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Abstract

Currently, the standardization of fifth-generation mobile communication system (5G), which realizes 10 Gbps transmission, is in progress. In mobile communications, it is generally difficult to perform high-capacity transmission because of channel fading. Therefore, an adaptive resource allocation scheme based on users’ channel conditions is adopted to enhance the system capacity. Recently, it has been shown that a non-orthogonal multiple access scheme can achieve a higher system capacity than orthogonal multiple access scheme. However, anticipating a continuous increase in mobile traffic, it is desired to further enhance the throughput of non-orthogonal multiple access scheme. Therefore, we propose an application of code division multiplexing to non-orthogonal multiple access scheme using successive interference canceler to improve the throughput performance. The improved performance is demonstrated through numerical simulations.

Keywords

Non-orthogonal multiple access code division multiplexing successive interference cancelation downlink proportional fairness

Introduction

Recently, the mobile traffic has increased 3.5 times in 3 years from 2012 to 2015.¹ This increase in mobile traffic is expected to continue and is expected to reach more than 1000 times in 2020 compared to 2010. In addition, the word Internet of Things (IoT) penetrates recently, and it is expected that everything around us will communicate in the future. Thus, the standardization of fifth-generation mobile communication system (5G), which accommodates this expanding traffic, is in progress. Figure 1 shows the performance index of 5G wireless access network.² For comparison, the performance index of 4G (IMT-Advanced) is also shown.³ It is supposed that the 5G accommodates a great variety of communication systems, and it is necessary to improve the performance such as peak data rate, mobility, capacity, number of connected device per cell, latency, and energy saving compared to 4G. To achieve these performance indexes, it is necessary to improve frequency utilization efficiency and develop high-frequency band by advancing the existing technologies and combining there. Generally, the technology to use limited frequency resources for communication is an important factor to realize 5G. 3.9 and fourth-generation mobile communication systems, named as long-term evolution (LTE) and LTE-Advanced, respectively, use orthogonal frequency division multiple access (OFDMA) as the downlink multiple access scheme.⁴ Because the OFDMA scheme uses subcarriers that are orthogonal to each other for the transmitted data, there are no interferences between the subcarriers, and OFDMA has a tolerance for frequency-selective fading because of multicarrier transmission. However, there is a need for further improvement of multiple access scheme in order to realize mobile communication system that accommodates mobile traffic expected in near future. Hence, non-orthogonal multiple access (NOMA) scheme is considered as a promising candidate for new multiple access schemes.^5,6 In orthogonal multiple access (OMA) scheme such as OFDMA, there are no interferences between users because base station (BS) allocates one user for each subcarrier. However, in the NOMA scheme, multiple users are multiplexed in the power domain for one subcarrier. This leads to interferences between multiplexed users. Figure 2 shows the principle of the NOMA scheme. In the figure, the BS allocates more than one user in each subcarrier in downlink. In the allocation, the users who have different channel gains are selected, for example, near user and far user. The user having low channel gain (far user) is allocated with higher levels of transmission power than the user having high channel gain (near user). The BS then transmits the superimposed signal. At the receiver side, a successive near user first decodes the far user data, subtracts it from the received signal, and then decodes his or her own data.⁷ In contrast, at the far user, the near user signal in the received superimposed signal is sufficiently attenuated because of the lower allocated power and low channel gain, and thus, the far user can just decode his or her own data. It is known that the system throughput can be increased using the NOMA scheme instead of the OMA scheme.

Figure 1.

Performance index of 5G wireless access network.

Figure 2.

Principle of NOMA.

Other than the power-domain NOMA described above, there are some techniques realizing NOMA, that is, spreading-domain, code-domain, and interlearver-domain NOMA schemes.⁸ In code-domain NOMA, low-density signature (LDS)⁹ and pattern division multiple access (PDMA)¹⁰ have been proposed. However, a sensitive design of spreading matrix is needed in these schemes. As a combination of power-domain and code-domain NOMA, power-domain sparse code multiple access (PSMA) has been proposed for throughput enhancement.¹¹ However, a complex design of code matrix is still needed and the decoding complexity increases in PSMA.

