I Introduction
Shortpacket communication (SPC) has been specified as one of key technologies for the fifth generation (5G) networks because of its ability to provide high reliability and low endtoend (e2e) latency [8]. SPC supports a wide range of ultrareliable lowlatency communication (URLLC) applications, such as intelligent transportation systems, highspeed trains, drones, factory automation, and InternetofThings (IoT) networks [1]. Recent works on URLLC mainly focused on SPCs with singlehop or dualhop transmissions in factory automation, where the stringent requirements on reliability and latency are and ms, respectively [1, 11].
Cisco forecasted around 75 billion IoT devices in 2025, which poses a great challenge in allocating limited spectrum to those connected devices. By allowing sensor nodes to opportunistically access the vacant licensed spectrum, cognitive radio (CR) has been recognized as a spectrumefficient networking solution for such a problem in dense IoT networks [9, 1]. Besides deploying CR, radiofrequency energy harvesting (EH) technique is an attractive solution to supply stable energy sources in SPCbased systems [6], which provides longterm operation for the massive number of IoT devices in harsh environments and inaccessible locations. In [5], EH and data transmission processes were considered in ultrareliable SPC scenarios. Recently, SPCs with EH have been investigated in a variety of network scenarios, e.g., ultrareliable communications [5], wirelesspowered IoT networks [1], and missioncritical IoT applications under finite blocklength regime [13]. However, SPCs in multihop cognitive IoT networks (MCINs) with multiple primary transceivers, which makes the performance analysis quite complex, have not been studied in these works. This prevents researchers from thoroughly examining the impact of finite blocklength and cognitive multihop transmissions under SPC study.
Recently, deep convolutional neural networks (CNNs) have been recognized as a powerful tool to solve various practical problems, such as resource allocation, queue management, and congestion control in modern wireless networks and IoT systems [7]. Since CNNs have the ability to accurately estimate high nonlinear functions with lowcomplexity, it has been employed in a wide variety of interesting applications, such as relay selection, resource allocation, and channel estimations [13, 14]. CNNbased performance prediction helps expedite realtime settings in IoT networks since CNN models can precisely estimate desired performance metrics from high dimensional raw data even with dynamic environments and complex radio conditions, where a mathematical derivation is intractable. This paper carries out a fresh and first attempt to study SPCs with new energy harvesting strategies considering multiple primary transmitters (s) and power beacon () in MCINs assisted by deep learning. The main contributions of the paper can be summarized as follows:

It is proposed a SumEH scheme in multihop cognitive IoT networks, where the source and relay nodes can harvest energy from either s or for their operations under short packet and cognitive radio constraints.

To support realtime settings, we design an efficient CNN with feature enhancementcollection blocks to estimate system performance of MCINs, where the formulated block error rate (BLER) and throughput are converted into a multioutput regression problem for a lowlatency and high accuracy estimation.

It is shown through simulation results that CNN framework achieves almost the same BLER and throughput with that of SumEH one, while it drastically reduces complexity and execution time. The SumEH scheme also outperforms other EH strategies, such as MaxEH and primary transmitterbasedEH schemes, which corroborates the efficiency of the proposed EH method.

It is also revealed that the designed CNN model provides the lowest rootmeansquareerror (RMSE) compared to the deep neural network (DNN) and stateoftheart machine learning (ML) approaches, arising as an excellent estimator for performance prediction.
Mathematical Notations
: Boldface represents vector and
symbolizes the Frobenius norm. and are the expectation operator and transpose conjugate, respectively.Ii System Model
Iia System Description and Operation
We consider a secondary multihop cognitive IoT network cognitively operating with a primary network, as shown in Fig. 1. A singleantenna source () sends its shortpackets to a singleantenna destination () through hop transmissions, where each relay , with , uses decodeandforward protocol to transmit its received signal to the next hop in the presence of primary receivers (s). Since source and relays can be seen as energylimited IoT devices, they must harvest energy from a with antennas and from s for their operations. We assume that perfect channel state information is available at each terminal.
