Error Successive Interference Cancellation Research Articles

Deep learning based detection of signal of interest of uplink NOMA multi-users in NOMA In-band Full-duplex Radio communication

The research focuses on investigating the symbol error rate (SER) performance of the Non Orthogonal Multiple Access (NOMA) In-band Full-duplex Radio communication system, which is considered a promising technology for 5G/6G. This system facilitates simultaneous transmission and reception of data over the same resource block for multiple users via power domain multiplexing. However, the system faces a significant challenge in the form of self-interference signal (SI). The SI signal transmitted from the NOMA In-band full-duplex radio transmitting antenna is also received by its own receiving antenna. It limits perfect successive interference cancellation (SIC) for channel estimation and signal detection of the signal of interest (SoI) from uplink NOMA multi-users at the receiver of NOMA In-band Full-duplex radio. Furthermore the SER performance is significantly degraded due to various SI and SoI channel imperfections. To address this, a three-phase-based efficient approach has been proposed for simultaneous non-linear SI cancellation and detection of the SoI from uplink NOMA two users under aforementioned SI and SoI channel imperfections. The approach uses the Least Square-SIC Estimator, Minimum Mean Square Error-SIC Estimator, and deep learning (DL) methods. The reported 4 dB SNR gain compared to least square-SIC/minimum mean square error SIC and DNN-based methods demonstrate the robustness of the proposed DL-aided approach against various SI and SoI channel imperfections for NOMA In-band Full-duplex Radio communication.

Downlink Learning-aided Precoding for Cell-Free networks Specially D esigned for beyond 5G Communication System

Objectives: With increase in number of access points in Cell-Free Massive Multiple Input Multiple Output (CFMM) system, spatial complexity of calculating precoding vector increases with traditional precoding schemes. So, to reduce computational complexity, network cost, and run time, a new deep learning -aided precoder is specially designed for CFMM system. The performance of downlink (DL) Cell-Free Massive Multiple Input Multiple Output (CFMM) system operating under Rayleigh fading channel model is analyze using new deep learning-based precoding scheme. Methods: We introduce new deep learning-aided precoder and an improved version of basic scalable pilot assignment algorithm which enhances system performance. We derive closed- form expression for average DL spectral efficiency (SE) for the proposed scheme, which is then compared with Minimum Mean Square Error Successive Interference Cancellation (MMSESIC), Regularized Zero Forcing (RZF), Least Square (LS) and Maximum Ratio (MR) combining techniques. We analyze the proposed scheme with perfect channel state information (CSI), instantaneous CSI, coherent transmission, non-coherent transmission, different pilot configuration. Findings: The spectral efficiency obtained with CFMM-MMSESIC and the proposed scheme is 3 bits/s/Hz, and 2.5bits/s/Hz respectively, which clearly indicates the difference of 20 % only. So, the proposed scheme gives near optimal results, and we can use simple linear combining techniques instead of complex non-linear combining techniques. Also, the proposed scheme with coherent data transmission gives performance curve, which is very close to MMSESIC scheme as desired. The performance of the proposed system is improved by reducing run time and computational complexity as compared to conventional linear precoding schemes. Novelty: The proposed precoder improves performance by reducing run time and computational complexity. Advanced pilot assignment algorithm enhances performance by reducing pilot contamination. Keywords: Cell-Free Massive Multiple Input Multiple Output, Pilot Contamination, Precoding, Minimum Mean Square Error Successive Interference Cancellation, Maximum Ratio, Regularized Zero Forcing (RZF), Least Square (LS)

Unequal Error Protection-based Rate-Splitting precoding for VLC systems: BER analysis

Rate-Splitting Multiple Access (RSMA), as a promising next-generation multiple access technique, can be integrated with Visible Light Communication (VLC) to address the challenge of accommodating multiple users under limited modulation bandwidth of Light Emitting Diodes (LEDs). However, most of the current works about RSMA assume perfect Successive Interference Cancellation (SIC) during the decoding procedure and neglect the error propagation problem due to SIC errors, which will greatly affect the performance in real applications. In view of this, we consider the design of Rate-Splitting (RS) precoder for downlink Multi-User Multiple-Input Single-Output (MU-MISO) VLC systems in the presence of SIC errors. For the first time in the literature, we derive analytic Bit Error Rate (BER) expressions in this case and analyze the error performance of a conventional RS precoder, which unveils the error performance degradation due to SIC errors. To mitigate this effect and improve the robustness of the system, we propose a novel RS precoding scheme by providing Unequal Error Protection (UEP) for common and private streams, which is achieved by changing an error protection factor. By this means, the transmission power is flexibly allocated to the common and private symbol stream, which can reduce the error probability as a whole. Simulation results indicate that the proposed RS precoder can provide significant error performance gains (up to 82.9%) over the baseline.

