VerylowSNR cognitive receiver based on wavelet preprocessed signal patterns and neural network
 Husam Y. Alzaq^{1}Email author and
 B. Berk Ustundag^{1}
https://doi.org/10.1186/s1363801709027
© The Author(s) 2017
Received: 24 January 2017
Accepted: 12 June 2017
Published: 4 July 2017
Abstract
A patternbased cognitive communication system (PBCCS) that optimizes nonperiodic RF waveforms for security applications is proposed. PBCCS is a crosslayer approach that merges the channel encoding and modulation. The transmitter encodes sequences of bits into continuous signal patterns by selecting the proper symbol glossaries. The cognitive receiver preprocesses the received signal by extracting a limited set of wavelet features. The extracted features are fed into an artificial neural network (ANN) to recover the digital data carried by the distorted symbol. The PBCCS system offers a flexible management for robustness against a high noise level and increases the spectral efficiency. In this study, the spectral efficiency and robustness of a PBCCS scheme for an additive white Gaussian noise (AWGN) channel is investigated. The results show that at an SNR of −5 dB, a 3bit glossary achieves a bit error rate (BER) of 10^{−5}. Also, the link spectral efficiency (LSE) of the proposed system is 2.61 bps/Hz.
Keywords
Cognitive radio (CR) Patternbased cognitive communication system (PBCCS) Artificial neural network Wavelet decomposition Digital signal processing (DSP) VerylowSNR1 Introduction
The efficiency of bandwidth utilization takes an important role in spectrum management [1, 2]. Due to fixed spectrum assignment policies and its inadequate to meet an unexpected increase in the number of higherdatarate devices, the spectrum is inefficiently used. Cognitive radio (CR) [3–6] was proposed as a promising solution to alleviate the spectrum scarcity problem through dynamic management of the available spectrum. The pioneer work of Mitola et al. [3] led to an efficient utilization of the spectral bandwidth by allowing the secondary user (SU), who is not serviced, to detect and access the primary network spectrum gaps. CR allows detection of the state of the spectrum to adjust its own system parameters (transmission power, frequency band, throughput and modulation scheme) in real time [7]. The result is that the utilization of the spectral bandwidth is performed with the software flexibility in an adaptive manner with respect to the system parameters.
However, efficient spectral bandwidth usage under the influence of higher noise is not the major consideration of CR. Claude Shannon [8] showed that the SNR is a leading factor that influences the link spectral efficiency (LSE), η=C/B, (in bps/Hz). SNR also limits the channel capacity. Therefore, the utilization of spectral bandwidth and the robustness to high SNR level are the keys to maximize the channel capacity.
Thus, a patternbased cognitive communication system (PBCCS) was introduced to optimize the overall spectral efficiency with respect to SNR [9, 10]. It is inspired by the recognition capability of humans to concentrate on a single conversation irrespective of the surrounding loudness. If human ears hear sounds from different sources, the brain chooses to pay attention to a particular voice amongst a whole range of sound streams in an environment. Similar to human cognitive capabilities, the communication system in PBCCS selectively recognizes and recovers the communication signal(s) a into known symbol(s), even within the same frequency range.
1.1 Related work
Conventional cognitive radio is equipped with various techniques for making wireless systems more flexible and robust to channel variation. Mitola, in his dissertation [11], stated that, although many aspects of wireless networks are artificial, they may still be enhanced by machine learning (ML). Recently, machine learning algorithms have become one of the key enabling features of cognitive radio in many applications. In previous literature, many techniques and algorithms have been applied to the cognitive radio engine [12, 13], such as the artificial neural network (ANN), hidden Markov model (HMM), fuzzy logic control, metaheuristic algorithms (evolutionary/genetic algorithm) and rulebased systems [14–16].
Comparison between pattern based cognitive communication system and cognitive radio
PBCCS  Cognitive radio  