We denote by , , , and the channel coefficients from th antenna at to , with , from th to , with , from to , and from to th , with , respectively. The propagation channels experience both largescale path loss and smallscale fading. Thus, the channel coefficient is modeled as , with , where and present the largescale path loss and smallscale fading, respectively. The smallscale channel is modeled by Rayleigh fading such that the channel gain
follows an exponential distribution with parameter
. On the other hand, the largescale path loss is modeled as , where , , , and denote the distance between two nodes, the path loss exponent, the reference distance, and the power attenuation at , respectively.We consider SPCs in multihop cognitive IoT networks with two consecutive phases, which include EH and information transmission (IT) phases. We denote by and the total number of channel uses and duration of each channel use, respectively; thus, the hop transmissions in one block time are denoted by . Moreover, the number of channel uses of EH is denoted by ; thus, the period of is spent for EH and the remaining one, , is used for IT process.
IiB Energy Harvesting Phase
Considering the deployment of and s, three energy harvesting strategies can be presented as follows:
IiB1 Primary Transmitterbased Energy Harvesting Scheme
In this scheme, the relay nodes harvest energy only from the s since the is located very far from the multihop network. The energy harvested by , with , from s can be expressed as
(1) 
where and are the energy conversion efficiency and the transmit power of each , respectively. The IT process is performed after the EH process during the time period of , where the transmit power of can be calculated from (1) as
(2) 
where and presents the transmit power of each in the primary network.
IiB2 MaxEnergy Harvesting Scheme
In this scheme, relay nodes harvest the highest amount of energy between s and for their operation. The EH of can be expressed as
(3) 
where denotes the transmit power of each antenna at , and are the beamforming and channel coefficient vectors between and , respectively. employs an efficient maximalratio transmission criterion based on beamforming design for powering the source and relay nodes, where it is formulated as [13]. Thus, the transmit power of can be expressed as
(4) 
IiB3 SumEnergy Harvesting Scheme
The SumEH criterion is deployed to combine the harvested energy from either s or for the operations of source and relay nodes, where the EH at can be expressed as
(5) 
Based on (5), the transmit power of can be expressed as
(6) 
IiC Information Transmission Phase
To guarantee the qualityofservice of primary communications, the transmit power of relays in multihop networks should be lower than a predefined threshold required by the PRs. The transmit power of can be expressed as
(7) 
where .
Upon receiving the signal transmitted from
, the instantaneous signaltonoise ratio (SNR) at
can be formulated as(8) 
where indicates the interference from PTs at .
Iii Performance Evaluation
Considering finite blocklength transmission condition, the performance of multihop network is analyzed and evaluated in terms of average block error rate (BLER) and throughput.
Iiia Block Error Rate
The source transmits a packet of information bits (message size) via hops over the blocklength , with [6], and the e2e SNR equals to , with transmission rate given by . Thus, the average BLER at hop can be tightly approximated by [5, 13]
(9) 
where represents the Gaussian Qfunction, and denote the Shannon capacity and the channel dispersion, respectively. The e2e BLER of multihop network can be expressed as
(10) 
IiiB Throughput
We consider the delaylimited transmission scenario, where the throughput is determined by evaluating the e2e BLER. For a fixed data transmission rate bits per channel use (BPCU) and the effective communication time over total transmission time , the e2e throughput in delaylimited transmission mode can be expressed as
(11) 
To support realtime settings, we design an efficient CNN model for BLER and throughput predictions in the next section.
Iv Deep CNN Design for Performance Prediction
Iva Description of CNN
We design a deep CNN to accurately estimate the throughput in the considered system setup. The network is initialized by an input layer with size to process input data, which includes the number of antennas at (), the number of relays (), the number of PTs (), the number of PRs (), the positions of PTs (), PRs (), and (), the transmit powers of (), (), the threshold at the PRs (), the channel uses for EH (), and the target data rate (). Based on the range of input variables shown in Table I, the dataset is generated over samples for training and testing.