Fuwa et al.¹² have proposed a code division multiplexing (CDM)-OFDMA in which the frequency diversity effect is obtained for the allocated subcarriers by code-spreading in the frequency domain. Adopting this principle, we proposed an application CDM to the NOMA-SIC scheme for throughput performance improvement in Kitagawa and Okamoto,¹³ and it was shown that the throughput enhancement was obtained compared to the conventional NOMA scheme. This NOMA-CDM-SIC uses a simple spreading matrix such as Walsh code matrix, and no additional structure other than spreading/despreading operations is required in scheduling and decoding. However, the scheduling algorithm in Kitagawa and Okamoto¹³ was rather simple and more performance improvement was expected. In addition, the user fairness was not considered. Therefore, in this article, we propose a NOMA-CDM-SIC scheme with improved scheduling algorithm to further enhance the performance of NOMA in terms of throughput and user fairness, and show its performance by numerical simulation.

This article is organized as follows. Section “Downlink NOMA system” describes the downlink NOMA system with successive interference cancelation (SIC). The details of the proposed NOMA scheme with CDM is described in section “Proposed NOMA scheme using CDM,” and the numerical results are shown in section “Numerical results.” Section “Further improvement of scheduling algorithm” describes about the advancement of scheduling algorithm for NOMA scheme. Finally, section “Conclusion” presents the conclusion.

Downlink NOMA system

Figure 3 shows the concept of downlink NOMA system. In the downlink from the BS to user equipment (UE), BS allocates users in each subcarrier while taking into account the proportional fairness (PF). In the NOMA scheme, more than two users can be allocated in one subcarrier, while allowing interference with each other. In the example of Figure 3, UE1 and UE5 are superposed in subcarrier 1, and UE2 and UE4 are superposed in subcarrier 3. Throughout this article, we assume a multiple-input-multiple-output (MIMO) spatial multiplexing transmission, in which the number of transmit antennae in the BS and receiver antennas in UE are $N_{t}$ and $N_{r}$ , respectively. There are $K$ users per cell, and $S$ subcarriers are used for multiuser transmission. Each of the $S$ subcarriers uses OMA or NOMA. In this article, the maximum number of non-orthogonally multiplexed users is $m_{s}$ . The BS selects a set of users, $U_{s} = {i_{s} (1), i_{s} (2), \dots, i_{s} (l)}$ , from $K$ users for a subcarrier $s$ $(1 \leq s \leq S)$ , where $i_{s} (l)$ indicates the index of the lth $(1 \leq l \leq m_{s})$ user allocated to the subcarrier $s$ . Note that the formulae in this article are based on the study of Benjebbour et al.¹⁴ The transmit signal $N_{t} \times 1$ vector $x_{s}$ at the subcarrier $s$ is given as

$x_{s} = \sum_{l = 1}^{m_{s}} \sqrt{p_{s} (i_{s} (l))} d_{s} (i_{s} (l))$ (1)

where $p_{s} (i_{s} (l))$ is the allocated transmit power to user $i_{s} (l)$ and $d_{s} (i_{s} (l))$ is the $N_{t} \times 1$ coded modulation vector of user $i_{s} (l)$ . The $N_{r} \times 1$ received signal vector of user $i_{s} (l)$ at the subcarrier $s$ is given as

$y_{s} (i_{s} (l)) = h_{s} (i_{s} (l)) x_{s} + w_{s} (i_{s} (l))$ (2)

where $h_{s} (i_{s} (l))$ is the $N_{r} \times N_{t}$ channel matrix of user $i_{s} (l)$ and $w_{s} (i_{s} (l))$ is the $N_{r} \times 1$ noise plus inter-cell interference vector of user $i_{s} (l)$ at the subcarrier $s$ . At the receiver side, the minimum mean square error (MMSE) equalization is processed by multiplication of channel inverse matrix to the received vector. The channel inverse matrix $W_{s} (i_{s} (l))$ is given by

