# A Methodology to Design Quantized Deep Neural Networks for Automatic Modulation Recognition
## 1 Introduction  
Next-generation wireless communications are geared towards versatility and adaptability to different radio environments and channel dynamics. CR is an enabling technology that extends the functionality of SDR by providing the mechanism to adapt intelligently to its environment [1]. One of the critical features of CR is DSA, which allows radios to access and use the unused spectrum dynamically [2]. DSA involves several tasks that a radio should execute to improve its performance automatically. Among these tasks, AMR is one of the most studied in the literature [1; 3; 4]. One of the main challenges in AMR is to classify a received signal into a modulation type without (or with limited) prior information about the transmitted signal under dynamic channel conditions [5]. Traditionally, AMR has been mainly tackled via LB and expert FB methods combined with pattern recognition methods [6]. While LB methods find optimal solutions by minimizing the probability of false classification at the cost of high computational complexity, FB methods have lower complexity, and their performance is (near-)optimal when appropriately designed. However, these features are usually chosen by an expert and are basedon a specific set of assumptions that are typically unrealistic [5]. In recent years, some limitations of such techniques have been solved by applying DL techniques such as DNN, which allow both automatically extracting the relevant features from raw time-series data and performing the classification task [7] on the extracted features. More recently, several approaches based on DL have been proposed to solve the AMR task using raw time, frequency, and time-frequency data, outperforming traditional methods [5; 7; 8; 9]. However, the primary assumption when using such models is the availability to train and run such models on high-end computational devices with hardware accelerators [10; 11]. While this can be acceptable on traditional deployments where the radio is co-allocated with dedicated high-end servers, this is not the case for new approaches such as the desegregated RAN [12] for private deployments in dense environments. In such cases, DL models trained in the cloud/core network will not be able to run on the DU or RU of such desegregated RAN, since such components are intended to run at the edge or far edge, where computational resources are constrained and shared. Therefore, there is a clear need to adapt models trained in high-end devices such that they can run on constrained ones by trading performance (e.g., classification accuracy) against model complexity (e.g., model size) [13]. Recently, several frameworks and tools have been proposed to decrease the computational complexity of DNN using techniques such as quantization. Quantization reduces the models' size by truncating the value of parameters such as inputs, activations, and weights. This truncation is achieved by moving from floating-point precision (e.g., 32 or 64 bits) representation of such parameters to a more straightforward and reduced representation using fewer bits as integers (e.g., 2, 4, and 8 bits). The main computational argument for quantization is that quantized weights and activations occupy much less memory space while trading-off model performance. The resulting quantized model can be housed entirely in the FPGA of the SDR device, allowing signal processing tasks, including DL-based ones, to be performed close to the radio. In addition, power consumption is reduced due to the simplification of the process by not having to work with floating-point modules [14]. The available literature on how to design, implement, and evaluate the performance of quantized DL for AMR is very limited [13; 15]. Most of these works focus on the performance of the proposed DL model when all layers are quantized with the same quantization value.