# Mine Intelligent Receiver: MIMO-OFDM Intelligent Receiver for Mine Information Recovery
## 2 Theoretical Basis
### MIMO-OFDM Communication System Model  
The MIMO-OFDM system uses multi-antenna technology to transmit OFDM modulated signals, which can effectively use the multipath effect to overcome signal fading, improve data transmission rate, and reduce the BER of signal transmission. In this paper, a centralized MIMO-OFDM system was used with the number of antennas, \(N_{t}\) and \(N_{r}\), at the transmitter and receiver ends, respectively, as shown in Figure 1. The original information bit stream was encoded into \(N_{t}\) binary bit stream by constellation modulation and MIMO coding to be OFDM modulated data, and then the signal transmitted to the wireless channel by the transmitting antenna after being OFDM modulated. After the wireless channel transmission to the receiver side to obtain \(N_{r}\) received signals, OFDM demodulation to obtain the MIMO-OFDM system of multiplexed subcarriers, and finally MIMO decoding, demodulation and other operations obtain the recovery information bit stream.  
Considering the channel as a flat fading channel, the channel pulse between the \(n_{t}\)-th transmitting antenna and the \(n_{r}\)-th receiving antenna is correspondingly \(\text{h}_{n_{r},n_{t}}(t)\). If frequency bias and initial time delay are neglected, the signal received at the \(n_{r}\)-th receiving antenna can be expressed as:  
\[y_{n_{t}}(t)=\sum_{n_{t}=1}^{N_{t}}\text{h}_{n_{r},n_{t}}(t)s_{n_{t}}(t)+v_{n_{ t}}(t) \tag{1}\]  
In terms of a matrixm this can be denoted as:  
\[\mathbf{Y}=\mathbf{H}\mathbf{S}+\mathbf{N} \tag{2}\]  
where \(\mathbf{S}\) denotes the signal after MIMO coding and OFDM modulation, \(\mathbf{N}\) is Gaussian white noise with zero mean and variance \(\sigma^{2}\), and \(\mathbf{H}\) is the channel matrix, which can be expressed as:  
\[\mathrm{H}=\left(\begin{array}{ccc}h_{1,1}&\dots&h_{1,N_{t}}\\ \vdots&\ddots&\vdots\\ h_{N_{t},1}&\dots&h_{N_{t},N_{t}}\end{array}\right) \tag{3}\]  
where \(h_{i,j}(1\leq i\leq N_{r},1\leq j\leq N_{t})\) is the channel coefficient with respect to the channel between the \(i\)-th receive antenna and the \(j\)-th transmit antenna.  
There are two implementations of MIMO technology: spatial diversity and spatial multiplexing. Space-time coding is the most commonly used spatial diversity technique. Among them, space-time packet coding (STBC) is a widely used space-time coding scheme with its concise coding method. STBC is a reliable high-speed wireless communication transmission optimization scheme, which can effectively reduce the bit error rate and expand the channel capacity. Alamouti space-time coding [21] is a classic two-antenna transmit diversity method in which two symbols, \(s_{1}\) and \(s_{2}\), are transmitted in two consecutive time slots; in the first time slot, \(s_{1}\) and \(s_{2}\) are radiated to the wireless channel by the first antenna and the second antenna, respectively; in the second time slot, \(-s_{2}^{*}\) is transmitted by the first antenna and \(s_{1}^{*}\) is transmitted by the second antenna. The coding matrix can be expressed as follows:  
\[s=\left[\begin{array}{cc}s_{1}&-s_{2}^{*}\\ s_{2}&s_{1}^{*}\end{array}\right] \tag{4}\]  
where each line represents the transmit data of each antenna in each time slot. With a single receive antenna, the signal received in the first time slot can be expressed as:  
\[y(1)=h_{1,1}s_{1}+h_{2,1}s_{2}+n_{1} \tag{5}\]  
Figure 1: Conventional MIMO-OFDM system architecture.  
The signal received in the second time slot can be expressed as:  
\[y(2)=-h_{1,1}s_{2}^{*}+h_{2,1}s_{1}^{*}+n_{2} \tag{6}\]  
where \(y(k)\) denotes the signal received at the \(k\)-th time slot.