Objective  To improve data transmission performance under bandwidth limitations by maximizing the LSE value with respect to SNR level.  To efficiently manage the spectrum by using the unoccupied spectrum band when it is not used by the licensed user. 
Transmitter side  It selects one signal pattern from the glossary space in adaptive manner.  It uses the frequency bandwidth in an adaptive manner with respect to channel availability. 
Receiver side  The distorted signal is recovered by a trained ANN. Recovering the information without separate demodulation, decoding and error recovery operations.  Receiver must have a wideband frontend to detect spectrum holes. It should take into account the adaptive modulation feature, since some receivers employs AMC. Many ML algorithms can be used. 
Modulation technique  AFPSK^{a}  QAM, QPSK, BPSK, …etc. 
Cognition manager  Glossary selector (GS)  Cognitive engine(CE) 
ANN within cognitive radio
Reference  Brief summary 

[21]  Wavelet cyclic feature has been proposed to reduce the complexity of calculating classical cyclic spectrum and a FFNN^{a} has been used to classify the received signals into BPSK^{b}, QPSK^{c}, MSK,^{d} and 2FSK^{e}. Cons: limited to loworder modulation schemes. 
[22]  Based on the instantaneous temporal features (the maximum value of the spectral power density, the standard deviation of the direct and absolute instantaneous phase values and the standard deviation of the normalized instantaneous amplitude), the authors have proposed a FFNN and probabilistic ANN to classify the received signals into 2 and 4ASK^{f}, BPSK, QPSK, 2, and 4FSK, 8PSK^{g}, 16QAM^{h}. Cons: Large ANN architecture and requires prior information on some specific parameters to guarantee the highest accuracy and reliable recognition. 
[23]  Based on the instantaneous temporal features (the maximum value of the spectral power density, the standard deviation of the direct and absolute instantaneous phase and the standard deviation of the normalized instantaneous amplitude), the authors have proposed a simple FFNN to classify the received signals into five classes, namely; 2 and 4ASK, BPSK, and QPSK. Cons: loworder modulations were considered. This approach requires prior information on some specific parameters to guarantee the highest accuracy and reliable recognition. 
[25]  Based on the extracted CWT instantaneous features (the mean, variance and central moments values), the authors have proposed an ANN to classify the modulation scheme into kASK, kPSK, kFSK, kQAM, OOK,^{i} and MSK. 
[26]  Based on the extracted instantaneous temporal features, the authors proposed a rulebased approach to discriminate between 15 modulation schemes (AM^{j}, FM^{k}, DSB^{l}, LSB^{m}, USB^{n}, VSB^{o}, combined AM–FM, CW, Noise, 2, and 4ASK, 2 and 4PSK, 2, and 4FSK). Cons: due to limited number of features and signal sensitivity, the approach was unable to classify the same modulation schemes of different order. 
[37]  FFNN, radial basis function ANN and multiclass support vector machine (SVM) have been suggested to classify the modulation technique of the received signal into 2 and 4FSK, 4ASK, 8ASK, 2PSK, 4PSK, 8PSK, V32, 8, 16, 32, and 64QAM. Cons: it requires prior information on specific parameters to guarantee the highest accuracy and reliable recognition. 
[38]  An expert discrete wavelet adaptive network based on fuzzy inference system has been proposed for classifying the digital modulated signals into 8ASK, 8FSK, 8PSK, and 8QAM. Cons: very large ANN structure, with four hidden layers. 
[39]  A system that is only based on wavelet transform has been developed, where a comparison between signals and templates in wavelet domain has been adapted to classify the received signals into 2ASK, 2FSK, and BPSK. Cons: binary digital modulation schemes were considered. It also requires prior signal information, such as, carrier frequency and symbol duration. 
[40]  A system that is based solely on DWT and signals statistics was used to classify the modulated received signals into 16QAM, QPSK and BPSK. Cons: degradation of performance at SNR appeared when the ANN was trained on signals with lower SNR. 
In this work, we choose to use the ANN model at the PBCCS receiver owing to its powerful capabilities. ANN can predict the correct class of the received signal even if the input signals have not been seen before, which allow the model to learn from training dataset and generalize the model to any received signal. Moreover, ANN is a nonlinear model and hence can predict the nonlinear received signal better than the linear model. Finally, the ANN parallel processing and the appropriate simple structure are two important properties for realizing ANN on hardware.
Furthermore, we have implemented a cognitive radio solution, which offers flexibility between the available spectrum and SNR. This solution has the capability to balance between LSE and the overall channel capacity under a very low SNR. It constructs optimal communication symbols, which compensate for the difference in data rates under various noise levels. In addition, the PBCCS system integrates the modulator and channel encoder through a crosslayer approach. The binary data is encoded into the appropriate waveform according to the selected glossary. Each binary word is assigned to the artificially constructed patterns. The transmitter selects the appropriate set of patterns that maximize LSE.
1.2 Contribution

We analyzed various DWT approaches, which have an influence on the recognition rate of the ANN.

