Achievable Ergodic Rate Research Articles

Impact and Calibration of Nonlinear Reciprocity Mismatch in Massive MIMO Systems

Time-division-duplexing massive multiple-input multiple-output (MIMO) systems estimate the channel state information (CSI) by leveraging the uplink-downlink channel reciprocity, which is no longer valid when the mismatch arises from the asymmetric uplink and downlink radio frequency (RF) chains. Existing works treat the reciprocity mismatch as constant for simplicity. However, the practical RF chain consists of nonlinear components, which leads to nonlinear reciprocity mismatch. In this work, we examine the impact and the calibration approach of the nonlinear reciprocity mismatch in massive MIMO systems. To evaluate the impact of the nonlinear mismatch, we first derive the closed-form expression of the ergodic achievable rate. Then, we analyze the performance loss caused by the nonlinear mismatch to show that the impact of the mismatch at the base station (BS) side is much larger than that at the user equipment side. Therefore, we propose a calibration method for the BS. During the calibration, polynomial function is applied to approximate the nonlinear mismatch factor, and over-the-air training is employed to estimate the polynomial coefficients. After that, the calibration coefficients are computed by maximizing the downlink achievable rate. Simulation results are presented to verify the analytical results and to show the performance of the proposed calibration approach.

Power Minimization Using Rate Splitting With Statistical CSI in Cloud-Radio Access Networks

Minimizing the power consumption in mobile communication networks while ensuring a minimum quality of service (QoS) for applications is essential in light of the unprecedented expected increase in the number of connected devices and the associated data traffic beyond the fifth generation of wireless networks (B5G). This paper considers a cloud-radio access network (C-RAN) model where a central processor (CP) is connected to the base stations (BSs) via limited capacity fronthaul links. In the context of our C-RAN setting, we consider the practical case where the CP has only statistical knowledge of channel state information (CSI). While conventional wireless systems adopt the treating interference as noise (TIN) strategy to deal with the interference in the network, this paper instead considers that the CP applies the rate splitting (RS) strategy by dividing each user’s message into two parts: a private part to be decoded by the intended user only and a common part to be decoded by a subset of users, for the sole reason of interference mitigation in the network. To best account for the channel estimation errors, this paper addresses the problem of transmit power minimization under minimum QoS constraints on the achievable ergodic rate per user, so as to determine the beamforming vectors of the private and common messages as well as the rate allocated to all the users. The considered problem is of stochastic, complex, and non-convex nature. This paper addresses the problem intricacies through an iterative approach that leverages both the sample average approximation (SAA) technique and the weighted minimum mean squared error (WMMSE) algorithm to obtain a stationary point of the optimization problem in the asymptotic regime. The numerical results demonstrate the gain achieved with the RS strategy as compared to TIN, especially under high QoS requirements.

Analytical Framework of CP-Free Multiuser OFDM System for Coordinated Multi-Point at mmWave

In this paper, a coordinated multipoint joint transmission (CoMP-JT) framework at mmWave for a cyclic prefix (CP)-free multiuser OFDM wireless communication system is developed and analyzed. The aim is to provide high-quality service to cell-edge users; otherwise, the cell-users would suffer from significant signal degradation due to undesired interference. The impact of complex Hadamard transform with block diagonalization channel precoding for multiuser interference reduction and designed subcarrier mapping for out-of-band (OOB) reduction are investigated. In addition, the paper studied the input back-off-aided high-power amplifier for peak-to-average power ratio (PAPR) reduction and forward error correction channel coding for improved bit error rate (BER) for cell-edge users at mmWave frequencies. Moreover, signal-to-interference-noise ratio and ergodic achievable rate are estimated both in the presence and absence of CoMP-JT-based transmission technique to verify their significance in terms of transmitted power. Numerical investigations showed an OOB reduction of 312 dB, PAPR reduction from 17.50 dB to 7.66 dB, and improved BER of 1×10−3 in 16-QAM for a signal-to-noise ratio of −6 dB. Hence, the simulation results demonstrated the effectiveness of the developed system.

