Hypergraph T-Coloring for Automatic Frequency ... - alexandre gondran
Channel Assignment in Wireless LAN based on SINR. 2. Necessary condition: Graph T-coloring Problem. 3. Quasi equivalent condition: Hypergraph T-coloring ...
Agenda 1. Channel Assignment in Wireless LAN based on SINR 2. Necessary condition: Graph T-coloring Problem 3. Quasi equivalent condition: Hypergraph T-coloring Problem 4. Results 5. Conclusions/Perspectives PIMRC’08
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Channel Assignment in WLAN Limit the interferences which degrade Quality of Service network by limiting its capacity. Not possible to avoid interferences to spread as well as possible interferences over the whole area SINR computation : long time
Channel Assignment in WLAN: SINR constraints fi frequency channel used by Access Point i sk SINR threshold necessary to satisfied user k SINR ≥ 20 dB
SINR ≥ 25 dB
f3 f1 f4
user
f2 Access Point (AP)
SINR ≥ 15 dB
Determine fi Satisfied : ∀k, SINRk ≥ sk
PIMRC’08
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Channel Assignment in WLAN: SINR constraints Determine fi Satisfied : ∀k, SINRk(fi) ≥ sk IEEE 802.11g
fi
SINRk =
pik k
∑p i ≠ ik
ik
×γ
(f
ik
)
− fi + N PIMRC’08
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SINRk =
SINR constraints pik k
∑p i ≠ ik
ik
×γ
(f
ik
)
− fi + N
≥ sk
Graph T-coloring
| f j − fi |≥ tij pik k pik k −N −N −1 sk s −1 k tij = max γ , j = ik ; γ , i = jk k pik p jk
PIMRC’08
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Necessary condition: Graph T-coloring problem SINR ≥ 15dB Example 1
f3
- 73 dBm
- 60 dBm
- 72 dBm
f1
f2
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Necessary condition: Graph T-coloring problem
f3 2 2
f1
f2
| f1 − f 2 | ≥ 2 SINR ≥ 15 ⇔ | f1 − f3 | ≥ 2
PIMRC’08
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SINRk =
SINR constraints pik k
∑p
ik
i ≠ ik
(f
×γ
ik
)
− fi + N
≥ sk
equivalence ?
Graph T-coloring
| f j − fi |≥ tij Theorem: Yes, if ∀k , SINR k :=
pik k
∑p i ≠ ik
ik
( )
× γ tiik + N
≥ sk PIMRC’08
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Quasi equivalent condition: Hypergraph T-coloring problem - 63 dBm
Example 2
f3
- 73 dBm
- 60 dBm
- 72 dBm
f1
f2
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Quasi equivalent condition: Hypergraph T-coloring problem
f3 3 2
f1
f2
| f1 − f 2 | ≥ 2 SINR ≥ 15 ⇒ | f1 − f3 | ≥ 3
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Quasi equivalent condition: Hypergraph T-coloring problem | f1 − f 2 | ≥ 2 SINR ≥ 15 ⇔ f1 − f3 | ≥ 3 no equivalence It’s necessary to add a new constraint linear n-ary constraints : |
f1 − f 2 | + | f1 − f3 | ≥ 6
| f1 − f 2 | ≥ 2 SINR ≥ 15 ⇔ | f1 − f3 | ≥ 3 | f − f | + | f − f | ≥ 6 1 3 1 2
PIMRC’08
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SINRk =
SINR constraints pik k
∑p i ≠ ik
ik
×γ
Graph T-coloring
(f
| f j − fi |≥ tij
ik
)
− fi + N
≥ sk
Hypergraph T-coloring
∑α i ≠ ik
ik
| f i − fik | ≥ α iik
pik k 1 ∀k , ∀i ≠ ik , α ik = min p jk γ (t jik + t ) + ∑ pik γ (tiik ) ≤ −N t sk i≠ j
PIMRC’08
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SINRk =
SINR constraints pik k
∑p i ≠ ik
ik
×γ
(f
ik
)
− fi + N
≥ sk
equivalence ?
Graph T-coloring
| f j − fi |≥ tij Theorem: Yes, if ∀k , ∀i ≠ i , k
Hypergraph T-coloring
∑α i ≠ ik
α ik = 1
ik
| f i − fik | ≥ α iik
PIMRC’08
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Results
SINR constraints time (s)
Graph T-coloring time (s)
Hypergraph T-coloring time (s)
9 AP
15 AP
30 AP
40 AP PIMRC’08
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Conclusions / Perspectives • Automatic method to build a good T matrix for graph T-coloring problem. • Define a new problem: hypergraph T-coloring problem. • Results equivalents for a better computation time. • Benchmarks soon in Internet: http://alexandre.gondran.free.fr • Integrate this approach into a global WLAN planning process. PIMRC’08
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Remark
SINRk =
SINR constraints pik k
∑p i ≠ ik
ik
×γ
(f
ik
)
− fi + N
≥ sk
In real problem, threshold sk are unknown Only throughput demand per user (kilobit/s) are known
Graph T-coloring
| f j − fi |≥ tij
Hypergraph T-coloring
∑α i ≠ ik
ik
| f i − fik | ≥ α iik PIMRC’08
17 - 16/00/2008
SINRk =
SINR constraints pik k
∑p i ≠ ik
Capacity constraints
Capacity AP ≥ Demand
ik
×γ
(f
ik
)
− fi + N
≥ sk
In real problem, threshold sk are unknown Only throughput demand per user (kilobit/s) are known
Graph T-coloring
| f j − fi |≥ tij
Hypergraph T-coloring
∑α i ≠ ik
ik
| f i − fik | ≥ α iik PIMRC’08
18 - 16/00/2008
SINRk =
SINR constraints pik k
∑p i ≠ ik
Capacity constraints
Capacity AP ≥ Demand
ik
×γ
(f
ik
)
− fi + N
≥ sk
We define a new algorithm which determine dynamically the best threshold sk to transform the problem into graph and hypergraph T-coloring problem
Graph T-coloring
| f j − fi |≥ tij
Hypergraph T-coloring
∑α i ≠ ik
ik
| f i − fik | ≥ α iik PIMRC’08
19 - 16/00/2008
19th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications
Hypergraph T-Coloring for Automatic Frequency Planning problem in Wireless LAN Cannes – 16 September 2008
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spectrum usage in each environment. This problem is called. AFP problem ..... and channel assignment in wireless LANsâ, IEEE Conference on Local Computer ...
2. Frequency Assignment Problem. 3. Our approach. 4. ACP and AFP combination. 5. Conclusion/Perspectives. WLAN Planning. 1. selecting a location for each ...
an urban environment where vehicles move in a road topology extracted from a ... antenna, A is a fixed quantity corresponding to the free-space path loss where ...
problem structure and the final solution. B. Local interference approaches. Inside BSS ..... 858â862, 1994. [3] Lee Y., Kim K., Choi Y., âOptimization of AP ...
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