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A Shifting Strategy for Dynamic Channel Assignment under Spatially Varying Demand

Harish Rathi

Advisors: Prof. Karen Daniels, Prof. Kavitha ChandraCenter for Advanced Computation

and Telecommunications

University of Massachusetts Lowell

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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

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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

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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

Constant demand 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

maxmax ...1,0)1(][ max ckppk

ckNP kc

vkvv

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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 Ci

Cj

CORE-IP (CIP) [Liu01]

Assignment variable

Usage variable

Objective function

Demand constraint

Usage constraint

Co-channel Interference constraint

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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 withthe shift constraints

Idea: Locally optimal may be globally optimalIdea: Locally optimal may be globally optimal

Shift variables and constraints added to CIP to form CIP1:

Group Shift

A 2

B 0

C 1

D 2

1

0

2

1

0

1

1

1

2

2

2

2

20

0

0

0 0

1 0 1

0

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)L

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Let optimal SHIFT-IP solution = U1

* optimal CIP solution = U*

SHIFT-IP is infeasible if maxqQ{Uq*} < U*

If U1* = maxqQ{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*

SHIFT-IP Feasibility and Optimality

maxqQ{Uq*} ≤ U*

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GREEDY-IP

Idea: Locally optimal may be globally optimalIdea: Locally optimal may be globally optimal

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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.

X-axis: Channels required, kY-axis: Pr[Channels required = k]

Reuse distance: 2pv = 0.2 pon=0.57

Legend:• SHIFT-IP and GREEDY-IP • Sequential Greedy Algorithm

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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 optimum is 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

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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

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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.