$W_{s} (i_{s} (l)) = h_{s}^{H} (i_{s} (l)) {h_{s} (i_{s} (l)) h_{s}^{H} (i_{s} (l)) + N_{r} [N_{s} (i_{s} (l))] I_{N_{r}}}^{- 1}$ (3)

where $N_{s} (i_{s} (l))$ is the average power of $w_{s} (i_{s} (l))$ and $I_{N_{r}}$ is the $N_{r}$ -dimensional unit matrix. In addition, we assume that the total transmission power of each subcarrier $s$ is equal to $P$ as follows

$\sum_{l = 1}^{m_{s}} p_{s} (i_{s} (l)) = P$ (4)

It is assumed that the BS knows the channel matrix $h_{s} (i_{s} (l))$ at the subcarrier $s$ . Then, the channel power of user $i_{s} (l)$ at the subcarrier $s$ is obtained by

$G_{s} (i_{s} (l)) = \sum_{i = 1}^{N_{min}} λ_{s, i} (i_{s} (l))$ (5)

where $N_{min} = min (N_{t}, N_{r})$ and $λ_{s, i} (i_{s} (l))$ is the ith eigenvalue of $h_{s} (i_{s} (l))$ at the subcarrier $s$ . Therefore, non-orthogonal user allocation is carried out based on the channel gain of $G_{s} (i_{s} (l)) / N_{s} (i_{s} (l))$ . At the SIC receiver, we assume that the SIC receiver of user $i_{s} (l)$ can correctly decode the signal of other user(s) $j$ when its channel gain $G_{s} (j) / N_{s} (j)$ is lower than $G_{s} (i_{s} (l)) / N_{s} (i_{s} (l))$ . The decoding is carried out in the ascending order of channel gain (i.e. the far user is considered first), and the near users’ signal is treated as noise. For example, as shown in Figure 4, UE1 close to the BS performs an SIC, in which the UE5 signal with a large power reception is first decoded, eliminated from the received signal, and then, the UE1 signal is decoded. UE5, far away from the BS, simply carries out the UE5 decoding because the overlapped UE1 signal is sufficiently attenuated because of the long-distance propagation. There are several methods of interference cancelation for the NOMA-SIC receiver¹⁵ such as codeword-level interference cancelation (CWIC) in which channel decoding is conducted for interference signals and symbol-level interference cancelation (SLIC) in which only demapping of the interference signal is conducted. Because CWIC can obtain a good interference replica by channel decoding, SIC works better and desired decoding results are obtained. However, to decode the far user’s codeword, the subcarrier allocation information of the far user is needed, which increases the control traffic. However, SLIC requires only the symbol demapping of far user, which does not require additional allocation information. However, the quality of interference replica is lower than that of CWIC, which degrades the performance. In this study, we adopt SLIC for simplicity.

Figure 3.

Downlink NOMA system.

Figure 4.

UE receiver structure for two-user NOMA-SIC, where channel gain of UE1 is larger than UE5.

It is assumed that the near user can correctly decode and eliminate far user signals at the receiver side. The achievable rate of user $i_{s} (l)$ at the subcarrier $s$ per 1 Hz is given by

$\begin{matrix} R_{s} (i_{s} (l) | U_{s}) = \log_{2} \\ (1 + \frac{G_{s} (i_{s} (l)) p_{s} (i_{s} (l))}{\sum_{j \in U_{s}, \frac{G_{s} (i_{s} (l))}{N_{s} (i_{s} (l))} < \frac{G_{s} (i_{s} (j))}{N_{s} (i_{s} (j))}} G_{s} (i_{s} (l)) p_{s} (j) + N_{s} (i_{s} (l))}) \end{matrix}$ (6)

