## 3 PBCS Structure
### Receiver Structure and ANN Design  
In the PBCS receiver the signal distorted by the communication medium arrives at the RF Front-end, where, after a pattern separation (synchronization and elimination of multipath effect) process, it will be fed into the ANN as an input. Since ANN is pre-trained for the patterns, it can recover the distorted signal into known patterns, and outputs the associated bit sequences. These bit sequences are concatenated by the Bit Sequencer layer in order to come up with the original information. This procedure is described below in Figure 4.  
In the receiver, the layer that has the most crucial effect on the performance of the system is the ANN and specifically its design. The ANN design process includes the training and the test procedure. In the training phase, the ANN is trained offline according to the glossary patterns, which are called the training set. Distorted by the communication medium, the training set now becomes the test set, which is used to check the performance of the pre-trained ANN. The ANN concept was first proposed by [PERSON] [17] under the name of MLP (Multilayer Perceptron). Hierarchically structured, the ANN achieved successful results in complex classification and pattern recognition problems. Therefore, in this study, ANN is used in order to recognize the signal patterns, which are constructed based on the RF signal construction principles. The MLP has one input and one output layer, and in addition, it may have one or several hidden layers. Essentially, it is referred to as Black-box in some studies; it aims to determine any function between input and output values. The difference between the output of ANN and the expected output is fed into the system using the back-propagation algorithm. After a number of repetition, which is determined with respect to the user defined finishing criterion, a function can be formulated between the input and the output. Many methods are developed in the literature for back-propagation algorithms. Since it was the most applicable to the proposed system, the \"Steepest Descent\" one was chosen in this study. This method based on minimization of the quadratic cost function by tuning the network parameters. The mathematical expression is this algorithm as below:  
\[w_{j}^{(\kappa+1)}=w_{j}^{(\kappa)}-\eta\frac{\partial\varepsilon^{(\kappa)} }{\partial w_{j}^{(\kappa)}} \begin{bmatrix}\text{for j}=1,\ldots,\text{q}\\ \text{for i}=1,\ldots,\text{H}\end{bmatrix}  \tag{6}\]  
where \(w\) represents the weights of the ANN, \(k\) is the number of iterations, \(\varepsilon\) is error between the output of ANN and the actual value, \(\eta\) is the learning rate. Learning rate can be selected as a constant or an adaptive coefficient. An adaptive learning method is preferred for ANN in the PBCS receiver. The well-known adaptive method for the learning rate update is called as \"additive increment and multiplicative decrement\". This approach provides a cost effective solution in terms of simplicity and more robust behavior to find the best value of learning rate. The formulation of this procedure is in the following equation:  
\[\eta^{i}= \begin{cases}\eta^{i-1}\times 0.995&\text{if}\ \frac{\partial \varepsilon}{\partial w}<0\\ \eta^{i-1}+\left(0.0001\times\varepsilon\right)&\text{if}\ \frac{\partial \varepsilon}{\partial w}>0\end{cases}  \tag{7}\]  
Figure 4: PBCS receiver structure. Another important aspect in ANN design is to determine the number of hidden layers and of neurons located in these layers. From the low complexity and high applicability perspectives, a single hidden layer is chosen in PBCS design. The number of neurons in this layer is determined by the cross-validation method. On the other hand, the number of neurons at input layer is set as equal to the number of samples for each pattern. The number of neurons at the output layer is selected as equal to the number of patterns in the glossary.