We studied the effect of using 4 and 5level DWT, which reduce the size of the ANN.

We analyzed various backpropagation learning algorithms, which have an influence on system performance as well as the speed of learning.

Finally, we showed that the space complexity of the receiver exhibits a reduced ANN structure in terms of inputs and the hidden layer. As fewer resources were used, the receiver could be implemented with fewer hardware units.
1.3 Paper organization
The rest of this paper is organized in the following way. Section 2 describes the structure of the PBCCS model and its blocks in detail. It also gives a short introduction on wavelet and neural networks. In Section 3, we evaluate the performance of the PBCCS system. In Section 4, we conclude the paper and recommend directions for future work.
2 PBCCS structure
The proposed system consists of two main parts, the transmitter and receiver. Basically, the system employs patternbased encoding at the transmitter and a waveletpreprocessed artificial neural network based decoder at the receiver. In this section, we describe the details of the individual parts of PBCCS.
2.1 The transmitter of PBCCS
The transmitter of PBCCS is responsible for three tasks: 1) selecting the appropriate glossary with respect to the SNR level, 2) encoding the user data, and 3) transmitting the signal through the antenna. In PBCCS, the modulation is performed by using the sinusoidal pattern envelope construction (SPEC) algorithm [10]. The SPEC algorithm is used to prevent unwanted extra spectral usage, and it guarantees that the signal’s pattern ends at its initial point to ensure a zeropower density in average and has no highfrequency components.
The SPEC algorithm has two essential parameters—namely, “depth”, and “level”. Depth determines the length of the pattern in terms of the time—i.e., number of periods. Meanwhile, level identifies a value for each feature of the signal pattern. It represents the maximum and the minimum values of any signal characteristics (amplitude (A), frequency (F) or phase (P) at depth i. All possible outcomes in the SPEC algorithm are due to the changes in the A, F, and P features of the signal.
The transmitted symbol, m(t), contains a sequence of known data symbols, m _{1}(t),m _{2}(t),.... According to the selected glossary, the pattern that matches the data index is selected and applied to the RF frontend.
The glossary selector is the core component in the transmitter’s design, because it selects the most appropriate glossary from the glossary space as part of the adaptation process. It takes the glossary space information and channel spectral situation—i.e., the SNR value from the environment, as an input to determine the most proper glossaries set in the glossary space by computing the maximum likelihood value. For example, Fig. 1 shows that the measured SNR is 8 dB. Therefore, the glossary selector switches to a 3bit glossary and maps ‘101’ to the sixth pattern (shown in Fig. 2).
2.2 The receiver of PBCCS
The main modules of the receiver are the discrete wavelet transform unit and ANN, as illustrated in Fig. 1 b. The aim of using ANN at the receiver is to predict the original bits of the distorted received signal. The receiver does not construct a similar analog signal or estimate its parameter. Instead, it classifies the input samples to a known pattern, so that the correct bits can be inferred. In the following subsections, we briefly describe the functionality of each part of the receiver.
2.2.1 Features extraction and reduction
One of the aspects of signal classification is the selection of proper classification features. The goal of feature extraction is to obtain a set of features that can discriminate different received signals. In this work, the discrete wavelet transform (DWT) [28] is used to extract the signal features.
