A Zero-Sum Game Approach for Non-Orthogonal Multiple Access Systems: Legitimate Eavesdropper Case

SummaryThe next generation wireless access technology highly relies on nonorthogonal multiple access (NOMA) technique. This paper proposes a novel power domain cyclic spread multiple access (PDCSMA) scheme for the design of NOMA system with power domain superposition coding (SC) and cyclic spreading at the transmitter concurrent with symbol level successive interference cancellation (SL‐SIC) at the receiver. Based on acceptable difference in channel gain, the users are grouped together to form PDCSMA clusters, and the unique power is allotted to each user in a cluster. The user with good channel condition is allotted less power, and the user with poor channel condition is allotted more power. Each PDCSMA cluster has its own spreading code, and the data of every user in a cluster are cyclic spread with the same code. Each cluster supports the number of multipath components equivalent to the length of the spreading code. The use of cyclic spreading makes the signal suffered by multipath fading less prone to intra cluster interference. The user signal is decoded by minimum mean square error‐frequency domain equalization (MMSE‐FDE) or maximal ratio combining (MRC)–based receiver in which weak user is detected with hard decision, and strong user is detected with SIC. Compared with conventional power domain NOMA (PDNOMA) and interleaved NOMA, the proposed PDCSMA achieves better bit error rate (BER) performance and assures guaranteed detection.

This paper investigates the application of simultaneous wireless information and power transfer (SWIPT) to cooperative non-orthogonal multiple access (NOMA). A new cooperative multiple-input single-output (MISO) SWIPT NOMA protocol is proposed, where a user with a strong channel condition acts as an energy-harvesting (EH) relay to help a user with a poor channel condition. The power splitting (PS) scheme is adopted at the EH relay. By jointly optimizing the PS ratio and the beamforming vectors, the design objective is to maximize the data rate of the "strong user" while satisfying the QoS requirement of the "weak user". It boils down to a challenging nonconvex problem. To resolve this issue, the semidefinite relaxation (SDR) technique is applied to relax the quadratic terms related with the beamformers, and then it is solved to its global optimality by two-dimensional exhaustive search. We prove the rank-one optimality, which establishes the equivalence between the relaxed problem and the original one. To further reduce the high complexity due to the exhaustive search, an iterative algorithm based on successive convex approximation (SCA) is proposed, which can at least attain its stationary point efficiently. In view of the potential application scenarios, e.g., IoT, the single-input single-output (SISO) case of the cooperative SWIPT NOMA system is also studied. The formulated problem is proved to be strictly unimodal with respect to the PS ratio. Hence, a golden section search (GSS) based algorithm with closed-form solution at each step is proposed to find the unique global optimal solution. It is worth pointing out that the SCA method can also converge to the optimal solution in SISO cases. In the numerical simulation, the proposed algorithm is numerically shown to converge within a few iterations, and the SWIPT-aided NOMA protocol outperforms the existing transmission protocols.

The full-duplex (FD) cooperative nonorthogonal multiple access (NOMA) achieves a superior throughput over the conventional half-duplex (HD) cooperative NOMA, wherein the strong users (SUs) with good channel conditions can act as an FD relay node for the weak users with poor channel conditions. However, the energy efficiency (EE) of a cooperative NOMA may be degraded due to the additional power consumption incurred at the SUs. We are, therefore, motivated to investigate the EE maximization problem of an FD cooperative NOMA system. More importantly, we investigate the “signal-to-inference-noise ratio gap reversal” problem of cooperative NOMA systems, which imposes successive interference cancellation (SIC) performance degradation at the SUs. This problem has not been documented in the existing cooperative NOMA literature. A low-complexity algorithm is proposed for maximizing the system's EE while guaranteeing a successful SIC operation. Our numerical results show that the proposed algorithm achieves both a higher EE and throughput over the existing HD cooperative NOMA and nonadaptive FD cooperative NOMA. More importantly, the proposed scheme guarantees a successful SIC operation at the SUs.

