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* P. C. Weeraddana **M. Codreanu, **M. Latva-Aho, ***A. Ephremides

Multicell MISO Downlink Weighted Sum-Rate Maximization: A Distributed Approach. * P. C. Weeraddana **M. Codreanu, **M. Latva-Aho, ***A. Ephremides * KTH, Royal institute of Technology, Stockholm, Sweden ** CWC, University of Oulu, Finland ***University of Maryland, USA 2013.02.19.

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* P. C. Weeraddana **M. Codreanu, **M. Latva-Aho, ***A. Ephremides

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  1. Multicell MISO Downlink Weighted Sum-Rate Maximization: A Distributed Approach *P. C. Weeraddana **M. Codreanu, **M. Latva-Aho, ***A. Ephremides *KTH, Royal institute of Technology, Stockholm, Sweden **CWC, University of Oulu, Finland ***University of Maryland, USA 2013.02.19

  2. Motivation • Centralized RA requires gathering problem data at a central location -> huge overhead • Large-scale communication networks -> large-scale problems • Distributed solution methods are indeed desirable • Many local subproblems -> small problems • Coordination between subproblems -> light protocol CWC | Centre For Wireless Communications

  3. Motivation • WSRMax: a central component of many NW control and optimization methods, e.g., • Cross-layer control policies • NUM for wireless networks • MaxWeight link scheduling for wireless networks • power and rate control policies for wireless networks • achievable rate regions in wireless networks CWC | Centre For Wireless Communications

  4. Challenges 21.8.2014 CWC | Centre For Wireless Communications • WSRMax problem is nonconvex, in fact NP-hard • At least a suboptimal solution is desirable • Considering the most general wireless network (MANET) is indeed difficult • A particular case is infrastructure based wireless networks • Cellular networks • Coordinating entities • MS-BS, MS-MS, BS-BS • Coordination between subproblems -> light protocol 4

  5. Our contribution • Distributed algorithm for WSRMax for MISO interfering BC channel; BS-BS coordination required • Algorithm is based on primal decomposition methods and subgradient methods • Split the problem into subproblems and a master problem • local variables: Txbeamforming directions and power • global variables: out-of-cell interference power • Subproblems asynchronous (one for each BS) • variables: Txbeamforming directions and power • Master problem resolves out-of-cell interference (coupling) • P. C. Weeraddana, M. Codreanu, M. Latva-aho, and A. Ephremides, IEEE Transactions on Signal Processing, February, 2013 8/21/2014 CWC | Centre For Wireless Communications 5

  6. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 6

  7. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 7

  8. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 8

  9. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 9

  10. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 10

  11. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 11

  12. Key Idea 8/21/2014 CWC | Centre For Wireless Communications 12

  13. System model : number of BSs : set of BSs 10 11 3 : number of data streams 9 12 : set of data streams 7 1 2 6 3 : set of data streams of BS 4 8 2 5 1 : number of BS antennas : receiver node of d.s. : transmitter node of d.s. interference region Tx region 8/21/2014 CWC | Centre For Wireless Communications 13

  14. System model signal vector transmitted by BS : power : information symbol; , : beamforming vector; 8/21/2014 CWC | Centre For Wireless Communications 14

  15. System model signal received at intra-cell interference out-of-cell interference : channel; to : cir. symm. complex Gaussian noise; variance 8/21/2014 CWC | Centre For Wireless Communications 15

  16. System model received SINR of out-of-cell interference intra-cell interference : out-of-cell interference power; th BS to 8/21/2014 CWC | Centre For Wireless Communications 16

  17. System model 3 7 1 2 6 8 5 out-of-cell interference power, e.g., 8/21/2014 CWC | Centre For Wireless Communications 17

  18. System model 3 7 1 2 6 8 5 out-of-cell interference power, e.g., 8/21/2014 CWC | Centre For Wireless Communications 18

  19. System model 3 7 1 2 6 8 5 out-of-cell interference power, e.g., 8/21/2014 CWC | Centre For Wireless Communications 19

  20. System model 3 7 1 2 6 8 5 out-of-cell interference power, e.g., 8/21/2014 CWC | Centre For Wireless Communications 20

  21. System model 3 7 1 2 6 8 5 out-of-cell interference power, e.g., 8/21/2014 CWC | Centre For Wireless Communications 21

