Static-neighbor-Graph-based
prediction
Present by Yftah Ziser
January 2015
Description
• The Static-neighbor-Graph method predicts
the primary users spectrum utilization by
constructing an empirical probabilistic graph
of primary users mobility.
How to build the graph?
• 1)if SU observe PU movement from point I to
point j
1.1)if the edge (i,j) doesn't exist
1.1.1)add edge (i,j) with the weight of 1
1.2)else
1.2.1)add 1 to the weight of the edge (i,j)
Simple Example
Simple Example
Simple Example
Directed graph
Simple Example
Simple Example
Simple Example
Simple Example
How to use the graph for prediction?
• Assuming that the current location of the PU
is represented by vertex i, our prediction for
the next location is j such that edge (i,j) has
the maximum weight .
Simple Example
Simple Example
Simple Example – with a conflict
Simple Example – with a conflict
Reduction to our problem
• What we have
Algorithm for predicting the next PU location.
• What we want
Algorithm for predicting the spectrum holes.
The reduction is quite simple.
The reduction
• Assuming we know all the Primary users
locations we can know injectively which of
the spectrum beans are idle.
• We would like to relate to the option of
predicting that some of the stations stay in the
same frequency for the next few intervals.
For this purpose the algorithm allows selfloops.
Self-loops
• In order to differ as possible the SNG
algorithm from Hold, a the weights on selfloops edges will be factored (0.1 in our case).
pros
• The time and space complexity are very low
(predicting and training).
pros
• Can work with large number of data
representations (including all the
representations we introduced in the
seminar).
cons
• The prediction for the next step and N steps
ahead are the same.
cons
• The prediction for the next step and N steps
ahead are the same.
• Work well in absolute patterns but very
inaccurate for relative ones.
Results
• In the following tables we present the relative
error of the frequency prediction for each
time interval ahead (the "n" row).
i.e. the relative frequency error formula given
by
Results
• The NW lines means that for each interval the
window size used is 10*i.
The BW lines means that the window size is
the minimum sum of all the intervals errors
(for the SNG algorithm).
Results
101
n
SNG NW
SNG BW
Hold
1
2
3
4
5
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
The best window is 10
Results
201
n
1
2
3
4
5
6
7
8
9
10
0.3189 0.1764 0.2860 0.2435 0.3035 0.2247 0.2376 0.2481 0.2251 0.2824
SNG NW
0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764
SNG BW
0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764
Hold
The best window is 20
Results
301
1
2
3
4
5
6
7
8
9
10
n
SNG NW
SNG BW
0.2826 0.2822 0.2332 0.5565 0.1480 0.1093
0.1066 0.1060
0.1172 0.1239
0.1350 0.1454 0.1340
0.1311
0.1128 0.1303 0.1212 0.1313
0.1163 0.1093 0.1203 0.1203 0.1290
0.1149
0.126 0.1250 0.1407 0.1407 0.1337 0.1364
Hold
The best window is 60
Results
301
1
2
3
4
5
6
7
8
9
10
n
SNG NW
SNG BW
0.2826 0.2822 0.2332 0.5565 0.1480 0.1093
0.1066 0.1060
0.1172 0.1239
0.1350 0.1454 0.1340
0.1311
0.1128 0.1303 0.1212 0.1313
0.1163 0.1093 0.1203 0.1203 0.1290
0.1149
0.126 0.1250 0.1407 0.1407 0.1337 0.1364
Hold
The best window is 60
Results
401
1
2
3
4
5
6
7
8
9
10
n
SNG NW
0.1124 0.1213 0.1209 0.1567 0.2644 0.3227 0.2786 0.3787 0.4547 0.3991
0.1011 0.1167 0.1209 0.1272 0.1296 0.1624 0.1522 0.1530 0.1341 0.1238
SNG BW
Hold
0.0882 0.0953 0.0994 0.1071 0.1061 0.1451 0.1269 0.1277 0.1079 0.1027
The best window is 30
Results Analysis
• In "constant wave" stations such as "101" we
can clearly see that both algorithms SNG and
Hold are predicting the frequency perfectly.
• In "frequency hop" stations such as “201" the
SNG and the hold algorithms are practically
the same.
• When the station nature is less holdish we can
see improvement (301).
Alternative results
• For this section we allow the SNG to
accumulate knowledge
Alternative results
101
n
SNG NW
SNG BW
Hold
1
2
3
4
5
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
The best window is 10
Alternative results
201
n
1
2
3
4
5
6
7
8
9
10
0.3189 0.1764 0.2860 0.2435 0.3035 0.2247 0.2376 0.2481 0.2251 0.2824
SNG NW
0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764
SNG BW
0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764 0.1764
Hold
The best window is 20
Results
301
1
2
3
4
5
6
7
8
9
10
n
SNG NW
SNG BW
0.2826 0.2822 0.2332 0.5565 0.1480 0.1093
0.1128 0.1303 0.1212 0.1313
0.1066 0.1060
0.1172 0.1239
0.1163 0.1093 0.1203 0.1203 0.1290
0.0226 0.0654
0.1139 0.1347 0.1693 0.1581 0.1025 0.0781 0.0589 0.0590
A-SNG BW
The best window is 60
0.1149
Alternative results
401
1
2
3
4
5
6
7
8
9
10
n
SNG NW
0.1124 0.1213 0.1209 0.1567 0.2644 0.3227 0.2786 0.3787 0.4547 0.3991
0.1011 0.1167 0.1209 0.1272 0.1296 0.1624 0.1522 0.1530 0.1341 0.1238
SNG BW
A-SNG BW
0.1105 0.1170 0.1246 0.1345 0.1405 0.1854 0.1720 0.1742 0.1845 0.1921
The best window is 30
Future thoughts
• Predict frequency and time
Future thoughts
• Predict frequency and time - The prediction
for the next step and N steps ahead are the
same.
• Predict a probabilistic spectrum
Simple Example – with a conflict
Simple Example – with a conflict
Any questions ?