A New Multi-Dimensional Hybrid Deep Neural Network Based Spectrum Inference for Cognitive Radio Network

2.1 System model

In this paper we have used real time spectrum dataset collected from our previous spectrum measurement campaigns. This dataset features radio signal power spectral density values measured in dBm at frequency resolution of 200 KHz from 700 MHz to 2.7 GHz. This interval of 200 KHz represents a channel, collection of all such channels for a telecom service represent a band. After data pre processing we first convert the signal power data in time/frequency domain to a binary occupancy matrix using thresholding technique described in the study [17, 18]. This matrix is used to compute band wise spectrum occupancy.

In spectrum inference, spectrum occupancy states are predicted over frequency range based on the measured occupancy data in time and frequency domain. Each measured frequency point is considered to be representing a frequency channel with busy and free channel state given by following hypothesis Eq. (1):

$y=\left\{\begin{aligned} n, & \mathcal\,{H}_0: { Channel \,is \,free } \\ H x+n, & \,\mathcal{H}_1: { Channel \,is \,occupied }\end{aligned}\right.$          (1)

where, x denotes transmitted signal, n represents noise, $\mathcal{H}$ represents channel matrix and y denotes received signal.

Let O_t(k),f(n) represent multi-dimensional spectrum occupancy of telecommunication bands in two dimensions with time instant t(k) and frequency f(n). Following Eq. (2), shows hypothesis for classifying a channel band as occupied and free using real time measured Power Spectral Density (PSD) P_γ value in dBm and comparing with the decision threshold γ:

$O_{t(k), f(n)}= \begin{cases}0, & \mid \quad P_\gamma<\gamma \\ 1, & \mid \quad P_\gamma>\gamma\end{cases}$               (2)

Eq. (3) shows calculation of average occupancy of each spectrum band, N is the total number of the measured frequencies in complete band, K denotes the number of corresponding time samples at this frequency:

$O=\frac{1}{K N} \sum_{k=1}^K \sum_{n=1}^N O_{t(k), f(n)}$         (3)

The dataset generated is a multi-dimensional time/frequency occupancy matrix [18]. This data exhibits temporal and spectral correlation. Study has revealed short term dependency in terms of channel vacancy durations and long term dependencies with respect to service rate congestions [17]. These features can be used with the dataset for training, testing and validating machine learning, deep learning and hybrid deep learning models for inferring spectrum.

2.2 Artificial neural network based machine learning models

Multi-layer Perceptron (MLP) artificial neural networks employ single input/output layer and multiple hidden layers. It uses activation functions like sigmoid, tanh (hyperbolic tangent function) tanh, ReLU (Rectified Linear Unit) to learn complex patterns in the data. It uses back propagation algorithm and adjusts its weights and biases for error minimization via gradient descent. It has a complex structure and is difficult to interpret due to large number of parameters involved. It can suffer over fitting easily when handling high dimensional spectrum data and becomes computationally expensive when dealing with large datasets like spectrum data.

2.2.1 Radial basis function neural network (RBFNN)

RBF neural networks are feed forward neural networks in structure same as MLP network. It has only one hidden layer as shown in Figure 1. This hidden layer forms the feature vector. A non-linear transfer function called radial basis is applied to the feature vector to increase dimension before being fed for classification.As shown in Figure 1, nodes of hidden layer do radial basis transformation. Here hidden layer outputs are linearly combined with hidden layer outputs to generate final output value. The neural activation function for RBFNN is given by Eq. (4):

$\varphi(x)=e^{-\beta\left\|x-c_i\right\|^2}$          (4)

where, $\beta=\frac{1}{2 \sigma_j^2}$.

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Figure 1. Structure of radial basis function neural network

where, $\|.\|$ is the Euclidean norm, c denotes center and σ is a width parameter. The output of a node k of the output layer is given by Eq. (5):

$y_k=\sum_{j=1}^n w_{j k} \varphi_j(x)$          (5)

where normally, Least Mean Square (LMS) algorithm is employed for error minimization by continuous updating weights. Network training is terminated when error condition meets decision threshold criteria. Testing and validation of network is then done for newly updated weights.

RBF networks have been chosen for this study since they tend to be effective in dealing with dataset where data points tend to cluster around a center point. In spectrum data the occupancy tends to cluster in downlink, uplink and center frequencies. RBF networks tend to generalize better and quickly due to their abilities to focus around local clusters. This is an added advantage which makes them less susceptible to over fitting. In RBF networks initially numbers of radial basis functions are determined with their corresponding centers. In this case clustering algorithm like k-means may be used. The next step is to measure closeness of input data with the established center. This is done using a gaussian activation radial basis function. Here weights are determined using least square estimation or gradient descent. Training includes optimization of centers, widths of radial basis functions and weights.