  22. System model received SINR of out-of-cell interference intra-cell interference : out-of-cell interference power; th BS to 8/21/2014 CWC | Centre For Wireless Communications 22

  23. System model received SINR of out-of-cell interference intra-cell interference : out-of-cell interference power (complicating variables) : set of out-of-cell interfering BSs that interferes 8/21/2014 CWC | Centre For Wireless Communications 23

  24. System model 3 7 1 2 6 8 5 e.g., 8/21/2014 CWC | Centre For Wireless Communications 24

  25. System model 10 11 3 9 12 7 1 2 6 3 4 8 2 5 1 e.g., : set of d.s. that are subject to out-of-cell interference 8/21/2014 CWC | Centre For Wireless Communications 25

  26. System model 10 11 3 9 12 7 1 2 6 3 4 8 2 5 1 e.g., : set of d.s. that are subject to out-of-cell interference 8/21/2014 CWC | Centre For Wireless Communications 26

  27. System model 3 9 12 1 2 6 6 e.g., : set of d.s. that are subject to out-of-cell interference 8/21/2014 CWC | Centre For Wireless Communications 27

  28. Problem formulation variables: and 8/21/2014 CWC | Centre For Wireless Communications 28

  29. Primal decomposition subproblems (for all ) : variables: master problem: variables: 8/21/2014 CWC | Centre For Wireless Communications 29

  30. Subproblem (BS optimization) 8/21/2014 CWC | Centre For Wireless Communications 30

  31. Subproblem variables: • The problem above is NP-hard • Suboptimal methods, approximations 8/21/2014 CWC | Centre For Wireless Communications 31

  32. Subproblem: key idea • The method is inspired from alternating convex optimization techniques • Fix beamforming directions • Approximate objective by an UB function • resultant problem is a GP; variables • Fix the resultant SINR values • Find beamforming directions , that can preserve the SINR values with a power margin • this can be cast as a SOCP • Iterate until a stopping criterion is satisfied 8/21/2014 CWC | Centre For Wireless Communications 32

  33. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 33

  34. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 34

  35. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 35

  36. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 36

  37. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 37

  38. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 38

  39. Subproblem: key idea 8/21/2014 CWC | Centre For Wireless Communications 39

  40. Master problem 8/21/2014 CWC | Centre For Wireless Communications 40

  41. Master problem variables: • Recall: subproblems are NP-hard -> we cannot even compute the master objective value • Suboptimal methods, approximations • Problem is nonconvex -> subgradient method alone fails 8/21/2014 CWC | Centre For Wireless Communications 41

  42. Master problem: key idea • The method is inspired from sequential convex approximation (upper bound) techniques • subgradient method is adopted to solve the resulting convex problems 8/21/2014 CWC | Centre For Wireless Communications 42

  43. Integrate master problem & subproblem • Increasingly important: • convex approximations mentioned above are such that we can always rely on the results of BS optimizations to compute a subgradient for the subgradient method. • thus, coordination of the BS optimizations 8/21/2014 CWC | Centre For Wireless Communications 43

  44. Integrate master problem & subproblem 8/21/2014 CWC | Centre For Wireless Communications 44

  45. Integrate master problem & subproblem • out-of-cell interference: • objective value computed by BS at ‘F’ : • we can show that • optimal sensitivity values of GP -> construct subgradient F convex subproblem 8/21/2014 CWC | Centre For Wireless Communications 45

  46. Integrate master problem & subproblem subgradient method: 8/21/2014 CWC | Centre For Wireless Communications 46

  47. Integrate master problem & subproblem Algorithm 1 (subproblem) Algorithm 2 (overall problem) 8/21/2014 CWC | Centre For Wireless Communications 47

  48. An example signaling frame structure note: in Alg.1 or subgradient method, ‘BS optimization GP’ is always carried out in our simulations: - fixed Alg.1 iterations ( ) - fixed subgrad iterations ( ) per switch Algorithm 2 (overall problem) 8/21/2014 CWC | Centre For Wireless Communications 48

  49. Numerical Examples channel gains: : distance from to : small scale fading coefficients SNR operating point: 21.8.2014 CWC | Centre For Wireless Communications 49

  50. Numerical Examples • -> the degree of BS coordination • note -> subgradient is not an ascent method • out-of-cell interference is resolved -> objective value is increased • smaller performs better compared to large • light backhaul signaling 21.8.2014 CWC | Centre For Wireless Communications 50

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