*2.2. Precoding*

We consider the *n*th MIMO-NOMA cluster that contains *m* users, the channel matrix **H***n* ∈ C*m*×*<sup>N</sup>* could be defined [24]:

$$\mathbf{H}\_{\rm tr} = \begin{bmatrix} \mathbf{h}\_{n,1}, \mathbf{h}\_{n,2}, \cdots, \mathbf{h}\_{n,m} \end{bmatrix} \tag{7}$$

By taking the Singular Value Decomposition (SVD) of the channel matrix **H***n* we obtain:

$$\mathbf{H}\_n^T = \mathbf{U}\_n \sum\_n \mathbf{V}\_n^H \tag{8}$$

Each beam is utilized by a MIMO-NOMA cluster so that the channel corresponding to the nth beam is: **~**

$$\mathbf{h}\_n = \mathbf{H}\_n \mathbf{u}\_n^\* \tag{9}$$

where **<sup>u</sup>**<sup>∗</sup>*n* is the first column of **<sup>u</sup>***n*.The equivalent channel matrix can be expressed as follows:

$$\tilde{\mathbf{H}} = [\tilde{\mathbf{h}}\_1, \tilde{\mathbf{h}}\_2, \cdots, \tilde{\mathbf{h}}\_G] = [\mathbf{H}\_1 \mathbf{u}\_1^\*, \mathbf{H}\_2 \mathbf{u}\_2^\* \cdots, \mathbf{H}\_G \mathbf{u}\_G^\*] \tag{10}$$

Then, the precoding matrix can be written as:

$$
\tilde{\mathbf{W}} = [\tilde{\mathbf{w}}\_1, \tilde{\mathbf{w}}\_2, \dots, \tilde{\mathbf{w}}\_G] = \tilde{\mathbf{H}} (\tilde{\mathbf{H}}^H \tilde{\mathbf{H}})^{-1} \tag{11}
$$

After normalization of the precoding matrix, the precoding vector of the nth beam is:

$$\mathbf{w}\_{n} = \frac{\tilde{\mathbf{w}}\_{n}}{\left\| \tilde{\mathbf{w}}\_{n} \right\|\_{2}} \tag{12}$$

#### *2.3. Power Allocation*

In the NOMA system, the channel gain di fference between users can be converted to a multiplexing gain by superposition coding. Therefore, power allocation has an important impact on system performance [25]. We proposed a dynamic power allocation method for the MIMO-NOMA system. Firstly, the transmission power is allocated according to the number of beams, which is proportional to the number of users served by the beam. Each beam is used by all users of the cluster and each MIMO-NOMA cluster contains users with near-similar channel di fferences. Therefore, the power allocation of users in the cluster is very important. We allocate power to users within the cluster for maximizing the cluster communication rate. The proposed power allocation method is described as:

$$P\_{\mathcal{S}} = P \times \frac{\left| \mathcal{S}\_{\mathcal{S}} \right|}{|\mathcal{S}\_1| + |\mathcal{S}\_2| + \dots + |\mathcal{S}\_G|} \tag{13}$$

The first step is to allocate the transmit power between beams. *Pg* is the transmitted power in the *g*th beam, *g* = 1, 2 ··· *G*. *P* denotes the total transmitted power. After obtaining the transmit power of each beam, *Sg* is a set of the users served by the *g*th beam. The second step is to perform power allocation on the user cluster served by the beams. We assume that the interference between users is small within the same user cluster, and the problem can be defined as:

$$\max\_{p\_{\mathcal{S}^1}, p\_{\mathcal{S}^2} - p\_{\mathcal{S}, \mathcal{S}\_{\mathcal{S}}}} \mathbf{C}\_{\mathcal{S}} = \sum\_{n=1}^{|S\_{\mathcal{S}}|} \log\_2(1 + \frac{\left| \mathbf{h}\_{\mathcal{S}, n} \right|^2 p\_{\mathcal{S}, n}}{\sigma})$$

$$\text{s.t. } \mathbf{C}\_1 : \sum\_{n=1}^{S\_n} p\_{\mathcal{S}, n} = P\_{\mathcal{S}} \tag{14}$$

