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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
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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.