Successive Cancellation Integer Forcing via Practical Binary Codes

A new multiple-input multiple-output (MIMO) receiver scheme for practical binary codes is proposed that provides consistent gains over conventional linear receivers. We first develop a practical successive integer forcing (IF) scheme based on practical binary codes rather than lattice codes. We then present the successive cancellation integer forcing (SC-IF) scheme, which combines and enhances successive IF and minimum mean squared error successive interference cancellation (MMSE-SIC). In this scheme, the receiver first decides whether individual decoding or IF sum decoding is appropriate for each data stream, and then conducts successive IF sum decoding only for selected streams while decoding the remaining streams using MMSE-SIC. The proposed SC-IF methodology mitigates the performance loss caused by mismatched IF filtering in fading channels, while attenuating the noise amplification caused by MMSE filtering. Extensive link-level simulations demonstrate that the proposed successive IF significantly improves the basic IF, and the SC-IF improves both the successive IF and MMSE-SIC, offering uniform improvements over conventional linear receivers for most channel correlation and variation parameters and modulation orders at comparable computational costs. These results illustrate the viability of SC-IF as a fundamental building block for high-performance MIMO receivers in 5G-Advanced and/or subsequent-generation communication systems.

Throughput performance optimization of NOMA-assisted cooperative relay system with realistic impairments

Abstract This work aims to investigate the outage and throughput performance of non-orthogonal multiple access assisted cooperative relay system (CRS-NOMA) considering the realistic impairments caused due to in-phase and quadrature-phase imbalance (IQI), channel estimation errors (CEE), and successive interference cancellation (SIC) errors. More specifically, we investigate a model in which two-phase downlink transmission is carried out in two different modes: (i) CRS-NOMA without direct links and (ii) CRS-NOMA with direct links (CRS-DLNOMA). In CRS-NOMA mode, the source broadcasts a composite NOMA signal to destination users with the assistance of a decode-and-forward (DF) relay. In contrast, in CRS-DLNOMA, direct and cooperative links are available for transmission. We derive the analytical expressions of outage probability and throughput for both the NOMA destinations to evaluate the system performance of both CRS-NOMA and CRS-DLNOMA modes of transmission. Furthermore, numerical simulations also study and validate the influence of IQI, CEE, and SIC errors on the outage and throughput performance. The simulation results verify that realistic impairments degrade the system performance, but the presence of direct link has a positive impact on outage and throughput. Additionally, we use the golden search method to optimize the power allocation factor (PAF) and transmission rate to maximize the throughput at the near user while ensuring the throughput constraint at the far user.

RIS-Enhanced Secure Transmission in MTC Networks With Finite Blocklength

In this paper, we propose a reconfigurable intelligent surface (RIS) assisted secure finite blocklength transmission framework in machine-type communications (MTC) networks, where the integration of millimeter-wave (mmWave) communication and non-orthogonal multiple access (NOMA) technology is considered to alleviate the problem of insufficient spectrum resources caused by massive MTC devices (MTCDs). For improving the ability of anti-eavesdropping, we aim to maximize the achievable sum secrecy capacity (SC) by jointly optimize the MTCDs’ transmission power, RIS phase coefficient and receive beamforming design. To handle the nonconvexity of the proposed optimization problem, we decouple it into three sub-problems, where the first two are solved by successive convex approximation (SCA) method. A minimum mean squared error successive interference cancellation (MMSE-SIC) scheme is proposed to tackle the receive beamforming problem for uplink NOMA networks. Furthermore, an alternating optimization based joint power, phase, and beamforming allocation (AO-JPPBA) algorithm is developed to implement joint optimization. Simulation results show that: 1) the security performance of the proposed AO-JPPBA is improved by 612.26% than the baseline scheme; 2) the proposed MMSE-SIC beamforming scheme is more effective in improving sum-SC of uplink NOMA networks; 3) RIS’s location has an obvious impact on sum-SC when considering eavesdroppers with strong wiretapping ability.

