I Introduction
Nonorthogonal multiple access (NOMA) is introduced to serve multiple users on the same resource block by implementing superposition coding (SC) at transmitter and iterative successive interference canceler (SIC) at receivers [1]. Since NOMA provides a spectral efficient communication, the potential of NOMA for massive machine type communication (MMTC) led researchers to investigate NOMA involved systems and tremendous effort has been devoted to integrate NOMA in future wireless networks[2, 3].
In NOMA systems, since the SIC is implemented at the users with better channel conditions, they have priori knowledge of the symbols of users which are former in the decoding order. Hence, the cooperation within NOMA users is proposed in [4] and the outage probability of cooperativeNOMA (CNOMA) is analyzed. Then, the error probability of CNOMA within two users is derived for quadrature phase shift keying (QPSK) and binary phase shift keying (BPSK) modulations [5]. It is presented that error performance of CNOMA suffers from the error propagation and the diversity order cannot be achieved. Hence, to increase data reliability of CNOMA, in this letter, we propose thresholdbased selective CNOMA (TBSCNOMA) in which users with better channel conditions forwards symbols of the users with weaker channel conditions if the signaltointerference plus noise ratio (SINR) is greater than a predetermined threshold value. The main contributions of this paper are as follows

TBSCNOMA network is proposed to cope with the error propagation from intracell user to celledge user in CNOMA. Thus, endtoend (e2e) error performance is improved and full diversity order is achieved.

The exact e2e bit error probability (BEP) of proposed TBSCNOMA is derived in the closedform for different modulation constellations.

