In next-generation communications, it is necessary to provide high data rates to a large number of heterogeneous wireless devices with limited resources . To achieve this goal, nonorthogonal multiple access (NOMA) has recently emerged as a promising technology to improve both the efficiency of resource utilization and the system performance in 5G networks ,. Recently, 3GPP has also studied deployment scenarios and receiver designs for NOMA systems in Release 14 in the context of a work item called “multiple user superposition transmission” (MuST) . Orthogonal multiple access (OMA), mainly employed in 3G or 4G networks, allocates orthogonal resources to user terminals, thereby eliminating inter-user interference. On the other hand, NOMA superposes multiuser signals with the different power weights within the same frequency, time, and spatial domains. Thus, NOMA receivers should handle the interference from the superpositioned signals by successive interference cancellation (SIC) or maximum-likelihood (ML) detection. NOMA can provide significant benefits for cell throughput improvement compared to OMA with the assumption of ideal SIC .
NOMA has been widely developed with other technologies in various environments. The application of MIMO to NOMA has also been investigated [7, 8], and the ergodic capacity of MIMO-NOMA has been derived . In addition, the data rate of a cell-edge user can be increased by using NOMA in a cooperative system  or a distributed antenna system . Cooperative NOMA has been proposed in an environment where cooperation among users is possible [12, 13]. The fairness among the scheduled NOMA users is also studied in .
Before an attempt is made to handle interference in NOMA signals on the receiver side, the receiver has to know some signal information in advance, e.g., 1) signal identification, i.e., whether the signal is modulated by OMA or NOMA; 2) modulation classification; and 3) whether or not SIC is required for the received signal . All of this signal information can be transmitted to the receiver via a high layer. However, the required signaling overhead can be a concern, especially in cellular environments with a massive number of heterogeneous devices, e.g., Internet of Things (IoT) networks. Further, some high-layer signaling may or may not be used on the receiver side depending on the multiuser channel conditions. In this case, high-layer signaling for NOMA signal information can be an extremely large waste of valuable resources. This motivates blind signal classification on the receiver side. 3GPP has also discussed blind signal classification in NOMA systems [16, 17]. However, to the best of the authors’ knowledge, blind signal classification in NOMA systems has not been thoroughly investigated in a theoretical sense.
On the basis of an ML-based classifier, which has been researched for OMA for a long time [18, 19, 20], the performance of signal identification and modulation classification improves as the SNR increases. Therefore, the system is sufficient for scheduling users whose SNRs are larger than a certain threshold for guaranteeing reliable signal identification and blind modulation classification. As the reader will see in detail later, however, the performance of blind signal classification for the presence of interference even decreases with the SNR for the user who does not perform SIC. That is because the user who does not perform SIC has to determine that there is no interference in the received signal, even though the signals of multiple users are superposed at the transmitter. In this regard, more elaborate user scheduling and power allocation are necessary in a NOMA system where users perform blind signal classification for the presence of interference. Thus, this paper focuses on determining whether or not SIC is required on the user side, which can be regarded as blind signal classification for the presence of interference.
User scheduling and resource allocation for NOMA have been extensively researched. The impact of user pairing on NOMA transmissions in a hybrid multiple access system, which allows both OMA and NOMA users, has been researched in , and the optimal user pairing for downlink NOMA was proposed in . The power allocation problem has also been extensively researched with fixed user pairing for NOMA [14, 23, 24, 25, 26, 27, 28, 29], but user scheduling is not considered. The authors of [26, 27, 28] focus on joint optimization of the subchannel assignment and power allocation but consider the situation where the base station (BS) already determines which users will be served by NOMA; thus, user scheduling for NOMA transmissions in a hybrid multiple access system has not been investigated. The joint optimization of power allocation and user scheduling for a NOMA system has been researched in [30, 31, 32, 33]. The distributed matching algorithm was used for the optimal two-user schedulings and power allocation in . The authors of  studied the application of NOMA in millimeter wave communications, and the globally optimal two-user pairings and power allocation were studied in . In , a dynamic algorithm for user scheduling and power allocation is presented to maximize the sum rate while reducing the queuing delay. However, all of the above studies do not consider blind signal classification in an NOMA system.