Dual-Polarized Massive MIMO-RSMA Networks: Tackling Imperfect SIC

The polarization domain provides an extra degree of freedom (DoF) for improving the performance of multiple-input multiple-output (MIMO) systems. This paper takes advantage of this additional DoF to alleviate practical issues of successive interference cancellation (SIC) in rate-splitting multiple access (RSMA) schemes. Specifically, we propose three dual-polarized downlink transmission approaches for a massive MIMO-RSMA network under the effects of polarization interference and residual errors of imperfect SIC. The first approach implements polarization multiplexing for transmitting the users' data messages, which removes the need to execute SIC in the reception. The second approach transmits replicas of users' messages in the two polarizations, which enables users to exploit diversity through the polarization domain. The third approach, in its turn, employs the original SIC-based RSMA technique per polarization, and this allows the BS to transmit two independent superimposed data streams simultaneously. An in-depth theoretical analysis is carried out, in which we derive tight closed-form approximations for the outage probabilities of the three proposed approaches. Accurate approximations for the ergodic sum-rates of the two first schemes are also derived. Simulation results validate the theoretical analysis and confirm the effectiveness of the proposed schemes. For instance, under low to moderate cross-polar interference, the results show that, even under high levels of residual SIC error, our dual-polarized MIMO-RSMA strategies outperform the conventional single-polarized MIMO-RSMA counterpart. It is also shown that the performance of all RSMA schemes is impressively higher than that of single and dual-polarized massive MIMO systems employing non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) techniques.

Precoding Design for Multi-Group MIMO-NOMA Scheme With SIC Residual Analysis

This paper presents a precoder design for multiple-input multiple-output (MIMO) uplink communications with a multi-group non-orthogonal multiple access (NOMA) scheme. In this scheme, QR-decomposition-based detection is used to decode user signals of each group under imperfect successive interference cancellation (SIC). In the uplink, transmitted signals are encoded with the constellation of a symmetric quadrature amplitude modulation (QAM), and SIC residual errors are generated from symbol demodulation. The statistics of the SIC errors are derived, with which expressions of approximate SIC-residual-power coefficient and signal-to-interference-plus-noise ratio (SINR) are developed. Consequently, the effect of the SIC errors can be explicitly addressed in the precoder design for minimizing the total transmit power subject to users' symbol error probability (SEP) constraints. A suboptimal design algorithm with efficient “logarithmic” golden-section search is developed. Simulation results show the effectiveness of the design criterion and algorithm, and validate the detection error analysis. Unlike the conventional fractional-SIC-error model that suffers from underestimation/overestimation of SIC errors and infeasibility, our SIC error model can provide accurate effect of the SIC errors in the SINR analysis and enable the proposed method to give design solutions to satisfy the SEP constraints.

Resource Allocation in MU-MISO Rate-Splitting Multiple Access With SIC Errors for URLLC Services

Rate-splitting multiple access (RSMA) is promising to be developed as a key enabling technology for 6G. This paper investigates the resource allocation problem in a downlink multi-user and multiple-input single-output (MU-MISO) RSMA system with successive interference cancellation (SIC) errors for ultra-reliable and low-latency communications (URLLC). The single-carrier RSMA (SC-RSMA) resource allocation scheme with URLLC is first given, where the beamforming vector and the transmission rate are optimized to maximize the effective throughput (ET). To solve the non-convex optimization problem formulated in the SC-RSMA scheme, an iterative algorithm based on block coordinate descent (BCD) and successive convex approximation (SCA) is proposed to alternately optimize the beamforming factor and the transmission rate. Furthermore, the multicarrier RSMA (MC-RSMA) scheme is developed for the URLLC access of large-scale users. Based on the results of the SC-RSMA scheme, a low-complexity three-step optimization algorithm is proposed to solve the resource allocation problem formulated in the MC-RSMA scheme. Finally, the simulation results show that the RSMA scheme and MC-RSMA scheme can respectively achieve higher ET than the non-orthogonal multiple access (NOMA) scheme and multi-carrier NOMA (MC-NOMA) scheme in the URLLC scenario, and verify that RSMA can reduce the latency and improve the reliability of the system.

Joint Power Control and Phase Shift Design for Future PD-NOMA IRS-Assisted Drone Communications under Imperfect SIC Decoding.

