Deep Learning for Spectrum Prediction in Cognitive Radio Networks: State-of-the-Art, New Opportunities, and Challenges

Various frequency bands are allocated for diverse spectrum services, encompassing applications such as broadcasting TV, GSM900 (both uplink and downlink), ISM, GSM1800 (both uplink and downlink), and similar services. The interplay of factors such as the number of spectrum devices, user mobility, and patterns of usage imparts unique temporal and spectral correlations to each spectrum service. The intricacies of this multifaceted time-frequency correlation are notably nonlinear, presenting a challenge for conventional methodologies. To overcome this challenge, the application of DL-models becomes pertinent. These models prove effective in capturing the nuanced time-frequency correlations by directly assimilating spectrum correlations from measurements across distinct frequency bands, subsequently encapsulating this information in a parameterized format within the neural network architecture.

As an attempt, LSTM was employed to learn the temporal correlations of multiple spectrum channels. Gao et al. [3] utilized LSTM and attention mechanisms to design a sequence-to-sequence model for achieving multi-channel, multi-step spectrum prediction. Supervised learning is adopted for the model optimization. Once the model is adequately trained, supervised learning transitions to the prediction phase. In this stage, only a specific length of historical spectrum data is input into the prediction model to predict the future spectrum state without any prior information. To further improve predictive performance, Yu et al. [4] combined CNN and gated recurrent unit (GRU) (a variant of the LSTM) networks to design a model called DCG for spectrum availability prediction. Recognizing the local correlations among different channels within the same time slot and regional correlations across multiple time slots, Yu et al. employed one-dimensional convolution to delve into the occupancy patterns of local channels and two-dimensional convolution to explore the occupancy patterns of regional channels. Subsequently, GRU was leveraged to encapsulate both short-term and long-term temporal dependencies within the data processed by the dual CNN.

Given the extensive range of frequency bands utilized by wireless devices, the amalgamation of vast spectrum data inherently results in high-dimensional data. Simultaneously, there is a heightened demand for the model’s proficiency in extracting features. To tackle this challenge, Pan et al. [5] initially employed stacked autoencoders (SAE) to diminish the dimensionality of the high-dimensional spectrum data while automatically extracting features without disrupting its internal temporal and frequency relationships. The extracted features were then fed into a CNN and bidirectional LSTM (Bi-LSTM) fusion network to grasp the frequency and time dependencies. However, due to the constraints of the Bi-LSTM gating structure, it demonstrated excellent short-term predictive performance but relatively weaker long-term predictive performance. To surmount this limitation, Pan et al. [6], drawing inspiration from the Transformer architecture, devised a long-term spectrum prediction method named Autoformer-CSA. Autoformer-CSA employs a self-attention mechanism, integrating series spatial and channel attention modules with autocorrelation mechanisms. This enables the model to allocate varying degrees of attention to different positions in the spectrum sequence, effectively capturing the long-term trends and seasonal characteristics of spectrum data.

Fig. 2 presents a comparison of the root mean square error (RMSE) performance between the DL-based approach and the traditional HMM prediction method across various prediction ranges. The dataset utilized for these comparative experiments is derived from real-world spectrum data collected by sensors deployed in the city center of Madrid, Spain (obtained via the Electrosense open API, https://electrosense.org/). The scanned frequency range spans 600-640 MHz with a 2 MHz sampling interval. Data collection took place from June 1, 2021, to June 8, 2021, with a sampling interval of 1 mins. The division of the training set, validation set, and test set followed a 5:1:1 ratio. Fig. 2 shows that the RMSE errors of the DL-based prediction methods are significantly lower than those of the traditional HMM-based prediction method. For instance, at a prediction range of 96 mins, LSTM with attention, DCG, and Autoformer-CSA exhibit 14.66%, 30.58%, and 39.77% higher RMSE performance, respectively, compared to HMM.

Unlike traditional time-frequency prediction, DL-based spatiotemporal spectrum prediction faces two key challenges: reconstructing spectrum map data for large RoIs and capturing heterogeneous time-frequency-space correlations.

To overcome these challenges, Li et al. [7] initially delved into historical data collected from a network of sparsely distributed spectrum sensors. They employed an inverse-distance spatial interpolation method to extrapolate the spectrum map across the entire RoI. They utilized predictive recurrent neural network (PredRNN) to discern the spatial-temporal correlations embedded in the spectrum map. Employing three identical PredRNN components, they modeled the temporal proximity, daily cycle, and weekly trend of the spectrum image. Ultimately, Li et al. used parameter matrices to integrate the features extracted from these three components. This refined approach to feature extraction has proven effective in significantly enhancing the model’s predictive performance.

