A Shifting Strategy for Dynamic Channel Assignment under Spatially Varying Demand

1. A Shifting Strategy for Dynamic Channel Assignment under Spatially Varying Demand Harish Rathi Advisors: Prof. Karen Daniels, Prof. Kavitha Chandra Center for Advanced Computation and Telecommunications University of Massachusetts Lowell

2. Problem Statement • Wireless communication will increasingly rely on systems that provide optimal performance • Number of channels required • Assign channels to cells such that minimum number of channels are used while satisfying demand and cumulative co-channel interference constraints. • Cumulative interference threshold • Reuse distance • A method is needed which can optimize resources and maximize performance • Dynamic Channel Assignment (DCA) • Example • Each color represents a unique channel • 5 different channels required to satisfy the demand • No channel repetition within any 2 x 2 square

3. High-Level Approach • Generate demand • Bounds on minimum number of channels required to satisfy demand and cumulative co-channel interference constraints: • Lower: (assuming reuse distance = r) • r x r sized cell group • (r+1) x (r+1) sized cell group (Integer Programming solution) • Upper: based on Core Integer Programming (CIP) model • To avoid expense of solving full CIP, solve: • small sub-problems • highly constrained formulations • SHIFT-IP: Attempts to assemble a provably optimal solution for the entire cellular system using optimal solutions generated for sub-regions whose size is related to the reuse distance r • GREEDY-IP: Uses the CIP formulation iteratively by augmenting local solutions to an ordered list of ascending demand values • used if SHIFT-IP does not find an optimal solution

4. Demand • Cells generate constant demand (Typec) and variable demand (Typev) in time • The Typev cells demand channels according to a two state (on-off) Markov chain • In the “on” state, the channel demand is set to one and zero otherwise • Constantdemand cells, Typec, have 0 demand • Typev cells are distributed in space, characterized by a Bernoulli distribution with probability pv • pv governs the occurrence of Typev cells • cmax: max. number of cells, Nv: number of Typev cells

5. Co-Channel Interference • Cumulative signal strength ratio cannot be below a threshold value of B. This keeps co-channel interference at an acceptable level. • Produces a non-linear constraint • Minimum reuse distance r and can be used to calculate minimum B •  is path loss exponent • Prevents two cells within reuse distance r from using same channels Cj Ci

6. CORE-IP (CIP) [Liu01] Assignment variable  Usage variable  Objective function  Demand constraint  Usage constraint  Co-channel Interference constraint 

7. SHIFT-IP • Decompose the cellular system into disjoint (r+1)x(r+1) sized groups of cells ordered by non-increasing demand • r is reuse distance • Solution of each such group determines a family of isomorphic solutions • Replace every channel assignment f with (f + f’) mod fmax where f’ is some shift integer from 0 to fmax - 1 • fmax is maximum lower bound across all such groups • Shift’s should satisfy all the CIP constraints along with the shift constraints Idea: Locally optimal may be globally optimal

8. 1 2 0 1 0 0 2 0 2 1 1 0 1 0 1 0 2 2 0 1 0 2 Shift variables and constraints added to CIP to form CIP1:

9. PSEUDO-CODE Assign channels to each group with local interference constraints only Add shift constraints for each group Solve the whole model with new constraints

10. SHIFT-IP Feasibility and Optimality • Let • optimal SHIFT-IP solution = U1* • optimal CIP solution = U* • SHIFT-IP is infeasible if maxqQ{Uq*} <U* • If U1* = maxqQ{Uq*}then U* = U1* • Proof Sketch • U1* ≥ U* because CIP1 is CIP + additional constraints • U1* ≤ U* • Uq* ≤U* for each q  Q • Hence: U1* = U* maxqQ{Uq*} ≤U*

11. GREEDY-IP Idea: Locally optimal may be globally optimal

12. Results • Heuristics run for nine different spatial configurations. • Total of Typev cells ranges from 8 to 13 across these nine configurations. • Typev cells demand channels according to a two state Markov chain (on/off). • total of 256 to 8196 unique states of the network • all states are examined • Two cases with reuse distance 2 and 3 are studied. • Results are compared against a sequential greedy algorithm. • Sequentially allocates the first available channel that satisfies demand and interference constraints.

13. Legend: • SHIFT-IP and GREEDY-IP • Sequential Greedy Algorithm Reuse distance: 2pv = 0.2 pon=0.57 X-axis: Channels required, kY-axis: Pr[Channels required = k]

14. Results (contd.) • Sequential greedy algorithm sometimes benefits from fortuitous channel assignments. • Performs well for large and/or densely packed Typev cells. • IP performs both local and global optimization. • Global optimumis often achieved when cell groups are well separated. • Randomized SHIFT-IP: • Channels obtained by IP can be randomly permuted • Does not violate local interference constraints • Result: Optimal solution found for configuration F • Tight upper and lower bounds are achieved • Consistently fast execution times

15. Conclusion • SHIFT-IP finds optimal solutions for 72% - 100% of demand states for our nine spatial distributions • SHIFT-IP result is provably optimal if: • Shift is feasible • SHIFT-IP solution matches optimal channel requirement for maximal demand subgroup • GREEDY-IP often finds optimal assignments when SHIFT-IP fails • GREEDY-IP has longer execution time than SHIFT-IP • Randomized SHIFT-IP improves some results

16. Future Work • Larger channel demand values • Let Randomized-SHIFT use multiple permutations for each cell group • Compare results to replication heuristic [Liu01] • Solve CIP for small cluster • Replicate resulting assignments across grid • Remove assignments violating interference constraints • Add channels greedily to satisfy remaining demand • Consider a hybrid SHIFT-IP/cluster replication approach.