# A Deep Learning Approach for MIMO-NOMA Downlink Signal Detection
## 2 Fundamentals of MIMO-NOMA and the Deep Learning System
### MIMO-NOMA Basics  
NOMA can implement multiple-signal multiplexing by allocating unbalanced power within a same time/frequency/code resource. In contrast to traditional orthogonal multiple access (OMA) using orthogonal resources such as OFDM, NOMA utilizes power in a non-orthogonal form to substantially enhance the spectrum efficiency at the expense of receiver complexity. Figure 1 shows the overall architecture of the basic NOMA system.  
In conventional downlink multiuser MIMO, UEs generally occupy orthogonal resources. Interbeam interference can be completely eliminated when the number of base station (BS) transmit antennas is equal to or greater than the number of receive antennas [17]. In the MIMO-NOMA system, however, the total number of UE antennas is always greater than the number of transmit antennas, and these UEs have to share a cluster. Thus, interference from other UEs in the same cluster is inevitable. Multiple antennas at the base station (BS) can radiate multiple beams to form different directions via beamforming technology. A schematic is shown in Figure 2. For simplicity, in this paper, we focus on signal detection from UEs in a single cluster.  
Supposing that the number of users is \(K\), the \(i\)-th UE signal at the BS can be denoted as \(s_{i}(t)\), \((i=1,2,\cdots,K)\). The power allocated to user \(i\) is denoted as \(p_{i}\), and the transmission power is limited by the total power \(P\), where \(P=p_{1}+p_{2}+\cdots+p_{K}\). The total transmission signal can be expressed as:  
Figure 1: Non-orthogonal multiple access (NOMA) system architecture. AWGN: additive white Gaussian noise; SIC: successive interference cancellation.  
Figure 2: System block diagram of the multibeam multiple-input multiple-output (MIMO)-NOMA. BS: base station.  
\[s\left(t\right)=\sum_{i=1}^{K}\sqrt{p_{i}}s_{i}\left(t\right). \tag{1}\]  
During power allocation, various strategies can be followed for different situations and destinations. A detailed analysis of these strategies can be seen in [18]. The signal received through the fading channel and AWGN channel can be denoted as:  
\[\boldsymbol{y}\left(t\right)=\boldsymbol{h}\left(t\right)\ast\sum_{i=1}^{K} \sqrt{p_{i}}s_{i}\left(t\right)+\mathbf{n}\left(t\right). \tag{2}\]  
As mentioned previously, the detection of NOMA usually adopts the SIC method, and NOMA with a SIC has shown to be an optimal multiple-access scheme in terms of the achievable multiuser capacity region in both uplink and downlink [2]. The SIC processes are shown in Figure 3.  
At the receiver, the SIC process is executed in descending order of signal-to-noise ratio (SNR). For example, for \(p_{1}>p_{2}>\cdots>p_{K}\), user 1 will be decoded directly while the other signals are viewed as noise. The throughput can be expressed as:  
\[R_{1}=log_{2}\left(1+\frac{p_{1}\left|h_{1}\right|^{2}}{\sum_{i=2}^{K}p_{i} \left|h_{1}\right|^{2}+N_{0}}\right). \tag{3}\]  
For user \(k\in\left[1,K\right]\), assuming that the first \(k-1\) users are decoded perfectly, the throughput for user \(k\) is:  
\[R_{k}=log_{2}\left(1+\frac{p_{k}\left|h_{k}\right|^{2}}{\sum_{i=k+1}^{K}p_{i} \left|h_{k}\right|^{2}+N_{0}}\right). \tag{4}\]  
Hereby, the throughput for user \(K\) is:  
\[R_{K}=log_{2}\left(1+\frac{p_{K}\left|h_{K}\right|^{2}}{N_{0}}\right). \tag{5}\]  
Figure 3: SIC receiver architecture. SNR: signal-to-noise ratio.  
Clearly, the decoding error of the higher-power signal is accumulated and affects the decoding accuracy of the lower-power signal. This is a key problem of the SIC method that must be solved.