Ergodic secrecy sum rate for multiuser MIMO downlink systems using block diagonalization

Sparse code multiple access (SCMA) has been recognized as a promising candidate technique for fifth generation (5G) cellular network to improve spectral efficiency (SE). In this paper, physical layer security (PLS) in a downlink single-input single-output (SISO) SCMA system is investigated, which includes one base station (BS), multiple legitimate users and one eavesdropper. The aim of this paper is to maximize the ergodic secrecy sum rate (ESSR) of the SCMA system under the constraint of the transmit power of BS. A novel many-to-many two-side matching algorithm is then proposed. After a limited number of iterations, the algorithm converges to a pair-stable matching. Finally, simulation results indicate that the proposed algorithm outperforms the random scheme and the orthogonal multiple access (OMA) scheme.

In this paper, we study the performance of the two-way relay network (TWRN) with NOMA-based transmission, where the information is exchanged during three time slots. To provide a fair comparison, we also examine the performance of a three-time-slot (3T) OMA-based transmission scheme. In the following, these schemes are referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3T-NOMA-TWRN</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3T-OMA-TWRN</i> . In the 3T-NOMA-TWRN scheme, each transceiver simultaneously transmits two symbols with different powers to exploit the multiplexing gain, implemented through the power-domain NOMA technique. The performance of both schemes is analyzed in terms of the outage probability, the ergodic sum-rate, and their asymptotic behaviors. The outage and rate performances of the schemes are enhanced by optimizing the power allocation coefficients, especially in the NOMA-based scheme. The proposed power allocation algorithm imposes negligible overhead because of considering the closed-form expressions of the outage probability and the ergodic sum-rate as the objective function. For the NOMA-based scheme, we propose sub-optimal power allocation strategies that closely approximate the optimal solution. The validity of the analytical results is confirmed by extensive numerical examples. The results show that the 3T-NOMA-TWRN scheme outperforms its OMA-based counterpart in terms of the outage probability and the ergodic sum-rate, especially in the high-rate and high-SNR regimes. Additionally, the 3T-NOMA-TWRN scheme significantly outperforms the existing two-time-slot (2T)-NOMA-TWRN scheme in the high-SNR regime. However, in the low-SNR regime, only in some cases, the situation changes in favor of the 2T-NOMA-TWRN scheme. Surprisingly, the performance of the 3T-OMA-TWRN scheme can significantly surpass that of the 2T-NOMA-TWRN scheme in certain situations, depending on the rate and SNR regimes and the network geometry. Furthermore, the 3T-NOMA-TWRN scheme significantly reduces the TWRN performance sensitivity to the location of relay node, which is a critical concern in both the 3T-OMA-TWRN and 2T-NOMA-TWRN schemes, especially in the latter case.

Unmanned aerial vehicle (UAV) communication using non-orthogonal multiple access-based coordinated direct and relay transmission (NOMA-CDRT) supports both massive connectivity and wide-area coverage, becoming a key technology for future emergency rescue communications. However, relay forwarding and high-quality line-of-sight links may subject UAV-aided NOMA-CDRT to multiple eavesdropping attempts by saboteurs. Therefore, we propose a multi-node joint jamming scheme using artificial noise (AN) for the UAV-assisted NOMA-CDRT to improve the system’s physical layer security. In the proposed scheme, the base station directly serves a nearby user while using a UAV relay to serve a disaster-affected user, and both the users and the UAV relay utilize AN to jointly interfere with eavesdroppers around the users. To accurately characterize and maximize the ergodic secrecy sum rate (ESSR) of the proposed scheme, we derive the corresponding closed-form expressions and design a joint power allocation and interference control (JPAIC) algorithm using particle swarm optimization. Simulations verify the correctness of the theoretical analysis, the ESSR advantage of the proposed scheme compared with the conventional NOMA-CDRT, and the effectiveness of the proposed JPAIC.

