Performance Evaluation for UAV-Based UL-NOMA with Channel Coding

Ⅰ. Introduction

Fifth-generation (5G) technology has been the first communication technology that attempted to systematically integrate and support all types of connected and automated mobility^[1]. In addition, the 5G design of communication systems has led to the deployment of advanced systems to achieve improved spectrum efficiency, energy efficiency, quality of service (QoS), and reliability. In the future, new types of mobile devices will extend the uninterrupted coverage of the connectivity infrastructure and increase the density of connected devices.

To enhance the overall spectral efficiency, non-orthogonal multiple access (NOMA) is a predominant technology that superposes signals with different power coefficients, where a single-frequency resource is provided to multiple users^[2,3]. The performance of NOMA overwhelms that of conventional orthogonal multiple access (OMA) because it serves multiple users at the same time and frequency and mitigates interference by applying the successive interference cancellation (SIC) process.

Owing to these advantages, NOMA has recently been extended to non-terrestrial networks (NTNs) such as unmanned aerial vehicles (UAVs), high-altitude platforms (HAPs), and satellite networks^[4]. In particular, a UAV has many different requirements such as being efficient, secure, inclusive, and smart. Because a UAV provides the potential for connectivity between many devices, it contributes to extending the communication range and exchange of massive amounts of information. In addition, it can act as a bridge between satellites and ground terminals. Therefore, several studies have been conducted on UAV-based downlink NOMA (DL-NOMA).

Unlike DL-NOMA, in uplink NOMA (UL-NOMA), each user decides to transmit a signal with its own assigned transmit power. This is because the maximum transmission power is limited by the user’s battery capacity^[5]. It is crucial for the superposed signal in UL-NOMA to be distinct, because the channels of each user are different from those in DL-NOMA. Interference from multiple users affects weak channel users because the base station (BS) receives signals simultaneously. Consequently, the SIC process performance is critical for weak channel users.

Generally, two SIC processes have been suggested: symbol-level and codeword-level SIC. The main difference between the two is that codeword-level SIC includes channel coding and decoding, that is, error correction. Therefore, codeword-level SIC can achieve a better bit error rate (BER) performance than symbol-level SIC^[6].

Among the error corrections, the Reed–Solomon (RS) code has been employed in satellite communication for NTNs^[7]. The RS code is a burst error-correcting code because of the use of multibit symbols rather than individual bits to encode data. However, the error cannot be corrected using single-error correction. Thus, a concatenated error correction was presented in [8] for reliable data transmission in a code division multiple-access system. This error correction employs both RS and convolutional codes.

In this study, we evaluated the performance of a UAV-based UL-NOMA with the concatenation of RS and convolutional code (RSCC). The simulation results included a BER comparison between OMA and NOMA and the application of RSCC. To validate the performance of the SIC process, we considered perfect and imperfect conditions for the coded UL-NOMA with -ary phase-shift keying (PSK) for modulation.

The remainder of this paper is organized as follows: Section 2 describes the proposed system and channel models. The RSCC-applied codeword-level SIC receiver is presented in Section 3. In Section 4, the simulation results are presented to compare the performances in terms of the BER. Finally, the conclusions of this study are presented in Section 5.

Ⅱ. System Model

The system model consists of a UAV and total K number of users, as shown in Fig. 1. Let us assume that the total number of users is divided into M near users and (K -M) far users. The number of near and far users is equal to (M = K / 2) and M pairings are generated between a single near user and a single far user.

Following NOMA pairing, multiple users can superpose their signals on the same frequency resource at distinct power allocation levels. The transmission distance is limited to [TeX:] $$d_k\lt d_{\max }.$$ The pairings are compromised in the order of channel gains, [TeX:] $$\sum_{m=1}^M\left|h_m\right|^2\gt \sum_{k=M-K+1}^K\left|h_k\right|^2.$$ The channel gain can be a criterion for dividing near and far users and calculating the performance of UL-NOMA from the signal model, which is discussed later.

Fig. 1.

UAV based UL-NOMA System

2.1 Transceiver design

The main structure of the UL-NOMA transceiver is shown in Fig. 2. Every user can transmit its or own signal to the BS through a distinct channel and has an equivalent antenna. The transmitter consists of three parts: channel encoding, modulation, and power allocation. In this paper, the concatenated RSCC is utilized for error correction. Two encoders are used: inner convolution and outer RS codes. The convolutional code can be defined as CC (n, k, m), where n is the number of output bits, k is the number of input bits, and m is the length of the constraint. The code rate is k / n. The RS code is decomposed using RS (n, m), where n is the codeword length, and m is the number of bits per symbol. The codeword length is given by [TeX:] $$n=2^m-1.$$

Fig. 2.