Intelligent reflecting surfaces (IRS) and power-domain non-orthogonal multiple access (PD-NOMA) have recently gained significant attention for enhancing the performance of next-generation wireless communications networks. More specifically, IRS can smartly reconfigure the incident signal of the source towards the destination node, extending the wireless coverage and improving the channel capacity without consuming additional energy. On the other side, PD-NOMA can enhance the number of devices in the network without using extra spectrum resources. This paper proposes a new optimization framework for IRS-enhanced NOMA communications where multiple drones transmit data to the ground Internet of Things (IoT) devices under successive interference cancellation errors. In particular, the power budget of each drone, PD-NOMA power allocation of IoT devices, and the phase shift matrix of IRS are simultaneously optimized to enhance the total spectral efficiency of the system. Given the system model and optimization setup, the formulated problem is coupled with three variables, making it very complex and non-convex. Thus, this work first transforms and decouples the problem into subproblems and then obtains the efficient solution in two steps. In the first step, the closed-form solutions for the power budget and PD-NOMA power allocation subproblem at each drone are obtained through Karush-Kuhn-Tucker (KKT) conditions. In the second step, the subproblem of efficient phase shift design for each IRS is solved using successive convex approximation and DC programming. Numerical results demonstrate the performance of the proposed optimization scheme in comparison to the benchmark schemes.

Uplink Performance of Cell-Free Massive MIMO With Multi-Antenna Users Over Jointly-Correlated Rayleigh Fading Channels

In this paper, we investigate a cell-free massive MIMO system with both access points (APs) and user equipments (UEs) equipped with multiple antennas over jointly-correlated Rayleigh fading channels. We study four uplink implementations, from fully centralized processing to fully distributed processing, and derive their achievable spectral efficiency (SE) expressions with minimum mean-squared error successive interference cancellation (MMSE-SIC) detectors and arbitrary combining schemes. Furthermore, the global and local MMSE combining schemes are derived based on full and local channel state information (CSI) obtained under pilot contamination, which can maximize the achievable SE for the fully centralized and distributed implementation, respectively. We study a two-layer decoding implementation with an arbitrary combining scheme in the first layer and optimal large-scale fading decoding (LSFD) in the second layer. Besides, we compute novel closed-form SE expressions for the two-layer decoding implementation with maximum ratio (MR) combining. In the numerical results, we compare the SE performance for different implementation levels, combining schemes, and channel models. It is important to note that increasing the number of antennas per UE may degrade the SE performance.

Performance of NOMA‐assisted MRC receivers in presence of imperfect SIC and CSI errors

SummaryIn this paper, we analyze the performance of maximum‐ratio combining (MRC) receivers for single‐input multiple‐output (SIMO) non‐orthogonal multiple access (NOMA) system. We explore the aforesaid system performance in presence of impairments like imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. In general, receive diversity provides diversity gain and helps to maintain quality of service (QoS), while the NOMA system achieves higher spectral efficiency compared to orthogonal multiple access (OMA). Power‐domain NOMA system transmits superimposed‐coded signal, which utilize SIC detection method at the receiving users. Here, we derive the closed‐form expression of the average bit error rate (BER) for the MRC‐based NOMA system. We also analyze the performance of the system in high signal‐to‐noise ratio (SNR) regime through derived asymptotic expression. Furthermore, the outage probability, diversity order, and sum rate comparison between NOMA and OMA system are also presented. Simulation results also validate the derived theoretical expressions and confirm the diversity gain achieved for the considered system.

Toward UL-DL Rate Balancing: Joint Resource Allocation and Hybrid-Mode Multiple Access for UAV-BS-Assisted Communication Systems

In this paper, we investigate unmanned aerial vehicle (UAV) assisted communication systems that require quasi-balanced data rates in uplink (UL) and downlink (DL), as well as users’ heterogeneous traffic. To the best of our knowledge, this is the first work to explicitly investigate joint UL-DL optimization for UAV assisted systems under heterogeneous requirements. A hybrid-mode multiple access (HMMA) scheme is proposed toward heterogeneous traffic, where non-orthogonal multiple access (NOMA) targets high average data rate, while orthogonal multiple access (OMA) aims to meet users’ instantaneous rate demands by compensating for their rates. HMMA enables a higher degree of freedom in multiple access and achieves a superior minimum average rate among users than the UAV assisted NOMA or OMA schemes. Under HMMA, a joint UL-DL resource allocation algorithm is proposed with a closed-form optimal solution for UL/DL power allocation to achieve quasi-balanced average rates for UL and DL. Furthermore, considering the error propagation in successive interference cancellation (SIC) of NOMA, an enhanced-HMMA scheme is proposed, which demonstrates high robustness against SIC error and a higher minimum average rate than the HMMA scheme.