where **<sup>h</sup>***g*,*<sup>n</sup>* is the channel of the *n*th user in the *g*th beam (*g* = 1, 2, ··· *G*, *n* = 1, 2, ···*Sg*). *pg*,*<sup>n</sup>* denotes the transmitted power for the *n*th user in the *g*th beam. σ denotes noise power spectral density. To solve the convex optimization problem (14), we define the Lagrange function as:

$$L(\lambda, p\_{\mathcal{S},1}, p\_{\mathcal{S},2} \cdots p\_{\mathcal{S},S\_{\mathcal{S}}}) = \sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \log\_2(1 + \frac{|\mathbf{h}\_{\mathcal{S},n}|^2 p\_{\mathcal{S},n}}{\sigma}) + \lambda (\sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} p\_{\mathcal{S},n} - P\_{\mathcal{S}}) \tag{15}$$

where λ ≥ 0,

> By calculating the derivative (15):

$$\frac{\partial L}{\partial p\_{\mathcal{S},\mathcal{U}}} = \frac{\mathbf{h}\_{\mathcal{S},\mathcal{U}}}{(1 + p\_{\mathcal{S},\mathcal{U}} \mathbf{h}\_{\mathcal{S},\mathcal{U}})In2} - \lambda = 0 \tag{16}$$

we have:

0

$$p\_{\mathcal{S},n} = \frac{1}{\overline{\lambda}} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}\tag{17}$$

where λ = λ*In*2, // /**h***g*,*<sup>n</sup>* // / is the channel gain of the *n*th user in the *g*th beam. By substituting (17) into the constraint C1 in (14) we have:

$$\sum\_{n=1}^{S\_n} \frac{1}{\overline{\lambda}} - \frac{1}{\left| \mathbf{h}\_{\mathcal{S},n} \right|} = P\_{\mathcal{S}} \tag{18}$$

 λ can be written as:

0

$$\overline{\lambda} = \frac{|S\_{\mathcal{S}}|}{P\_{\mathcal{S}} + \sum\_{n=1}^{|S\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S}^n}|}} \tag{19}$$

Substituting (19) into (17), we have

$$p\_{\mathcal{S},n} = \frac{P\_{\mathcal{S}} + \sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}}{|\mathbf{S}\_{\mathcal{S}}|} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|} = \frac{P\_{\mathcal{S}}}{|\mathbf{S}\_{\mathcal{S}}|} + \frac{\sum\_{n=1}^{|\mathcal{S}\_{\mathcal{S}}|} \frac{1}{|\mathbf{h}\_{\mathcal{S}}|}}{|\mathbf{S}\_{\mathcal{S}}|} - \frac{1}{|\mathbf{h}\_{\mathcal{S},n}|}\tag{20}$$

where *Pg* is the transmitted power in the *g*th beam, ///*Sg*/// represents the number of users served by the *g*th beam, and ///**<sup>h</sup>***g*,*<sup>n</sup>*/// is the channel gain of the *n*th user in the *g*th beam. From (20) we obtain the transmitted power of the *n*th user in the *g*th beam and find that when the number of users in the group is larger, the power allocated to user would be reduced.

#### **3. Energy Harvesting Maximizing**

To maximize the harvested energy while meeting the minimum communication rate, we propose the addition of a power splitter for each user at the receiver to help implement SWIPT. This method is called SWIPT with power split [26], as shown in Figure 4. The signal received by each user is divided into two parts. One part is forwarded to the information decoder for information decoding, and the other part is subjected to Energy Harvesting (EH). The received signal to EH at the *m*th user in the *n*th beam can be can be formulated [27]:

$$
\Delta y\_{n,m}^{EH} = \sqrt{1 - \beta\_{n,m}} y\_{n,m} \tag{21}
$$

**Figure 4.** Simultaneous Wireless Information and Power Transfer (SWIPT) split receiver Power Split (PS) mode.

The harvested energy at the *m*th user in the *n*th beam is

$$P\_{n,m}^{EH} = \left. \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^{-2} \right) \tag{22}$$

where η is the energy conversion efficiency, β*<sup>n</sup>*,*<sup>m</sup>* is the power splitting factor at the *m*th user in the nth beam, 0 ≤ β*<sup>n</sup>*,*<sup>m</sup>* ≤ 1.

