Precoding for Nonorthogonal Multiple Access with User Equipment Pairing
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Abstract
Due to the tremendous throughput requirement, current spectrum allocation scheme of 4G long term evolutionadvanced system can’t satisfy the need for future communications applications. Hence, researches have proposed a nonorthogonal multiple access (NOMA) technique as a candidate for 5G access system recently. This paper proposes two precoding matrix selection methods for the NOMA system and also provides an appropriate user equipment (UE) pairing method for NOMA. Combining the UE pairing with the proposed precoding selection method, results show that system capacity for NOMA system can be further improved.
Keywords
NOMA MIMO system Precoding matrix UE pairing1 Introduction
Long term evolutionadvanced (LTEA) is currently the most widely deployed fourthgeneration (4G) wireless communication system. LTEA adopts the orthogonal frequency division multiple access (OFDMA) to improve the spectrum efficiency for the conventional wideband code division multiple access system (WCDMA) [1]. However, as the tremendous throughput demand required for the future wireless communication applications, the spectrum allocation scheme of the LTEA system can no longer satisfy the need. Therefore, researches have proposed a novel nonorthogonal multiple access (NOMA) technique [2, 3, 4] as the fundamental access method for future 5G system and it has become the working item for the 3rd generation partnership project (3GPP).
Different from the OFDMA system that each individual user occupies a different frequency spectrum, in the NOMA transmission, it allows multiple users to use the same frequency spectrum at the same time to transmit their signals. The advantage of the NOMA is to have better spectrum efficiency than the OFDMA system.
Besides, in LTEA system, transmitter (Tx) can adopt the precoding matrix to ease the channel fading and has the advantage of beamforming. Receiver (Rx) acquires the channel state information (CSI) via the reference signal (RS) and feedbacks the suitable precoding matrix index (PMI) based on some criteria, such as to maximize the mutual information (MI) or minimize the bit error rate (BER) [7]. Therefore, it is an intuitive and reasonable extension for the future 5G system to adopt the precoding matrix during transmission since that the precoding technique has been shown can efficiently avoid the interferences and increase the signal to noise ratio (SNR) at Rx. Hence, what is the performance of the precoding matrix if applied to the NOMA system and how to select a suitable precoding matrix become interesting problems for the NOMA system. In [8], authors described a precoding matrix selection method to maximize the SNR or MI. This method has excellent capacity performance. Nevertheless, this method requires large amount of calculations that make it impractical in real implementations. In [9], authors reported singular value decomposition (SVD) precoding matrix selection method based on the maximization of the trace of the equivalent channel matrix. Besides, also in [9], a low complexity precoding matrix selection method was proposed by using the QR decomposition of the channel matrix. NOMA communication can increase system capacity by reusing the same frequency spectrum resource among multiple user equipment (UE). In practical situations, there are often several UEs coexist nearby. Therefore, in this paper, how to choose the appropriate UE pairs for the NOMA communication is also addressed.
This paper is organized as follow, Sect. 2 formulates the considered problem and illustrates the proposed two precoding selection methods. Besides, an appropriate UE pairing method for the NOMA communication is also provided. In Sect. 3, computer simulations and the indoor channel measurements were conducted to evaluate the performances of the proposed schemes and the literature methods. Finally, some conclusions for this paper are given in Sect. 4.
2 Problem Formulation and Method Descriptions
2.1 Problem Formulation
The purpose of this paper is to appropriately select the precoding pair \(({\mathbf{W}}_{{\mathbf{1}}} {\mathbf{,W}}_{{\mathbf{2}}} )\) for Tx at the downlink to have a better SNR or capacity performance in NOMA communication.
2.2 Review of the Literature Precoding Selection Methods
2.3 Proposed Precoding Selection Methods for NOMA
In this paper, two precoding selection methods for NOMA system are proposed. One adopts the MI criteria incorporating the SIC operation. The other is a low complexity method to simplify the calculations via maximizing the equivalent channel gain at Rx.
2.4 Proposed Modify Maximum Mutual Information Selection
In NOMA, an important feature for UE1 is to use the SIC method for decoding its symbols. In [8], the calculations of the SINR consider only the received signals for the UE1 and UE2 directly. However, for the UE1, additional SIC procedure is conducted to decode its symbols. Therefore, the proposed modified MI method will incorporate the SIC procedure to determine the suitable precoding matrices for both users.
2.5 Proposed Low Complexity Precoding Selection
Same as the conventional MI method, the proposed modified maximum MI selection has also the concern of large amount of calculations. Hence, a low complexity precoding selection method is proposed.
The term \(\sqrt {\beta_{1} P} (\sqrt {\beta_{2} P} {\mathbf{h}}_{{\mathbf{2}}} {\mathbf{W}}_{{\mathbf{2}}} )^{  1} {\mathbf{h}}_{{\mathbf{2}}} {\mathbf{W}}_{{\mathbf{1}}} {\mathbf{x}}_{{\mathbf{1}}}\) is the interference from the UE1 and the \((\sqrt {\beta_{2} P} {\mathbf{h}}_{{\mathbf{2}}} {\mathbf{W}}_{{\mathbf{2}}} )^{  1} {\mathbf{w}}_{{\mathbf{2}}}\) is the resulted AWGN.
In Eq. (24), the minimization of the noise enhancement is approximated as the maximization of the equivalent channel gain. With this relation, the calculation of matrix inverse can be avoided and the precoding matrix for each UE can also be determined separately to reduce the required computational complexity.
2.6 Proposed UE Pairing Method for NOMA