Performance Analysis for RIS-Assisted D2D Communication Under Nakagami-$m$ Fading

Reconfigurable intelligent surface (RIS) is considered as a promising technology, which can effectively control the phase of signals with low-cost reflective elements. In this paper, we investigate the RIS-assisted D2D communication system under Nakagami-m fading. Overlay mode and underlay mode are discussed respectively. To characterize the performance of proposed communication system, we propose novel closed-form analytical expressions for outage probability under two modes, respectively. Based on the analytical results, we derive the diversity order of outage probability. We show that under overlay D2D mode, the diversity order depends on the number of elements and fading parameters. For the underlay D2D case, 0 diversity order is obtained due to the existence of interference. Furthermore, we study the ergodic achievable rate for each mode and the corresponding tight bounds are derived in closed form. High SNR slopes achieved by users under two modes are also discussed. We observe a high SNR slope of order 1 for overlay D2D mode and 0 for underlay D2D mode. In addition, we also investigate the energy efficiency (EE) of the considered system. Numerical results show that the optimal phase shift proposed in our paper enhance system performance effectively comparing to the traditional D2D communication and random phase shift scheme. Significant EE gains can be obtained for low to middle SNR region by passive reflectors with reconfigurable phase. Unlike relay system, the nearer RIS to the D2D transmitter/receiver, the better performance is obtained.

Large System Achievable Rate Analysis of RIS-Assisted MIMO Wireless Communication With Statistical CSIT

Reconfigurable intelligent surface (RIS) is an emerging technology to enhance wireless communication in terms of energy cost and system performance by equipping a considerable quantity of nearly passive reflecting elements. This study focuses on a downlink RIS-assisted multiple-input multiple-output (MIMO) wireless communication system that comprises three communication links of Rician channel, including base station (BS) to RIS, RIS to user, and BS to user. The objective is to design an optimal transmit covariance matrix at BS and diagonal phase-shifting matrix at RIS to maximize the achievable ergodic rate by exploiting the statistical channel state information at BS. Therefore, a large-system approximation of the achievable ergodic rate is derived using the replica method in large dimension random matrix theory. This large-system approximation enables the identification of asymptotic-optimal transmit covariance and diagonal phase-shifting matrices using an alternating optimization algorithm. Simulation results show that the large-system results are consistent with the achievable ergodic rate calculated by Monte-Carlo averaging. The results verify that the proposed algorithm can significantly enhance the RIS-assisted MIMO system performance.

Performance analysis for large intelligent surface assisted vehicular networks

Large intelligent surface (LIS) is considered as a new solution to enhance the performance of wireless networks[1]. LIS comprises low-cost passive elements which can be well controlled. In this paper, a LIS is invoked in the vehicular networks. We analyze the system performance under Weibull fading. We derive a novel exact analytical expression for outage probability in closed form. Based on the analytical result, we discuss three special scenarios including high SNR case, low SNR case, as well as weak interference case. The corresponding approximations for three cases are provided, respectively. In order to gain more insights, we obtain the diversity order of outage probability and it is proved that the outage probability at high SNR depends on the interference, threshold and fading parameters which leads to 0 diversity order. Furthermore, we investigate the ergodic achievable rate of LIS-assisted vehicular networks and present the closed-form tight bounds. Similar to the outage performance, three special cases are studied and the asymptotic expressions are provided in simple forms. A rate ceiling is shown for high SNRs due to the existence of interference which results 0 high SNR slope. Finally, we give the energy efficiency of LIS-assisted vehicular network. Numerical results are presented to verify the accuracy of our analysis. It is evident that the performance of LIS-assisted vehicular networks with optimal phase shift scheme exceeds that of traditional vehicular networks and random phase shift scheme significantly.

Channel Estimation and Robust Detection for IQ Imbalanced Uplink Massive MIMO-OFDM With Adjustable Phase Shift Pilots

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.