The optimum threshold value which minimizes the e2e BEP of TBSCNOMA is derived.
The remainder of this paper is given as follows. In section II, we introduce TBSCNOMA. Then, in section III, error analysis^{1}^{1}1BEP is derived for only celledge user since BEP of intracell user remains the as with conventional NOMA. of TBSCNOMA is provided. The optimum threshold for TBSCNOMA is derived in section IV. In section V, the validation of derivations is presented via simulations. Finally, in section VI, results are discussed and the paper is concluded.
Ii System Model
We consider a downlink CNOMA scheme with a basestation (BS) and two mobile users (i.e., UE1 and UE2) where each node is equipped with single antenna^{2}^{2}2Singleantenna situation is considered in this letter, however the analysis can be easily extended for multipleantenna situations and for also different channel fadings. as shown in Fig. 1. We assume that channel fading of each link follows where , and denote the links between BSUE1, BSUE2 and UE1UE2, respectively, and is determined by the distance (largescale fading) between nodes. In the first phase of communication, BS implements SC and transmits the total signal of users, hence the received signals by users are given as follow:
(1) 
where and denote the complex channel fading coefficient and the additive white Gaussian noise (AWGN), respectively. is distributed as . and pairs are the power allocation (PA) coefficients and the complex baseband symbols of users. Without loss of generality, UE1 and UE2 are assumed to be intracell user and celledge user according to their distances to the BS i.e., , thus, is determined. The SINR at UE1 is given as
(2) 
where is the average signaltonoise ratio (SNR). In order to increase data reliability of UE2, we propose that UE1 forwards the symbols of UE2 obtained during SIC process only if the SINR is greater than a threshold value i.e., . Hence, the received signal by UE2 in the second phase of TBSCNOMA is given as
(3) 
where is the power of the relayUE1 and is the fading coefficient between the users. denotes the detected symbols of the UE2 at UE1. The UE2 implements a maximumratio combining (MRC) for the received symbols in two phases and the total received symbol by UE2 is given as
(4) 
where
denotes complex conjugate operation. Finally, UE2 implements a maximumlikelihood (ML) detector to estimate its own symbols.
Iii Error Analysis of TBSCNOMA
Iiia The Probability SINR’s being greater than the threshold
The probability of the event that SINR is greater than the predetermined threshold value is obtained as
(5) 
where and are defined. We note that condition should be accomplished otherwise UE1 always remains idle. In case the channel coefficient is Rayleigh distributed,
will be exponentially distributed with the probability density function (PDF)
, where . The probability for is determined as(6) 
IiiB Bit Error Probability of UE2 during SIC for TBSCNOMA
The BEP for arbitrary modulation/fading is given as . However, in case SC is implemented, the users encounter interuserinterferences (IUI), thus the conditional BEP of the UE2 is given
(7) 
where , and depend on the modulation constellations of UE1 and UE2 which are given in section III.E for various constellation pairs whereas is dependent on channel fading. Considering and by using (7), we formulate the average BEP (ABEP) of UE2 symbols at UE1 as
(8) 
By taking steps in [6, appendix B], we define
(9) 
and we apply partial integration by substituting into (8). Then, with the aid of the Leibniz’ rule [7, eq. (0.42)] and after simplifications, it yields
(10) 
Considering channels are Rayleigh distributed and the symbol of UE2 is forwarded by UE1 only if the condition is succeeded in TBSCNOMA, we define
(11) 
where is the scaling factor to ensure PDF to have unit area. Substituting (11) into (9) and then into (10), the ABEP of UE2 at UE1 is derived as
(12) 
IiiC Bit Error probability of Direct Transmission
When , the UE1 stays idle in the second phase of communication and only the direct transmission from BS to UE2 remains. In this case, with the aid of (7), the conditional BEP for symbols of UE2 is given as
(13) 
where . The ABEP is obtained by averaging over instantaneous as . The ABEP for direct transmission is derived as
(14) 
IiiD Bit Error probability of Diversity Transmission
We assume that the condition is succeeded and the symbols of UE2 are detected correctly at the UE1. Since MRC is implemented at UE2 for the signals received in two phases, by using (7) and utilizing [8, eq. (14411)], the conditional BEP is given as
(15) 
where . The ABEP for diversity transmission is obtained by averaging over instantaneous and . It is formulated as . By using the ABEP of 2branch MRC [8, eq. (14415)], the ABEP of diversity transmission turns out to be
(16) 
IiiE Endtoend (e2e) Error Performance of TBSCNOMA
To obtain the e2e ABEP, we consider all the possibilities. Hence, with the aid of the law of total probability, the e2e ABEP of TBSCNOMA is given as
(17) 
where is defined as the error probability at UE2 when UE1 detects UE2’s symbols erroneously and forwards to UE2. It is given for BPSK in [5], by utilizing [5, eq.(13)] and [9, Appendix C], for Mary constellations, we provide a tight approximation as
(18) 
where
(19) 
We note that depends on the symbols of UE2 transmitted by BS and detected erroneously by UE1, hence we have averaged all the possibilities. The e2e ABEP of TBSCNOMA is derived by substituting (6), (12), (14), (16) and (18) into (17).
Throughout the paper, the analyses are provided for arbitrary modulation pairs of UE1 and UE2 which are adaptively determined according to channel qualities in wireless networks [10]. We provide the BEP coefficients (i.e., , , ) for six different uncoded mode of [10] in Table I by utilizing the deductions of error probability for NOMA networks in [11].
mode  Constellations  BEP 
UE1  
UE2  Coefficients  
1  BPSK  
BPSK  
2  BPSK  
QPSK  
3  QPSK  
BPSK  
4  QPSK  
QPSK  
5  16QAM  
BPSK  
6  16QAM  
QPSK 
Iv The Optimum Threshold for TBSCNOMA
The optimum threshold is defined as the value which minimizes the e2e ABEP of UE2 in TBSCNOMA. Since the has to be determined according to PA coefficients ,e.g. if , UE1 always remains idle for transmission to UE2, the optimum value which includes PA coefficient effects is given as
(20) 
and it is derived as
(21) 
Firstly, we apply Leibniz’ rule [7, eq. (0.42)] to (21).Then, with the aid of [12] and after some simplifications, the expression (21) turns out to be
(22) 
where
(23) 
is defined. The optimum value which minimizes the e2e ABEP is obtained by substituting (14), (16) and (18) into (22). Finally, the optimal threshold value is derived as
(24) 
The in (24) is given in Fig. 2 for two different scenarios when . One can easily see that optimum threshold value also depends on the transmit SNR in addition to channel states and PA coefficients. To minimize the e2e ABEP of UE2, low threshold in low SNR region and high threshold in high SNR region should be implemented.
V Numerical Results
In this section, the derived expressions are validated via simulations. In all figures, the lines denote the analytical curves whereas simulations are represented by markers. We assume that the power of UE1 relay is equal to .
In Fig. 3, we present the error performance of proposed TBSCNOMA for all six modes in a network where dB. The PA coefficients are chosen as and and threshold value is fixed to 2. It is noteworthy that the simulations match perfectly with the analytical derivations for all modes.
In Fig. 4, to emphasize the effect of the threshold, we provide the error performance of TBSCNOMA for different fixedthreshold values and optimum threshold value. It is assumed to be dB, dB. We assume that mode 3 is chosen and the PA coefficients are and . We also present error performances of conventional NOMA (noncooperative), CNOMA and CNOMA with perfectSIC where it is assumed that relay detects the far user’s all symbols correctly (genieaided/perfectdecoding) and no error propagation occurs. TBSCNOMA outperforms significantly CNOMA since TBSCNOMA copes with the error propagation better than CNOMA. Nevertheless, the error performance of TBSCNOMA highly depends on the threshold value. Using a low threshold value decreases the reliability of the relay UE1 and this causes decay in the error performance in the high SNR region due to error propagation. On the other hand, using a higher threshold value causes the relay to be silent in the low SNR region, hence the error performance of TBSCNOMA gets worse. Nevertheless, this can be solved by the implementation of optimum threshold which is derived in section IV. In Fig. 4, one can easily see that with the use of optimum threshold TBSCNOMA has better error performance than the use of fixedthreshold values in whole SNR region. Hence, full diversity order is achieved and the error performance of TBSCNOMA gets close to CNOMA with perfect SIC.
Vi Conclusion
In this letter, the TBSCNOMA is proposed to cope with error propagation in CNOMA. In TBSCNOMA, the data reliability of cooperative phase is increased by implementing a condition that SINR of intracell user to be greater than a threshold value. The e2e ABEP of TBSCNOMA is derived for different modulation constellations. Then, the optimum threshold value is obtained in order to minimize the ABEP of TBSCNOMA. TBSCNOMA outperforms CNOMA and full diversity order is achieved. In this letter, fixed PA is assumed. Nevertheless, optimum PA algorithms for conventional NOMA can be adapted for TBSCNOMA. TBSCNOMA provides a reliable communication for celledge user, and the achievable rate and outage performance of this reliable communication need to be analyzed. In addition, TBSCNOMA proves that introducing threshold value for such networks as NOMA and cooperative communication are involved together, can achieve better error performance. These are considered as the directions of future research.
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