The main contributions of this paper are as follows:
Two types of incorrect blind signal classification for the presence of interference in two-user NOMA are analyzed. In the first type, the SIC user determines that it should not perform SIC, and in the second type, the non-SIC user classifies itself as the SIC user. In addition, mathematical forms of the probabilities for these two errors are derived.
The effects of blind signal classification for the presence of interference on user scheduling and power allocation in a hybrid multiple access system are investigated. The trade-off between the data rate and the classification error probability is studied, and we show that appropriate user scheduling and power allocation can control the trade-off.
The joint optimization problem of user scheduling and power allocation in a hybrid multiple access system is formulated. We then solve the optimal power allocations given user scheduling, and iteratively find the appropriate user scheduling.
We numerically investigate how many data samples should be used to guarantee reliable blind signal classification for the presence of interference.
Our extensive simulation results show that the proposed scheme outperforms other existing user scheduling methods.
The rest of this paper is organized as follows. In Section II, the system model is described. Section III derives the mathematical forms of the classification error probabilities for the presence of interference. The joint optimization problem of user scheduling and power allocation is formulated, and an algorithm is proposed to solve this problem in Section IV. Simulation results are presented in Section V. Finally, the conclusion follows in Section VI.
Ii System Model
Ii-a Cellular Model and Downlink NOMA Transmission
Consider downlink communications in a cellular model where a BS transmits signals to users simultaneously on the basis of hybrid multiple access. We focus on the downlink scenario without any high-layer signaling that communicates the necessity of SIC use on the NOMA user side. Therefore, NOMA users should perform blind signal classification for the presence of interference. Suppose that users and are scheduled for NOMA at the BS, . The BS intentionally superposes the signals for both users with different power weights; thus, the signal received by user is given by
where and correspond to the received signal, transmitted symbol, channel, and noise, respectively, and the subscripts and indicate the users’ indices. Denote and as the power allocation ratios for users and , respectively; therefore, . In addition, a normalized power is assumed; i.e., . Let and be the power weighted constellation sets of users and , respectively; then, and . Moreover, , where is the composite constellation set of the superpositioned NOMA signal. means that the set consists of the sums of all combinations of elements in and .
The Rayleigh fading channel from the BS to user is defined as for , where controls the path loss; is the BS-user- distance; and
represents the fast fading component having a complex Gaussian distribution,. Without loss of generality, assume that and . In addition, suppose that the BS knows the instantaneous channel gains, and , where
is the normalized noise variance.
A larger power is usually allocated to the user with weak channel conditions in the NOMA system, . With a large power allocation, user does not perform SIC and just decodes without cancellation of . Therefore, the data rate of user is given by
Meanwhile, SIC is necessary for user to cancel user ’s signal component, , and its SINR is . However, remains the same as (2) because . After performing SIC, the data rate of user becomes
OMA is the general baseline multiple access scheme; therefore, the fair allocation of frequency resources is reasonable in a hybrid multiple access system. Therefore, since a normalized frequency resource is assumed for two NOMA users, the data rate of user served by OMA is given by
Since (2) and (3) depend on the power coefficients, finding the optimal power allocation ratios is as important as appropriate user scheduling. Thus, this paper considers the joint optimization of user scheduling and power allocation for an NOMA system to maximize the sum rate when all users perform blind signal classification. In a hybrid multiple access system, several user groups consisting of more than two users can be created for power-multiplexing NOMA. However, this paper considers only two-user groupings for NOMA transmissions and assumes that other users are served by OMA, owing to the excessive complexity of blind signal classification, as we will see later.
Here, the problem is how to schedule two users for NOMA transmissions among users while guaranteeing reliable blind signal classification for the presence of interference without any high-layer signaling. The multiple groups for NOMA can be generated in a hybrid multiple access system, but this paper focuses on scheduling only two users for NOMA transmissions among users, for simplicity. The joint optimization of multiple user groupings and power allocations under the constraint of reliable blind signal classification is exceedingly complicated. In addition, even though it is not optimal, a suboptimal user scheduling policy can be found by iterative methods, e.g., the deferred acceptance procedure for stable matching . In this paper, however, we leave the optimal method of making multiple user groups for NOMA as a future work.
