Ergodic capacity of internet of things’ devices in presence of channel state information imperfection

Non-orthogonal multiple access (NOMA) is deployed to improve spectral efficiency for applications in fifth generation networks. NOMA system splits power domain to many parts to further serve massive users by relaxing the orthogonal use of radio-resources. In this paper, a relay is required to help the source communicate with destinations with a fixed power allocation scheme. We derive expressions to highlight ergodic performance of two users the deployment of NOMA is suitable to different rate requirements from destinations (e.g., a cellular users have different requirements compared with internet of things devices). By conducting Monte-Carlo simulations, we find main system parameters which have crucial impacts on ergodic capacity. This paper is different other recent studies since we emphasize on imperfect channel state information (CSI) and Rician fading model for our analytical results. This is an open access article under the CC BY-SA license.


INTRODUCTION
In recent years, power-domain based non-orthogonal multiple access (NOMA) has recently studied as a promising system to enhance system performance in terms of low latency, high efficiency, and massive users [1]- [3]. Since only a fraction of total transmit power is assigned to NOMA user is allocated, the limited coverage of NOMA-based system is raised compared with the traditional (OMA)-based system. As one of the effective methods is to improve the coverage, once might integrate the cooperative approaches into NOMA systems. To assist the transmission between the transmitter and NOMA users, such system needs assistance from a certain number of intermediate nodes. By owing to the spatial diversity gain, NOMA relaying systems have benefits of the reception reliability [4]. The two kinds of cooperative NOMA networks are the dedicated-relay cooperation and the user cooperation, which depends on the role of relay. In the dedicated-relay cooperation, relays are required to forward signal from the source to destinations [5]- [12]. In the user cooperation, relays are strong users which help foster communication from the source to weak users [13].
In the perspective of internet of things (IoT) for sixth-generation (6G), the system in [14] needs cover spectrum access for huge number of users relying on allowed spectrum resources. In traditional systems, the overuse of spectrum resources related to access of orthogonal multiple signal is challenging [14] proposed 6Genabled cognitive IoT (CIoT) by exploiting a NOMA-adied hybrid spectrum access approach. In this scenario, both the busy and idle spectrum are accessed by the CIoT without considering the primary users' state. The work in [15] studied system to serve massive IoT devices in extremely differentiated IoT applications for 6G. Such system is able to provide communication in air-space-ground integrated system. To support IoT deployment in remote and disaster areas, by deploying unmanned aerial vehicle (UAV), such UAV can act as aerial base station to communicate with users in cluster of UAV-supported clustered users. In addition, an aerial base station along with wireless powered communication (WPC)-based UAV provides higher energy efficiency. Different from aforementioned conventional NOMA systems, half-duplex and relay stations (RSs) schemes benefit to NOMA approach since they exhibit further gains in term of spatial diversity [16]- [23]. Yue et al. in [18], Kader et al. [20], and Liang et al. [21], the transmission from transmitters to receivers needs assistance of a single relay. Main results in [18], [21] indicated that the orthogonal multiple access (OMA) is likely worse than the system relying on NOMA when we mentioned system performance metrics including throughput and outage probability. The popular models of channels namely Nakagami-m fading channels [18] and Rayleigh fading channels [21] are considered as best fit to characterize advances of NOMA systems. Kader et al. in [20], ergodic sum capacity with perfect and imperfect successive interference cancellation (SIC) are analysed to highlight performance of the cooperative NOMA relaying system including two transmitters, a single shared relay and two destinations. However, there is still open problem regarding how we can achieve exact channel information at receivers. Motivated by recent work [20], this paper focuses on the impact of imperfect channel state information (CSI) in downlink dual-hop NOMA system. Importantly, we characterize channels as Rician fading model to provide analytical computations of outage probability for destinations.