Step 1: For the existing N users (\(UE_{1}\) ~ \(UE_{N}\)), using the precoding matrix selection to decide a suitable pair of the matrices \(({\mathbf{W}}_{{\mathbf{1}}} {\mathbf{,W}}_{2} )\) with the \(UE_{N + 1}\). There will be N pairs of \(({\mathbf{W}}_{{\mathbf{1}}} {\mathbf{,W}}_{{\mathbf{2}}} )\).

Step 2: Calculate the \(SINR_{1}\) and \(SINR_{2}\) for each pair, and use Eq. (25) to decide the system capacity \(C_{n}\).
$$C_{n} = B[\log_{2} (1 + SINR_{1} ) + \log_{2} (1 + SINR_{2} )]\quad n = 1 \ldots N$$(25) 
Step 3: The \(\hat{n}\)th user with the largest capacity is the final decision to conduct the NOMA with \(UE_{N + 1}\), i.e.,
$$\hat{n} = \mathop {\arg }\limits_{n} \hbox{max} \{ C_{n} \}$$(26)
3 Computer Simulations and Experiments
In this section, the capacity performances of the proposed precoding selection methods are evaluated and compared with the related literature methods [8, 9, 10]. The required computation complexities are also analyzed to have fair comparisons.
3.1 Capacity Performance of Precoding Selection
Simulation parameters
Parameter  Value 

Number of Tx antenna  4 
Number of Rx antenna  1 
Channel  Rayleigh fading channel 
Bandwidth  5 kHz 
Power Ratio  \(\beta_{1} = 0.2\,\,\beta_{2} = 0.8\) 
SNR  0–20 (dB) 
Capacity  \(C = B(\log_{2} \left( {1 + SINR_{1} } \right) + \log_{2} (1 + SINR_{2} ))\) 
Complexity analysis
Complexity required  Example  

Proposed maximum mutual information selection  16,896  100% 
\(\begin{aligned} & S^{2} \times \{ 6 \times [N_{r} lN_{t} + N_{r} l(N_{t}  1)] + 3 \times [N_{r}^{2} l + N_{r}^{2} (l  1)] \\ & \quad + N_{r}^{3} + N_{r}^{2} (N_{r}  1) + N_{r}^{2} l + N_{r} l(N_{r}  1) \\ & \quad + 2 \times [N_{r} lN_{t} + N_{r} l(N_{t}  1) + N_{r} ]\} \\ \end{aligned}\)  
SVD based selection  2336  13.8% 
\(2S \times (N_{r} lN_{t} + N_{r} l(N_{t}  1) + N_{r}^{2} l + N_{r} l(Nr  1) + N_{r} + R)\)  
Singular value decomposition selection criterion  352  2% 
\(2S \times (N_{t} lN_{t} + N_{r} l(N_{t}  1) + K)\)  
Max–min selection criterion  320  1.9% 
\(2S \times (N_{t} lN_{t} + N_{t} l(N_{t}  1) + N_{r} + Q)\)  
Proposed low complexity method  256  1.5% 
\(2S \times (N_{t} lN_{t} + N_{t} l(N_{t}  1) + N_{r} )\) 
From above analysis, we can conclude that the proposed modified MI precoding selection method has better capacity performance that the conventional maximum MI method. And the proposed low complexity method has the similar capacity performance than the literature methods [9, 10]. Nevertheless, it requires the least computations among these methods.
3.2 Performance Analysis of the Proposed UE Pairing
Consider a scenario that there are five UEs has been allocated the whole spectrum and system has to decide which user is suitable to conduct the NOMA with the additional 6th user (UE6). The parameters in this simulation are the same as Table 1.
3.3 Measured Experiments
4 Conclusions
In this paper, two precoding selection methods for the NOMA system are proposed. One is to maximize the MI after SIC and the other is to enhance the equivalent channel gain at Rx. Besides, a UE pairing method is also provided for the NOMA system.
Based on the results of simulations and the experiments, it shows that the proposed MI precoding selection method has excellent performance in the system capacity. For the proposed low complexity method, it has the least required complexity among the compared methods. Besides, with the help of the proposed UE pairing method, system capacity can be further improved about 30% in average for NOMA system.
Notes
Acknowledgements
Funding was provided by Ministry of Science and Technology, Taiwan (Grant No.: 1052119M019006).
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