Frequency Assignment for Cellular Mobile Systems Using Constraint Satisfaction Techniques

1. Frequency Assignment for Cellular Mobile Systems Using Constraint Satisfaction Techniques Yokoo & Hirayama principles and practice of constraint programming-2000 Mythri Telakapalli Lecture slides x

2. Outline • Introduction • Problem description:Constraints • CSP formulation • Mathematical representation • Optimization task • Strategy • Basic algorithm • Ordering heuristics • Example • Limited discrepancy search • Evaluation and conclusions • Future research Lecture slides x

3. Introduction • Mobile Communication Systems • Division of geographical region into cells (areas) • Base Station controls mobile users in each cell The network is divided into 7 cells a 2 3 4 1 b Basestation 5 6 7 Lecture slides x

4. Introduction • Satisfying demands (call requests) of the mobile users by assigning frequencies to each cell • Frequency (bandwidth or spectrum) assignment problem Lecture slides x

5. 1 1 2 Figure The network is divided into 7 cells Co-site constraint f1 d f2 Co-channel constraint f 1 2 f1 f2 f 7 Adjacent channel constraint Lecture slides x

6. 1 Problem description: Constraints • Co-site constraint: pair of frequency assigned to same cell should have some separation f1 d f2 Lecture slides x

7. 1 2 Problem description: Constraints Adjacent channel constraint: Adjacent frequencies cannot be assigned to adjacent cells f1 f2 Lecture slides x

8. 1 1 2 Figure The network is divided into 7 cells Co-site constraint f1 d Co-channel constraint f2 f 1 2 f1 f2 f 7 Adjacent channel constraint Lecture slides x

9. Problem description: Constraints • Co-channel constraint: same frequency cannot be assigned to pairs of cells that are geographically close (interference) f 1 2 f 7 Lecture slides x

10. CSP formulation • Each cell is taken as a variable • The set of available frequencies is taken as a domain • Based on the three types of interference constraints mentioned before, the separation constraints are formed for all variables • The solution is said to be found if the demands are fully satisfied for all cells, i.e. if the number of call requests in each cell is equal to the number of frequencies assigned in that cell by satisfying the constraints. Lecture slides x

11. 1 2 3 4 5 6 7 8 9 10 fmax a a Cell1 a Cell2 a a Cell3 Cell4 a a a Mathematical representation • N : Number of Cells • 1,2,3,…, : Frequencies as positive integers • : The number of requested calls (demands) in cell I • : The frequency separation between a call in cell I and a call in cell j d1 = 2 d2=1 d3=2 d4=3 Lecture slides x

12. Optimization task The Goal is to find, • The frequency assigned to the kth call in cell i • satisfying the separation constraints, • for all i,j,k,l except for i = j and k = l, • While minimizing the maximum number of frequencies used in each cell Lecture slides x

13. Cell1 Cell2 3 2 1 2 2 3 1 Cell3 Cell4 Basic algorithm Example:- Lecture slides x

14. 1 2 3 4 5 6 7 8 9 10 11 f u u a a Cell1 a Cell2 f a a Cell3 Cell4 a f a a Basic Algorithm a: assigned u: unused f: forbidden Lecture slides x

15. Strategy • Depth-first search, backtracking and forward checking • Branch & bound • Various ordering heuristics • Main procedures • Reduce-Frequency • Backtrack • cell-ordering heuristic • frequency-ordering heuristic:limited-discrepancy search • Tools: • Labels: assigned (a), unused (u), forbidden(f) • Stack for storing assignments <label, Cp, Fp> • Vector for the frequencies Lecture slides x

16. Basic algorithm 1. If (Demands satisfied), call Reduce-Frequency 2. If (~Demand satisfied), call Backtrack 3. CpCell-ordering heuristic 4. Fpfrequency-ordering heuristicfor CELLp 5. Set the vector element of the corresponding to Fp to assigned Vector-Cp[Fp]  a 6. Push (“a”, Cp, Fp) to stack 7.Propagate the constraints and go to step-1 Lecture slides x

17. Ordering heuristics • Cell-ordering heuristic • Least Domain • Smallest Average Available Frequencies AAF = , i is the cell number • Largest Generalized Weighted Degree GWD = • Combination of smaller AAF and larger GWD • Frequency-ordering heuristic • First Free Frequency • Least-Impact • Limited-Discrepancy Search Lecture slides x

18. Cell1 Cell2 3 2 1 2 2 3 1 Cell3 Cell4 Basic Algorithm Example:- Lecture slides x

19. 1 2 3 4 5 6 7 8 9 10 11 a a Cell1 a Cell2 a a Cell3 Cell4 a a a Basic Algorithm a: assigned u: unused f: forbidden Lecture slides x

20. Limited-Discrepancv seach Lecture slides x

21. Evaluation • Tested with standard benchmark problems called as Philadelphia problems • His method obtains better equivalent solutions compared to other methods implemented in FASoft • Tabu search, • Simulated annealing, • Sequential methods and • NN Lecture slides x

22. Comparison of Solution Quality (Philadelphia Problems) Lecture slides x

23. Conclusion • A new algorithm (depth-first branch and bound search) for solving frequency assignment problem • Powerful cell ordering heuristic and limited discrepancy search • Better solutions found on standard benchmark problems • Appropriate problem representation and heuristics are required when applied to realistic problems Lecture slides x

24. Future Research • Setting algorithm parameters dynamically based on problem instances desired • Including local consistency algorithm • Applying limited discrepancy search for cell ordering heuristic • Using hybrid algorithms of backtracking and iterative improvement Lecture slides x