1. Static-neighbor-Graph-based prediction Present by Yftah Ziser January 2015

2. Description The Static-neighbor-Graph method predicts the primary users spectrum utilization by constructing an empirical probabilistic graph of primary users mobility.

3. 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)

4. Simple Example

6. Directed graph

7. Simple Example

11. 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.

12. Simple Example

14. Simple Example – with a conflict

16. 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.

17. 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 self- loops.

18. Self-loops In order to differ as possible the SNG algorithm from Hold, a the weights on self- loops edges will be factored (0.1 in our case).

19. pros The time and space complexity are very low (predicting and training).

20. pros Can work with large number of data representations (including all the representations we introduced in the seminar).

21. cons The prediction for the next step and N steps ahead are the same.

22. 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.

23. 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

24. 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).

25. Results 101 10987654321 n 0000000000 SNG NW 0000000000 SNG BW 0000000000 Hold The best window is 10

26. Results 201 10987654321 n 0.28240.22510.24810.23760.22470.30350.24350.28600.17640.3189 SNG NW 0.1764 SNG BW 0.1764 Hold The best window is 20

27. Results 301 10987654321 n 0.13130.12120.13030.11280.10930.14800.55650.23320.28220.2826 SNG NW 0.11490.12900.1203 0.10930.11630.12390.11720.10600.1066 SNG BW 0.13640.13370.1407 0.1250 0.126 0.13110.13400.14540.1350 Hold The best window is 60

28. Results 301 10987654321 n 0.13130.12120.13030.11280.10930.14800.55650.23320.28220.2826 SNG NW 0.11490.12900.1203 0.10930.11630.12390.11720.10600.1066 SNG BW 0.13640.13370.1407 0.1250 0.126 0.13110.13400.14540.1350 Hold The best window is 60

29. Results 401 10987654321 n 0.39910.45470.37870.27860.32270.26440.15670.12090.12130.1124 SNG NW 0.1238 0.13410.15300.15220.16240.12960.12720.12090.11670.1011 SNG BW 0.10270.10790.12770.12690.14510.10610.10710.09940.09530.0882 Hold The best window is 30

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).

31. Alternative results For this section we allow the SNG to accumulate knowledge

32. Alternative results 101 10987654321 n 0000000000 SNG NW 0000000000 SNG BW 0000000000 Hold The best window is 10

33. Alternative results 201 10987654321 n 0.28240.22510.24810.23760.22470.30350.24350.28600.17640.3189 SNG NW 0.1764 SNG BW 0.1764 Hold The best window is 20

34. Results 301 10987654321 n 0.13130.12120.13030.11280.10930.14800.55650.23320.28220.2826 SNG NW 0.11490.12900.1203 0.10930.11630.12390.11720.10600.1066 SNG BW 0.05900.05890.07810.10250.1581 0.1693 0.13470.11390.06540.0226 A-SNG BW The best window is 60

35. Alternative results 401 10987654321 n 0.39910.45470.37870.27860.32270.26440.15670.12090.12130.1124 SNG NW 0.1238 0.13410.15300.15220.16240.12960.12720.12090.11670.1011 SNG BW 0.19210.18450.17420.17200.18540.14050.13450.12460.11700.1105 A-SNG BW The best window is 30

36. Future thoughts Predict frequency and time

37. Future thoughts Predict frequency and time - The prediction for the next step and N steps ahead are the same. Predict a probabilistic spectrum

38. Simple Example – with a conflict

40. Any questions ?