Meanwhile, the signal used to carry out the information decoding is expressed as

$$y\_{n,m}^{ID} = \sqrt{\beta\_{n,m}} y\_{n,m} + u\_{n,m} \tag{23}$$

Substituting (1) into (23), we have

$$\begin{split} \mathbf{y}\_{n,\mathbf{m}}^{ID} &= \sqrt{\beta\_{\mathbf{n},\mathbf{m}}} \Big( \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sqrt{\mathbf{p}\_{\mathbf{m},\mathbf{n}}} \mathbf{s}\_{\mathbf{m},\mathbf{n}} + \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sum\_{j=1}^{\mathbf{m}-1} \sqrt{\mathbf{p}\_{i,\mathbf{n}}} \mathbf{s}\_{i,\mathbf{n}} \\ &+ \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \mathbf{w}\_{\mathbf{n}} \sum\_{i=m+1}^{|\mathcal{S}\_{i}|} \sqrt{p\_{i,\mathbf{n}}} \mathbf{s}\_{i,\mathbf{n}} + \mathbf{h}\_{\mathbf{n},\mathbf{m}}^{H} \sum\_{i \neq n}^{|\mathcal{S}\_{i}|} \sum\_{j=1}^{|\mathcal{S}\_{i}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} \mathbf{s}\_{i,j} + \boldsymbol{\nu}\_{n,\mathbf{m}} \bigg) + \boldsymbol{u}\_{n,\mathbf{n}} \end{split} \tag{24}$$

where *un*,*<sup>m</sup>* is the noise the distribution CN(0, <sup>σ</sup>*u*<sup>2</sup>). By applying NOMA in each beam, intra-beam superposition coding of the transmitter and the receiver is realized. The *m*th user in the *n*th beam can eliminate the interference of the *i*th user (for all *i* > *m*) in the *n*th beam by performing SIC, and the remaining received signal of the *m*th user in the *n*th beam to information decoding can be rewritten as

$$\mathbf{y}\_{n,m}^{ID} = \sqrt{\beta\_{n,m}} \Big| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sqrt{p\_{n,m}} s\_{n,m} + \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sum\_{j=1}^{m-1} \sqrt{p\_{i,n}} s\_{i,n} + \mathbf{h}\_{n,m}^{H} \sum\_{i \neq n}^{G} \sum\_{j=1}^{|\mathcal{S}\_{i}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} s\_{i,j} + \boldsymbol{\upsilon}\_{n,m} \bigg) + \boldsymbol{\mu}\_{n,m} \tag{25}$$

Then, according to (25), the SINR at the *m*th user in the *n*th beam can be written as

$$\gamma\_{n,m} = \frac{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m}}{\xi\_{n,m}} \tag{26}$$

where,

$$\boldsymbol{\xi}\_{n,m} = \left\| \mathbf{h}\_{n,m}^H \mathbf{W}\_n \right\|\_2^2 \sum\_{j=1}^{m-1} p\_{n,j} + \sum\_{i \neq n}^G \left\| \mathbf{h}\_{n,m}^H \mathbf{W}\_i \right\|\_2^2 \sum\_{j=1}^{|S\_j|} p\_{i,j} + \sigma\_v^2 + \frac{\sigma\_u^2}{\beta\_{n,m}} \tag{27}$$

The achievable rate of the *m*th user in the *n*th beam can be written as

$$R\_{n,m} = \log\_2(1 + \gamma\_{n,m})\tag{28}$$

We have grouped users, designed a precoding matrix, and allocated power to users in Sections 2 and 3. According to (22), we know we need to find the power splitting coefficient of each user for making the harvested energy at the receiver is maximized. We formulate the problem as

$$\begin{array}{l}\underset{\{\beta\_{n,m}\}}{\max}P^{EH}\\\text{s.t. C}\_{1}:\,\mathcal{R}\_{m,n}\geq\mathcal{R}\_{\text{min}}\\\text{C}\_{2}:\,0\leq\beta\_{n,m}\leq1\end{array} \tag{29}$$