Due to the successive interference cancellation (SIC) technique, Non orthogonal multiple Access (NOMA) users have the capability of decoding the other paired users sharing the same resource bloc. As a result, NOMA technique is not only exposed to external eavesdropping, but also to internal eavesdropping which raises security risks regarding NOMA users' privacy. Therefore, this research aims to analyse a Multi-antenna cooperative NOMA system where both Decode and Forward (DF) and Amplify and Forward (AF) strategies are studied. In this context, we investigate the secrecy performance of our system with both internal and external eavesdropping scenarios. Closed-form expressions of the secrecy outage probability (SOP) and the strictly positive secrecy capacity (SPSC) metrics are derived. Numerical results are given to illustrate the validity of the obtained theoretical results.

The increasing number of consumers with diverse data rate needs is leading to increased heterogeneity in traditional cellular networks. Nonorthogonal multiple access (NOMA) has emerged as a promising method to serve a large number of users, but research shows that weak users (WU) and strong users (SU) have different throughputs. Intra-group interference reduces WUs throughput due to the superposition of signals. Improper power distribution impacts NOMA performance and lowers the total system rate. The multi-objective sum rate dwarf mongoose optimization algorithm (M-SRDMOA) is implemented as a solution to the NOMA network power allocation problems. The DMOA approach distributes adequate power to all NOMA users to increase the large sum rate. The effectiveness of the M-SRDMOA approach is supported by existing studies on fair NOMA scheduler (FANS) and multi-objective sum rate-based butterfly optimization algorithm (M-SRBOA). The M-SRDMOA’s potential sum rate with an SNR of 9dB and a noise variation=2 is 14.06 bps/Hz, which is high compared to M-SRBOA and FANS.

Non-Orthogonal Multiple Access (NOMA) is known as one of the promising techniques in the fifth generation of wireless communication. The classification of users in (NOMA) is based on power, while it is based on time, frequency and code in Orthogonal Multiple Access (OMA). In this study the downlink NOMA includes two users, one strong and one weak. The comparison of NOMA and OMA properties shows a range of Power Allocation Factors (PAF) for the two users within which NOMA properties have proved to be better than OMA. It was also shown that the achieved PAF is a function of channel gains of two users. Then, the coverage region is defined for multiple access channel; and by considering the Base Station (BS) as a fixed one in the center of the cell, the coverage region for both NOMA and OMA is calculated. The theoretical and analytical results show that the achieved coverage region of NOMA for both weak and strong users has been increased compared to OMA.

In this paper, a novel approach is introduced to study the achievable delay-guaranteed secrecy rate, by introducing the concept of the effective secrecy rate (ESR). This study focuses on the downlink of a non-orthogonal multiple access (NOMA) network with one base station, multiple single-antenna NOMA users and an eavesdropper. Two possible eavesdropping scenarios are considered: 1) an internal, unknown, eavesdropper in a purely antagonistic network; and 2) an external eavesdropper in a network with trustworthy peers. For a purely antagonistic network with an internal eavesdropper, the only receiver with a guaranteed positive ESR is the one with the highest channel gain. A closed-form expression is obtained for the ESR at high signal-to-noise ratio (SNR) values, showing that the strongest user’s ESR in the high SNR regime approaches a constant value irrespective of the power coefficients. Furthermore, it is shown the strongest user can achieve higher ESR if it has a distinctive advantage in terms of channel gain with respect to the second strongest user. For a trustworthy NOMA network with an external eavesdropper, a lower bound and an upper bound on the ESR are proposed and investigated for an arbitrary legitimate user. For the lower bound, a closed-form expression is derived in the high SNR regime. For the upper bound, the analysis shows that if the external eavesdropper cannot attain any channel state information (CSI), the legitimate NOMA user at high SNRs can always achieve positive ESR, and the value of it depends on the power coefficients. Simulation results numerically validate the accuracy of the derived closed-form expressions and verify the analytical results given in the theorems and lemmas.