Furthermore, the user set $U_{s}$ is selected as follows

$Q_{s} (U) = \sum_{k \in U} (\frac{R_{s} (k | U, t)}{L (k, t)}) U_{s} = max_{U} Q_{s} (U)$ (7)

where $U_{s}$ is the selected user set at the subcarrier $s$ , $U$ is the candidate user set, $Q_{s}$ is the PF scheduling metric, which is given by the summation of users to be allocated, and $R_{s} (k | U, t)$ is the achievable rate of equation (6) at time instance $t$ .¹⁴ Equation (7) is the metric of maximizing system sum rate by taking into account the PF.¹⁶ $L (k, t)$ is the average throughput of user $k$ at time $t$ defined by

$L (k, t) = (1 - \frac{1}{t_{c}}) L (k, t - 1) + \frac{1}{t_{c}} (\frac{1}{S} \sum_{s = 1}^{S} R_{s} (k, t - 1))$ (8)

where $t_{c}$ is an averaging parameter in the time direction and is set to $t_{c} = 20$ in this study. The number of user candidate sets in $U_{s}$ is given by

$N_{U} = (\begin{matrix} K \\ 1 \end{matrix}) + (\begin{matrix} K \\ 2 \end{matrix}) + \dots + (\begin{matrix} K \\ m_{s} \end{matrix})$ (9)

Equation (7) provides a high-capacity allocation while taking into account the PF. In the NOMA scheme, because the user signals are superimposed in the power domain, the power allocation to each user significantly affects the system throughput. As described above, to make SIC work effectively, more power should be allocated to far user and less power should be allocated to near user. As one of its allocation schemes, fractional transmit power control (FTPC)¹² is adopted in this study. In FTPC, the transmit power of user $k$ at the subcarrier $s$ is given as follows

$p_{s} (k) = \frac{P}{\sum_{j \in U_{s}} {(G_{s} (j) / N_{s} (j))}^{- α_{FTPC}}} {(\frac{G_{s} (k)}{N_{s} (k)})}^{- α_{FTPC}}$ (10)

where the parameter $α_{FTPC} (0 \leq α_{FTPC} \leq 1)$ denotes the same parameter of the power allocation. When $α_{FTPC} = 0$ , the transmit power is equally allocated to each superimposed user, and when it is close to 1, more power is allocated to the far user.

Proposed NOMA scheme using CDM

CDM is a technique in which multiplexed transmission is realized by multiplying spreading code to the transmitted signals. In multicarrier transmission, when the code-spreading is carried out in the frequency domain, the frequency diversity effect is obtained. In this study, we use the orthogonal Walsh code, often used in code division multiple access (CDMA) as the spreading code. The Walsh code is iteratively calculated by the following equation

$\begin{matrix} C w_{L} = (\begin{matrix} C w_{\frac{L}{2}} & C w_{\frac{L}{2}} \\ C w_{\frac{L}{2}} & - C w_{\frac{L}{2}} \end{matrix}) \\ {}_{\forall}L = 2^{γ}, γ \geq 1, C w_{1} = 1 \end{matrix}$

The NOMA transmit signal before spreading is denoted as $x = {(x_{1}, x_{2}, \dots, x_{L})}^{T}$ , and the transmit signal of NOMA-CDM is given by

$x_{w} = C w_{L} x$ (12)

