**1. Introduction**

Non-Orthogonal Multiple Access (NOMA) is one of the key technologies of fifth generation (5G) networks, which can significantly improve the overall performance of the system. Through time and frequency resource reuse and user grouping for large-scale connection, NOMA can improve spectral efficiency [1]. Multiple-Input Multiple-Output (MIMO) is regarded as a promising technique for 5G wireless communication systems. The principle of MIMO is the use of multi-antenna technology to achieve spatial diversity. The multi-receiving and multi-transmitting mechanisms can effectively combat multipath interference and increase system capacity. The author proposed a new low complexity arrival direction estimation algorithm in MIMO system for meeting the needs of green communication in [2]; this algorithm is based on a new downlink transmission frame structure that can make full use of the prior information under the channel codebook feedback mechanism. NOMA superimposes multiple user signals in the power domain, superimposes coding on the transmitter, performs serial interference cancellation on the receiver, and eliminates inter-user interference for grouped users [3]. NOMA can be divided into two categories: NOMA in power domain and NOMA in code domain. The power domain NOMA scheme can provide service to multiple users with different channel conditions simultaneously in the same time, frequency, coding, and space [4–7]. Uplink and downlink NOMA transmission of single cellular network is studied in [8], the author also analyzed the effect of distance on performance of the system. The influencing factors of NOMA, such as user power allocation, new order cost, and Serial Interference Cancellation (SIC) error propagation were discussed in [9].

NOMA combined with MIMO technology has attracted considerable research interest. The basic principle of NOMA and MIMO combination in downlink transmission was studied in [10]. The MIMO-NOMA could improve spectrum reuse efficiency, transmission throughput, and energy efficiency. In MIMO-NOMA, it is essential to make user grouping efficient. If the user is grouped by appropriate methods, the error rate of the system can be reduced [11]. In the existing MIMO-NOMA system, users are divided into multiple groups. The group uses the NOMA principle to serve users. The precoding between groups is used to eliminate interference. The user grouping of the downlink NOMA system is studied in [12]; the user clustering problem is formalized into a semi-definite programming problem which can be solved using numerical toolbox [13]. The accuracy of power allocation a ffects the system performance. In [14], the author derived the closed expressions for the traversal, rate, and interrupt probability of the two-user NOMA system for static power allocation. A dynamic power allocation solution is provided in [15] with the goal of maximizing the total unit capacity.

Wireless communication devices still use electric cables or batteries to obtain electric energy. The battery storage capacity and usage period are often limited, which will cause the development and application of new technologies in specific scenarios to be deeply bounded. Harvesting energy from radio frequency (RF) signals has become an attractive strategy to address the critical challenges of limited battery life in wireless communication networks. An advanced technology called Simultaneous Wireless Information and Power Transfer (SWIPT) emerged in [16], by which the energy transmission and information transmission using RF signals can be achieved. Therefore, SWIPT is considered a potential energy-saving solution for 5G [17], which has attracted widespread attention in academia and industry. A capacity-energy function was defined and the receiver can perform both information decoding and energy harvesting (EH) without any restrictions [16]. The work [18] considered the sum rate and the per-user optimized data rate of the SWIPT-enabled NOMA system, in which two information decoding schemes are proposed, "fixed decoding order" and "time sharing", respectively, and proved that system performance could be significantly improved by integrating SWIPT on NOMA. The work of [19] jointly optimized the transmission power of the Base Station (BS), as well as the length of time for energy acquisition and data transmission. The application of SWIPT technology in NOMA is studied and a new cooperative SWIPT NOMA protocol is proposed in [20]. By jointly optimizing the power allocation coe fficient of MIMO-NOMA and the power splitting factor of SWIPT, the achievable sum rate can be maximized [21].

The issue of energy conservation is also an issue that recently has attracted considerable attention. To meet the needs of green communication and realize the recycling of energy, we implement energy-saving wireless communication in MIMO-NOMA system integrated with SWIPT. Specifically, each user uses a power splitter to split the received signal into two parts. The receiver performs information retrieval and energy storage to implement SWIPT simultaneously. In this paper, we also studied the user clustering, precoding design, and power allocation to optimize the power-splitter factor of SWIPT. The harvested energy is maximized under the premise of satisfying the minimum communication rate of the user.

The main contributions of this paper are as follows:


*Notation*: Within this paper, the upper-case boldface letters denote matrices; lower-case boldface letters are vectors. (·)*<sup>T</sup>*,(·)−1,(·)*<sup>H</sup>* denotes the transpose, matrix inversion, and conjugate transpose. CN(*<sup>a</sup>*, *b*) denote the complex Gaussian distribution with mean a and covariance b. ·*n* is *ln* norm operation. |Γ| denotes the number of elements in set Γ. *E*{·} denotes the expectation.

