Joint Fixed Power Allocation and Partial Relay Selection Schemes for Cooperative NOMA

In the future wireless systems, non-orthogonal multiple-access (NOMA) with partial relay selection scheme is considered as developing research topic. In this paper, dual-hop relaying systems is deployed for NOMA, in which the signal is transfered with the assistance of decode-and-forward (DF) scheme. This paper presents exact expressions for outage probability over independent Rayleigh fading channels, and two partial relay selection schemes are provided. Using matching analytical result and Monte-Carlo method, we introduce forwarding strategy selection for fixed user allocation and exactness of derived formula is checked. The presented simulations confirm the the advantage of such considered NOMA, and the effectiveness of the proposed forwarding strategy.

1958 as analysis in [19]. It is shown that error floor exists in the FD-based RS scheme and a zero diversity order is obtained. The outage probability performance of the cognitive radio networks related to relay selection scheme was considered [20].
To the best of our knowledge, few of the existing works have studied the partial relay selection (RS) for a NOMA, this paper presents two specific schemes related to partial relay selection [21][22][23][24][25]. In particular, in this paper we investigate a new scheme assuming joint power allocation for NOMA and partial relay selection. To evaluate system performance, the outage performance of partial relay selection applied in NOMA schemes with DF relay scheme is investigated. To look insight in considered schemes, the closed-form expressions for the outage probabilities (OPs) are derived, and it is shown that, for a proper minimum desired target rate, the OP can decrease significantly with appropriate select of the power allocation assigned to users. Finally, Matlab simulation results are offered to corroborate the correctness of the attained analytical results.

System Model and Relay Selection Scheme 2.1. System model
As illustration in Figure 1, we determine a downlink cooperative NOMA network with one base station (BS), K relays, and only selected relay serve for two NOMA users. It is noted that the relay operates in half-duplex mode and decode-and-forward (DF) protocol is applied. We denote P as the transmit power for both the BS and relays. In this scenario, a single antenna is equipped in each node. Meeting deep fading, it can not existence of direct link between the BS and the NOMA users and helping relay with relay selection is required for such transmission. We denote SRi h and 12 , RiD RiD hh as the frequency flat channel coefficients from the BS to i th  relay and from i th  relay to user D1, D2 respectively,   1, 2, , . iK  Figure 1. System model of partial relay selection NOMA As many previous works, such channel quantities satisfy unchanged during one fading block but independently vary from one fading block to another independent or they also called as slowly Rayleigh fading. These channel gains' averages are assumed as: It is worth noting that we have assumed in (1) that the K relays are clustered relatively closely together such that they have equivalent distances to the same node, and hence the channel gains between a certain node and the relays are independent identically distributed (i.i.d.), as commonly assumed in the past work. However, the proposed RS schemes do not depend on this assumption, and it is used to simplify the analysis only. Moreover, each relay is assumed to know channel state information (CSI) of SRi h and

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RiD RiD hh, whereas no CSI is known by the BS. The BS will send a message to each user within each fading block, and each fading block is divided into two time slots. During the first time slot, the BS transmits a codeword In this paper, fixed power allocation will be considered as it is simply processed without require instantaneous CSI, reducing overhead usage in signal frame transfer.
Regarding on Relay Selection Schemes, the subset of the relays is confirmed in the first stage by concentrating on correctly decoding the mixed message 0 s : Next, the best relay from K relays can be found in the second stage to transmit messages to the users D1 and D2. Two partial RS schemes will be considered according to the channel condition compared with target rates.
In such scenario, fixed power allocation is assumed at each relay, power allocation coefficients retain unchanged within each fading block; it means that 12 In the second stage, the optimal partial RS scheme can be expressed as:    

Outage performance analysis
In general, to adapt to the users' quality-of-service (QoS) requirements, outage performance of the two users are determined with respect ot the target SNRs. In particular, each user has its own preset target SNR. Based on the NOMA scheme, an outage event occurs in considered transmission links in the proposed model.

Partial relay selection scheme I
With condition   Furthermore, based on the probability density function of channel, it can be shown:   Combining (14) and (15), the outage probability of partial relay selection scheme I can be expressed as:

Outage performance
The overall OPs for the two partial RS schemes can be summarized in the following theorem. Theorem 1: The overall outage probability for the two partial RS schemes, denoted by ,1 P n COP and ,2 P n COP , respectively, can be expressed as: Note that ther overall COPs for the two partial RS schemes can be expressed as follows:

Simulation Results
In this section, by using Matlab simulations, we evaluate the outage performance of cooperative NOMA with several RS schemes. The two considerd RS are illustrated and compared to show system performance. Specifically, the averages of the channel gains in (1)   The curves of outage probabilities versus transmit SNR is presented in Figure 2 for Scheme I and in Figure 3 for Scheme II, the analytical results can match the simulations very well. Obviously, compared with the target rate with different values it can be obtaind different outage performance. When the transmit SNR comes to higher value case, the outage peformance will be enhanced. It coincides with the analysis in previous section and leads to choose a target rate which can yield lower outage probability. In this figure, lower target rate for signal of D1, outage performance is the best case among considered scenarios. It is confirmed that the achievable data rate for each user in NOMA becomes the bottleneck of the outage performance. As can be further observation as Figure 4, the effect of the selection relay scheme on outage probability can be seen, in which the system parameters are set as   1 0.1; 0.5 R  and 2 2 R  . Note that all the configurations fall in the first case of Theorem 1, and the outage probability decreases at high transmit SNR. The reason is that, in this case, more power for signal processing and outage will become enhanced. The RS in scheme II better than Scheme I as the transmit SNR greater than about 22 dB. This result is guidline for design of NOMA where RS is selected for optimal performance.
Next, the influence of relay numbers K on the outage probability of the considered system with two RS schemes is shown as Figure 5 and 6, respectively. As observation in these two figures, it can be seen that the outage performance can be improved by increasing the number of relay of two RS schemes. In addition, compared to the three cases regarding on the number of relay in considered schemes, the performance gap achieves a similar performance among these schemes.

Conclusion
In this paper, an optimal selection algorithm was proposed to improve the outage probability of cooperative NOMA networks with joint power allocation and partial relay selection. The system performance was analyzed by deriving the closed-form analytical expressions. From the outage probability, we found that the number of relays and the target data rate which exhibit crucial effects on the outage performance. Such relay selection of NOMA users is helpful to expand the transmission quality, it beneficial for the outage probability.