2.2.2 LSTM neural network

LSTM based on Recurrent Neural Network (RNN) architecture deals excellently with data which is temporally correlated; it cannot handle long term time dependency in practice. Basic LSTM cell unit comprises of three gates namely input (i), output (o) and forget (f). These gates have control over what is being read, written and stored in the cell unit. Additionally candidate cell unit (g) is used to add information to cell. An LSTM layer has an output state (called hidden state) and intermediate cell state. LSTM cell unit shown in Figure 2 retains information from past states. At every time step LSTM layer adds or deletes information using gates. In this way long-term dependencies amongst different time steps are learned for time series or sequence data.

Different weights involved in learning include W (Input Weights), R (Recurrent Weights) and b (Bias).

$\boldsymbol{W}=\begin{gathered}W_i \\ W_f \\ W_g\end{gathered}, \, \boldsymbol{R}=\begin{gathered}R_i \\ R_f \\ R_g\end{gathered}, \,\boldsymbol{b}=\begin{gathered}b_i \\ b_f \\ b_g\end{gathered}$,

For every time step t cell state is given by Eq. (6):

$c_t=f_t \odot c_{t-1}+i_t \odot g_t$         (6)

where, ⊙ being the Hadamard product.

For time step t the hidden state is given by Eq. (7):

$\mathrm{h}_{\mathrm{t}}=\mathrm{O}_{\mathrm{t}} \odot \sigma_{\mathrm{c}}\left(\mathrm{c}_{\mathrm{t}}\right)$         (7)

where, σ_c is the state activation function normally hyperbolic tangent function (tanh).

The formulae’s used for computation at different gates are shown in Table 1.

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Figure 2. LSTM cell unit

Table 1. Mathematical formulae for computation at gates

where, σ_g is gate activation function normally sigmoid function $\varphi(x)=\frac{1}{1+e^{-x}}$.

2.2.3 BiLSTM neural network

Individual ANNs like MLP and RBF are prone to vanishing gradient problems when subjected to long sequential data. They are inefficient to capture long term dependencies. To overcome this LSTM/BiLSTM networks are particularly designed to learn from long sequence data. They have memory cell gate units to remember long term dependencies and forget gate mechanism to discard redundant information. This mechanism of selectively remembering and discarding information makes these networks efficient for long datasets like spectrum data.  MLP and RBF are suitable for dataset where data points are independent of each other but in case of spectrum dataset where data is sequential a recurrent neural network like LSTM and BiLSTM can offer better results. With this intuition these deep neural networks have been investigated for their performance for spectrum dataset.

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Figure 3. BiLSTM network

Better training can beachievedin Bidirectional LSTM (BiLSTM) model by two way information flow one from past and another from future. The immediate advantage of such capability is additional training to enhance prediction accuracy. In Figure 3, a model structure for BiLSTM is shown with different layers and Input/Output.

2.3 Methodology

2.3.1 Proposed methodology

ANNs excel in extracting spatial features of data whereas RNN work very well for temporal dependencies. A hybrid approach thus tends to learn more information and has a better representation. ANNs can generalize data patterns effectively and RNNs can extract contextual information in long sequential data. The spectrum dataset has short term dependencies given by channel vacancy durations and have long term dependencies across locations, services given by service congestion rates [17]. In this work the hybridization of ANN and RNN is being motivated by intrinsic characteristics of data dependencies in spectrum dataset both short term and long term. Our research questions are aimed at determining whether it is possible to produce hybrid models that outperform single models with different domains and types of datasets.

LSTM and BiLSTM are proven algorithms in many applications domains. Here we investigate use of a hybrid model based on these networks for spectrum occupancy inference. We have investigated deep integration of two major recurrent neural networks namely LSTM and BiLSTM to build a hybrid model with RBF. In our proposed model Hybrid RBF-BiLSTM (Hyb R-BiLSTM) has been further analyzed to investigate its competitiveness with existing classical neural networks MLP, RBF, HNN and deep neural networks LSTM, BiLSTM, Hybrid MLP-LSTM (Hyb M-LSTM) and Hybrid MLP-BiLSTM (Hyb M-BiLSTM). The proposed methodology is as illustrated in Figure 4.

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Figure 4. Methodology of the proposed Hybrid model

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Figure 5. Hybrid R-BiLSTM based spectrum occupancy prediction model architecture

In order to hybridize two different neural network architectures we use a Flatten mechanism to convert the MLP/RBF output to a single featured vector data to be processed by fully connected layer of LSTM/BiLSTM. This mechanism basically reshapes the data vectors to match the mini batch dimensions of underlying layers. The evaluation metrices under consideration includes F₁ score, RMSE (Root Mean Square Error), Recall and Precision. This proposed Hybrid R-BiLSTM based spectrum occupancy prediction model architecture is as seen in Figure 5.

The detail steps for predicting future spectrum occupancy states in time and frequency dimensions are outlined in the proposed algorithms. In the first algorithm we train our model with RBFNN model as the first step and then combine the result in second algorithm with Hybrid BiLSTM based prediction.