#### **2. System Model**

In this paper, we consider a single-cell downlink Millimeter-Wave massive MIMO-NOMA system, as shown in Figure 1. The base station is equipped with *N* antennas and *NRF* RF chains, and *K* single antenna users are served by the base station. By using NOMA, each beam can support multiple users. *Sg* represents the set of users served by the *g*th beam. To fully realize the multiplexing gain, we assume that the beam number *G* is equal to the number of RF chains *NRF*. The received signal at *m*th user in the *n*th beam is [21]:

$$\begin{split} y\_{n,\mathfrak{m}} &= \mathbf{h}\_{n,\mathfrak{m}}^{H} \sum\_{j=1}^{G} \sum\_{i=1}^{|\mathbf{S}\_{n}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} \mathbf{s}\_{i,j} + \boldsymbol{\nu}\_{n,\mathfrak{m}} \\ &= \mathbf{h}\_{n,\mathfrak{m}}^{H} \mathbf{w}\_{n} \sqrt{p\_{n,\mathfrak{m}}} \mathbf{s}\_{n,\mathfrak{m}} + \mathbf{h}\_{n,\mathfrak{m}}^{H} \mathbf{w}\_{n} \sum\_{j=1}^{\mathfrak{m}-1} \sqrt{p\_{i,j}} \mathbf{s}\_{n,j} + \mathbf{h}\_{n,\mathfrak{m}}^{H} \mathbf{w}\_{n} \sum\_{i=\mathfrak{m}+1}^{|\mathbf{S}\_{i}|} \sqrt{p\_{i,i}} \mathbf{s}\_{i,i} \\ &+ \mathbf{h}\_{n,\mathfrak{m}}^{H} \sum\_{i=\mathfrak{m}}^{G} \sum\_{j=1}^{|\mathbf{S}\_{i}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} \mathbf{s}\_{i,j} + \boldsymbol{\nu}\_{n,\mathfrak{m}} \end{split} \tag{1}$$

where the interference within the cluster and the interference between the cluster are existing. **<sup>h</sup>**m,*n* represents the channel of the *m*th user in the *n*th beam, **w***n* is precoding vector of the *n*th beam. *sn*,*<sup>m</sup>* is the transmitted signal and *pn*,*<sup>m</sup>* denotes transmitted power for the *m*th user in the *n*th beam, and <sup>υ</sup>*n*,*<sup>m</sup>* is the noise following the distribution CN(0, <sup>σ</sup>*u*<sup>2</sup>).

**Figure 1.** Millimeter-Wave massive Multiple-Input, Multiple-Output, Non-Orthogonal Multiple Access (MIMO-NOMA) system.

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 Serial Interference Cancellation (SIC). The remaining signal received by the *m*th user in the *n*th beam can be rewritten as:

$$\widetilde{\mathbf{y}\_{n,m}} = \left( \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sqrt{p\_{n,m}} \mathbf{s}\_{n,m} + \mathbf{h}\_{n,m}^{H} \mathbf{w}\_{n} \sum\_{j=1}^{m-1} \sqrt{p\_{n,j}} \mathbf{s}\_{n,j} + \mathbf{h}\_{n,m}^{H} \sum\_{i \neq n}^{G} \sum\_{j=1}^{|S\_{[i]}|} \mathbf{w}\_{j} \sqrt{p\_{i,j}} \mathbf{s}\_{i,j} + \boldsymbol{\nu}\_{n,m} \right) \tag{2}$$

The Signal to Interference plus Noise Ratio (SINR) at the *m*th user in the *n*th beam is:

$$\gamma\_{n,m} = \frac{\left\|{\mathbf{h}\_{n,m}^H \mathbf{w}\_n}\right\|\_2^2 p\_{n,m}}{\xi\_{n,m}} \tag{3}$$

where,

$$\mathbf{k}\_{\mathbf{n},\mathbf{m}}^{\boldsymbol{\xi}} = \left\| \mathbf{h}\_{\boldsymbol{n},\mathbf{m}}^{H}, \mathbf{W}\_{\boldsymbol{n}} \right\|\_{2}^{2} \sum\_{j=1}^{\mathbf{m}-1} p\_{\mathbf{n},j} + \sum\_{i \neq \mathbf{n}}^{G} \left\| \mathbf{h}\_{\boldsymbol{n},\mathbf{m}}^{H} \mathbf{W}\_{i} \right\|\_{2}^{2} \sum\_{j=1}^{|\mathbf{S}\_{i}|} p\_{i,j} + \sigma\_{\upsilon}^{2} \tag{4}$$

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

$$R\_{n,m} = \log\_2(1 + \gamma\_{n,m})\tag{5}$$

Finally, the achievable sum rate is:

$$R\_{sum} = \sum\_{n=1}^{G} \sum\_{m=1}^{|S\_i|} R\_{m,n} \tag{6}$$