Ii-B ML-Based Blind Signal Classification
The concept of ML-based modulation classification  is applied to blind signal classification for the existence of interference in this paper. For simplicity, we call the user for which SIC is necessary and the user who does not perform SIC as the SIC user and non-SIC user, respectively. Let two hypotheses, and , represent the cases where the user who receives the signal is the SIC user and the non-SIC user, respectively. The likelihood probabilities of the SIC user and non-SIC user are then given by
respectively, where the symbol is assumed to be equally probable, and the cardinalities of the constellation sets and are denoted by and , respectively. Since the SIC user should detect both superposed signals, and , in (5) is calculated throughout the composite constellation . On the other hand, the non-SIC user detects only ; therefore, it is enough to scan the constellation set of user , i.e., , for obtaining (6). If one sample of received signals, i.e., , is used for blind signal classification and , the receiver classifies itself as the SIC user; otherwise, it classifies itself as the non-SIC user.
Note that since the received signal is originally generated from , increases, but decreases as the SNR grows. Therefore, it is beneficial to schedule the user with a high SNR and the user with a low SNR as the SIC user and the non-SIC user, respectively, for reliable blind signal classification for the presence of interference. In this case, however, there is a risk that the data rate of the non-SIC user would not be sufficiently large to satisfy the minimum data rate constraint. Thus, this paper considers two conflicting constraints for the non-SIC user, the minimum data rate and the maximum error probability of blind signal classification for the presence of interference.
Remark: In practice, the classification steps for whether the received signal is based on OMA or NOMA, i.e., signal identification, and which modulation scheme is employed, i.e., blind modulation classification, should also be considered . The performance of the ML-based classifiers for those steps increases with the SNR on every NOMA user side ; therefore, the BS needs to schedule just the users with sufficiently large SNRs to guarantee the reliability of signal identification and blind modulation classification. Meanwhile, the performance of blind classification for the presence of interference at the non-SIC user decreases with the SNR. As in (6), the received symbols should be closer to than to , in order for the non-SIC user to determine that it should not perform SIC. However, since the received signal is superposed and generated on the basis of at the transmitter side, the received symbols become close to as the SNR increases, as shown in Fig. 1(a). At rather low SNRs, it is highly probable that the non-SIC user classifies itself correctly, because more received symbols are closer to than to compared to the high-SNR scenario. In this regard, more elaborate user scheduling and power allocation are necessary in an NOMA system where users perform blind signal classification for the presence of interference. Accordingly, we only consider blind signal classification for the presence of interference in this paper. From now on, the term “blind signal classification” means the determination of whether or not SIC is required for decoding the received signal on the user side.
Ii-C Extension to -User Grouping for NOMA
Although this paper mainly focuses on a two-user NOMA system, blind signal classification can be performed in the general -user NOMA model. Again, ; then, the largest power is allocated to user , and user decodes without cancellation of any interfering signal. By contrast, user 1 should cancel all other users’ signals. In general, user decodes its data after canceling the interference components of user , user , , user in order. Denote as the composite constellation set of , , , and , i.e., . Let be the hypothesis that indicates that the target user is user ; i.e., SIC steps are required. The likelihood probability of user is given by
The receiver then determines itself to be user , where
However, as the number of hypotheses increases, i.e., the number of NOMA users increases, the classification performance is expected to be significantly degraded. In addition, a massive number of computations is required to obtain the likelihood probabilities of all users; therefore, blind signal classification is not preferred when a large number of users is served by NOMA. Thus, it is reasonable to focus on a two-user NOMA system where blind signal classification for the presence of interference is performed on the user side.
|SIC user||non-SIC user|
Iii Error Types of Blind Signal Classification for the Presence of Interference
Iii-a Classification Error at the SIC User
In this section, we focus on the probability that user (i.e., the SIC user) incorrectly determines that it should not perform SIC, denoted by , where indicates that the receiver classifies itself as the non-SIC user. In practice, the transmitter and the receiver share the table of usable modulation and coding schemes (MCS). As shown in Table I, the MCS table of a NOMA system should include combinations of the MCSs of the SIC and non-SIC users and their power weightings. Therefore, when the SIC user determines that it should not perform SIC, the signal detection would be totally incorrect even if the correct channel quality indicator (CQI) index is given.
Suppose that and are the transmitted signal components for users and , respectively, for and . The superpositioned signal becomes for , and the received signal is . For simplicity, we define two hypotheses as follows:
The classification error probability at user is then given by
where all constellation points are equally probable; therefore, in (10). If dominates the summation over in (5), i.e., , then . In a similar way, when ; then, (9) can finally be approximated by (10). Here, represents the probability density function of the received signal when the transmitted symbol is .
