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 (Type c ) and variable demand (Type v ) in time  The Type v 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 Constant demand cells, Type c, have 0 demand  Type v cells are distributed in space, characterized by a Bernoulli distribution with probability p v p v governs the occurrence of Type v cells c max : max. number of cells, N v : number of Type v 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 CiCi CjCj

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 f max where f ’ is some shift integer from 0 to f max - 1 f max 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

Shift variables and constraints added to CIP to form CIP 1 : GroupShift A2 B0 C1 D

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

10  Let optimal SHIFT-IP solution = U 1 * optimal CIP solution = U *  SHIFT-IP is infeasible if max qQ {U q *} < U*  If U 1 * = max qQ {U q * } then U * = U 1 * Proof Sketch  U 1 * ≥ U * because CIP 1 is CIP + additional constraints  U 1 * ≤ U * U q * ≤ U * for each q  Q  Hence: U 1 * = U * SHIFT-IP Feasibility and Optimality max qQ {U q *} ≤ U*

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

12 Results  Heuristics run for nine different spatial configurations.  Total of Type v cells ranges from 8 to 13 across these nine configurations.  Type v 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.

X-axis: Channels required, k Y-axis: Pr[Channels required = k] Reuse distance: 2 p v = 0.2 p on =0.57 Legend: SHIFT-IP and GREEDY-IP Sequential Greedy Algorithm

14 Results (contd.)  Sequential greedy algorithm sometimes benefits from fortuitous channel assignments. Performs well for large and/or densely packed Type v cells.  IP performs both local and global optimization.  Global optimum is often achieved when cell groups are well separated. Global optimum  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 Tight  Consistently fast execution timesexecution times

15 Conclusion  SHIFT-IP finds optimal solutions for 72% - 100% of demand states for our nine spatial distributions72% - 100%  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.