# Training from Zero: Forecasting of Radio Frequency Machine Learning Data Quantity
### Machine Learning Concepts
#### 1.1.3 Automatic Modulation Classification  
The RF problem presented in this work is then the classification of the modulation present in the original transmitted waveform \(s_{BB}(t)\). AMC is then the problem of being able to identify how information (or lack thereof) is being applied to a specific time and frequency slice of the overall spectrum. When coupled with the problem of signal detection, whether a waveform present or not in a time and frequency slice, the problem space is often referred to as Automatic Modulation Recognition; however, in this work, the trained network is determining what is there, rather than the additional task of where is it, so AMC is a better category for the task. While AMC is one of the oldest disciplines within RFML, traditional approaches have relied on expert analysis and feature extraction [35; 36; 37; 38], though over the last three decades, heavier reliance on ML has been used for feature fusion and decision -making [39], as well as direct application to raw waveforms [40; 41]. To help understand how data quantity and quality affect the performance of the system, there are three primary datasets used while training, and one unique evaluation set for evaluating the performance of all models that are trained. The four datasets are described in Table 1. Captured data make up the first dataset (\(\Omega_{C}\)), along with the evaluation set (\(\Omega_{TC}\)) such that the two sets are disjoint (\(\Omega_{C}\cap\Omega_{TC}=\emptyset\)). This dataset was collected at Virginia Tech's Kentland Farms in 2019 over a four-month window. It consists of narrowband transmissions between two Ettus Research B210s stationed at two setup points, which were approximately 110m and 1 km apart in their locations, with the first being line-of-sight and the latter having natural occlusions in between them. Data generation occurred using the out-of-tree module \"gr-signal_excitter\" [42], producing collections of over 20 waveforms with more than 2.1 million examples per class of 1024 complex-baseband samples with sample separations between any two observations being another 1024 samples apart in time. The second set is a synthetic dataset (\(\Omega_{S}\)) that makes the waveforms in their pure form, as shown in (7) using the same setup as with the captured dataset's transmissions except saved to a file rather than transmitted. To increase the practical usage of the synthetic data, synthetic errors are added to the saved data that can be associated with detection algorithms such as Frequency Offset (FO) and Sample Rate Mismatch (SRM), as well as varying the SNR to indicate different received power levels in the dataset. The second and third datasets make use of a Joint Kernel Density Estimate (KDE) on \(\Omega_{C}\) to mimic the distortions of FO, SRM, and SNR within them to attempt to minimize changing the distributions in the data to any extreme. The third dataset, by contrast with \(\Omega_{S}\), applies synthetic permutations to observations from \(\Omega_{C}\), thereby creating an augmented dataset. These permutations are similar, if not identical, to the synthetic errors introduced in the synthetic dataset. Additionally, in order to observe greater diversity in the application of dataset quality and quantity, the work shows the classification performance of three classification groups given in Table 2. These waveforms are selected for the typical usage in qualifying AMC approaches, with the comparison in \(\Phi_{3}\) between BPSK (Binary Phase-Shift Keying) and QPSK (Quadrature PSK) being considered the simplest problem as BPSK carries information only on the in-phase, or real, component while QPSK makes use of both the in-phase and quadrature (IQ) components of a complex baseband signal. The inclusion of Quadrature Amplitude Modulation (QAM) waveforms with 16 and 64 constellation points in \(\Phi_{5}\) increases the difficulty of classification significantly under the same power constraints, with lower SNR values typically completely obscuring the difference between the two QAM modulations.