According to the path loss model in [8], it’s clear that wireless signals follow exponential decay with distance. As the average received power at nearby locations tends to be similar, there’s a higher spatial correlation. In simpler terms, only sensors close to the unsensed area can provide signal power information that has a certain correlation with the data in the unsensed area. Therefore, Ren et al. [8] went a step further and employed a neighboring spatial interpolation method to estimate the spectrum map for the entire RoI. This method is compared with a tensor completion, and the proposed approach achieves the minimum error rate at a low sparsity level. Note that in addition to the above methods there are Kriging, kernel-based, and improved tensor completion methods. Ren et al. proposed a spatiotemporal spectrum prediction method combining CNN and ResNet to capture spectrum matrix spatiotemporal features, using skip connections to improve performance and prevent gradient vanishing.

A deep GAN (DGAN) consists of a generator and a discriminator. The GAN’s aim is to train the generator network to produce realistic data, while the discriminator network distinguishes between generated and real data. These two networks engage in mutual adversarial training, propelling the learning and improvement of the model. Consequently, GAN can be employed to boost the quantity of trainable data for the target band.

Peng et al. [9] introduced a spectrum data conversion GAN to generate realistic data for the target band. Initially, they used Fréchet inception distance (FID) to measure differences between the target band and other bands, pinpointing the source band with the least difference from the target predictive band. Peng et al. then crafted a generator using a blend of CNN and LSTM to transform data from the source band to the target predictive band. Subsequently, the prediction model utilized both the transformed data and the original data from the target band for training and prediction.

It’s essential to note that this method doesn’t directly generate the target prediction data but leverages highly similar data from other bands. This is because traditional GANs have specific requirements for the quantity of target samples, and insufficient target samples can lead to GAN instability. Additionally, this approach reduces the dependency of the GAN on existing data from the target band. Lin et al. [10] similarly utilized FID to identify a source band with high similarity to the target band. They then devised a deep convolutional GAN (DCGAN) for pre-training using the source band. Subsequently, transfer learning was employed to fine-tune the pre-trained model onto the target band, generating data with minimal differences. Finally, the generated data for the target band, along with the original data, was used for training and prediction in a residual prediction model.

Transfer learning (TL) aims to distill knowledge from one or multiple source tasks and apply that knowledge to related but different target tasks. Building upon this TL concept, deep transfer learning (DTL) has emerged as a secondary approach to tackle this challenge. DTL efficiently achieves cross-band spectrum prediction by transferring pre-trained models from the source band to the target task.

Lin et al. [11] implemented cross-band prediction through a naive TL approach by transferring a prediction model comprised of LSTM units. To ensure positive TL, Lin et al. analyzed the similarity between source and target bands and used dynamic time warping to measure the similarity of each frequency point between source and target bands. Subsequently, Lin et al. employed a transfer component analysis method, utilizing maximum mean discrepancy as the distance measurement, based on the marginal distribution of features to obtain features with strong transferability.

For an additional performance enhancement, Li et al. proposed a transfer time-frequency fusion attention network (T-TF²AN) to achieve cross-band spectrum prediction. The primary challenge in applying TL for TF²AN stems from the gaps between source and target bands, resulting from variations in spatial, temporal, or spectral domains. Li et al. addressed these challenges through weighted TL, adaptively discovering and transferring shared knowledge while mitigating the negative impact of specific domain patterns from the source spectrum. The core components of the designed weighted TL are the shared pattern learner and the loss with adaptive weights. The shared pattern learner assigns higher weights to source spectrum data similar to the target spectrum, incorporating more shared patterns. Adaptive weights are determined by appropriately weighting the loss from the source domain, diminishing the risk of negative transfer and effectively enhancing the model’s performance on the target domain dataset. It’s noteworthy that the T-TF²AN model not only considers cross-band prediction but also takes into account spatial and temporal transferability.

Assuming that there are $S$ sparsely distributed spectrum sensors in a RoI divided into $M(\text{rows})\times N(\text{columns})$ grids to measure the radio signal power in the area. Considering the hardware cost, it is not feasible to deploy sensors at every location. Therefore, we adopt the commonly used inverse-distance spatial interpolation method to fill in the missing signal power at unmeasured locations. These measurements at any given time step $t$ can be represented as a tensor $\mathcal{X}_{t}\in\mathbb{R}^{C\times M\times N}$, where the measurements are mapped to three channels ($C=3$) using a common Jet colormap. The spatiotemporal spectrum prediction problem involves predicting a spectrum sequence of the most probable length-$K$ time steps in the future based on a spectrum sequence of historical length-$J$ time steps, including measurements at the current time step, represented as

In spatiotemporal spectrum prediction, most works adopt convolutional structures to capture spatial correlations, such as PredRNN used in [7]. However, due to the limitations of convolutional kernel size, convolutional structures may struggle to capture global information. The fixed parameter-sharing mechanism in convolution operations makes it challenging for the model to handle spatiotemporal correlations at different locations. Compared to convolutional structures, vision Transformers (ViTs) excel at capturing spatial correlations due to their self-attention-based global learning patterns. Inspired by this, we integrate ViT and PredRNN to propose an extended spatiotemporal spectrum prediction framework called ViTransLSTM. The innovation of this framework lies in replacing the core component ST-LSTM in PredRNN with our designed ViT-LSTM component. The overall structure of the ViT-LSTM component is shown on the left of Fig. 3.