The desired signal is obtained in the receiver after despreading using the same $C w_{L}$ . Figures 5 and 6 show the system block diagrams of transmitter and receiver, respectively, for the proposed NOMA scheme with CDM. In the BS, input data for each user are non-systematic convolutional (NSC) coded and modulated by quadrature phase shift keying (QPSK). Then, data are allocated to subcarriers according to the channel condition, and mapping to frequency domain. At this time, in NOMA scheme, data are superimposed according to equation (1). After a frequency-spreading is done, transformed by inverse fast Fourier transform (IFFT), a guard interval (GI) is inserted, and data are transmitted from each antenna. In the receiver, after removing GI, the SIC to be described later and frequency despreading are conducted. Then, data are decoded by soft-decision Viterbi algorithm, and desired data are obtained. In the multicarrier and multiuser CDM, the frequency diversity effect is obtained by extracting allocated subcarriers for each user and code-spreading them. In the case of NOMA, because multiple users are allocated at one subcarrier, extract and spreading need to be conducted for the same user pair. Figure 7 illustrates the example of the proposed code-spreading in the NOMA scheme. The non-orthogonal user-scheduling is conducted for each subcarrier. Then, the subcarriers of the same user combination are extracted, code-spread, and reallocated to the original subcarriers. Here, the number of allocated subcarriers for each combination is different according to the users’ channel condition. However, as shown in equation (11), the length of the Walsh code is limited to the power of two, and the Walsh code cannot be directly applied to the different length subcarriers. Therefore, in the proposed scheme, all subcarriers for each user set are divided into a power of 2 and spread individually. For example, if the number of allocated subcarriers is 40, it is divided into 32 and 8, and the Walsh codes of 32 and 8 are applied into each subcarrier group for spreading. In the receiver, when the near user subtracts the far user signal in SIC, that signal is code-spread and cannot be directly canceled by simple subtraction. Therefore, as shown in Figure 8, the near user first despreads the received signal, decodes the far user signal, and again code-spreads the decoded far user signal. After that, the interference replica is subtracted from the received signal, and the interference is canceled. By this CDM, the noise and interference are averaged and the frequency diversity effect is obtained.

Figure 5.

System block diagram of transmitter for the proposed NOMA with CDM.

Figure 6.

System block diagram of receiver for the proposed NOMA with CDM.

Figure 7.

Example of code-spreading in the proposed NOMA with CDM.

Figure 8.

SIC in proposed NOMA with CDM.

Numerical results

We evaluate the performance of the proposed scheme through numerical simulations. As the performance criterion, the average user throughput is calculated. Table 1 shows the simulation conditions. A non-sectorized hexagonal 19-cell model is used, and the users in the center target cell receive an interference signal from the adjacent 18-cell BSs, which have the same transmit power as the target BS. We assume that the cell radius is 500 m. It is assumed that the channel state information of the users in the target cell and the interference channel coefficients to each user from adjacent BSs are perfectly known to the target BS. The number of sub-bands $S$ and the size of fast Fourier transform (FFT) are both 256. The propagation loss is given by

$L_{d} = 128.1 + 37.6 \log_{10} (r) dB, rin kilometers$

Table 1.

Simulation conditions.

Cell layout	Hexagonal 19-cell model
Frequency reuse factor	1
No. of Tx and Rx antennas	$(N_{t}, N_{r}) = (2, 2)$
No. of user/cell $K$	8
Power decay factor $α_{FTPC}$	0.4
No. of subcarrier	256
FFT size	256
Channel	16 path 1 dB decay, quasi-static Rayleigh
Path loss exponent	3.5
Standard deviation of shadowing loss	7 dB
Carrier frequency	2 GHz
BS total transmit power	37 dBm
BS antenna gain	3 dBi
Feed system loss	1 dB
Total bandwidth	5 MHz
UE antenna gain	0 dBi
UE noise figure	4 dB
UE noise density	–169 dBm/Hz
UE SNR at cell edge	20 dB
Channel estimation	Ideal
Scheduling algorithm	Proportional fair
Cell radius	500 m
Channel coding	Non-systematic convolutional code, rate 1/2
Maximum code length	512
Decoding algorithm	Soft-decision Viterbi decoding
Primary modulation	QPSK
SIC receiver	SLIC
Spread code	Walsh code
No. of simulation iteration of user distribution	800
No. of simulation iteration per one user distribution	100
Throughput averaging factor $t_{c}$	20

FFT: fast Fourier transform; BS: base station; UE: user equipment; SNR: signal-to-noise ratio; SIC: successive interference cancelation; QPSK: quadrature phase shift keying; SLIC: symbol-level interference cancelation.

and the receiver noise density is –169 dBm/Hz, which are the typical values in 4G systems. The link budget parameters are also shown in Table 1. The carrier frequency is 2 GHz band, and the transmit power of BS is 37 dBm. The bandwidth is 5 MHz, and the average received signal-to-noise ratio (SNR) at the cell edge becomes 20 dB. In the simulation, the users were randomly distributed within the target cell, and the capacity was calculated based on 100 times channel generations. The user distribution was then iteratively changed to 800 times. The number of antennas is 2 × 2 MIMO, and SLIC is used for SIC in the receiver.