The discrete wavelet transform is a linear signal processing technique that transforms a signal r(t) from the time domain to the “wavelet” domain—i.e., wavelet coefficients. A transformation from the time domain to the “wavelet” domain is analogous to the Fourier transform. The key difference between wavelet transform and Fourier transform is that wavelets are local in both time (via translation) and frequency (via dilation), whereas Fourier analysis is local only in frequency but not in time. Because the generated waveforms contain numerous nonstationary or transitory characteristics, which are often the most important parts of signals, Fourier analysis is unsuitable to describe such characteristics. Moreover, the received pattern signal can be represented by a compact form and hold most features that distinguish it from other patterns. As a result, the wavelet analysis is appropriate to capture the changes in the pattern’s frequency over time and achieves better lossy compression, which dramatically reduces the size of ANN.
where n becomes 2n representing the downsampling process. The output of the lowpass filter, y _{ low }[ k], provides approximation signal, whereas the output of the highpass filter, y _{ high }[ k], provides detailed signal. In addition, Eqs. (7) and (8) show that using DWT can not only greatly reduce the number of input nodes, but also effectively expresses the features of the received signal, thereby enhancing the ability of neural networks to recognize the signal.
2.2.2 Recognition layer
After extracting the proper features from the received signal, classifying these patterns into appropriate classes is the final step to recognize the symbol. In this work, the artificial neural network (ANN) [30, 31] is considered as a recognition layer to recover the transmitted data, and it forms the cognitive part of the PBCCS receiver.
In this work, the most common ANN model, namely multilayer perceptron (MLP), is used. MLP is a type of feedforward neural network (FFNN) model that maps the input data onto a set of appropriate outputs. It consists of at least three layers—i.e., the input layer, one or more hidden layers and an output layer. The network is fully connected from one layer to the next as a directed acyclic graph (Fig. 5). Each neuron is capable of multiplying the inputs by its weight and sum up the results. In other words, the neuron operations are performed by multipliers and adders.
Mathematically, for n arbitrary distinct received samples (x _{ i },t _{ i }), where x _{ i } is the extracted features’ vector from the received signal, \( x_{i} = [x_{i1},x_{i2},{\ldots },x_{in}]^{T} \in \mathbb {R}^{n}\) and t _{ i } is the target vector, \( t_{i} = \left [t_{i1},t_{i2},{\ldots },t_{im}\right ]^{T} \in \mathbb {R}^{m} \). n and m are the size of the input feature and the target vectors, respectively. The target vector t _{ i } represents the actual sequence of bits that the recognition layer must produce.
where w _{ ji }=[w _{ j1},w _{ j2},…,w _{ jk }]^{ T } is the weight vector connecting the j ^{ t h } hidden neurons with the inputs and b _{ j } is the bias value of the j ^{ t h } hidden neuron. The bias allows the sigmoid function curve to be shifted horizontally along the input axis while leaving the shape of the function unchanged. w _{ ji }·x _{ i } denotes the inner product of w _{ ji } and x _{ j }.
where M is the total number of output neurons. β _{ j } i=[β _{ j1},β _{ j2},…,β _{ jm }]^{ T } is the weight vector connecting the j ^{ t h } hidden neurons and output neurons and b _{ j } is the bias value of the j ^{ t h } output neuron.
The backpropagation algorithm (BP) [30] is used to compute the weights and biases of the ANN by minimizing the error function in weight space using gradient descent.
where O _{ j } is the j ^{ t h } the output neuron.