Widely-Linear Processing for the Uplink of the Massive MIMO With IQ Imbalance: Channel Estimation and Data Detection

In this paper, we investigate widely-linear channel estimation and data detection for the uplink of the massive multiple-input multiple-output (MIMO) with in-phase or quadrature-phase imbalance (IQI). We firstly investigate widely-linear minimum mean square error (WL-MMSE) estimation for the effective channel which is the product of the IQI coefficients and the wireless channel. We reuse pilots among different user terminals (UTs) to reduce pilot overhead and derive a lower bound of the estimation MSE. Based on the optimal condition under which the lower bound is achieved, we show that if we assign the same pilot for the UTs of which the covariance matrices are orthogonal, the pilot interference does not affect the MSE performance. Then according to the obtained estimates of the effective channel, we further propose WL-MMSE data detection that is robust to the estimation error. The proposed widely-linear approach can cope with the IQI and multi-user interference jointly. With some results of operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed robust WL-MMSE data detection. The performance of the proposed widely-linear processing approach is verified by the numerical results.

Uplink and Downlink MIMO-NOMA With Simultaneous Triangularization

In this paper, we consider the uplink and downlink precoder design for two-user power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. We propose novel uplink and downlink precoding and decoding schemes that lower the decoding complexity at the receiver by decomposing the MIMO-NOMA channels of the users into multiple single-input single-output (SISO)-NOMA channels via simultaneous triangularization (ST) of the MIMO channels of the users and a low-complexity self-interference cancellation at the receiver. The proposed ST MIMO-NOMA schemes avoid channel inversion at transmitter and receiver and take advantage of the null spaces of the MIMO channels of the users, which is beneficial for the ergodic achievable rate performance. We characterize the maximum ergodic achievable rate regions of the proposed uplink and downlink ST MIMO-NOMA schemes, and compare them with respective upper bounds, baseline MIMO-NOMA precoding schemes, and orthogonal multiple access (OMA). Our results illustrate that the proposed schemes significantly outperform the considered baseline MIMO-NOMA precoding schemes and OMA, and have a small gap to the respective upper bounds for most channel conditions and user rates. Moreover, we show that a hybrid scheme, which performs time sharing between the proposed uplink and downlink ST MIMO-NOMA and single-user MIMO, can improve performance even further.

Interference Analysis and Mitigation for Aerial IoT Considering 3D Antenna Patterns

Due to dense deployments of Internet of things (IoT) networks, interference management becomes a critical challenge. With the proliferation of aerial IoT devices, such as unmanned aerial vehicles (UAVs), interference characteristics in 3D environments will be different than those in the existing terrestrial IoT networks. In this paper, we consider 3D topology IoT networks with a mixture of aerial and terrestrial links, with low-cost cross-dipole antennas at ground nodes and both omni-directional and cross-dipole antennas at aerial nodes. Considering a massive-access communication scenario, we first derive the statistics of the channel gain at IoT receivers in closed form while taking into account the radiation patterns of both ground and aerial nodes. These are then used to calculate the ergodic achievable rate as a function of the height of the aerial receiver and the cumulative interference. We propose a low-complexity interference mitigation scheme that utilizes 3D antenna radiation pattern with different dipole antenna settings. Our results show that using the proposed scheme, the ergodic achievable rate improves as the height of the aerial receivers increases. In addition, we also show that the ratio between the ground and aerial receivers that maximizes the peak rate increases with the height of the aerial IoT receiver.

Distributed IRS With Statistical Passive Beamforming for MISO Communications

Intelligent reflecting surface (IRS) has recently been identified as a prominent technology with the ability of enhancing wireless communication by dynamically manipulating the propagation environment. This letter investigates a multiple-input single-output (MISO) system deploying distributed IRSs. For practical considerations, we propose an efficient design of passive reflecting beamforming for the IRSs to exploit statistical channel state information (CSI) and analyze the achievable rate of the network taking into account the impact of CSI estimation error. The ergodic achievable rate is derived in a closed form, which provides insightful system design guidelines. Numerical results confirm the accuracy of the derived results and unveil the performance superiority of the proposed distributed IRS deployment over the conventional centralized deployment.