Transceiver system model for UAV-based UL-NOMA with channel coding

At the BS, the receiver comprises a single antenna and four parts: the minimum mean-square error (MMSE) detector, demodulation, and the SIC process. In the RSCC decoder, scatter errors are corrected using the Viterbi decoder and burst errors are corrected using the RS decoder. Hence, the error propagation of coded NOMA can be dramatically reduced compared with that of uncoded NOMA.

2.2 Signal model

This paper considers a UL-NOMA scenario with multiple users and a BS. Users superpose different signals with distinct power levels on different channels. The location of the k-th user is denoted by the 3D Cartesian coordinates [TeX:] $$L_{\mathrm{UE}, k}=\left(a_k, b_k, 0\right)$$ and the location of the UAV is denoted by LA = (x, y, H). The locations of the users and UAV are shown in Fig. 1. The Euclidean distance between the UAV and the k-th user is expressed as follows:

Generally, air-to-ground links are widely used in line-of-sight (LoS) and non-LoS (NLoS) channel models. In this paper, a Rician fading channel is assumed for the UL-NOMA system to consider both LoS and NLoS channels. The channel between the UAV and k-th user can be denoted as

where [TeX:] $$\beta_k$$ is the large-scale channel power gain given by [TeX:] $$\beta_k=d_k^{-v}$$ with pathloss v. [TeX:] $$g_k$$ is the small-scale fading coefficient, expressed as

where g is the LoS channel component with [TeX:] $$|g|=1,$$ [TeX:] $$\tilde{g}$$ is the NLoS channel component, and [TeX:] $$\mathcal{K}_k$$ is the Rician factor. Adopting the equations in [9,10], the angle-dependent Rician factor can be defined as

where [TeX:] $$A_1 \text { and } A_2$$ are constant coefficients. Here, we set the Rician factor as [TeX:] $$\mathcal{K}_{\min } \leq \mathcal{K}_k \leq \mathcal{K}_{\max }$$ where [TeX:] $$\mathcal{K}_{\min }=A_1 \text { and } \mathcal{K}_{\max }=A_2 \exp \left(A_2 \pi / 2\right)$$^[10]. [TeX:] $$\theta_k$$ denotes the elevation angle given by [TeX:] $$\theta_k=\arcsin (H/d_k).$$

Without loss of generality, let two users create a pairing to superpose the signals for the near and far users. The superposed signal of the near and far users is given as follows:

where [TeX:] $$x_m \text { and } x_k$$ represent the messages from M near users and (K -M) far users, respectively. [TeX:] $$p_m \text { and } p_k$$ denote the transmission power based on the user’s condition.

The received signal at the BS is given as follows:

where w denotes Gaussian noise with zero mean and unit variance, and denotes the Hadamard product, which is known as the element-wise product.

Ⅲ. SIC Receiver in UL-NOMA

3.1 Perfect and Imperfect SIC

We highlight UL-NOMA challenges, such as SIC errors and channel coding. The performance of NOMA depends on perfect SIC to avoid strong interference signals. Consequently, an imperfect SIC is applied to the superposed signal, and the subtracted signal may also be an error.

The channel state information (CSI) for each user should be perfect, and measured CSI can be ordered such as [TeX:] $$\left|h_1\right|>\left|h_2\right| \cdots>\left|h_M\right|>\left|h_{M-K+1}\right|>\cdots>\left|h_K\right|.$$

The near users' signal detection applying MMSE receiver can be expressed as follows

where [TeX:] $$\widetilde{w}=w / h_k$$

Generally, perfect and imperfect SIC are applied to far users to decode near user’s signals. The far user’s signal detection is expressed as follows:

where the case for [TeX:] $$x_k=\hat{x}_k$$ is perfect SIC and that for [TeX:] $$x_k \neq \hat{x}_k$$ is imperfect SIC.

3.2 Upper bound of error probability

We formulate a performance upper bound of the coded BER for a far user with perfect SIC. For the convolutional code with hard decision decoding, the performance upper bound of the coded BER after the Viterbi decoder is given by^[11]

where [TeX:] $$d_{\text {free }}$$ represents the free distance of the convolutional code. [TeX:] $$\alpha_d$$ is the total number of paths of distance d from the all-zero path that merges with the all-zero path for the first time^[11]. [TeX:] $$P_e$$ denotes the theoretical BER for -PSK with a Rician fading channel, i.e., the uncoded bit error probability, which can be expressed as [12]

where [TeX:] $$M_\gamma$$ is the moment generating function, which is given by [12]

where [TeX:] $$\bar{\gamma}$$ is the average SNR per bit. For RS codes, the probability of a bit error at the output of the RS decoder can be upper-bounded as [8]

where [TeX:] $$P_b$$ is the m-bit symbol error probability. For RSCC, the simple upper bound for [TeX:] $$P_b$$ is given by [13]

Ⅳ. Numerical Results

This section presents the performance evaluations of the proposed RSCC-based UL-NOMA under both perfect and imperfect SIC scenarios and compares it with the OMA system. In this study, we set the simulation parameters as listed in Table 1. We considered the Rician factor to be 8. For channel coding, a convolutional code was used as the inner code with a restriction length of 7 and a code rate of 1/2, whereas the RS code was used as an external code with a codeword length n of 7 and message length m of 3 as RS(7,3), where the parity length was 2t = (n -m) = 4.