Input neurons: the number of neurons is equivalent to the sample size of the DWT vector.

Hidden neurons: due to low complexity and high applicability perspective [10], a single hidden layer with few number of neurons should be used. The number of neurons will be determined by the cross validation method.

Output neurons: The number of output neurons should be identical to the size of the glossary space—i.e., total number of patterns. However, each glossary differs in the number of symbols that it represents. For instance, the 3−bit glossary has 8 symbols while 4−bit glossary has 16 symbols. Therefore, the size of the glossary can be added to determine the width of the output sequence bits.
3 Experimental results
In this section, the performance of the proposed PBCCS based on the extracted features (discussed in Section 2) is verified in an AWGN channel. At the end of this section, the proposed approach complexity is presented.
3.1 Simulation settings
Simulations were carried out to transmit 2^{ k } different symbols (kbit glossary) at various SNR levels. The SNR levels were in the range of [ −15,25] dB. The ANN parameters are shown in Table 4. All experiments were performed using Matlab software.
3.2 Constructing the glossary
Base signal specifications
Feature  L2  L1  L0  L1  L2 

Frequency (kHz)  4.600  5.000  5.600  6.600  7.400 
Phase (rad)  −π/2  −π/4  0  π/4  π/2 
Amplitude (V)  0.1  0.2  0.45  0.7  0.9 
ANN parameters
Parameters  Value 

Number of layers  2 
Number of input nodes  220,55,27 
Number of output neurons  3,4,5 
Activation function  Sigmoid 
Training algorithm  Scaled conjugate gradient 
Gradient error level  1×10^{−6} 
Performance function  Mean squared error 
Number of neurons in hidden layer  Varied from 8 to 40 
Maximum number of epochs to train  3000 
3.3 Learning process and model evaluation
where N is the total number of test symbols and x _{ i } is an indicator whose value is 1 if the i ^{ t h } symbol is correctly received. In other words, S u c c e s s R a t e measures the symbol error rate (SER).
In addition to the success rate, the BER performance is used to assess the accuracy of the whole system. It expresses the number of bit errors per second divided by the total number of transferred bits.
3.4 Classification performance of different wavelet families
In this section, we study the effect of applying different wavelet families on the performance of the receiver for 3bit glossary. The received signal has 880 samples. The number of input nodes was subsequently reduced from 220 to 55 and 27 to identify the most relevant input features to ANN by employing 2, 4, and 5level DWT decomposition (j=2,4 and 5). The ANN model was then trained for different numbers of neurons in the hidden layer. These experiments were repeated 10 times, and the success rate was averaged.
In Fig. 8 b, the effect of using a triangle wavelet is shown, which is similar to Fig. 8 a. However, the success rate of the model with 55 neurons outperforms the model that has 220 inputs. The improvement of the input size reduction to 55 inputs by using DB2 is illustrated in Fig. 8 c. The success rate is greater than 97% with more than 12 hidden neurons (with the exception of the case with 27 inputs).
DB5 wavelet has similar performance compared to the DB2, as shown in Fig. 8 d. Similar result was also obtained by using a coiflets (C6) wavelet as shown in Fig. 8 e. The figure shows that with 55 input nodes and 10 hidden nodes, the performance is improved compared with the experiment of 220 input nodes.
In summary, we found that for 3bit glossary the DB2 wavelet has better performance compared with other wavelet families studied in our tests. It is also found that with a 27−input ANN, the performance is better than that when using many extracted features. Furthermore, the use of 14 hidden neurons or more has a similar recognition rate to a network that contains 8 hidden neurons. As a result, an ANN that is based on 5level DWT can be realized with 27 inputs and as minimum as 14 hidden neurons. This reduction will use fewer resources during the hardware design realization.
3.5 Classification performance of various learning algorithms
ANN parameters
Parameter  Value 

Maximum number of epochs to train  25 
Initial μ value  0.1 
Decrease factor (α)  0.2 
Increase factor (β)  6 
Minimum performance gradient  10^{−5} 
Performance function  Mean squared error 
The average MSE versus number of hidden neurons are shown in Fig. 10 d. Smaller values that are close to zero are better because they indicate that the MLP had fitted the data well. SCG, GDX, and BR learning algorithms have better performance compared with LM algorithm because the number of iterations of LM was limited to 25 iterations. Increasing the number iterations will improve the MSE values but has dramatically effect on learning time.
3.6 System performance with kbit glossary spaces in AWGN Channel
Figure 11 shows a strange behavior as the BER carve reaches 10^{−5}, where some errors increases again. We expect that the ANN could not distinguish between the samples either because the learning process is not enough or it overfits the data.
In summary, we found that the best performance of 4 and 5bit glossary space is achieved when the number of hidden neurons is between 20 and 40 neurons. This means that the BER of an ANN with a hidden layer of 20 neurons is approximately equal to an ANN configuration with higher hidden units. This phenomenon indicates that an increasing number of hidden neurons does not always improve the performance. As a result, the best PBCCS performance can be realized with a fixedstructure ANN of 27 inputs nodes and 20 hidden neurons for 3, 4, and 5bit glossaries.
3.7 Spectral efficiency
Spectral efficiency of PBCCS at P _{ e }=10^{−5} bit error probability
Glossary  3bit  4bit  5bit 