Substituting (22), (28), into (29), we have

$$\begin{aligned} \max\_{\{\boldsymbol{\beta}\_{n,m}\}} & \sum\_{i=1}^{G} \sum\_{j=1}^{|S\_j|} \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^2 \right) \\ \text{s.t.} & \,\mathbf{C}\_1: \log\_2(1 + \chi\_{n,m}) \ge R\_{\min} \\ & \mathbf{C}\_2: 0 \le \beta\_{n,m} \le 1 \end{aligned} \tag{30}$$

where *PEH* is the total harvested energy. *R*min denotes the minimum achievable rate of the user.

To maximize the total harvested energy, the energy harvested by each user is maximal, the problem is converted to maximize the energy harvested by each user:

$$\begin{aligned} \max\_{\{\beta\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_\upsilon^2 \right) \\ \text{s.t.} &\,\mathbf{C}\_1: \log\_2(1 + \gamma\_{n,m}) \ge R\_{\min} \\ &\mathbf{C}\_2: 0 \le \beta\_{n,m} \le 1 \end{aligned} \tag{31}$$

Substituting (26), (27) into (31), we have

$$\begin{split} \max\_{\{\boldsymbol{\beta}\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2} p\_{n,m} + \sigma\_{v} \boldsymbol{\varepsilon} \right) \\ \text{s.t. } \mathbb{C}\_{1}: \log\_{2} \left( 1 + \frac{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2} p\_{n,m}}{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \right\|\_{2}^{2m-1} p\_{n,j} + \sum\_{j=n}^{G} \left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{i} \right\|\_{2}^{2} \sum\_{j=1}^{[S\_{i}]} p\_{i,j} + \sigma\_{v}^{2} + \frac{\sigma\_{u}^{2}}{\rho\_{n,m}}} \right) \geq R\_{\text{min}} \\ \text{C}\_{2}: 0 \leq \beta\_{n,m} \leq 1 \end{split} \tag{32}$$

By simplifying C1 in (32),

$$1 + \frac{\left\|\mathbf{h}\_{n,m}^H \mathbf{w}\_n\right\|\_2^2 p\_{n,m}}{\omega\_{n,m} + \frac{\sigma\_n^2}{\beta\_{n,m}}} \ge 2^{R\_{\text{min}}} \tag{33}$$

where,

$$\boldsymbol{\omega}\_{n,\rm m} = \left\| \mathbf{h}\_{n,\rm m}^{\rm H} \mathbf{W}\_n \right\|\_2^2 \sum\_{j=1}^{m-1} p\_{n,j} + \sum\_{i \neq \rm n} \left\| \mathbf{h}\_{n,\rm m}^{\rm H} \mathbf{W}\_i \right\|\_2^2 \sum\_{j=1}^{|S\_i|} p\_{i,j} + \sigma\_v^2 \tag{34}$$

By simplifying (33),

$$\beta\_{n,m} \ge \frac{\sigma\_u^2 (2^{R\_{\min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{u,m} - \alpha\_{n,m} (2^{R\_{\min}} - 1)}\tag{35}$$

Then, the constraint C1 in (32) can be rewritten as

$$\begin{aligned} \max\_{\{\beta\_{n,m}\}} P\_{n,m} &= \eta (1 - \beta\_{n,m}) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_\upsilon^2 \right) \\ \text{s.t. } \mathbf{C}\_1: \beta\_{n,m} &\ge \frac{\sigma\_u^2 (2^{R\_{\min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} - \omega\_{n,m} (2^{R\_{\min}} - 1)} \\ \mathbf{C}\_2: 0 &\le \beta\_{n,m} \le 1 \end{aligned} \tag{36}$$

