## 3 Neural-Network-Based Interference Cancellation in LIS Systems
### Neural Network Architecture  
The neural network model was designed considering the trade-off between computational complexity and performance improvement. Extensive testing showed that increasing the network depth beyond three fully connected layers did not lead to significant performance improvements, while a shallower network resulted in a degraded signal recovery. As such, the proposed architecture consists of three key fully connected layers, each serving a specific role in feature extraction and signal reconstruction. The proposed Multi-Layer Perceptron (MLP) architecture is well-suited for interference cancellation in LISs using MRC/EGC due to its ability to learn non-linear mappings between the received signals and the transmitted signals. Since interference is generated during the decoding process rather than being a direct function of the channel matrix inversion, the primary goal is to estimate and remove this interference rather than reconstruct the original transmitted signal through explicit channel equalization. The MLP effectively captures the complex signal relationships introduced by MRC/EGC processing while maintaining a manageable computational cost. Other architectures, such as Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks, were also evaluated but found to be less appropriate, as the interference structure lacks significant spatial or temporal correlations. Additionally, the structure of the MLP network, with three fully connected layers and ReLU activations, ensures a sufficient level of non-linearity to model the interference effects while avoiding unnecessary complexity that could lead to overfitting. The aim of the neural network relies on removing interference (see Figure 2). To ensure robust learning, the dataset is structured such that each transmit antenna has a dedicated neural network trained independently. Note that the aim is to estimate the signals transmitted by each one of the transmit antennas. This design choice was motivated by the observation that training a single network for all antennas introduced inconsistencies due to the varying channel conditions across antennas. The choice to train independent networks for each antenna was based on the variability of channel conditions across antennas. This ensures that the network can adapt more accurately to the specific conditions of each antenna, resulting in more efficient signal reconstruction. As inputs, the network receives the received signals at the output of the MRC/EGC detector \(\widehat{S}_{n}^{(t)}\), corresponding to the estimation of the \(t\)th transmitted antenna, where the in-phase (I) and quadrature (Q) components are treated as separate features. Note that the neural network processes signals in the time domain. These two components (I and Q) are jointly fed to the network, in a new dimension of the matrix, to achieve the required correlation during training and prediction processes. The input to the neural network is structured as a two-dimensional vector, where the **I** and **Q** parts of the received signal are presented as separate features but concatenated to maintain correlation during training, as follows:  
\[\widehat{S}_{n}^{(t)}= \begin{bmatrix}\mathfrak{R}(\widehat{S}_{n}^{(t)})\\ \mathfrak{I}(\widehat{S}_{n}^{(t)})\end{bmatrix}  \tag{4}\]  
The length of the dataset is \(N\), the block size during training. The architecture consists of the following layers:  
* Feature Input Layer: A featureInputLayer with two input features (I and Q components), ensuring compatibility with the structure of complex-valued signals, compatible with QPSK (Quadrature Phase-Shift Keying) complex modulation. * Fully Connected Layer 1: A fullyConnectedLayer with 20 neurons, responsible for the initial feature extraction. * ReLU Activation: A reluLayer to introduce non-linearity, improving the network's ability to capture complex signal relationships. * Fully Connected Layer 2: A fullyConnectedLayer with 10 neurons, further refining the extracted features.