Cell-free massive multiple-input multiple-output (MIMO) is considered as a promising technology for satisfying higher rate requirement of users in beyond-5G networks. This paper investigates the impact of phase noise on the performance of cell-free MIMO systems which employ a large number of multi-antenna access points (APs). For both downlink and uplink transmissions, we derive the tractable closed-form achievable rate expressions when signal detection with channel state information (CSI) and channel distribution information (CDI), respectively, by utilizing the extended deterministic equivalence method in random matrix theory. The closed-form achievable rate expressions provide efficient evaluation for the impact of phase noise on system performance. The analytical results indicate that the phase noise influences the power of the desired signal, the beamforming uncertainty gain, and the inter-user interference increment caused by the pilot contamination. In addition, the special cases that only APs have phase noise and only users have phase noise are discussed. It is found that the impact of phase noise at users is more severe than that at APs. Besides, we discuss the system performance at low and high SNR regimes. It demonstrates that the phase noise is the major limitation of the system performance in high SNR regime while it can be neglected in low SNR regime. Furthermore, we formulate the max-min power control problem for both downlink and uplink transmissions to guarantee the users' fairness and prove that the downlink max-min problem is a quasi-concave problem while the uplink max-min problem is a geometric programming (GP) problem. Then, the phase noise-aware max-min power control schemes for both downlink and uplink transmissions are proposed to ensure the users' fairness. Finally, numerical results are provided to validate the analytical results and the proposed phase noise-aware power control scheme.

Rate-Splitting Multiple Access (RSMA) has recently appeared as a powerful and robust multiple access and interference management strategy for downlink Multi-user (MU) multi-antenna communications. In this work, we study the precoder design problem for RSMA scheme in downlink MU systems with both perfect and imperfect Channel State Information at the Transmitter (CSIT) and assess the role and benefits of transmitting multiple common streams. Unlike existing works which have considered single-antenna receivers (Multiple-Input Single-Output–MISO), we propose and extend the RSMA framework for multi-antenna receivers (Multiple-Input Multiple-Output–MIMO) and formulate the precoder optimization problem with the aim of maximizing the Weighted Ergodic Sum-Rate (WESR). Precoder optimization is solved using Sample Average Approximation (SAA) together with the proposed vectorization and Weighted Minimum Mean Square Error (WMMSE) based approach. Achievable sum-Degree of Freedom (DoF) of RSMA is derived for the proposed framework as an increasing function of the number of transmitted common and private streams, which is further validated by the Ergodic Sum Rate (ESR) performance using Monte Carlo simulations. Conventional MU–MIMO based on linear precoders and Non-Orthogonal Multiple Access (NOMA) schemes are considered as baselines. Numerical results show that with imperfect CSIT, the sum-DoF and ESR performance of RSMA is superior to those of the two baselines, and is increasing with the number of transmitted common streams. Moreover, by better managing the interference, RSMA not only has significant ESR gains over baseline schemes but is more robust to CSIT inaccuracies, network loads and user deployments.

The stack-based iterative precoding (SBIP) is an efficient algorithm that achieves a tradeoff between bit error rate (BER) performance and computational complexity in multi-user MIMO downlink systems. In this paper, we propose an adaptive SBIP algorithm with variable candidate set and statistically derived threshold for pruning. By analyzing the upper bound of accumulated metric, the range of candidate set is calculated. The probability distribution is also derived for statistical pruning of the tree search. Applying these ideas, the number of undesirable node visit is significantly reduced. Monte-Carlo simulations show that the proposed algorithm considerably reduces the computational complexity whereas the performance is close to that of sphere encoder (SE).

