A cognitive network with users seeking access to the spectrum in an opportunistic manner is modelled, where ܰௌ out of the possible ܰ users in the system are competing for ܰ unlicensed channels (where ܰ is the number of available channels). A multi-channel
scenario (ܰ> 1) is modelled using an uplink scenario. Users that require the use of the spectrum submit a bid based on their belief using the OBB. Two types of beliefs are used in this chapter as explained earlier. The bid of each user is either taxed or subsidized using the concept of green payments as used in chapters 4 and 5. The channel is allocated to the highest bidder(s) represented asܰௐ using the first price sealed bid auction with a reserve price. The transmit power of the user depends on the group in which the user belongs as explained in chapter 4. All users in the same group transmit at the power level. The WINNER II B2 propagation model is used as detailed in [89]. The remaining parameters used in the simulations are as given in table 7.1 in addition to the ones in table 3.1.
Table 7.1 Parameters used
Parameters Value
ܣ௦ 12
݀ 0.001
߱ 1
The truncated Shannon equation is used to model the transmission rates of each of the users as detailed in [86]. The Dirichlet distribution is used in generating the prior and the posterior distribution for the learning players and the flow chart is as shown below shown.
Chapter 7 A Game Based Energy Sensitive Spectrum Auction and Bid Learning Process for Dynamic Spectrum Access
198 Abdulkarim A. Oloyede, PhD Thesis, Department of Electronics, University of York. Figure 7.3. System Flow Chart
The algorithm for the learning process is summarised below:
1. Treat the unknown parameter (Probability of the bids) as a uniform random variable 2. Assume the prior distribution for the unknown parameter
3. Update the distribution of the parameter based on data(ܤ(ߙ)) 4. Compute the hyper parameter (ߙ)
5. Finally compute prior probability and the posterior probabilitiesܲ(ܤ|ܣ)
For the LPU the prior distribution in step 2 is provided by the WSP. The users compute the posterior probability for all the possible value of OBB. The user picks a random bid from the distribution of the OBB with the highest ܲ(ܣ|ܤ). This is repeated until a steady state is reached. During the iterations, the utility obtained is repeated for a number of times before another OBB is examined.
7.4.1 Efficient Exploration Based on Transfer Learning
In order to understand the effects of transfer learning on the time taken for the learning process to converge, the models with and without the transfer learning are considered. Figure 7.4 shows the energy consumed by the system when the traffic load is 4 Erlangs. In this model, all the users in each of the two groups are allowed to learn individually as they arrive in the system. The players are not allowed to share information about what they have learnt. This led to the long learning period compared to figure 7.5 where the users are allowed to transfer what they have learnt to others provided they belong to the same group.
Figure 7.4. Energy consumed per file sent against number of iteration using the individual learning scheme
The longer learning period in figure 7.4 is because the learning process converges after all the learning users in the system have completed their learning process individually rather than having a sort of information exchange as done in figure 7.5.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 2 4 6 8 10 12 14 16 18 20 Iteration T ot al E ne rg y C on su m ed (W h)
HPU Using the Learning Model LPU Using the Learning Model
Chapter 7 A Game Based Energy Sensitive Spectrum Auction and Bid Learning Process for Dynamic Spectrum Access
200 Abdulkarim A. Oloyede, PhD Thesis, Department of Electronics, University of York. Figure 7.5. Energy consumed per file using transfer learning between users in the same
group
Hence, in order to reduce the exploration period transfer learning is introduced, where the players in the same group can share information regarding the reserve price, the traffic load in the system and the optimal bidding price. The Bayesian learning model used in this work also incorporates a form of transfer learning due to the prior knowledge involved. However, the users in this model went further by processing the prior information collectively. Transfer learning is used in the remaining results in this chapter
7.4.2 Performance Analysis
In order to understand the reasons behind the game formulation, a scenario where only the WSP and one of the user group is learning while the other players are using the greedy model is examined. This is done mainly because of two reasons. First, it enables the understanding of the behaviour of each of the players. Second, it helps in examining if the players can learn different parameters about each other. The result obtained is the average for each of the
0 5 10 15 20 25 30 4 6 8 10 12 14 16 Iteration T ot al E ne rg y C on su m pt io n (W h)
LPU Using the Learning Model HPU Using the Learning Model