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

Abstract

Despite the increasing role of machine learning in various fields, very few works considered artificial intelligence for frequency estimation (FE). This work presents comprehensive analysis of a deep-learning (DL) approach for frequency estimation of single tones. A DL network with two layers having a few nodes can estimate frequency more accurately than well-known classical techniques can. While filling the gap in the existing literature, the study is comprehensive, analyzing errors under different signal-to-noise ratios (SNRs), numbers of nodes, and numbers of input samples under missing SNR information. DL-based FE is not significantly affected by SNR bias or number of nodes. A DL-based approach can properly work using a minimal number of input nodes N at which classical methods fail. DL could use as few as two layers while having two or three nodes for each, with the complexity of O{N} compared with discrete Fourier transform (DFT)-based FE with O{Nlog2 (N)} complexity. Furthermore, less N is required for DL. Therefore, DL can significantly reduce FE complexity, memory cost, and power consumption, which is attractive for resource-limited systems such as some Internet of Things (IoT) sensor applications. Reduced complexity also opens the door for hardware-efficient implementation using short-word-length (SWL) or time-efficient software-defined radio (SDR) communications.

Using Sequence-to-Sequence Models for Carrier Frequency Offset Estimation of Short Messages and Chaotic Maps

“…Further indication that DL can provide good frequency offset estimation for sinusoidal waveforms in low SNR is described in [3]. The network architecture was constrained specifically to the fully connected network (FCN) with the number of input nodes representing the length of the signal to be processed and being dependent on the range of the frequency offset, requiring larger dimensions for wider ranges of frequency [3]. FCN networks require a larger number of connections between layers as opposed to the CNN [16], hence consideration of CNN layers would provide flexibility for processing multiple signal lengths with a constant number of layer parameters.…”

“…Further indication that DL can provide good frequency offset estimation for sinusoidal waveforms in low SNR is described in [3]. The network architecture was constrained specifically to the fully connected network (FCN) with the number of input nodes representing the length of the signal to be processed and being dependent on the range of the frequency offset, requiring larger dimensions for wider ranges of frequency [3].…”

“…Short sample message lengths are advantageous in low power Internet of Things (IoT) applications and pilot signals used for signal detection and synchronisation. Deep Learning (DL) methods have demonstrated to outperform FFT-based methods under similar constraints [2], [3]. However, much of the experimentation to date has focused largely on phase amplitude modulation (PAM) or M -ary phase shift keying (M -PSK) modulations, and has not investigated the potential application to chaotic modulation techniques.…”

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time-Frequency Analysis

“…Symmetric α-Stable distribution noise requires 4 parameters (𝛼𝛼, 𝛾𝛾, 𝛽𝛽, and µ), with characteristic function defined as [20,21]:…”

Frequency Estimation from Compressed Measurements of a Sinusoid in Moving-Average Colored Noise

“…Recently, the emerging artificial intelligence technique of deep learning (DL) found application in frequency estimation of noisy sinusoidal signals [29,30] with promising performance. However, no results were reported for frequency estimation of compressed sinusoids using DL; this remains a topic for future research.…”