A key feature of the non-orthogonal multiple access (NOMA) technique is that users with better channel conditions have prior information about the messages of other users. The technique to exploit the prior knowledge of strong users in order to improve the performance of weak users is known as cooperative NOMA. In this paper, we study the physical layer security in such a cooperative NOMA system. In order to reduce the complexity, the considered system in this paper has two users. Through the cooperative NOMA concept, the performance of the weak user is enhanced by the strong user. Given that there is an eavesdropper in the system that can hear all transmissions, we study the secrecy rate of the strong and the weak users. More specifically, we make an attempt to derive the secrecy outage probability (SOP) of both the users. Due to the intractable nature of the exact analysis for the weak user, we provide the closed form expression for the SOP of this user in high SNR regime while keeping the exactness for the strong user. Through numerical simulations, we verify the correctness of our analytical derivations under different scenarios. Besides, we provide the insights of achieving optimal secrecy performance in such a system.

With the gradual promotion of the fifth generation (5G) mobile communication and Internet of Things (IoT) applications, wireless communication transmission will be more vulnerable to illegal interceptions and/or attacks. To ensure communication security, we study covert communication of downlink nonorthogonal multiple access (NOMA) systems, where the channel knowledge of users is uncertain. A multiantenna transmitter tries to covertly transmit information to a covert user (strong user) through the shield of a public communication link (weak user), while the warden tries to detect the communication behavior between the transmitter and the covert user. To improve security and energy efficiency, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> th best antenna of the transmitter is selected, since the optimal antenna may be not available due to some schedule and/or other reasons. Aiming to evaluate the proposed framework performance, we start by deriving exact expressions for the minimum detection error probability and the optimal detection threshold of the warden, followed by a calculation analysis of the expected minimum detection error probability (EMDEP) and the outage probability of NOMA users. The asymptotic behavior for the outage probability is investigated at high signal-to-noise ratio (SNR) to acquire greater useful insights. With the goal of improving the system covertness performance, we propose that a scheme is optimized to enhance the covert throughput of the system to the maximum. Simulation results show that the following hold: 1) channel estimation errors have a significant effect on system performance; 2) reliability performance tends to build up, as the total number of antennas grows large; and 3) as the transmitting power and number of antennas increases, there is an upper bound for maximizing the covert throughput.

SummaryThe simultaneous wireless information and power transfer or energy harvesting (EH) can be combined in nonorthogonal multiple access (NOMA) as green applications towards 5G. This paper investigates a new cooperative EH‐NOMA protocol, where the intermediate relay has not equipped the fixed power source and acts as a wireless powered relay to help signal transmission to representative weak user and strong user in NOMA. However, impacts of imperfect channel estimation contribute to outage system performance evaluations. We formulate the power resource assignment paradigms as two schemes, namely, fixed power allocation and dynamic power allocation, by considering imperfect channel state information (CSI). To solve this problem, we derive the closed‐form expressions of outage probability under imperfect CSI and the power allocation constraints. The expected numerical results related to the derived expressions for the outage probability are examined that numerical and the Monte Carlo simulations are strictly matching lines.

In this paper, we present the joint optimization of sum rate and fairness for contention based uplink multiple access with non-orthogonal multiple access (NOMA) communication system by resource allocation and user grouping. In particular, we study the cases of many users sharing the same resources that address application of the the internet of things (IoT). The key feature of contention based multiple access is to serve multiple users at the same time and frequency. With different power levels and user grouping, it can achieve better spectral efficiency over conventional orthogonal multiple access (OMA). However, unlike the OMA system, NOMA results in additional inter-user interference (IUI). It has also been shown that, without proper resource allocation for users in the uplink NOMA, the weak users can always be in outage. In this work, we have developed algorithms on subbands assignment, user grouping, and power allocation for joint optimization of sum rate and fairness. The algorithm allocates resources iteratively to handle the IUI in each iteration. Given a number of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> subbands allocation to each user, we could prevent starvation of poor users, e.g. cell edge users. We have also compare and analyze the sum rate and fairness performance with different combination of L and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . We also find that, by properly limiting the maximum number of subbands each user can use, the system could better exploit multi-user diversity to improve the sum rate and hence the energy efficiency. The numerical simulations are also conducted to verify the results.