2.3.2 Proposed algorithms

Algorithm 1: To design a radial basis function network for spectrum inference in cognitive radio network

Input: Historical spectrum occupancy data in time and frequency dimensions with feature vectors

Output: RBFN neural network

Load dataset with feature vectors frequency wise

1. Initialize design parameters for two layer Radial basis network (RBFN) model
2. Select inputs
   
   1. X$\leftarrow$P-by-Q matrix for the input N vectors
   2. V$\leftarrow$R-by-S matrix of M vectors as targets
3. Set MSE (mean square error) as design goal
4. Add neurons in steps to radial basis network’s hidden layer and compute MSE and evaluate the set goal.
5. Set second parameter ‘spread’ for radial basis function

RBFN Simulation steps

1. Set ‘radbas’ neurons for first layer
2. Calculate weights ‘dist’ and ‘netprod’ for net input
3. Set purelin neurons for second layer
4. Calculate ‘dotprod’ for weighted input and ‘netsum’ for net inputs
   
   1. do while (input vector has high error)
      
      1. add radbas neuron to vector with corresponding weights
      2. update ‘purelin’ layer weights such that error is minimum
   2. Return (new radial basis network)
   3. end
5. Save RBFN network

Algorithm 2: To design a hybrid RBFN based BiLSTM network for spectrum inference in cognitive radio network

Input: Historical spectrum occupancy data in time and frequency dimensions with feature vectors

Output: Predicted spectrum occupancy states

Start

#Import predesigned RBFN network from Algorithm 1

1. Initialize
2. Load RBFN designed network
3. Assign inputs xdata1$\leftarrow$ data1 and target $\leftarrow$data2
4. Simulate the specified model RBFN using existing model configuration parameters

#Database creation

1. Create Database with feature vectors and target vector.
2. Initialize Sequence Length to create dataset input for BiLSTM model
3. Create a Hybrid Database by combining feature vectors from input dataset feature file and targets from simulated RBFN network model as per Sequence Length.
4. Flatten the data input of RBFNN to compact it with HybridInput
5. Initialize ResultDatabase to Hybrid Database
6. Select training & testing samples from Hybrid Database as per training & testing sample ratio.
   
   1. resTrain$\leftarrow$Feature vector inputs from Hybrid Database
   2. occTrain$\leftarrow$Target output from Hybrid Database

#Training

1. Initialize learning parameters for Hybrid R-BiLSTM network
   
   1. set numFeatures$\leftarrow$ no. of feature vectors
   2. set numHiddenUnits$\leftarrow$no. of hidden layers
   3. set numResponse$\leftarrow$ occupancy
2. set MaxEpoch$\leftarrow$ maximum no. of iterations
3. set miniBatchSize$\leftarrow$ no. of observations for each iteration
4. Initialize different layers of deep neural network
   
   1. sequenceInputLayer with numFeatures
   2. BiLSTM layer with numHiddenUnit
5. fullyConnectedLayer
6. regressionLayer
7. Set options for training the network
8. Choose appropriate solver (optimizer) for training network ‘adam’
9. Set the ExecutionEnvironment
10. Turn on Plots and training-progress
11. Train HybridDeepNeuralNetwork model for regression with
    
    1. occTrain$\leftarrow$ time series predictors
    2. restrain $\leftarrow$ responses
12. Save HybridDeepNeuralNetwork model as HybRBiLSTM net

#Testing

1. Initialize 
   
   1. occTest$\leftarrow$ target samples form Database
   2. resTest$\leftarrow$testing samples from ResultDatabase
2. Predict responses YPred using the trained HybridDeepNeuralNetwork model and update the network          
3. Stop

#Error & Accuracy Performance Analysis

1. Compute error e = (resTest-YPred)
2. Compute all network performance functions of the designed network
   
   1. Mean of Squared Errors
   2. Mean of Absolute Errors
   3. Root of Mean of Squared Errors
3. Compute network performance accuracy of the designed network with confusion matrix as a metric to evaluate precision, accuracy and F₁-score

Stop

2.3.3 Performance metrics for evaluation and comparison

Confusion matrix is used here for quantifying accuracy with performance metrics f₁-score, precision and recall. To compare error performance following metrics given by Eqs. (8-10) have been computed.

Mean Absolute Error (MAE):

$M A E=\frac{1}{n} \sum_{\text {sum }}|y-\hat{y}|$        (8)

where, y is true output value and $\hat{y}$ is predicted output value.

Mean Square Error (MSE):

$M S E=\frac{1}{n} \sum_{i=1}^n\left(y_i-\widehat{y}_l\right)^2$        (9)

Root Mean Squared Error (RMSE):

$R M S E=\sqrt{\frac{1}{n} \sum_{i=1}^n\left(y_i-\widehat{y}_l\right)^2}$          (10)