Since the user with a high SNR is chosen as the SIC user, we could further assume that and
, which means that the transmitted symbol gives the largest likelihood probability. For simplicity, let the following functions represent normal distributions given onlyand , respectively;
In addition, we assume that -QAM is used for both users. Multiuser superposition transmission (MUST) adopted by 3GPP also considers only -QAM for modulation candidates . Owing to the symmetric structure of -QAM, we can reduce the computations required to obtain (12) by taking summations only in the first quadrature of and , denoted by and . Let the index sets of and be and ; then, can be further approximated in (13).
Iii-B Classification Error at the Non-SIC User
The classification error probability at user (i.e., the non-SIC user) is denoted by . When the non-SIC user classifies itself as the SIC user, it appears good because the interfering signal from the SIC user may be canceled, but it is not so. Again, from Table I, it is evident that the modulation order and/or power weightings of the non-SIC and SIC users could be different, and so the decision to perform SIC at the non-SIC user makes signal detection incorrect.
is obtained in a similar manner as that in Section III-A:
Equation (15) is an approximation of (14) under the assumptions that dominates the summation over all in (5), and dominates the summation over all in (6). Equation (15) is further approximated to (16) by , which means that the decoding result of based on is the same as that based on . Since the non-SIC user usually experiences weak channel conditions, the high-SNR approximation is not available. The first term of (15) can be computed as shown in (17).
The second and third terms of (15) depend on the decision regions of modulation. In the case of -QAM, all decision regions have square shapes. In other words, the decision region of each constellation point can be defined by two intervals of real and imaginary components. Denote as the decision region of the constellation point , defined as . and are lower and upper decision boundaries for the real component of , and and are the lower and upper decision boundaries for the imaginary component of . In other words, and . A matched filter is considered to remove the channel effect. Let ; then the noise variance also changes to . Let and be the real and imaginary components of ; then, the second term of (15) is expressed by
where , , , and .
Likewise, the third term of (15) becomes
where , , , and .
Incorporating (17), (20), and (23) into (15), the BS could expect on the basis of the instantaneous CSI. However, an extremely large computational load is required to derive (15). Since the power allocated to the non-SIC user is relatively large, if the SNR is not very low, it would be highly likely that ; i.e., symbol detection of the non-SIC user is correct, and (15) could be further approximated by
As in Section III-A, can be approximated by taking only the first quadratures of and owing to the symmetric structure of -QAM, as given by (25). According to (17) and (20), the first and second terms in the approximated version in (25) can be respectively obtained by (26) and (27), respectively, where .
Iii-C Number of Data Samples Required for Blind Signal Classification
In practical environments, it is also important to determine how many data samples are required for the reliable performance of classification for the presence of interference. Only one data symbol is used for blind signal classification in prior sections, but more samples can provide better performance. However, the use of many data samples may result in heavy signal processing tasks and a very large computational complexity. Assume that samples are used for blind signal classification and that all samples experience the same channel gain . The likelihood probabilities of the SIC user and non-SIC user are then given by
where and are vectors of the received signals and transmitted symbols, respectively. However, the numbers of summations in (28) and (29) exponentially increase with ; thus, a large number of computations are required to compute (28) and (29).
Therefore, we independently compute the likelihood probability of each , denoted by for . The probability that all of data samples are likely to predict for becomes . Since all data samples are based on the same hypothesis, it would be reasonable that is true if more than half of the data samples predict . Let and be the classification error probabilities computed from . Assuming that all elements of are independent, and , because samples experience the same channel gain. The classification error probabilities can then be approximately computed by
with the odd number. Since the receiver does not have to know any information about the data samples required for blind signal classification, the information bits can be used as samples for blind signal classification. Thus, the system does not need additional signaling overhead for blind signal classification.
Iv Joint Optimization Problem of User Scheduling and Power Allocation
In this section, the effects of blind signal classification on user scheduling and power allocation in NOMA systems are presented. For the joint optimization problem of user scheduling and power allocation, the sum-rate gain of NOMA over OMA is considered an optimization metric. The gains at users and are given by
Again, users and are scheduled for NOMA as the non-SIC user and SIC user, respectively, and . The total sum-rate gain of NOMA over OMA is