In addition, to suppress the performance degradation of SLIC, we introduce a parameter $β$ , which is the threshold of the channel gain ratio between multiplexed users. If the channel gain ratio between two users in a candidate user set is less than $β$ , that user set is eliminated in the NOMA scheduling. Figure 9 shows the average user throughput versus $β$ , where the average SNR at the cell edge is assumed to be 20 dB. It can be seen that when $β$ is small, the throughput significantly decreases because of SLIC. In SLIC, the channel decoding of interfered user is not conducted, resulting in incorrect cancelation of the other user when the channel gains between the two users are close. In contrast, when $β$ becomes large, that is, the channel gains of the two users become different, the average throughput increases and saturates at $β$ = 50. Because the pass loss exponent is 3.5, the condition of $β$ = 50 is equivalent to 3.62 times the difference in the distance from the BS to the user on average between the two users. Furthermore, we also compare the average user throughput when the number of maximum superposed users is two and three. In the three-user case, $β$ is applied between adjacent users, in which the difference between the first and the third users is $β^{2}$ . As a result, it is found that the user throughput is almost the same in both cases, and $β$ = 50 is the best configuration. However, the probability of three-user superposition was about 0.5% in the simulation but the number of combinations in scheduling largely increases. Therefore, we only consider the two-user superposition in the following.

Figure 9.

Average user throughput versus $β$ .

To evaluate the fairness among users in terms of allocated resources, we used Jain’s fairness index (JFI)¹⁷ in this article. JFI is a value between 0 and 1, and is closer to 1 when the difference in the capacity of each user channel is small, that is, fairness is achieved. JFI is calculated by the following equation

$JFI = {(\sum_{k}^{K} C_{k})}^{2} / K \sum_{k}^{K} C_{k}^{2}$ (13)

where $C_{k}$ is the total channel capacity of user $k$ . Figure 10 shows JFI of each transmission scheme. In the figure, JFI of NOMA when $β = 0$ is also shown. From Figure 10, it can be seen that JFI of NOMA is almost the same as OFDMA. In addition, JFI slightly deteriorates when $β$ = 50 because the user pair which maximizes JFI cannot satisfy the condition $β$ = 50, and the subcarrier is allocated to other user. Figure 11 shows the average user throughput versus SNR at the cell edge when $β$ = 50. For comparison, the performance of OFDMA and NOMA without CDM is also plotted. From the result, it can be seen that NOMA improves the performance compared to OFDMA because of the superimposed user multiplexing. In addition, NOMA with CDM effectively improves the throughput because of the frequency diversity effect.

Figure 10.

Comparison of Jain’s fairness index.

Figure 11.

Average user throughput versus average SNR at the cell edge when $β$ = 50.

Further improvement of scheduling algorithm

In conventional scheduling algorithm, $L (k, t)$ is fixed in advance as in equation (8) and eliminated as a parameter of equation (7). By making fairness index in equation (8) fixed, the search of equation (7) becomes independent on the order of scheduling, and the allocation can be conducted in ascending order of $1 \leq s \leq S$ . Using this method, calculation complexity can be reduced. However, there is room for improvement in the average user throughput and fairness. Then, to improve the performance of the average user throughput and fairness, we change scheduling metric of equation (7) as follows allowing a slight increase in the calculation complexity

$\begin{matrix} Q_{s} (U) = \sum_{k \in U} (\frac{R_{s} {(k | U, t)}^{\frac{3}{2}}}{L (k, t) + \sum_{i = 1}^{s} R_{s_{i}} (k, t)}) \\ U_{s} = max_{U} Q_{s} (U) \end{matrix}$ (14)

where $s_{i}$ is the subcarrier index during the ith subcarrier allocation. In the proposed method, because the allocation history at target time $t$ is taken into account, and the previously allocated capacity is included in the metric, equation (14) depends on the allocation order. Therefore, we use a suboptimal algorithm to conduct equation (14) as follows.¹⁸

$L (k, t)$ is calculated using equation (8) and transmission power for all $s$ . Let $s = 1$ .