In this paper, a bidirectional relaying (BR) non-orthogonal multiple access (NOMA) with simultaneous wireless information and power transfer (SWIPT) termed as BR NOMA-SWIPT is proposed and investigated for the Internet of Things (IoT) relay networks. Here, multiple NOMA users in one group can communicate or exchange information with multiple NOMA users in another group through a common energy harvesting (EH) based relay. The EH based relay exploits the radio frequency (RF) energy supplied by the two NOMA user groups to recharge itself, and then it exchanges the information between them. Specifically, the two groups of NOMA users transmit the information intended for the exchange to the relay node using the uplink NOMA protocol. The relay node first harvests the RF energy through the signals of the two group of NOMA users, and then it carries out the exchange of information between two NOMA user groups by using the downlink NOMA protocol. To the best of our knowledge, there is no existing study or research on BR NOMA with SWIPT. Therefore, in this paper, we examine in detail, the performance of BR NOMA-SWIPT enabled IoT relay networks. Specifically, we study a popular EH time switching (TS) relaying architecture with BR and NOMA. We also study the effect of both perfect successive interference cancellation (pSIC) and imperfect SIC (ipSIC) on the proposed BR NOMA-SWIPT system. Analytical expressions for the outage probability and ergodic capacity are mathematically derived. The analytical results of our proposed system model are validated by the simulation results, and representative performance comparisons are presented thoroughly, which not only provides practical insights into the effect of different system parameters on the overall network performance, but it also demonstrates that our proposed BR NOMA-SWIPT can attain significant throughput and capacity gains as compared to conventional BR multiple access schemes.

This work proposes a multiuser hybrid beamforming scheme for non-orthogonal multiple access (NOMA) systems using the minimum mean square error (MMSE) approach to weighted sum rate maximization. While NOMA may be effective in terms of enhancing user fairness, hybrid beamforming is necessary to reduce the transceiver cost as the system moves towards higher frequency. The design is divided into two stages. In the first stage, a fully digital multiuser beamformer is derived by maximizing the weighted sum rate of all users under no constraint on the number of RF chains. This problem is then transformed into a weighted sum MSE minimization problem, which facilitates the use of alternating optimization to obtain an efficient local solution. In the second stage, the previously obtained multiuser beamformer is then split into RF and baseband beamformers by using orthogonal matching pursuit (OMP). A user role selection algorithm is then proposed to determine the role of strong and weak users. Simulation results are provided to demonstrate the effectiveness of the proposed schemes.

In this paper, we investigate a downlink non-orthogonal multiple access (NOMA) system consisting of a base station (BS) and two users, where each user decodes its own signal through successive interference cancellation (SIC). When the signal of one user, called the weak user (WU) who has a bad channel, is being decoded, the signal of the other user, called the strong user (SU) who has a good channel, acts as interference. In an interference channel, we can increase the achievable rate by applying improper Gaussian signaling (IGS). Therefore, we apply IGS to SU, aiming to mitigate the interference. We also consider imperfect SIC at SU, which is a more general assumption for a NOMA system. For the considered NOMA system model, we derive the outage probability of each user in a closed form, provide its asymptotic expression, and obtain its diversity order. We also derive the ergodic rate of each of the two users in a closed form. We propose two algorithms to maximize the fairness of the NOMA system based on the primal decomposition method. Through simulation, we verify that our analysis is correct, and confirm that applying IGS improves the fairness of the NOMA system.

Non-orthogonal multiple access (NOMA) attracts much attention from industry and academia as it promises more connections. One interesting yet important question is, “What is the number of maximally admissible users in NOMA?” In this letter, a lower bound of admissible user equipment (UE) number is derived, which relates to the spreading factor, the required signal to interference and noise ratio, and the noise power only. Also, the overloading factor, i.e., the normalized admissible UE number, can be presented as 1 $ {+}{\Delta }$ , where ${\Delta }$ denotes the capability of interference tolerance in NOMA. Further, with considering Rayleigh-distributed fading channels, stochastic analysis is used to get a clean expression of the probability of accessing the network successfully in NOMA. Numerical results show the current demodulation reference signal pattern in 5G needs to be enhanced and a lower modulation and coding scheme is more suitable to achieve a higher overloading.