Fig. 3 compares the simulated BER and upper bound for UE1 under perfect SIC with and without RSCC using the expressions in (12) for the coded case and (10) for the uncoded case. We set the transmit power [TeX:] $$p_1=1,$$ and the modulation used was BPSK. The results for the uncoded case perfectly matched the entire SNR range. However, the coded bounds were tight in the high-SNR region.

Fig. 3.

Comparison of BER of [TeX:] $$\mathrm{UE}_2$$: BPSK, pSIC

Fig. 4 depicts the BER with respect to SNR for UE2 comparison with and without RSCC, namely coded (C) and uncoded (UC), where modulation set as BPSK (=2) and the SNR for [TeX:] $$\mathrm{UE}_1$$ was [TeX:] $$\mathrm{SNR}_1=8\mathrm{dB} .$$ The SNR of the OMA user was the same as [TeX:] $$\mathrm{SNR}_2.$$ The normalized distance between users and the BS were [TeX:] $$d_1=0.8 \text { and } d_2=1 \text {, }$$ respectively. The transmit powers were [TeX:] $$p_1=0.7 \text { and } p_2=1 \text {. }$$ As shown in the figure, the difference in SNR between the two users affected the BER performance. As [TeX:] $$\mathrm{SNR}_2$$ increased, the BER of [TeX:] $$\mathrm{UE}_1$$ increased significantly because the interference from [TeX:] $$\mathrm{UE}_2 \text { to } \mathrm{UE}_1$$ increased as [TeX:] $$\mathrm{SNR}_2$$ increased. The BER of [TeX:] $$\mathrm{UE}_2$$ compared both perfect SIC (pSIC) and imperfect SIC (ipSIC) condition. Basically, with the increase in [TeX:] $$\mathrm{SNR}_2$$, the BER trend of [TeX:] $$\mathrm{UE}_2$$ with perfect SIC was similar as that of OMA. In contrast, the BER of [TeX:] $$\mathrm{UE}_2$$ with imperfect SIC decreased to the bottom at [TeX:] $$\mathrm{SNR}_2=5\mathrm{dB}$$ and gradually increased again owing to the [TeX:] $$\mathrm{UE}_1 \text {'s }$$ error propagation^[14]. Note that the trend was the same with and without RSCC. Based on that, the uncoded result for [TeX:] $$\mathrm{UE}_1$$ performed better BER than the coded one in low SNR, whereas the coded result for [TeX:] $$\mathrm{UE}_1$$ had a significantly better BER than the uncoded result because the number of occurrences of erroneous bits may have exceeded the error correction capability of RSCC code in lower SNR. In particular, the BER of [TeX:] $$\mathrm{UE}_2$$ under imperfect SIC improved after RSCC coding.

Fig. 4.

Comparison of BER : BPSK, [TeX:] $$\mathrm{SNR}_1=8\mathrm{dB}$$

Similarly, Fig. 5 compares the BER performances with and without RSCC when [TeX:] $$\mathrm{SNR}_1=10\mathrm{dB} .$$ The other simulation parameters were set as shown in Fig. 4. As [TeX:] $$\mathrm{SNR}_1$$ increased, the BER performance of the coded results further improved compared with that of the uncoded results.

Fig. 5.

Comparison of BER : BPSK, [TeX:] $$\mathrm{SNR}_1=10\mathrm{dB}$$

Fig. 6 shows the BER performance using QPSK (=4), where [TeX:] $$\mathrm{SNR}_1=10\mathrm{dB} .$$ and the other parameters were the same as those in Fig. 5. In contrast to the BPSK results, the BER performance of a coded SIC had less performance improvement for an imperfect SIC.

Fig. 6.

Comparison of BER : QPSK, [TeX:] $$\mathrm{SNR}_1=10\mathrm{dB}$$

Fig. 7 shows the BER with respect to the power allocation factor for [TeX:] $$\mathrm{UE}_2$$. The power allocation factor varied [TeX:] $$p_2$$ varied as [0.1 1.0] and [TeX:] $$p_1$$ was fixed at 1.0. As shown in the figure, as the power factor increased, the BER for [TeX:] $$\mathrm{UE}_2$$ improved.

Fig. 7.

Comparison of BER vs power factor

V. Conclusion

In this study, we evaluated the performance of a UAV-based UL-NOMA system using a channel coding scheme. Here, the channel coding scheme considered was the concatenated Reed–Solomon and convolutional coding (RSCC). Moreover, we obtained the BER of UL-NOMA under perfect and imperfect SIC processes with different modulation orders. These results will be useful for integrating terrestrial and non-terrestrial networks in future studies.