As a variant of ST-LSTM, spatiotemporal ViT-LSTM consists of two sets of gate structures: a standard temporal ViTransMemory and a spatiotemporal ViTransMemory. In the standard temporal ViTransMemory, all the inputs $\mathcal{X}_{t-J+1}$, $\cdots$, $\mathcal{X}_{t}$, hidden states $\mathcal{H}_{t-J+1}$, $\cdots$, $\mathcal{H}_{t}$, cell outputs $\mathcal{C}_{t-J+1}$, $\cdots$, $\mathcal{C}_{t}$, and gates, i.e., input ViTransGate $i^{vit}_{t}$, input-modulation ViTransGate $g^{vit}_{t}$, forget ViTransGate $f^{vit}_{t}$ are 3D tensors in $\mathbb{R}^{C\times M\times N}$. In the spatiotemporal ViTransMemory, all the inputs $\mathcal{X}_{t-J+1}$, $\cdots$, $\mathcal{X}_{t}$, hidden states $\mathcal{M}^{l-1}_{t-J+1}$, $\cdots$, $\mathcal{M}^{l-1}_{t}$, cell outputs $\mathcal{M}^{l}_{t-J+1}$, $\cdots$, $\mathcal{M}^{l}_{t}$, and gates ${i^{{}^{\prime}}}^{vit}_{t}$, ${g^{{}^{\prime}}}^{vit}_{t}$, ${f^{{}^{\prime}}}^{vit}_{t}$, $o^{vit}_{t}$ are also 3D tensors in $\mathbb{R}^{C\times M\times N}$. The equations of ViT-LSTM in the $l$-th layer are shown as follows:

where $\sigma$ is the sigmoid activation function, $\ast$ is the convolution operator, $\odot$ is the Hadamard product, $[\cdot,\cdot]$ is the operation of concatenating two tensors, and $\text{vit}(\cdot)$ is two consecutive Swin Transformer [13] blocks (see Fig. 3, right), which includes a standard multi-head self-attention module with non-overlapping window (W-MSA), a MSA module with non-overlapping shifted window (SW-MSA), and a feed-forward network (FFN, is a 2-layer multilayer perceptron (MLP), with Gaussian error linear unit (GELU) non-linearity in between) following each MSA module. Layer normalization (LN) is applied before each MSA module and FFN, and a residual connection is applied after each module.

As shown in (2), unlike ST-LSTM, ViT-LSTM introduces two new designs: ViTransGate and ViTransMemory. Specifically, 1) ViTransGate: This design replaces the convolutional networks in all gate structures of the original ST-LSTM with ViT (i.e., Swin Transformer). Taking the input ViTransGate $i^{vit}_{t}$ (see Fig. 3, right) as an example, it is obtained by feeding $\mathcal{X}_{t}$ and $\mathcal{H}_{t-1}^{l}$ into the $\text{vit}(\cdot)$ module, followed by the activation function. 2) ViTransMemory: From (2), this design feeds the tamporal memory unit $\mathcal{C}_{t}^{l}$ and the spatiotemporal memory unit $\mathcal{M}_{t}^{l}$ separately into the $\text{vit}(\cdot)$.

Compared to the original ST-LSTM, the advantages of ViT-LSTM include: 1) The ViTransGates in ViT-LSTM capture local and global spectral pattern features of the spectrum map by computing self-attention within the standard window and the shifted window, respectively. In contrast, the original ST-LSTM can only capture local features through convolution operations, which may lead to the loss of critical spatial spectrum pattern features. 2) The ViTransMemory also employs the self-attention mechanism to integrate spectral information from different positions, capturing more diverse feature representations to enhance memory. Additionally, it works in conjunction with LSTM to store long-range spatiotemporal spectrum dependencies. In contrast, convolution operations may exhibit biases toward local patterns, potentially leading to the loss of specific memory features.