A physical layer security scheme for full-duplex communication systems with residual self-interference and non-eavesdropping CSI

We discuss the physical layer security scheme in the Full-Duplex (FD) MIMO point-to-point two-way communication system with residual self-interference, in which legitimate nodes send confidential information and null space Artificial Noise (AN) while receiving information. Because the Channel State Information (CSI) of the eavesdropper is unavailable, we optimize the covariance matrices of the information signal as well as the allocation of the antenna for transmitting and receiving to minimize the signal power consumption under the target rate constraint. As a result, the power of AN is maximized within the limit of total power, so the interception capability of the eavesdropper is suppressed as much as possible. Since self-interference cannot be completely eliminated, the optimization process of one legitimate node depends on the optimization result of the other. By substituting self-interference power in the secrecy rate formula with its average value, the joint optimization process at the two nodes is transformed into two separate and solvable optimization processes. Then, the Water-Filling Algorithm (WFA) and bisection algorithm are used to get the optimal covariance matrices of the signal. Furthermore, we derive the theoretical lower bound of ergodic achievable secrecy rate under rayleigh channels to evaluate the performance of the scheme. The simulation results show that the theoretical derivation is correct, and the actual achievable rate is very close to the target rate, which means that the approximation in the optimization is feasible. The results also show that secrecy transmission can be realized because a considerable secrecy rate can be achieved.

Physical Layer Security of In-Home PLC Systems: Analysis Based on a Measurement Campaign

This article investigates the physical layer security (PLS) of a broadband in-home power line communication (PLC) system when a malicious and passive PLC device tries to eavesdrop upon private information sent by a PLC transmitter to a legitimate PLC receiver. In this setting, the ergodic achievable secrecy rate, secrecy outage probability, effective secrecy throughput, and wiretap code rates are numerically evaluated with the use of a data set obtained from a measurement campaign carried out in several Brazilian houses. This data set comprises PLC channel estimates and measured additive noises considering four distinct sets of transmitter, legitimate receiver, and eavesdropper positions. Numerical results, covering three distinct frequency bands (1.7–30 MHz, 1.7–50 MHz, and 1.7–86 MHz), quantitatively show, in practice, the level of vulnerability of broadband in-home PLC systems in terms of PLS and offer some directions for an appropriate design of PLC modems to improve PLS.

Precoder Design and Statistical Power Allocation for MIMO-NOMA via User-Assisted Simultaneous Diagonalization

In this paper, we investigate the downlink precoder design for two-user power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA). We propose a novel user-assisted (UA) simultaneous diagonalization (SD) based MIMO-NOMA scheme that achieves SD of the MIMO channels of both users through a combination of precoder design and low-complexity self-interference cancellation at the users, thereby considerably lowering the overall decoding complexity compared to joint decoding. The achievable ergodic user rates of the proposed scheme are analyzed for Rayleigh fading channels based on a finite-size random matrix theory framework, which is further exploited to develop a statistical power allocation algorithm. Simulation and numerical results show that the proposed UA-SD MIMO-NOMA scheme significantly outperforms orthogonal multiple access and a benchmark precoder design performing SD via generalized singular value decomposition in terms of the achievable ergodic rate region for most user rates. The ergodic rate region is further enhanced by a hybrid scheme which performs time sharing between the proposed UA-SD MIMO-NOMA scheme and single-user MIMO.

Joint user association and power allocation for massive MIMO HetNets with imperfect CSI

Since Massive multiple-input and multiple-output (MIMO) and heterogeneous networks (HetNets) have significantly improvement in spectrum efficiency, Massive MIMO enabled HetNets have emerged as a promising technique for the fifth-generation cellular networks. Most previous studies focus on energy-efficient resource allocation of Massive MIMO HetNets by assuming perfect channel state information (CSI). In this paper, we investigate the α-fairness network utility optimization problem of joint user association and power allocation for a downlink Massive MIMO HetNet with imperfect CSI. By utilizing zero-forcing beamforming, we show a new closed-form lower bound expression on the ergodic achievable rate. Furthermore, we formulate the optimization problem as a mixed-integer nonlinear programming problem, which is non-convex and NP-hard, to achieve the maximization of α-fairness network utility. Consequently, a joint iterative algorithm with respect to user association and power allocation is developed by decomposing the original problem and relaxing the constraints. Simulation results show that our proposed algorithm can yield much better network utility performance than the other algorithms.

