A shifting strategy for dynamic channel assignment under spatially varying demand
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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. Problem Statement.

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A shifting strategy for dynamic channel assignment under spatially varying demand

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


Problem statement
Problem Statement Spatially Varying Demand

  • 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


High level approach
High-Level Approach Spatially Varying Demand

  • 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


Demand
Demand Spatially Varying 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


Co channel interference
Co-Channel Interference Spatially Varying Demand

  • 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


CORE-IP (CIP) [Liu01] Spatially Varying Demand

Assignment variable 

Usage variable 

Objective function 

Demand constraint 

Usage constraint 

Co-channel Interference constraint 


Shift ip
SHIFT-IP Spatially Varying Demand

  • 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


1 Spatially Varying Demand

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:


PSEUDO-CODE Spatially Varying Demand

Assign channels to each group with local interference constraints only

Add shift constraints for each group

Solve the whole model with new constraints


Shift ip feasibility and optimality
SHIFT-IP Feasibility and Optimality Spatially Varying Demand

  • 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*


Greedy ip
GREEDY-IP Spatially Varying Demand

Idea: Locally optimal may be globally optimal


Results
Results Spatially Varying Demand

  • 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.


  • Legend: Spatially Varying Demand

  • 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]


Results contd
Results (contd.) Spatially Varying Demand

  • 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


Conclusion
Conclusion Spatially Varying Demand

  • 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


Future work
Future Work Spatially Varying Demand

  • 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.


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