Variable  Value  Variable  Value  Variable  Value 

With regard to the network architecture, there are four feature enhancementcollection blocks, denoted by , which are sequentially linked together to extract the intrinsic features as the correlations between system variables, as illustrated in Fig. 2. Our deep network starts with the input size of indicating the system variables in Table I. We next specify a convolutional () layer with kernel size of
, followed by a batch normalization (
) layer and a rectified linear unit (
) layer to effectively enrich the feature diversity. To emphasize the high impact features resulted by the preceding layers, is designed to possibly improve accuracy of prediction. As the core of network architecture, each has three multiplication layers.Given the input of , its operating principle can be described as follows. At the first multiplication layer, the output is obtained as
(12) 
where , in which and , respectively, indicate the global average pooling and the convolution operation; and
denote the sigmoid function and elementwise multiplication, respectively. The output
is passed through a fully connected () layer, where the result is used as input of the second multiplication layer, i.e.,(13) 
The output of is identical to the output of the third multiplication layer, which can be expressed as
(14) 
The
function greatly accelerates the convergence of optimization algorithm during training process compared to the sigmoid or tanh activation functions
[4]. The network is finalized with a layer between two layers, denoted by and in Fig. 2, wherein the number of neurons in
is identical to the number of estimation variables at the output. Here, the BLER and throughput variables need to be estimated and they are arranged into a vector . With regard to the layer configurations, we specify 64 kernels in each layer and 64 neurons in each layer. Based on the universal approximation theory [2], the heuristicbased scaling approach is applied in this design, where the number of kernels and neurons are heuristically chosen by experimental trials until the minimal training error is achieved
[12]. It is worth noting that the zero padding is automatically added when processing convolution with different kernel sizes to keep the spatial size of output feature maps unchangeable.
For the regression problem, the loss function indicating the error between predicted and expected values, which can be expressed as
[15](15) 
where is the number of training samples, and and
are the expected and predicted values, respectively. The weights and biases are iteratively updated during the backpropagation procedure by using the adaptive moment (Adam) estimation optimization algorithm to minimize the loss function of the entire training set.
IvB RealTime Prediction
Once the offline training is completed, the resulting CNN model consisting of weights and biases can be represented in a compact mapping function as . In general, when the CNN is well trained, it can provide realtime and highly accurate predictions. We use the resulting CNN model to predict the throughput value whenever any new information is available at the input. In particular, we input serially each sample, which is arranged as a vector , and the resulting CNN will output the predicted BLER and throughput sorted into vector , which can be expressed as
(16) 
Through a lowlatency inference process in (16), the BLER and throughput can be predicted by the CNN model within a short time. Since the capacity of CNN can be improved by going a deeper (more hidden layers) or wider (more neurons/hidden units) network, the settings of CNN can be aptly designed to achieve the lowest error during training process. If the predicted throughput is not close to the expected one, the CNN will need to be retrained with new appropriate settings until achieving the smallest error in (15).
V Simulation Results and CNN Predictions
In this section, we present illustrative examples to evaluate the BLER and throughput of the proposed system model. MonteCarlo simulations and CNN prediction results are provided to validate our designed approach. We consider a twodimensional plane, where , , , and are located at coordinates , , , and , respectively. We set the reference distance m and the pathloss at dB. Unless otherwise stated, we set in simulations the number of antennas at as , the number of relays as , the number of PTs as and PRs as , the energy conversion efficiency as , the pathloss exponent as , the total channel uses as with bits, the channel uses for EH as
, and the normalized noise variance as
. To prevent the overfitting issue while network goes deeper, hidden layers and hidden neurons are selected for DNN model [1]. The entire dataset is split into for training and the remainder for testing. The holdout crossvalidation method is used, where the model is trained on the training set and evaluated on the test set. We also heuristically set epochs for training of the CNN model to prevent the overfitting on the training set and achieve a good accuracy on the test set. The weights and biases are randomly initialized using Adam optimizer with the gradient decay factor of . The initial learning rate is set as (dropped after epochs). The performance is measured on a system equipped by a 3.60GHz CPU, 32GB RAM, and a single NVIDIA GeForce GTX 1060 6GB GPU.Va RMSE Evaluation
To evaluate the estimation performance of the proposed CNNbased estimation scheme for predicting the target BLER and throughput, the RMSE is used to measure the differences between actual values and predicted ones over the entire test set. The RMSE can be calculated by using the samples in the test set as follows:
(17) 
We compare the RMSE of the CNNbased model with that of MLbased regression models, such as SVM [3]
, decision tree learning
[14], and ensemble learning [10]. It is noted that such MLbased regression models share the same dataset with the proposed CNN one. We follow the standard fold crossvalidation () to measure the performance of traditional ML regression models [3].We first present the RMSE versus the number of samples with different regression models, as shown in Fig. 3. The linear SVM regression model has the highest RMSE, while the proposed CNN model gets the lowest RMSE, showing the best performer. The reason is that the linear SVM model is infeasible to estimate a moderatetohighdimensional dataset, resulting in the lowest performance. The SVM model with Polynomial, Gaussian, and FBF kernels yield almost a similar RMSE result since they share the same backbone architecture. The RMSE values of the ensemble, DNN, and the proposed CNN models are progressively reduced and eventually reach , , and , respectively, over the entire test set. The proposed CNN model has the ability to map the original dataset into a higher dimensional space through the versatile design of and attention connection. This shows the beneficial feature of deep learning approach for effectively dealing with big communication datasets. On the contrary, the RMSE of the SVM, decision tree, and ensemble models is nearly unchanged even when the number of samples is increased, showing that they have poor predictive ability in large datasets.