M (symbols)  8  16  32 
SNR value (dB)  5  2  4 
Data rate (kbps)  2.508  3.553  4.6 
Average BW (kHz)  0.960  0.881  0.9135 
LSE, η, (bps/Hz)  2.61  4.0318  5.03 
Equation 14 states the condition of reliable communication in terms of bandwidth efficiency, η, and power efficiency in terms of E _{ b }/N _{0}. Figure 12 shows the minimum value of E _{ b }/N _{0}=−1.59 for which reliable communication is possible. The marks in the figure show the best working point regarding the glossary at a 10^{−5} bit error rate and M−QAM. This figure depicts that the 4bit glossary and 16QAM have the same spectral efficiency, but the 4bit glossary is more robust to high levels of AWGN than 16QAM. Similarly, 5bit glossary is more robust than 32−QAM at the same spectral efficiency, η=5.
However, the most interesting finding is that the 3−bit glossary breaks down the Shannon limits. This phenomenon occurs because the ANN can perfectly discriminate among the eight signals of the 3−bit glossary. In the learning step, the ANN model has constructed a model that allows the PBCCS to classify any unseen signal, in a manner analogous to memory. Another reason for breaking down the Shannon limit is the usage of nonperiodic signals. Shannon’s law is restricted to periodic signals [34]. The PBCCS constructs a nonperiodic and uncorrelated communication waveforms that provide a manageable SNR capability between high noise redundancy and high data bandwidth requirements under observed spectrum conditions.
It is worth mentioning that this result depends on the difference between the bandwidth of recovered digital data based on a priori information in the glossary and the raw physical data bandwidth inside the communication medium. In addition, the synchronization overhead between the transmitted symbols is not considered.
3.8 Bit error rate comparison
where Q(x) is the Qfunction. Q(.) is a monotonically decreasing function of its argument; the probability of error decreases as the ratio \(\frac {4E_{b}}{5N_{o}} \) increases. This means that the decision boundary of the QAM technique depends on increasing the signal energy, which makes the binary signals dissimilar. However, the PBCSS depends not only on the signal energy but also on the extracted features from the received signal by DWT and the nonlinear model of ANN, which enable the PBCCS model to reduce the probability of error.
3.9 System performance comparison with AMC
Comparison between different works in terms of features, ANN model and the achieved SNR with the recognition accuracy
Reference  Application  Applied features  Type of ANN  Recognition accuracy (%) 

[22]  AMC  Instantaneous temporal featurebased  FANN (5,19,8) and PANN (5,1800,8)  Overall success rate at 5 db are 65.63% and 55.5% respectively. 
[23]  AMC  Instantaneous temporal featurebased modulation  FANN (4,7,5)  the overall success rate at 5 dB is 99.65%. 
[25]  AMC  Continuous wavelet transform (CWT)  N/A  The overall success rate at 0 dB is 99.6% (using 10 features). 
[26]  AMC  Instantaneous information and signal spectrum  N/A  The overall success rate at 3 dB is 98.6% (using 10 features). 
[37]  AMC  Combination of the higher order moments, higher order cumulants and instantaneous characteristics of digital modulations  Radial basis function (RBF) probabilistic neural network (PNN)  The overall success rate at 3 dB is 87.50%. The overall success rate at 3 dB is 86.45%. 
[38]  AMC  7level DWT  Adaptive Network Based Fuzzy Inference Systems of 5 hidden layers  The overall success rate using DB2 at 5 dB is 98%. 
[39]  AMC  Haar Wavelet Transform  N/A  The overall success rate at 7 dB is 99.71%. 
[40]  AMC  Haar Wavelet Transform  N/A  The overall success rate at 5 dB is 97.93%. 
[27]  Modulation classification and signal encoding  1level DB2 DWT  FFNN(30,14,3)  The overall success rate a 11 dB for 3bit glossaries is 96.0%. 
PBCCS  Modulation classification and signal encoding  5level DB2 DWT  FFNN(27,14,3), FFNN(27,14,4), FFNN(27,14,5)  The overall success rate at 11 dB for 3bit, 4bit and 5bit glossaries are 99.0%, 90.3% and 72.79%, respectively. 
3.10 Receiver space complexity
After simulating the proposed approach, the next step is to verify the design on real hardware such as a fieldprogrammable gate array (FPGA) and applicationspecific integrated circuit (ASIC). We prefer using FPGA because the parallel structure of an ANN and the similarity of neurons makes its design simple and straightforward.
Each FPGA comes with limited resources, which poses challenges for real implementation. Space complexity gives an indication of the number of used functional units. It approximates the numbers of connections, multipliers and adders that the real design will occupy when it is implemented on an FPGA.
At the receiver, each neuron of the implemented ANN has a set of multipliers that are used to multiply the weight of the connections with the received data values. For example, if there are 26 2input nodes, then each hidden neuron requires 26 multipliers and 26 2input adders (including one adder to the bias). Because multipliers are more expensive than the adders and each FPGA comes with a limited number of them, they, in fact, significantly influence the design. For instance, Xilinx Virtex VI xc6vlx240t1ff1156 has 768 multipliers (named DSP48E1) [33].
Space complexity comparison between the proposed approach and time delay ANN [10]
Parameters  Wavelet and ANN  Time delay ANN  