SYSTEM MODEL
We consider a downlink dual-hop NOMA network which consists a base station (S) and two devices U i (i{1, 2}), shown in in Figure 1. To extend coverage, the destinations need the help of a relay (R) which operates in a decode-and-forward (DF) mode. We denote the distances from S to R and R to U i are d SR and d RUi , respectively. In addition, we denote h SR , h RUi are the Rician fading channel form S to R and R to U i respectively [22]. This paper emphasizes on the impact of CSI on system performance analysis. In particular, the channel estimation error can be modeled as [23]: where . In this first phase, S send superimposed signal to R. The received signal at R is expressed as: where P S is the transmit power at S, τ denotes the path-loss exponent, x i is the the intended message to U i , δ is the power allocation coefficient with δ > 0.5, and n SR is the additive white Gaussian noise (AWGN) with CN (0, N 0 ). To compute the outage probability, we need to determine the signal-to interference-plus-noise ratio ❒ ISSN: 2302-9285 (SINR) which is used to detect signal x 1 at R, and such SINR is formulated by: where η = P S N0 is the transmit signal-to-noise ratio (SNR). By doing SIC to delete interference, the SNR at R is used to detect signal x 2 and it is expressed by: In the second phase, the received signal at U i when R forwards signal from S to U i is formulated by: where P R is the transmit power at R and n RUi is AWGN with CN (0, N 0 ). At user U 1 , two steps are conducted. Firstly, U 1 detects the signal x 1 with SINR is given by: where η = P R N0 . Secondly, U 1 decodes the signal x 1 after performing SIC and the SINR is expressed as: Similarly, U 2 detects the own signal x 1 and the SINR is given by: To further compute ergodic capacity, we will apply result reported in [24], i.e. the probability distribution function (PDF) ofĥ v is given by: where K v is the Rician factor, Ω v is the average fading power and I 0 denotes the Bessel function of the first kind [25].

THE ANALYSIS OF ERGODIC CAPACITY
In this section, we evaluate the closed-form expression of ergodic capacity for users U i . The ergodic capacity of U 1 can be expressed as [26]:

Ergodic capacity of U 1
Similarly, the ergodic capacity of of U 2 is calculated by: where Similarly, the CDf of Z 2 is given as: Next, C x2 is rewritten as: ❒ ISSN: 2302-9285 Then, we express C x2 as: The CDF of Z 1 is calculated as: With the help of (4), the term A 1 is formulate by: Putting (9) into (19), (19) is rewrite as: Based on [25], we can write A 1 as: Moreover, with result in [25] A 1 can be obtained as: where β = (1+K SR )(ηd τ SRσ 2 SR +1) Ω SR ηd τ SR . Then, the second term A 2 of (18) is rewritten as: Similarly, we can obtain A 2 as: Putting (22) and (24)

NUMERICAL RESULTS
In this section, we set δ = 0.85,σ 2 =σ 2 SR =σ 2 RU1 =σ 2 RU2 K = K SR = K RU1 = K RU1 = 2, Ω SR = Ω RU1 = Ω RU2 = 1, τ = 2, d SR = 5m, d RD1 = 10m and d RD2 = 5m. We conduct 10 6 times for Monte-Carlo simulation. As can be seen in Figure 2, ergodic capacity increases significantly when value of SNR goes from 20 dB to 50 dB. Due to different power allocation factors and decoding procedure, two users show performance gap of ergodic capacity, i.e. at range SNR from 0 to 35 dB, performance of two users is similar, bigger gap among two users exist when SNR is greater than 35 dB. It is intuitively that Monte-Carlo simulation and analytical results are same, which shows the exactness of derivations.
We can see the impact of CSI imperfect levels on the ergodic performance, shown in Figure 3. At higher SNR region, SINR to detect signal at destination can be improved, then ergodic capacity is better as well. In this figure,σ 2 = 0.01 is reported as best case for both users.
In Figure 4, the performance gap among two users depends on power allocation factor δ. Therefore, by adjusting such factor δ, the gap will be changed. Since NOMA benefits to the fairness, this modification of factor δ will satisfy the users' demand properly. In Figure 5, the quality of channel decide the height of curves of ergodic capacity. In this circumstance, K = 5 is reported as the best etgodic performance for three considered cases.

CONCLUSION
This paper has explored the impact of CSI imperfection on the ergodic capacity of a two-user cooperative NOMA network. We conduct Rician fading model for wireless transmission from the source to destination with the assistance of relay. The fixed power allocation factor scheme is adopted and SIC is useful to detect signals at destinations. We derived the closed-form expression of ergodic capacity and verify all main system parameters to how they make influence on the system performance. In future work, we deploy multiple destinations to highlight how interference among many users in a group of destinations which get benefit from NOMA.