A layer-wise distribution analysis of the WLMMSE-SIC MIMO receiver for rectilinear or quasi-rectilinear signals

In this brief, we investigate the widely linear minimum mean square error (WLMMSE) successive interference cancellation (SIC) detector in multiple-input-multiple-output systems with rectilinear or quasi-rectilinear transmit signals. To this end, layer-wise approximate probability density functions (PDFs) of the post-detection signal-to-interference-plus-noise ratio are first derived. It is next shown that the so-derived PDFs enable explicit and concise performance evaluations in terms of the symbol error rate and the outage probability. For rigor, both the cases with and without inter-layer error propagation are addressed, and closed-form solutions are provided. Validity of theoretical analysis is demonstrated via Monte Carlo simulations.

BER analysis of NOMA with max-min relay selection

In contrast with orthogonal multiple access (OMA) technologies, non-orthogonal multiple access (NOMA) technology can achieve higher spectral efficiency and support more users simultaneously. Multiple relays can be deployed in NOMA networks, in order to combat fading and thus increase the transmission reliability. In the existing works on cooperative NOMA networks with multiple relays, the decoding error at the relays and the imperfect successive interference cancellation (SIC) are not taken into account simultaneously. In this work, we consider the bit error rate (BER) analysis of relay-aided NOMA networks, where max-min relay selection is employed. Particularly, closed-form BER expressions are derived for NOMA networks with Rayleigh fading, in the existence of the relay decoding error and imperfect SIC. The asymptotic BER performance is then obtained to provide some useful insights into the system design such as the diversity order. Finally, simulation results illustrate the correctness of the derived expressions. The presented results reveal the effects of imperfect SIC and relay decoding error on the performance of cooperative NOMA networks.

IRS-Assisted Massive MIMO-NOMA Networks: Exploiting Wave Polarization

A dual-polarized intelligent reflecting surface (IRS) can contribute to a better multiplexing of interfering wireless users. In this paper, we use this feature to improve the performance of dual-polarized massive multiple-input multiple-output (MIMO) with non-orthogonal multiple access (NOMA) under imperfect successive interference cancellation (SIC). By considering the downlink of a multi-cluster scenario, the IRSs assist the base station (BS) to multiplex subsets of users in the polarization domain. Our novel strategy alleviates the impact of imperfect SIC and enables users to exploit polarization diversity with near-zero inter-subset interference. To this end, the IRSs are optimized to mitigate transmissions originated at the BS from the interfering polarization. The formulated optimization is transformed into quadratically constrained quadratic sub-problems, which makes it possible to obtain the optimal solution via interior-points methods. We also derive analytically a closed-form expression for the users’ ergodic rates by considering large numbers of reflecting elements. This is followed by representative simulation examples and comprehensive discussions. The results show that when the IRSs are large enough, the proposed scheme always outperforms conventional massive MIMO-NOMA and MIMO-OMA systems even if SIC error propagation is present. It is also confirmed that dual-polarized IRSs can make cross-polar transmissions beneficial to the users, allowing them to improve their performance through diversity.

Performance Analysis of NOMA in Vehicular Communications Over i.n.i.d Nakagami-m Fading Channels

This paper investigates the performance of non-orthogonal multiple access (NOMA) in vehicular networks where a base station (BS) communicates with the vehicles moving away from the BS with single-input multiple-output. To combine the signals received at the antennas, diversity combining techniques such as maximal ratio combining (MRC) and selection combining (SC) are performed at the receiver of each vehicle. However, in practice, the expected performance from the diversity techniques may not be achieved due to the fact that all the diversity branches are not independent and identically distributed (i.i.d) all the time. In this context, analytical expressions of the outage probability and ergodic sum rate are derived for the considered vehicular networks with the assumption of independent but not necessarily identically distributed (i.n.i.d) Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> fading channels. The performance analysis of NOMA vehicular networks is also extended for multiple-input multiple-output antenna configurations and evaluated in the presence of successive interference cancellation (SIC) error propagation. The obtained analytical results are validated by Monte Carlo simulations. Furthermore, the performance of NOMA is verified with conventional orthogonal multiple access (OMA) for fading parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m=1$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m=2$ </tex-math></inline-formula> with perfect channel knowledge and channel estimation. Numerical results show that NOMA outperforms the conventional OMA by approximately 20% and has high sum rate with i.n.i.d as well as i.i.d channel consideration. However, i.n.i.d consideration degrades the performance of NOMA and OMA as the diversity gain achieved with i.n.i.d consideration is less as compared to i.i.d consideration. The performance is further deteriorated with SIC error and channel estimation.

