Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 59

1 Consider the binary antipodal signal detection model in the figure below where μ0 is the mean of the PDF expressing the receipt of the signal y when the symbol S0 is transmitted, and μ1 is the mean of the PDF expressing the receipt of the signal y when the symbol S1 is transmitted. The channel is assumed to introduce AWGN with variance σ and the two small shaded areas express the error probability on both sides of the decision threshold 0. The left‐hand part of the shaded area expresses the error probability when decoding S0 but S1 was transmitted, while the right hand part of the shaded area expresses the error probability when decoding S1 but S0 was transmitted. State some of the parallels (similarities) and differences between this binary antipodal signal detection model and the ROC basic model explained in Section 3.1.

2 Using Equations (3.7) and (3.8) drive the equivalent to Equations (3.7) and (3.8) for the case of same‐channel in‐band local decision fusion building on Equations (3.19)–(3.22). Does the signal overlay model simplify this ROC model? Why?

3 A set of nodes in a cognitive MANET are moving in tandem while using directional antennas, as shown in the figure below. This could be a row of vehicles, illustrated by the oval shapes. Assume that this convoy is driving along a road in a straight line with the distance between each two vehicles being the same, D. Let us assume the road width is W. Let us also assume that the frequency used for communication between vehicles needs to be used again after a distance W away from the road, as shown in the figure, i.e. the spatial separation is 2W. Consider a directional beam such that spectrum emission would reach the vehicle in front and the vehicle at the back and then fade away to the side of the road. Spectrum analysis of the directional beam power spectral density shows that D1 has to be 1.1 × D. The distance D1 defines the spatial separation regions such that when a node is communicating to the node ahead of it, the spectral density further away from D1 is negligible to allow for spectrum reusability.If we use sectored antennas for the vehicles, find the minim number of sectors per antenna we need in order to meet the above spectral pattern design. Note that you would need to round up your calculation to an even number of antenna sectors to find a symmetrical division of the full circle. Note that this will require some geometric analysis.Assume that we can apply power control on the antenna spectrum emission such that we can use a frequency after n hops. Find the number of frequencies we need for any number of nodes driving on this road.Based on the nulling matrix explained in Section 3.3.1.2, do you recommend a higher number of sectors than estimated by (a) above? Why?

4 A cognitive military MANET is implementing a directional antenna technique with a sectored antenna with N equal sectors. Let us assume that there is no overlapping between the sectors. This directionality technique is evaluated based on its ability to avoid enemy eavesdropping nodes. Let us assume that we have node a that is communicating to node b. The maximum area of coverage (AoC) for node a is defined by a circle of diameter d where the radius R is the maximum distance for node a reachability to and beyond node b, as shown in the figure below. As the figure shows, at a certain point in time, the distance between nodes a and b was L.What is the sector angle of this sectored antenna as a function of N?Let us assume that the enemy is able to put eavesdropping nodes randomly within the AoC of node a. What is the probability of the enemy succeeding in receiving the radio signal if the radio uses an omnidirectional antenna with the same AoC?If the enemy succeeded in deploying a single eavesdropping node randomly in the AoC, what is the probability of the enemy succeeding in receiving the military signal if the military node used described the directional antenna with a single active sector?If the enemy was able to deploy 1, 2, 3, and 4 eavesdropping nodes randomly within the AoC, create a table showing the probability of the enemy succeeding in receiving the radio signal for each of these four cases if the radio used the prescribed directional antenna with a single active sector.If the number of sectors used by the military node N = 12, find the number of eavesdropping nodes the enemy would have to drop randomly so that the probability of the enemy succeeding in receiving the radio signal approach 0.5.

5 Refer to Appendix 3A. Let us assume we have two ROC curves as shown in the figure below. Are both curves in the “use” region? Based on these intersected curves, will you consider the area under the curve a good metric to assess a ROC curve? Why?

6 In military communications, is DSA alone sufficient to overcome an enemy's follower jammer? Why?