k=3  k=4  k=3  k=4  
Number of layers  2  2  2  2 
bit size of glossary space  3  4  3  4 
Input neurons  27  27  120  120 
Hidden neurons  20  20  20  50 
Output neurons  3  4  3  4 
Number of multipliers  600  620  2460  2480 
In addition to the impact of the neural network, the wavelet decomposition has effect on the space complexity of the receiver. Similar to the finite impulse response (FIR) filter, the wavelet decomposition convolves wavelet coefficients with the received signals. This convolution process requires as many multiplication resources as the number of filter taps. For example, DB2 and DB5 can be implemented as 4tap and 10tap FIR filters, respectively. Furthermore, it is an iterative process—i.e., the output of one stage is an input to the next stage (Fig. 3). The direct implementation DWT, known as the multiplyaccumulate structure (MAC), requires as many resources as the number of stages times the numbers of filter taps—i.e., 5level DB2 requires 20 multipliers. An alternative but efficient implementation could be achieved by means of the distributed arithmetic algorithm (DAA) [35, 36]. DAA efficiently realizes the sumofproducts computation by means of memory (LUT), adders and shift registers, without employing any multipliers. That is, the total number of multipliers at the receiver will not be affected by the DWT implementation.
4 Conclusions
PBCCS was designed to increase the spectral efficiency by constructing a secure and nonperiodic communication signals. In addition, PBCCS minimizes the bit error rate through optimized signal patterns that are decoded solely by DWT preprocessed signals and artificial neural network.
In this article, we analyzed the performance of ANN to recover original transmitted symbols using wavelets as a feature extractor. We applied different wavelet decomposition techniques to study their effects. Several experiments were conducted to find the most appropriate wavelet family for PBCCS. The results obtained are intended to be a guidance tool in selecting the most appropriate operating point of the glossary selector with the discrete wavelet family at the receiver. We found out that the DB2 wavelet decomposition filter shows better performance compared with the other studied wavelet families. Thanks to DWT, a simple ANN structure was constructed with few hidden neurons, which is impossible for a thirdparty to predict. In addition, we studied the effect of various backpropagation learning algorithm. We could conclude that in terms of learning time and performance, both SCG and GDX are better to handle large dataset that includes thousands of signals. Finally, because of robustness to stationary noise, the proposed approach has a great advantage of less bit error, unlike the standard modulation techniques, which has higher bit error rate.
The simulation results also reveal that by using 5level DWT and a neural network, SNR values of 5 dB, 2 and 4 dB are achieved at a BER of 10^{−5} for 3bit, 4bit and 5bit glossary spaces, respectively. The advantage is obvious, because the transmitter can adapt the bit rate according to SNR values. Therefore, adaptive glossary and its performance can be considered in a future work.
An initial evaluation of hardware implementation was demonstrated, and the applicability of the proposed modulation technique and the recognition layer were discussed. In brief, according to our preliminary works on the FPGA platform, the system can be realized with limited level glossaries in the existing technology. The next future step of this work is validating the simulation and preliminary laboratory testbed results under real application and environmental conditions.
Declarations
Acknowledgements
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the article.
Funding
There are no sources of funding body reported for this manuscript.
Authors’ contributions
All authors contributed to the work. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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