I would like to express my gratitude to my supervisor Dr. Mohammed Zafar Ali Khan for the helpful comments, remarks and engagement throughout the learning process of this master's thesis. Furthermore, I would like to thank Mohammad Fayazur Rahaman for introducing me to the topic as well for the support along the way. I would also like to thank my friends at IIT Hyderabad, who supported me throughout the process, both by keeping me harmonious and helping me put pieces together.
I would like to dedicate my thesis to my parents, teachers and friends who inspired me to be a part of my success. Distributed sensing is an important part of many applications such as wireless sensor networks, cooperative spectrum sensing in cognitive radio network. In the CSS scheme, multiple secondary users (SUs) connected via communication links to a fusion center (FC) cooperate to increase the detection efficiency of the binary hypothesis test to identify a hole in the spectrum.
According to the Bayesian criterion, the calculation of the single threshold for the LR test is simple when the a priori probabilities of the hypothesis and the Bayes costs are available. We exploit local monotonic properties exhibited in a special case of non-monotonic decision fusion problems, which reduces the size of the optimal solution space. We provide a numerical comparison of the performance (ROC) and complexity of (i) the proposed variable reduction technique and (ii) the solution of the generalized decision fusion problem (GDFP) presented in [13].
Furthermore, we would like to use the proposed method for performance improvement of FC under faulty channel between SUs and FC with MIMO technique.
Fusion rule
Dynamic programing
Then we define Idm =I(PDm), Ifm =I(PFm) and Iα=I(α). Let V(i, j) be the maximum value of the set of the first i vectors ums, for which the restriction applies that the sum of Ifms vectors in the set is ≤j. To find out if vectors are involved in the solution here is a step-by-step process of the algorithm. At the end of the algorithm, all items in the solution are in the set S.
Example: Let's try to fill the Backpack of capacity W=5 with items mentioned in Table 2.1 Table 2.1: List of items.
Branch and Bound
Following the step-by-step process mentioned in Algorithm 2, we can prepare a graph as shown below. Where xi = 0 indicates that the object is not in the backpack, xi = 1 indicates the ith object that is in the backpack. And p,w denotes the gain or weight at that particular node and ub denotes the upper bound estimated at that particular node.
Likelihood ratio test
Semi -Monotonic Property
The SU index set S(ut) of the observation vector at the tail of an arbitrary arrow is the subset of the corresponding SU index set S(uh) of the vector at the head of this arrow, i.e.,S(ut)( S( uh), where,uh denotes the observation vectors at the tail and head of any arbitrary arrow.
Variable Reduction in GDFP
Using (2.7), the reduced variable GDFP is now defined as. 2.20) The proposed DP-based solution can now be applied to (2.20) to obtain the optimal value of the free variables in x. In the next section we present the numerical results confirming the correctness of the proposed solution and the reduced dimensionM0 obtained for different N andα. To demonstrate the effectiveness of the proposed algorithm, we considered individual SUs as an example based on the probability of false alarmpfi ∈U[0.2,0.4] and the probability of detectionpdi ∈U[0.6,0.8].
In DP (2.7) M∗Iαmathematical operations are required and to know the vector in the solution M operations are required. In BB Greedy approach, we can check whether a particular node can provide us a better solution or not. This minimizes the number of nodes we have to travel. But in the worst case, we have to cover all the nodes, which determines the complexity of BB.
In LRT, sort probability by Merge sort algorithm requires O(M∗log(M)) operations and (2.10) in worst case requires M operation. Therefore, the overall complexity for LRT will be O(M ∗log(M)). In reduced variable approach we try to reduce the number of vectors given to DP or BB to solve GDFP problem which in return reduces the time it takes to solve the problem compared to when DP or BB with all the vectors be given. Distributed detection in Cognitive radio network is used to detect the presence of the primary user with the help of secondary users (SUs) which are geographically diversely distributed.
These SUs collect the necessary information and send it to the Fusion Center, where further processing takes place and a better decision is made about the presence of the primary user. In general, the channel between SU and FC is considered to be noiseless and fadeless, but it is not the same in real life. If the channel between SU and FC is considered as a wireless channel, the channel will definitely undergo fading and the system model would be as shown in Figure 4.1.
Here we use multiple antennas at FC and single antenna at individual SUs as shown in Figure 4.2. Since only one US transmits at a time, we can consider a single antenna transmitter and multiple antenna receiver system.
Alamouti code
Lety1andy2 are two symbols received in the first and second time slots, then we have. After simplifying (4.5), we get 4.7) we know that hi∀i is an independent identically Rayleigh distributed random variable as term. The coded symbols transmitted via the two antennas in the first and second time slots are as follows Tx1 Tx2.
At the receiver during the first time and the second time we get the symbols as follows. To calculate the BER or Probability of Error from equation (4.12) which will be similar to the calculation of. Figure 5.1 shows how the Probability of Detection (Pd) varies with respect to the signal-to-noise ratio (SNR) using the SNR enhancement methods discussed in the previous chapter on FC to improve the quality of the received data being sent. . from SUs over the wrong channel.
To draw this graph we have considered individual SUs with the following false alarm probability pfi ∈U[0.2,0.4] and detection probability pdi ∈U[0.6,0.8] where U is the uniform distribution. With the total allowed false alarm probability α= 0.1. For the Rayleigh fading channel without using any performance improvement method, we have considered the error probability = 12 1−q. We have used MRC in FC with 2,3 and 4 receive antennas and single transmit antenna in SU and use () for error probability.
The aforementioned methods are helpful in improving the data vectors received at the FC, and global decision making is done by reducing the variables using dynamic programming to solve the GDFP problem. We used the semi-monotonic property shown in the special case of the decision fusion problem to reduce the dimensions in the space of feasible solutions. Furthermore, we have seen the effect of using multiple antenna schemes such as the MRC and Alamouti code at FC with the reduced complexity rule.
Khan, Reduced Complexity Optimal Hard Decision Fusion under Neyman-Pearson Criterion, 26th IEEE SIU 2018 Conference, Turkey. Haykin, Cognitive Radio: Brain-Empowered Wireless Communications, IEEE Journal on Selected Areas in Communications, vol. Weak, Spectrum Exploration and Exploitation for Cognitive Radio: Recent Advances, IEEE Signal Processing Magazine, vol.
Weak, Spectrum Sensing for Cognitive Radio: Latest and Latest Advances, IEEE Signal Processing Magazine, Vol. Khan, Low Complexity Optimal Fusion of Hard Decision According to the Neyman-Pearson Criterion, IEEE Signal Process.