Radio-frequency (RF) energy harvesting presents a viable solution to prolong the lifetime of wireless communication devices. In this paper, we study downlink multiuser scheduling for a time-slotted system with simultaneous wireless information and power transfer. In particular, in each time slot, a single user is scheduled to receive information, whereas the remaining users opportunistically harvest the ambient RF energy. We devise novel online scheduling schemes in which the tradeoff between the users' ergodic rates and their average amount of harvested energy can be controlled. In particular, we modify the well-known maximum signal-to-noise ratio (SNR) and maximum normalized-SNR (N-SNR) schedulers by scheduling the user whose SNR/N-SNR has a certain ascending order (selection order) rather than the maximum one. We refer to these new schemes as order-based SNR/N-SNR scheduling and show that the lower the selection order, the higher the average amount of harvested energy in the system at the expense of a reduced ergodic sum rate. The order-based N-SNR scheduling scheme provides proportional fairness among the users in terms of both the ergodic achievable rate and the average harvested energy. Furthermore, we propose an order-based equal throughput (ET) fair scheduler, which schedules the user having the minimum moving average throughput out of the users whose N-SNR orders fall into a given set of allowed orders. We show that this scheme provides the users with proportionally fair average harvested energy values. In this context, we also derive feasibility conditions for achieving ET with the order-based ET scheduler. Using the theory of order statistics, the average per-user harvested energy and ergodic achievable rate of all proposed scheduling schemes are analyzed and obtained in closed form for independent and nonidentically distributed Rayleigh, Rician, Nakagami- $m$, and Weibull fading channels. Our closed-form analytical results are corroborated by simulations.

We consider a fully digital massive multiple-input multiple-output architecture with low-resolution analog-to-digital/digital-to-analog converters (ADCs/DACs) at the base station (BS) and analyze the performance trade-off between the number of BS antennas, the resolution of the ADCs/DACs, and the bandwidth. Assuming a hardware power consumption constraint, we determine the relationship between these design parameters by using a realistic model for the power consumption of the ADCs/DACs and the radio frequency chains. Considering uplink pilot-aided channel estimation, we build on the Bussgang decomposition to derive tractable expressions for uplink and downlink ergodic achievable sum rates. Numerical results show that the ergodic performance is boosted when many BS antennas with very low resolution (i.e., 2 to 3 bits) are adopted in both the uplink and the downlink.

In this paper, we investigate channel estimation and robust detection for uplink massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with in-phase and quadrature-phase imbalances (IQI). We represent the received signal with a real-valued model, where the combination of the IQI and the wireless channel is treated as the effective channel. Based on the real-valued model, we then perform the minimum mean square error (MMSE) criterion based estimation for the effective channel. We use adjustable phase shift pilots (APSPs) to reduce the pilot overhead and verify that the MSE of the effective channel estimation can be minimized by scheduling the pilot phase shifts properly. We propose a pilot phase shift scheduling algorithm based on the covariance matrices of the effective channels. Since the channel estimation performance might be degraded due to using APSPs, we develop an MMSE criterion based data detection scheme which is robust to the channel estimation error. Using operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed detection scheme. The performance of the channel estimation with APSPs and the robust data detection is demonstrated via extensive numerical results.

Communication systems with low-resolution analog-to-digital-converters (ADCs) can exploit channel state information at the transmitter and receiver. This paper presents codebook designs and performance analyses for limited feedback MIMO systems with finite-bit ADCs. A point-to-point single-user channel is firstly considered. When the received signal is sliced by 1-bit ADCs, the absolute phase at the receiver is important to align the phase of the received signals. A new codebook design for beamforming, which separately quantizes the channel direction and the residual phase, is therefore proposed. For the multi-bit case where the optimal transmission method is unknown, suboptimal Gaussian signaling and eigenvector beamforming is assumed to obtain a lower bound of the achievable rate. It is found that to limit the rate loss, more feedback bits are needed in the medium SNR regime than the low and high SNR regimes, which is quite different from the conventional infinite-bit ADC case. Second, a multi-user system where a multiple-antenna transmitter sends signals to multiple single-antenna receivers with finite-bit ADCs is considered. Based on the derived performance loss due to finite-bit ADCs and finite-bit CSI feedback, the number of bits per feedback should increase linearly with the ADC resolution in order to restrict the rate loss.

A null space constraint based block Tomlinson-Harashima preceding technique (NS-BTHP technique) is proposed for the downlink of multi-user MIMO systems. Employing non-linear pre-processing at the base station this technique pre-eliminates multi-user interference (MUI) among different mobiles. Therefore, an equivalent point-to-point MlMO channel is realized for each mobile, and the spatial interference among the multiple data streams directed to each user (self-interference) can be eliminated using signal processing algorithms developed for point-to-point MlMO systems. The proposed nonlinear preceding approach results in an improvement of the null space constraint technique (NS technique), in which linear pre-processing is used to pre-eliminate the MUI at the base station. The advantage of the NS-BTHP technique over the NS technique is explained and demonstrated by simulations.