According to (36), we know that when β*<sup>n</sup>*,*<sup>m</sup>* is the minimum that meets constraint C1, 1 − β*<sup>n</sup>*,*<sup>m</sup>* is the maximum. Then we obtain the maximum *Pn*,*m*. Accordingly, we ge<sup>t</sup> the optimal power splitting coefficient at the *m*th user in the *n*th beam:

$$\beta\_{n,m} = \frac{\sigma\_{\rm u}^{2} (2^{K\_{\rm min}} - 1)}{\left\| \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{\rm n} \right\|\_{2}^{2} p\_{n,m} - \omega\_{n,m} (2^{R\_{\rm min}} - 1)} \tag{37}$$

Substituting (37) into (22), The maximal harvested energy at the *m*th user in the *n*th beam is

$$P\_{n,m\_{\rm max}} = \eta \left( 1 - \frac{\sigma\_u^2 (2^{R\_{\rm min}} - 1)}{\left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} - \omega\_{n,m} (2^{R\_{\rm min}} - 1)} \right) \left( \left\| \mathbf{h}\_{n,m}^H \mathbf{w}\_n \right\|\_2^2 p\_{n,m} + \sigma\_v^2 \right) \tag{38}$$

#### **4. Simulation Results**

We consider a typical downlink mmWave massive MIMO-NOMA system, the spectral efficiency is defined as the reachability rate in equation (6), and the energy efficiency is defined as the ratio of reachability to total power consumption [28],

$$EE = \frac{R\_{sum}}{P + N\_{RF}P\_{RF} + P\_{BB}} \tag{39}$$

where *P* is the total transmitted power,*PRF* is the power consumed by each RF chain, *PBB* is the baseband power consumption, *NRF* is the number of the RF chain, *Rsum* is from (6).Simulation parameters are shown in Table 1.


**Table 1.** Simulation parameters.

In the simulation, we first consider three kinds of mmWave massive MIMO systems and compare them by using two different user grouping methods proposed in Section 2.1:


The power allocation method proposed in this paper is applied to the MIMO-NOMA system and we compare the performance with the system using traditional average power allocation method that it allocated equal power to all users. Finally, the SWIPT technology is integrated into the system to compare the power harvested by the MIMO-NOMA and MIMO-OMA.

Figure 5 shows the spectral efficiency against Signal to Noise Ratio(SNR)of the considered five schemes mentioned above, where the number of users *K* is set to 32 and the number of antennas is set to 256. From the figure, we can see that the proposed MIMO-NOMA scheme has a higher spectral efficiency than the MIMO-OMA scheme. It is intuitive that the fully digital MIMO can achieve the best spectrum efficiency, as shown in Figure 5. However, the number of RF chains required in the full digital MIMO scheme is equal to the number of antennas (*NRF* = *N*), and the number of RF chains required in MIMO-NOMA is 8. The full digital MIMO scheme needs higher hardware costs and overhead. Through the simulation diagram, we can obtain that the UC\_CG algorithm gives higher spectral efficiency than the UC\_FAG algorithm. Given the users that are matched according to the correlation between all channels of the user and the cluster-head user in UC\_CG algorithm, in the UC\_FAG algorithm, the users are matched according to the correlation between the part of the channel of the user and the cluster-head user. In comparison with the UC\_FAG algorithm, the interference between users in the group is smaller in the UC\_CG algorithm.

*Electronics* **2020**, *9*, 32 correlation between all channels of the user and the cluster-head user in UC\_CG algorithm, in the UC\_FAG algorithm, the users are matched according to the correlation between the part of the channel of the user and the cluster-head user. In comparison with the UC\_FAG algorithm, the interference between users in the group is smaller in the UC\_CG algorithm. 

**Figure 5.** Spectral efficiency of the considered five schemes system against SNR **Figure 5.** Spectral efficiency of the considered five schemes system against SNR

