# Efficient Deep Learning-Based Detection Scheme for MIMO Communication Systems
## 1 Introduction
### Related Work  
DL-based signal detection for MIMO systems has recently been investigated in different configurations using various modulation schemes to encode symbols during transmission. When the NN architecture considers multiple models, a single training strategy can be used to unify the models, improving the BER performance of the zero-forcing (ZF) and semi-definite relaxation approaches [16]. Motivated by these findings, the authors in [17] present a study that compares the performance of a fully connected NN architecture and a customized DL scheme that unfolds the stochastic gradient descent (SGD) iterations in a network. The authors in [18] find that vector quantization (VQ) presents a similar performance compared to the MIMO-DL detection. This approach uses NN to reduce the quantization loss as the number of transmit (Tx) antennas increases.  
DL has also been investigated to improve other MIMO detection approaches, such as sphere decoding [19; 20; 21] and polar decoding [22; 23]. The ML detector is a well-known optimal method that has been implemented with a convolutional neural network (CNN)-based architecture for vehicular networks in a correlated fading channel scenario [24]. In addition, CNN can be applied for the joint design of channel estimation and signal detection in MIMO systems [25]. The CNN model for a MIMO signal detector can also be used in the Internet of Things (IoT) [26; 27]. However, a CNN has higher complexity when the levels of the signal-to-noise (SNR) ratio are up to 10 dB [28].  
The authors of [29] present different methodologies for the design of a DL-based MIMO detection. The study compares a fully connected long-short-term memory (LSTM) and a CNN-based architecture. For generating labeled data, each index is encoded using a OH strategy for each index. The labeling approach reported in [30] implements Gray encoding when adjacent symbols are presented to help differentiate the loss function. However, if higher-order modulations are required, a DL demodulation with \(M\)-QAM signals can be considered [31]. In addition, different ML strategies have been implemented for demodulation in MIMO systems, including reinforcement learning [32], and unsupervised learning [33]. Since the multiple NNs designed are not directly connected, several NN-adapted receiver architectures, such as dual-multilevel detection [34] and the design of a parallel NN signal demodulator with the design of a specific loss function, have been proposed. The revised DL-based MIMO signal detection schemes present promising results in BER compared to optimal ML detection. Furthermore, DL-based algorithms have shown highly efficient, robust, and scalable solutions that provide near-optimal performance with lower computational cost, once trained.  
However, to the best of our knowledge, there is an absence in the reported results of an appropriate strategy to improve the system considering the training data generated. In this work, we compare two proposals for labeling input data for training DL networks, with the OH strategy in [29] and the optimal ML criterion used in MIMO communication systems.