User $k$ having the smallest throughput of

$L' (k, t) = (1 - \frac{1}{t_{c}}) L (k, t) + \frac{1}{t_{c}} (\sum_{s = 1}^{S} R_{s_{i}} (k, t))$ (15)

is selected from $K$ users.

The subcarrier $s_{i}$ , in which user $k$ can increase the throughput at maximum throughput, is selected from subcarriers not allocated yet.

For subcarrier $s_{i}$ , the user(s) are allocated based on equation (14). Let $s \to s + 1$ and return to step 2. If all $S$ subcarriers are allocated, the process is finished.

First, in step 1, the initial average throughput of all users is calculated. Next, in step 2, user $k$ having the minimum average throughput is selected, and subcarrier $s_{i}$ , in which user $k$ can increase the throughput at maximum, is set as the subcarrier to be allocated. Then, in step 4, subcarrier $s_{i}$ is allocated to the user(s) based on the NOMA scheduling of equation (14). This algorithm does not guarantee that user $k$ will always be selected in subcarrier $s_{i}$ . However, when this user is selected, their throughput is increased the most compared to the other subcarriers. In addition, in equation (14), it is known that the value of the power of throughput $R_{s}$ in a numerator significantly affects the system throughput.¹⁶ Therefore, in the proposed scheme, to take into account the spreading effect of CDM and $β$ , we assumed that $R_{s}$ is 3/2. The drawback of the proposed scheme is the increase in complexity. When $S$ is the number of subcarriers, the calculation complexity for scheduling of equation (7) is $O (S)$ . In contrast, that of the proposed scheduling of equation (14) becomes $O (S^{2})$ due to the adaptive subcarrier selection.

We evaluate the performance of the proposed scheme. Simulation conditions are equal to Table 1. Figure 12 shows JFI of each scheduling algorithm, where the schemes of equations (7) and (14) are labeled as “ascending order method” and “sequential update method,” respectively. From the result, it can be seen that the proposed scheme can improve the fairness index compared to the conventional scheme. This improvement of JFI is due to sequential update.

Figure 12.

Comparison of Jain’s fairness index for different scheduling algorithms.

Figure 13 shows the average user throughput versus SNR at the cell edge of the proposed scheme and the conventional scheme. The proposed scheme is shown to have a slightly better performance. This is because the probability of users with a small resource allocation decreased using equation (14). It should be noted that the throughput is basically in a tradeoff with the user fairness index, and in this regard, the proposed sequential update method that improves both is effective even though the throughput enhancement is not large.

Figure 13.

Average user throughput versus average SNR at the cell edge for different scheduling algorithms.

From Figures 12 and 13, we show that the proposed scheme can achieve higher performance in terms of both the average user throughput and the fairness index compared to the conventional scheme.

Conclusion

In this article, we proposed a new NOMA scheme utilizing CDM for downlink cellular systems. After PF-based scheduling, the subcarriers of the same user set are extracted, code-spread, and reallocated. In the receiver, CDM-based SIC is conducted. Numerical results show that an improved average user throughput was obtained because of the frequency diversity effect, particularly when the channel gains of the two superimposed users are significantly different.

In addition, we proposed an improved scheduling scheme, in which both the average user throughput and the fairness index were improved allowing a slight increase in the calculation complexity.

Future studies will consider the user-scheduling scheme for CDM and the application of CWIC.

Footnotes

Handling Editor: Sang-Woon Jeon

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

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