# EVM Loss: A Loss Function for Training Neural Networks in Communication Systems
## 1 Introduction  
Visible light communication (VLC) is an area of sustained research interest, as it can provide a supplementary spectrum to high-capacity wireless internet access networks. Operating on the visible wavelengths in the electromagnetic spectrum, VLC offers low-cost, rapid network deployment using white light-emitting diodes (LEDs) [1]. In general, LEDs are low bandwidth devices and as the demand for data is ever-increasing, methods to improve spectral efficiency are currently in high demand. Candidates to do this in VLC have either been through equalization [2], or through advanced modulation schemes [3]. Of the latter, of the most promising is spectrally efficient frequency division multiplexing (SEFDM), a modification of orthogonal frequency division multiplexing (OFDM) first proposed in 2006 by [PERSON] and [PERSON] in [4]. In SEFDM, orthogonality between subcarriers is broken by compressing the overall bandwidth at the cost of inter-carrier interference (ICI) [5], and machine learning is a promising topic to compensate for this.  
The use of machine-learning and neural networks for communication systems is a topic of ever-increasing interest. One of the key aspects missing from the current state-of-the-art is domain-related methods of training and evaluating these systems within the communication system context [6]. Communication systems are typically evaluated via their bit error rate (BER) after forward error correction (FEC), however, evaluation of BER as an objective function for an optimization target is not feasible, for example when training models in machine learning. Due to this, in the literature for machine learning in communications, authors typically use the mean square error (MSE) or the related \(l_{2}\) norm as a loss function to train their models [7, 8]. This causes a disconnect between the objectivefunction of the model, and the eventual metrics that will be reported when the model is deployed. Thus, it is clear that a performance gain would be obtained when the objective function of the training process is aligned with the metrics that the communication system will be evaluated against.  
To this end, in this paper, we propose the exploitation of the error vector magnitude (EVM) in the training process as the objective loss function and show how it can be effectively utilized to improve the performance of symbol receivers. We will be doing this with a physical implementation using a VLC link. Since EVM is a common key performance indicator used in communication systems since it was first proposed in [9], and is closely related to the BER [10]. In a machine learning scenario, EVM is useful because it gives an error value in relation to a known ideal value, and is available instantly for any batch size used in the system, unlike the unit-less BER metric that requires vast numbers of bits to converge. The EVM requires knowledge of both the in-phase and quadrature parts of a signal, therefore to aid this method, we will also be using the 'concatenated-complex' approach. Whilst not the main contribution of this work, there exists mixed literature between this and the'split-complex' approach [11; 12], i.e., splitting a complex signal into its in-phase and quadrature components and training a separate, independent model for each, this paper will also demonstrate how including both can aid a model's learning ability due to indirect retention of the phase information.