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Edholm's Law predicts exponential growth in data rate and spectrum bandwidth for communications and is forecasted to remain true for the upcoming deployment of 6G. Compounding this issue is the exponentially increasing demand for deep neural network (DNN) compute, including DNNs for signal processing. However, the slowing of Moore's Law due to the limitations of transistor-based electronics means that completely new paradigms for computing will be required to meet these increasing demands for advanced communications. Optical neural networks (ONNs) are promising DNN accelerators with ultra-low latency and energy consumption. Yet state-of-the-art ONNs struggle with scalability and implementing linear with in-line nonlinear operations. Here we introduce our multiplicative analog frequency transform ONN (MAFT-ONN) that encodes the data in the frequency domain, achieves matrix-vector products in a single shot using photoelectric multiplication, and uses a single electro-optic modulator for the nonlinear activation of all neurons in each layer. We experimentally demonstrate the first hardware accelerator that computes fully-analog deep learning on raw RF signals, performing single-shot modulation classification with 85% accuracy, where a 'majority vote' multi-measurement scheme can boost the accuracy to 95% within 5 consecutive measurements. In addition, we demonstrate frequency-domain finite impulse response (FIR) linear-time-invariant (LTI) operations, enabling a powerful combination of traditional and AI signal processing. We also demonstrate the scalability of our architecture by computing nearly 4 million fully-analog multiplies-and-accumulates for MNIST digit classification. Our latency estimation model shows that due to the Shannon capacity-limited analog data movement, MAFT-ONN is hundreds of times faster than traditional RF receivers operating at their theoretical peak performance.