Sum-Throughput Maximization in NOMA-Based WPCN: A Cluster-Specific Beamforming Approach

Wireless power transfer is a promising solution for wireless networks composed of Internet-of-Things (IoT) devices that may suffer from insufficient battery capacity. A wireless powered communication network (WPCN) is a framework to design energy-constrained networks such as IoT networks. In this article, we consider WPCNs consisting of a hybrid access point (H-AP) and energy harvesting users, all equipped with multiple antennas. A H-AP transfers energy to the users using energy beamforming in the downlink, and the users transmit information using the harvested energy in the uplink, where nonorthogonal multiple access (NOMA) transmission is employed. For the uplink NOMA transmission, users are grouped into multiple clusters by cluster-specific beamforming. In particular, signal alignment is exploited for the beamforming so that the channels of users in a cluster are aligned in the same direction. By signal alignment, the number of messages decoded by successive interference cancellation (SIC) is reduced, which can be effective at lowering the decoding complexity and SIC error propagation. Due to the difficulty of jointly optimizing cluster-specific beamforming and time/energy resources for sum-throughput maximization, we determine the beamforming relying on signal alignment first, and then the resources are optimized for given beamforming. To be more specific, we propose a novel iterative algorithm for cluster-specific beamforming design followed by the sum-throughput maximization algorithm. Numerical results show the sum-throughput performance of the proposed scheme and its robustness toward SIC error propagation compared to existing schemes.

Hardware and Interference Limited Cooperative CR-NOMA Networks Under Imperfect SIC and CSI

The conflation of cognitive radio (CR) and non-orthogonal multiple access (NOMA) concepts is a promising approach to fulfill the massive connectivity goals of future networks given the spectrum scarcity. Accordingly, this paper investigates the performance of a cooperative CR-NOMA network in the presence of system impairments and interference. Our analysis is involved with the derivation of the end-to-end outage probability for primary and secondary networks by accounting for channel state information (CSI), hardware imperfections, and residual interference caused by successive interference cancellation errors as well as coexisting primary/secondary users. Moreover, a mathematically tractable upper bound on spectral efficiency (SE) with its high-SNR approximations are derived. Besides, we propose an optimal power allocation scheme for CR-NOMA users to guarantee their outage and SE fairness. The numerical results validated by Monte Carlo simulations show that the CR-NOMA network provides a superior outage performance over orthogonal multiple access. Furthermore, the higher level of system imperfections leads to the performance degradation of the CR-NOMA networks. As imperfections become more severe, the CR-NOMA is observed to deliver relatively inferior outage and SE performance as compared to the perfect system scenario.

1-bit feedback-based beamforming scheme for an uplink FSO-NOMA system with SIC errors.

In this paper, we study the effect of a beamforming scheme for a multiple-input-single-output (MISO) uplink free-space optical (FSO) communication system with nonorthogonal multiple access (NOMA) over negative exponential fading channels. 1-bit feedback about the channel state information is required by the proposed beamforming scheme. The feedback is considered to be error-free in this work; however, an error due to successive interference cancellation (SIC) is taken into consideration. It is inferred by bit error rate (BER) analysis that a higher weight given to the channel with higher channel gain and a slightly lower weight given to the channel with lower channel gain gives the best performance as compared to all arbitrary schemes in a 2×1 FSO-NOMA system. Further, it is also analytically shown that using a 1-bit feedback-based beamforming scheme in an FSO-NOMA system suppresses the effect of SIC error; hence the BER performance of both the transmitters (TXs) is the same, which is not the case for a conventional NOMA scheme. A simplified asymptotic upper bound of BER of the proposed scheme is obtained by using the order statistics, and an optimized beamforming vector is found by minimizing this upper bound. It is then established analytically as well as through simulations that the beamforming vector is independent of average signal-to-noise ratio as long as the two channels remain independent and identically distributed. We further compare the proposed scheme with an FSO-NOMA system without feedback and beamforming and with single-input single-output FSO system using 4-ary pulse amplitude modulated signaling. It is shown by simulations that the proposed scheme outperforms both of them and has a huge coding gain advantage. A numerical analysis of this scheme is also provided for gamma-gamma (GG) and log-normal (LN) turbulence regime. The proposed scheme is extended to 3×1 and 4×1 MISO systems, and it is revealed that the performance of the system degrades as the number of TX increases.