Vizing s theorem holds! Maximum degree determines the number of colors Problem Only one vertex with large degrees can cause color (resource) explosion! 15

16 Edge-cutting algorithm u If one vertex (BS) that has large Δ can cause resource explosion u Can improve the network performance by sacrificing a few users P 7 d 4 P 1 P 7 d 4 P 1 Save the resource of P 6 P d P 6 P 1 P P 4 Edge Cutting P d P 6 P 1 P P 4 d 0 P 3 d 5 d P 5 P 0 d 5 5 P 5 d 6 P 5 d 6 P 4 P P 1 P 4 P 1 P 1 P P 1 d P 5 8 d 7 P P 3 d P 5 8 d 7 P Users here cannot be protected 16

17 Models for analysis u Signal model y` = kd 0 k / T h`0 V`0s`0 + kd j k / T h`j V`js`j + X kd v k / T h`v V`vs`v +n` {z } {z } d v N`\C` desired signal intra cluster interference {z } out of cluster interference Distance from a BS Channel vector to our user hì C N, CN (0, 1) u Intra-cluster interference management method ª Coordinated beamforming (CBF) maximize : h`0 T v`0,k Precoding matrix Vì = vì,1,...,vì,k, vì,k C N, vì,k =1 ` : cluster pattern index subject to : h`0 T v`0,k 0 = 0 for k 0 6= k h`j T v`j,k 00 = 0 for dj C` and 1 apple k 00 apple K 17

18 Analyzing bounds on average achievable rates u Lower bound on ergodic spectral efficiency (fixed geometry) E apple 1 L log 1 + SINR ` 1 L log 1+ exp ( (N K + 1)) K P d v D` (kd v k / kd 0 k) + kd 0 k /SNR! # of users where D` = {d v d v N`\C`} # of used colors (resources) cluster pattern cluster u Lower bound on ergodic spectral efficiency (random geometry, PPP) E apple apple 1 1 L log 1 + SIR ` E L log K exp ( (N K + 1))! J. Park, N. Lee, and R. W. Heath, Cooperative Base Station Coloring for Pair-wise Multicell Coordination, submitted to IEEE Transactions on Communications, available on ArXiv 18

19 Proof sketch u Lower bound ª For non-negative random variable S and I, E applelog 1+ S I +1 u Calculating E [I], E 4kd 1 k =KE r1,r X d i \B(0,kd k) 4E \B(0,r ) =KE r1,r appler 1 = 8K 4 Z 1 4r 1 kd i k X log 1+ hì d i \B(0,r ) r r 1 dr = K T Vì 3 ee[ln S] E [I + 1]. 5 = KE 4kd 1 k X d i \B(0,kd k) 33 kd i k kd 1 k = r 1, kd k = r 55 Z 1 r =0 Z r r 1 =0 4( ) e kd i k r r +1 1 r 3 dr 1 dr User communicates with two nearest BSs = protection ball B (0, kd k)

20 Other approaches for performance comparison Robert W. Heath Jr. (015) BS 1 BS BS 1 BS BS 1 BS BS 3 BS 4 BS 3 BS 4 BS 3 BS 4 Single cell operation No interference management is applied Fractional frequency reuse Adjacent BS uses different sub-band Random clustering BS cluster is made with arbitrary rule (No coloring) Conventional strategies - square grid model application example 0

21 Comparison results u Ergodic spectral efficiency of edge users Performance improvement by edge-cutting Sum ergodic spectral efficiency (bps/hz) Proposed Clustering (simulation) Proposed Clustering (analytical lower bound) Random Clustering Fractional Frequency Reuse Single Cell Operation SNR (db) Symmetric network case No need edge-cutting x Ergodic spectral efficiency (bps/hz) Proposed Clustering (simulation Proposed Clustering (analytical lower bound) Proposed Clustering with EC =7 Proposed Clustering with EC =10 Proposed Clustering with EC =3 Random Clustering Fractional Frequency Reuse Single Cell Operation SNR (db) Asymmetric network case More irregular Edge-cutting might be needed 1.5 1

22 Concluding remarks u Main benefits ª Any active user can communicate with two nearest BSs ª No BS is conflicted ª Can be combined with scheduling for greater gains u Possible drawbacks and solutions ª Only useful for pairwise cooperation? Two is enough* ª Edge-coloring demands too much complexity? No done frequently ª Too many resources can be required? Edge cutting u Application ª Carrier aggregation u Future direction ª Application to millimeter wave to reduce blockage effects N. Lee, D. Morales, A. Lozano, and R. W. Heath, Spectral Efficiency of Dynamic Coordinated Beamforming, IEEE Transactions on Wireless Communications, 015

23 Questions 3