In this paper, we propose a general method to analyze the achievable rate and to characterize the optimal power-allocation (PA) scheme for a wide range of half-duplex single-relay amplify-and-forward (AF) protocols over Rayleigh fading channels in high and low signal-to-noise-ratio (SNR) regimes. These include one-way (OW) dual-hop AF (DHAF) systems, OW nonorthogonal AF (NAF) systems, and two-phase two-way AF (2P TWAF) systems using either fixed-gain (FG) or variable-gain (VG) amplification coefficients. At high-SNR regimes, our main idea is to exploit the capacity of a two-branch maximal-ratio combining (MRC) system to obtain tight yet simple approximations to the achievable rates. In low-SNR regions, we use a simple approximation to the logarithm to compute the asymptotic achievable rates. For all considered AF protocols, the closed-form approximations are tight and easy to analyze since they involve only the exponential integral. Then, using the derived approximations, we analytically quantify the asymptotic PA schemes among the nodes to achieve the maximum rate and the sum rate for OW and TW schemes, respectively. The OW and TW protocols of interest are finally compared with the direct transmission (DT) scheme. Although OW relaying is inferior in terms of capacity in high- and low-SNR regimes, the 2P TW system might become advantageous in terms of sum-rate performance at high SNRs under the right channel conditions.

We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.

We consider the reciprocity of the information-theoretic channel of Time Division Duplex (TDD) Multi-User-Multiple Input Multiple Output (MU-MIMO) systems in the up- and downlink. Specifically, we assume that the transmit and receive chains are reciprocal. We take the mutual coupling between the antenna elements at the base station and at the mobiles into account. Mutual coupling influences how to calculate transmit power and noise covariance. The analysis is based on the Multiport Communication Theory, which ensures that the information-theoretic model is consistent with physics. It also includes a detailed noise model. We show that due to the coupling, the information-theoretic up- and downlink channels do not fulfill the ordinary reciprocity relation, even if the input-output relation of the transmit voltage sources and the receive load voltages, i.e., the channel which is estimated with the help of pilot signals in the uplink, is reciprocal. This is a fundamental effect that is not considered otherwise. We show via Monte Carlo simulations that both, using the ordinary reciprocity relation, and not taking the coupling into account, significantly decreases the ergodic rates in single-user and the ergodic sum rates in multi-user systems.

In this paper, a novel cooperative non-orthogonal multiple access (NOMA) system is proposed, where one near user is employed as decode-and-forward relaying switching between full-duplex (FD) and half-duplex (HD) mode to help a far user. Two representative cooperative relaying scenarios are investigated insightfully. The first scenario is that no direct link exists between the base station (BS) and far user. The second scenario is that the direct link exists between the BS and far user. To characterize the performance of potential gains brought by the FD NOMA in two considered scenarios, three performance metrics outage probability, ergodic rate, and energy efficiency are discussed. More particularly, we derive new closed-form expressions for both exact and asymptotic outage probabilities as well as delay-limited throughput for two NOMA users. Based on the derived results, the diversity orders achieved by users are obtained. We confirm that the use of direct link overcomes zero diversity order of far NOMA user inherent to FD relaying. In addition, we derive new closed-form expressions for asymptotic ergodic rates. Based on these, the high signal-to-noise ratio (SNR) slopes of two users for FD NOMA are obtained. Simulation results demonstrate that: 1) the FD NOMA is superior to the HD NOMA in terms of outage probability and ergodic sum rate in the low SNR region; and 2) in delay-limited transmission mode, the FD NOMA has higher energy efficiency than the HD NOMA in the low SNR region; However, in delay-tolerant transmission mode, the system energy efficiency of the HD NOMA exceeds the FD NOMA in the high SNR region.