# Hardware-Based Architecture for DNN Wireless Communication Models
## 2 System Model  
In this paper, we consider an \(M\times M\) MIMO OFDM system in Figure 1, where there are M antennas at the transmitter and receiver. The MIMO OFDM channel follows the multipath (15 taps) fading channel using the time-varying Rayleigh fading channel. The modulation scheme used is QPSK, the number of OFDM subcarriers is \(N(N=64)\), and the number of pilots is also \(N\) for total estimation of the channel information. We assume \(M\) is equal to 2 and 4 in this paper. For the \(n^{th}\) symbol \((1\leq n\leq N)\), the received signal at the \(mr^{th}\) receive antenna \(y_{mr}^{th}(n)\) can be described as follows  
\[y_{mr}^{th}(n)=\sum_{mt=1}^{M}(h_{mt,mr}(n)\oplus_{mt}(n))+w_{mr}(n) \tag{1}\]  
where \(s_{mt}(n)\) is the transmitted signal at the \(mt^{th}\) transmit antenna, \(\oplus\) denotes the circular convolution, \(w_{mr}(n\sim\mathcal{CN}(0,\sigma^{2})\) is the additive white Gaussian noise (AWGN) at the \(mr^{th}\) receive antenna. Notation \(h_{mt,mr}(n))\sim\mathcal{CN}(0,1)\) represents the channel coefficient between the \(mt^{th}\) transmit antenna and \(mr^{th}\) receive antenna. By using vector and matrix forms, (1) can be written as  
\[Y(n)=H\oplus S(n)+W(n) \tag{2}\]  
Furthermore, we also include LS as a channel estimator and ZF/MLD as a signal detector in some cases. In this paper, we divide the operation of our designs into two phases. Firstly, the training phase is done online with many simulation data samples. In the offline phase, our hardware design in this paper can run inference to output the data.  
We further explain the choice of system parameters. We have chosen the LS algorithm for the channel estimation process due to its simplicity. In addition, the authors in [12] use the LS algorithm, so we also use the LS algorithm to have similarities when comparing the results. For the signal detection process, we have chosen the ZF algorithm due to its simplicity and the MLD algorithm due to its high performance. In addition, the authors  
Figure 1: MIMO OFDM system.  
in [9; 10; 11] use the ZF, and MLD algorithms, so we also use these algorithms to have similarities when comparing the results. As we know, the LS and Zero-forcing algorithms have low BER performance due to their complexity. So if we use the QPSK modulation scheme with lower complexity, we get better results than models using 64-QAM or 128-QAM. Besides, 64-QAM or 128-QAM is quite challenging to apply to DL models, and the computational speed of a DL-based system would be very slow with today's computer technology. In addition, our work also focuses on testing the use of DL in particular and machine learning in general in wireless communication systems. Then, it can serve as a premise for the research and application of machine learning in future practical wireless communication systems. Our system uses 64 subcarriers because this number is commonly used in systems relevant to OFDM such as [13]. During simulation, the CP (Cyclic prefix) length must be greater than the number of taps for the simulation to function properly for a MIMO OFDM system. Therefore for the use of 64 subcarriers, we used a CP of length 16. Thus, 15 taps are the maximum number that can be selected. The multipath fading channel is considered in our system, then 15 taps are selected. Lastly, the reason why we use the point-to-point model (the number of antennas at the transmitter and receiver are equal) is that in our referred papers [9; 10; 11] the authors also use the point-to-point model. So we do that to have similarities when comparing to [9; 10; 11].