The effects of different MLbased estimation schemes on the ability of throughput prediction are shown in Fig. 4. It is observed that the proposed CNNbased estimation framework provides the best fit curve of the throughput to the SumEH scheme while the linear SVMbased estimation one has a high error prediction and fails to evaluate the throughput. The decision tree, ensemble, and DNNbased estimation schemes perform better than SVM (linear, RBF, and polynomial kernels) one; however, they cannot exactly predict throughput at high SNRs since their nature is shallow learning network. Contrarily, a novel architecture designed for deep CNN allows it to explore and learn the interfeature correlations, which prevents the network from vanishing gradient by deploying batch normalization layer. Owing to this fact, the CNNbased estimation framework demonstrates the best prediction ability among DNN and MLbased estimation schemes.
VB BLER and Throughput Evaluation
In Fig. 5(a), we show the BLER of all schemes with different values of . When the number of antennas at the increases, the EH capability enhances at relay nodes as (4) and (6), thus improving the BLER for SumEH and MaxEH schemes. However, when increases, its harmful effect counterbalances the benefits gained from EH; thus, the BLER of all schemes suffers outage at dB. It is observed in Fig. 5(b) that the throughput of all schemes increases when is large. The source and relays will have more energy budget if the allowable interference level at the PRs is large, leading to the enhancement of system throughput. Moreover, the SumEH scheme gives the best performance while the PTEH scheme is the lowest performer. The reason is that relay nodes in SumEH scheme can harvest a total of energy from PTs and PB while the PTEH scheme mainly harvests from PTs. Moreover, the negative effects caused by the interference from PTs on relays offsets the positive effects given by EH from PTs; thus, PTEH has poor BLER and throughput performances. It is also evident that the MonteCarlo simulation results of the SumEH scheme perfectly coincide with the CNN prediction ones, verifying our excellent deep model design.
VC Reliability and Latency Evaluation
In Fig. 6, the message with 256 bytes has higher reliability and lower latency than long one (i.e., with 512 or 1024 bytes). To achieve high reliability (over ), the 512byte message can be framed into packets by using channel uses, as shown in Fig. 6(a), but its latency is about s, as shown in Fig. 6(b), which exceeds the maximum latency budget for URLLC applications [11]. The 1024byte message is transmitted with the latency of s and reliability of at channel uses, which does not meet the stringent requirements of latency and reliability. Thus, the longmessages are not able to support URLLCs in IoT networks and lowlatency transmission in factory automation.
VD Execution Time Evaluation
Scenarios  Sim.  CNN  RMSE 

s  s  
s  s  
s  s 
Finally, we evaluate the execution time of the throughput prediction in Table II. Each sample of MonteCarlo is obtained by averaging independent channel realizations. When the network scale increases in terms of the number of devices and antennas , the CNN still guarantees an execution time of less than s in all scenarios, while the execution time of simulation method increases with the network scale and it consumes s for the last scenario. These results reveal the excellent ability of the proposed CNN framework in dealing with large scale network settings.
Vi Conclusions
In this paper, we proposed a novel deep CNNbased relay selection scheme in multihop cognitive IoT networks to evaluate and improve the e2e BLER and throughput. Simulation results showed that the proposed CNNbased estimation scheme achieved almost exactly the throughput of SumEH one, which by its turn outperformed the MaxEH, and PTEH schemes. Furthermore, the design of deep CNN model shown the perfect estimation capability with the smallest RMSE compared to DNN and machine learning approaches. In future works, we will study the hybrid relayreflecting intelligent surfaces for multihop IoT systems embedding various advanced deep learning models to solve the joint power allocation, beamforming, and relay selection problem in future IoT cognitive wireless networks.
Acknowledgment
The work of B. An was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF2019R1A2C1083996). The work of V.D. Nguyen was supported in part by the ERC AGNOSTIC project, ref. H2020/ERC2020POC/957570. Prof. Beongku An is the corresponding author.
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