# Deep Learning versus Spectral Techniques for Frequency Estimation of Single Tones: Reduced Complexity for Software-Defined Radio and IoT Sensor Communications

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## Abstract

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## 1. Introduction

- The performance of the DL approach is compared with the performance of still-active classical techniques that are based on Fourier analysis.
- In many situations, SNR estimation can be inaccurate or unavailable. Hence, system performance is investigated in case of unavailable SNR information.
- The DL approach is SNR-dependent; hence, an investigation of system performance under various SNRs is presented.
- The more the nodes in the DL approach are, the better the accuracy of estimation could be. Hence, this work investigated the effect of changing the number of nodes in the hidden layers of the network.
- The number of input samples (signal length or duration) has significant impact on the complexity and the performance of classical and DL-based methods. This point was fully investigated in this work.
- The effect of different realizations while training was handled in the literature of DL-based approaches, as it is a necessary step in the training process. However, the possibility of different realizations in the working environment (application phase) was not previously handled. In this work, we discuss the effect of different realizations during the application phase.
- The reduced complexity introduced by DL-based FE, in addition to avoiding complex-valued arithmetic operations, makes FE easier and cheaper for IoT communications, sensors, sensor networks, and software-defined radio (SDR). This work presents a discussion on such possibilities.

## 2. Motivation and Related Work

- The network was trained for a specific SNR. There should be a clarification whether different networks should be present in the case that different SNRs are expected.
- The effect of SNR on estimation error was unclear.
- The number of input nodes was chosen as N = 2000. It is not clear whether this choice of the input samples (nodes) is frequency-, duration-, or network-dependent.
- The division of the frequency range was not clear. The effect of this division on estimation error should be addressed. The relation of this division to the time–frequency uncertainty principle should also be clarified.
- The number of nodes in the hidden layers was 2. The effect of this number on estimation accuracy should be clarified. The possibility that this effect is SNR-dependent should be addressed.
- Classical techniques for frequency estimation have been well-studied for decades. There should be a clear reasoning why one should choose DL-based estimation instead.

## 3. Problem Statement

- Comparing the performance of DL-based approach with classical techniques.
- Investigating system performance in case of unavailable SNR information.
- Investigating system performance under various SNRs.
- Investigating the effect of changing the number of nodes in the hidden layers of the network.
- Investigating the effect of input signal length (duration) on the performance of both classical and DL-based methods. This factor has significant impact on overall performance and complexity.
- Investigating the effect of different realizations during the application phase (not only during the training phase).
- Investigating the impact of DL-based FE on IoT, sensors, sensor networks, and software-defined radio (SDR).

## 4. A Brief Overview of Classical FE for Single Tones

#### 4.1. Maximum of DFT Estimator

#### 4.2. Quadratic Interpolator

#### 4.3. Barycentric Estimator

## 5. Deep Learning for Single-Tone FE: Network Structure and Training

#### 5.1. DL Network Structure

#### 5.2. Training Data

#### 5.3. Training Function: Scaled Conjugate Gradient Backpropagation

_{k+1}= ν

_{k}+ α

_{k}ρ

_{k},.

## 6. Results: Deep Learning vs. Classical Single-Tone FE

#### 6.1. Performance under Different Input Lengths

#### 6.2. Performance under Insufficient SNR Information

#### 6.3. Effect of Increasing Nodes at Hidden Layers

#### 6.4. Impact on IoT, Sensors, and SDR

#### 6.5. Future Directions: DL in the SWL Domain

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Performance of FE methods for different input lengths. Bold curves are for larger duration $T=2$ s, $N=201$ input samples; plain curves are for smaller duration $T=0.1$ s, N = 11.

**Figure 3.**DL vs. barycentric discrete Fourier transform (DFT)-based FE for different input lengths with $J=K=5$. Note that DFT-based FE failed when $N=11$, while DL-based FE gave reasonable results even at low signal-to-noise ratio (SNR).

**Figure 4.**DL vs. barycentric DFT-based FE for different input lengths with $J=K=3$. Bold curves used for DL.

**Figure 7.**Performance of DL-based FE under different sizes of hidden layers. No significant difference in DL performance between networks with sizes $J=K=5$ and $J=K=3$.

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**MDPI and ACS Style**

Almayyali, H.R.; Hussain, Z.M. Deep Learning versus Spectral Techniques for Frequency Estimation of Single Tones: Reduced Complexity for Software-Defined Radio and IoT Sensor Communications. *Sensors* **2021**, *21*, 2729.
https://doi.org/10.3390/s21082729

**AMA Style**

Almayyali HR, Hussain ZM. Deep Learning versus Spectral Techniques for Frequency Estimation of Single Tones: Reduced Complexity for Software-Defined Radio and IoT Sensor Communications. *Sensors*. 2021; 21(8):2729.
https://doi.org/10.3390/s21082729

**Chicago/Turabian Style**

Almayyali, Hind R., and Zahir M. Hussain. 2021. "Deep Learning versus Spectral Techniques for Frequency Estimation of Single Tones: Reduced Complexity for Software-Defined Radio and IoT Sensor Communications" *Sensors* 21, no. 8: 2729.
https://doi.org/10.3390/s21082729