p Plt+1 = 1, glt+1 = 0 Plt = 0, glt = qm in Java Generating QR-Code in Java p Plt+1 = 1, glt+1 = 0 Plt = 0, glt = qm

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p Plt+1 = 1, glt+1 = 0 Plt = 0, glt = qm using none toaccess none on web,windows application Microsoft Office Official Website = pl0 1 ,. (8.4). since the transitio none none n does not depend on the gain glt at time t. In the above, we have discussed the dynamics of primary users returning/vacating the licensed bands and the gains associated with utilizing the licensed spectrum. Clearly, these dynamics will affect the secondary users decisions about how to allocate the channels for transmitting control and data messages.

For instance, in order to obtain higher utilization of the spectrum opportunities, the secondary users tend to allocate more channels with higher gains as data channels and those with lower gains as control channels. However, their channel allocation decisions should also depend on the observations about the malicious attackers strategies, which can be conjectured from knowledge of which channels are jammed by the attackers. Thus, the secondary users should maintain a record of which channels have been jammed by the attackers and what types of messages have been transmitted in the jammed channels.

Since the channels within the same licensed band are assumed to have the same gain, what matters to the secondary users is only the number and the type of the jammed channels. On the basis of these assumptions, the observations of the secondary user network are denoted t t t t by Jl,C , Jl,D , where Jl,C and Jl,D denote the numbers of control and data channels that are jammed in the lth band observed at time slot t, and l {1, 2, . .

. , L}. Such.

8.3 Formulation of the stochastic anti-jamming game observations can be none none obtained when the secondary users do not receive con rmation of message receipt from the receiver. The secondary users cannot tell whether an idle channel gets jammed or not, since no messages are transmitted in those channels. Thus, the number of idle channels that get jammed is not an observation of the secondary users, and will not be considered in the state of the stochastic game.

In summary, the state of t t t the stochastic anti-jamming game at time t is de ned by st = s1 , s2 , . . .

, s L , where t t slt = Plt , glt , Jl,C , Jl,D denotes the state associated with the lth band. After observing the state at each stage, both the secondary users and the attackers will choose their actions for the current time slot. The secondary users might no longer choose the previously jammed channels as control or data channels if they believe that the attackers will stay in the jammed channels until they detect no activity of the secondary users.

On the other hand, if the attackers believe that the secondary users will hop away from the jammed channels, they will choose the previously unattacked channels to jam; then, for the secondary users, remaining in the previously jammed channels may be a better choice. When facing such uncertainty about each other s strategy, both the secondary users and the attackers should adopt a randomized strategy. The secondary users will still transmit control or data messages in some of the previously jammed channels in case the attackers choose to jam the previously unattacked channels, and start transmitting in some of the previously unattacked channels in case the attackers keep jamming the previously jammed channels for a while.

Similarly, the attackers will keep jamming some of the previously jammed channels and start to jam the channels that were not jammed in the previous time slot. In addition, as discussed in Section 8.2, the secondary users may need to perform channel switching to make their channel access pattern more unpredictable to the attackers and alleviate the potential damage due to jamming.

Thus, at every time the secondary users can switch a control channel to a data channel or an idle channel, and vice versa. If so, when there are Nl channels in each licensed band l, the secondary users will have 3 Nl different actions to choose from for the lth band and L Nl actions in total. This will complicate the decision making of the secondary l=1 3 users.

To have the decision making computable in a reasonable time, we formulate the action set for both players as follows. Note that more complicated action modeling will only affect the performance, while not affecting the stochastic anti-jamming game framework. Mathematically, the actions of the secondary users are de ned as at = t t t t t t t t t a1 , a2 , .

. . , a L , with alt = al,C1 , al,D1 , al,C2 , al,D2 , where action al,C1 (or al,D1 ) t means that the secondary network will transmit control (or data) messages in al,C1 (or t al,D1 ) channels uniformly selected from the previously unattacked channels, and action t t al,C2 (or al,D2 ) means that the secondary network will transmit control (or data) mest t sages in al,C2 (or al,D2 ) channels uniformly selected from the previously jammed chant t t nels.

Similarly, the actions of the attackers are de ned as at = a1,J , a2,J , . . .

, a L ,J , J t = at , at t t ) means that the attackers will jam with al,J l,J1 l,J2 , where action al,J1 (or al,J2 t t ) channels uniformly selected from the previously unattacked (or attacked) al,J1 (or al,J2.
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