Figure 6 shows the energy efficiency of the five schemes considered under different SNR, where the number of users is set to 32, the number of antennas is set to 256. From Figure 6, we know that the MIMO-NOMA scheme has a higher energy efficiency than MIMO-OMA and fully digital MIMO, where the number of RF chains of the fully digital MIMO is equal to the number of base station antennas, which results in very high energy consumption. In contrast, in the MIMO-NOMA scheme, the number of RF chains is much smaller than the number of antennas. Therefore, the energy consumption of the RF chain can be significantly reduced when compared with the fully digital MIMO scheme. Figure 6 shows the energy efficiency of the five schemes considered under different SNR, where the number of users is set to 32, the number of antennas is set to 256. From Figure 6, we know that the MIMO-NOMA scheme has a higher energy efficiency than MIMO-OMA and fully digital MIMO, where the number of RF chains of the fully digital MIMO is equal to the number of base station antennas, which results in very high energy consumption. In contrast, in the MIMO-NOMA scheme, the number of RF chains is much smaller than the number of antennas. Therefore, the energy consumption of the RF chain can be significantly reduced when compared with the fully digital MIMO scheme. *Electronics* **2019**, *8*, x FOR PEER REVIEW 13 of 16

According to Figure 5, the communication rates of UC\_CG with MIMO-NOMA is higher than UC\_FAG with MIMO-NOMA. When the total power consumption of the system is the same, UC\_CG

A comparison of the performance of energy efficiency with the number of users is shown in Figure 7 in which the SNR is set to 10dB. We can see that, as the number of users increases, the energy efficiency is gradually reduced. Even with a very large number of users, the proposed MIMO-NOMA scheme is more energy efficient than MIMO-OMA and the fully digital MIMO scheme. **Figure 6.** Energy efficiency against SNR

**Figure 7.** Energy efficiency against the number of users K. **Figure 7.** Energy efficiency against the number of users K.

The next experiment considers the spectral efficiency of the SNR under two different power allocation algorithms. From Figure 8, we obtain that the power allocation algorithm proposed in this paper has higher spectrally efficient than the traditional average power allocation algorithm. We understand that the power allocation algorithm proposed is better than the traditional average allocation algorithm. The next experiment considers the spectral efficiency of the SNR under two different power allocation algorithms. From Figure 8, we obtain that the power allocation algorithm proposed in this paper has higher spectrally efficient than the traditional average power allocation algorithm. We understand that the power allocation algorithm proposed is better than the traditional average allocation algorithm.

Figure 9 shows the energy harvesting performance against SNR. To enable the user to maximize harvested power and meet the communication requirement, in Section 3, we proposed a method that finds the power splitting optimization. From Figure 9, we can see that, when signal power is low, the received signal performs information decoding. The receiver can start harvesting energy when the signal becomes larger. In comparison with the MIMO-OMA scheme, MIMO-NOMA can harvest more energy. Therefore, the proposed MIMO-NOMA scheme with SWPIT is superior to MIMO-OMA scheme, which can realize the recycling of energy.

Figure 9 shows the energy harvesting performance against SNR. To enable the user to maximize harvested power and meet the communication requirement, in Section 3, we proposed a method that finds the power splitting optimization. From Figure 9, we can see that, when signal power is low, the received signal performs information decoding. The receiver can start harvesting energy when the signal becomes larger. In comparison with the MIMO-OMA scheme, MIMO-NOMA can harvest more energy. Therefore, the proposed MIMO-NOMA scheme with SWPIT is superior to MIMO-OMA scheme, which can realize the recycling of energy. 

**Figure 9.** Energy harvesting against SNR. In this paper, we designed two different user grouping methods for MIMO-NOMA system: the UC\_CG algorithm and the UC\_FAG algorithm. From the simulation, we can see that the UC\_CG algorithm is better than the UC\_FAG algorithm, which improves spectral efficiency. We proposed a new power allocation method. The simulation results show that the algorithm is superior to the traditional average power allocation algorithm. Finally, we apply the SWIPT for MIMO-NOMA system. Under the premise of satisfying the minimum communication rate of each user, we proposed the method based on maximizing the harvested energy to find the optimal power splitting factor for each user. This method allows the system to harvest more energy and meets the user's minimum communication rate, thereby achieving the recycling of energy and green communication.

**Author Contributions:** Conceptualization, S.L.; Methodology, Z.W.; Supervision, L.J. and J.D.; Writing—review & editing, S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by National Nature Science Funding of China (NSFC): 61401407, 61601414 and the Fundamental Research Funds for the Central Universities.

**Conflicts of Interest:** The authors declare no conflict of interest.