To validate the effectiveness of the proposed ViTransLSTM, we use spectrum data collected by four sensors via the Electrosense open API (https://electrosense.org/) as the dataset. This dataset is reconstructed into $64\times 64$ spectrum maps based on inverse distance spatial interpolation of the data from these four sensors (sensor ID: $\text{test}\_\text{yago}\_3$, $\text{test}\_\text{yago}$, $\text{rack}\_3$, and $\text{rack}\_2$). The data collection period spans from Jun. 1 to Jun. 3, 2021, with a frequency band of 610 MHz and a sampling interval of 1 mins. The dataset (a total of 3200 samples) is divided into training, validation, and test sets in a ratio of 4:1:1. In the ViTransLSTM, the window size of the $\text{vit}(\cdot)$ network is $4\times 4$, the patch size is $4\times 4$, and the number of heads is 8. We select recently proposed spectrum prediction models, including ConvLSTM, PredRNN [7], and the upgraded version PredRNN V2 [14], as baseline comparisons. We run all the experiments on a PC with 3.30 GHz Intel Core i9-10940X CPU, NVIDIA GTX 3090Ti graphic, and 64 GB RAM using the Pytorch 1.8.0. All models are trained using the Adam optimizer with a starting learning rate of 0.001. The training process is stopped after 1000 iterations. Unless otherwise specified, batch size is 4.

Under the setup of input-10-predict-10, Fig. 4 presents the comparison results of the proposed ViTransLSTM and all baselines in terms of average MSE and PSNR. As shown in Fig. 4, the proposed ViTransLSTM outperforms all baselines across all evaluation metrics. For example, in Fig. 4(a), the average MSE of ViTransLSTM is 28.99%, 19.70%, and 15.58% lower than that of ConvLSTM, PredRNN, and PredRNN V2, respectively. Similarly, in Fig. 4(b), the average PSNR of ViTransLSTM is 5.29%, 3.13%, and 2.72% higher than that of ConvLSTM, PredRNN, and PredRNN V2, respectively. These results demonstrate that the proposed ViTransLSTM, which integrates visual self-attention with LSTM, can effectively capture deeper spatiotemporal correlation features of spectrum usage patterns, thereby achieving more accurate predictions.

Owing to interference from spectrum measuring equipment, signal propagation environments, and other variables, spectrum measurements may contain missing and abnormal data. This compromise in data quality amplifies the complexity of modeling. In an initial exploration, tensor completion is used to address this challenge. However, tensor completion algorithms struggle to estimate nonlinear missing data accurately. Fortunately, the diffusion model uses a stepwise de-noising approach to grasp the distribution of nonlinear spectrum data, resulting in the generation of high-quality spectrum data that is robust to deletions and anomalies.

Despite achieving impressive accuracy, existing DL-based spectrum prediction methods rely only on uni-modal data, highlighting the need for a robust DL-based multi-modal fusion framework to integrate features from each modality (such as spectrum occupancy series and spectrogram). To the best of our knowledge, deep multi-modal learning has yet to be applied in the field of spectrum prediction, despite its successful implementation in other domains such as weather and traffic predictions. However, a significant challenge involves the necessity to assign relative weights to different modalities. A viable approach could use a multi-objective optimization algorithm to balance the optimal weight of each modal by treating each weight as an optimization objective.

Multi-tasking spectrum prediction is often considered to meet the customization needs of massive spectrum users. However, when various DL-based spectrum prediction models are deployed in multiple spectrum prediction tasks, the intrinsic complexity of the models often necessitates substantial computational resources for training. To address this issue, it is recommended to customize lightweight DL models for spectrum prediction to achieve a flexible balance between performance and complexity through pruning and knowledge distillation techniques. Further, the lightweight model uses distributed learning [15] for each task node to improve computing efficiency.

Unlike cross-band spectrum prediction, cross-region spatiotemporal spectrum prediction extends into the time-frequency-space dimension. TL addresses this challenge, with cross-region TL going beyond time-frequency knowledge to include spatial information. This introduces complexity, leading to a challenge known as knowledge drift. As more knowledge transfers, the problem of knowledge drift becomes more severe. Enhancing transfer learning efficiency and spectrum prediction accuracy in the target region is a significant challenge. To address this, importance weight TL reweights source domain knowledge to improve model performance. Furthermore, cross-region cross-band spectrum prediction based on DTL presents an even more formidable problem. The relevance of the target domain to the source domain is lower compared to the previous challenge, intensifying the knowledge drift problem in transfer learning. Refinement TL emerges as a solution, involving the classification of transfer knowledge to improve transfer efficiency.

The electromagnetic spectrum is evolving, integrating space, air, and ground communication modes like vehicle-to-vehicle (V2V), unmanned aerial vehicle (UAV)-assisted, air-to-ground, and satellite communication. These modes create complex spectrum usage patterns. Joint spectrum prediction for space, air, and ground is challenging due to multi-domain information fusion, addressed by spectrum information semanticization. Additionally, traditional-DL struggles in dynamic wireless systems, requiring frequent retraining for changing data distributions, consuming time and memory. Deep reinforcement learning offers a solution by training intelligent agents to perform tasks and derive optimal strategies from experience. In highly dynamic wireless systems, where the environment constantly changes, the agent receives feedback through a reward mechanism and makes rational decisions.