Physical Layer Multicasting in Massive MIMO Systems With Statistical CSIT

We present a transmit design for physical layer multicasting in single-cell massive multiple-input-multiple-output (MIMO) systems using statistical channel state information at the base station (BS). We first establish the relationship between the transmit design problems under the quality of service (QoS) and max-min fair (MMF) criteria. According to the relationship between the QoS and MMF problems, we only focus on the transmit covariance optimizations under the latter criterion. We show that when the uniform linear array is equipped at the BS, the eigenvectors of the optimal transmit covariance are given by columns of the discrete Fourier transform matrix, which reveals the optimality of the beam domain transmission in massive MIMO multicasting. A dual algorithm together with stochastic programming is proposed to specify the eigenvalues of the transmit covariance. To reduce the complexity involved in stochastic programming, we further formulate two simplified MMF problems by using the deterministic equivalents and upper bound to approximate the ergodic achievable rate, respectively. We show that the optimality of the beam domain transmission still holds for the two simplified MMF problems. Then we present two low-complexity transmit designs. Simulation results demonstrate the performances of the proposed algorithms.

Vehicular Networks Under Nakagami-m Fading Channels: Outage Probability and Ergodic Achievable Rate

Vehicular networks are regarded as an effective solution for the traffic management and road safety. In this paper, the performance of the vehicular networks is investigated under Nakagami-m fading channels. The vehicular communication is considered to reuse the same time-frequency with another vehicular communication link, so that both interference and noise produce an effect on each vehicle and infrastructure. Firstly, we derive the closed-form expressions for the outage probability of vehicular links and particularly examine two special cases, that is, high SNR case and weak interference case. For both cases, approximate expressions for outage probability are provided in closed form. Then, we derive lower and upper bounds of ergoidic achievable rate, which are evident to be sufficiently tight to the Monte-Carlo simulated results. Based on these results, we further analyze the high SNR and weak interference scenarios and the asymptotic expressions of ergoidic achievable rate are also presented. All the analytical results are applicable for arbitrary locations, transmit power, as well as channel parameters. Finally, we propose the power optimization which aims at maximizing the ergodic achievable rate and guaranteeing the outage performance. Numerical results validate our analytical results via Monte Carlo simulations.

Performance Analysis of Linear Precoded MU-MIMO-OFDM Systems With Nonlinear Power Amplifiers and Correlated Channel

In this paper, we investigate the effect of power amplifier (PA) nonlinearity on a multi user multiple-input multiple-output orthogonal frequency division multiplexing (MU-MIMO-OFDM) system where the base station (BS) uses linear precoding to transmit data for single antenna users through a correlated channel. The signal to distortion, interference and noise ratio is derived for any order of PA nonlinearity. Our analysis shows that a correlated channel can result in correlated distortions at the output of PAs which increase the received distortion power of users. Approximations for the ergodic achievable rate of the users are provided when the BS transmits data through a correlated channel using maximum ratio transmission or zero forcing precodings and number of BS antennas and users are large. Also, closed form approximations for the ergodic achievable sum rate of the system are provided when the channel is not correlated. The simulation results agree with the derived approximations even when the number of transmit antennas and users are relatively small. The approximations can be used to find the achievable sum rate maximizing number of users or transmit power of the system.

Secure Quadrature Channel Modulation

In this paper, a physical layer security (PLS) scheme based on quadrature channel modulation (QCM) called secure QCM (SQCM) is proposed for time division duplex (TDD) multi-input multi-output (MIMO) media based modulation (MBM) systems to resist eavesdropping. By exploiting the abundant legitimate channel realizations generated by the radio frequency (RF) mirrors, secure mappings between the original information bits and the transmit patterns are designed, where the transmit patterns include the transmit antenna activation pattern (AAP), mirror activation pattern (MAP) and symbol modulation pattern. The secure mappings used by the transmitter change for each transmission and are unavailable at the eavesdropper due to the independent fading of the legitimate link and the eavesdropping link. Based on the secure mappings, the proposed SQCM conveys the source information bits securely through the complex modulation symbol and instantaneous channel realizations by using a single RF chain. The ergodic secrecy rate is analyzed and a closed-form approximation is derived. Simulation results show that the closed-form approximation coincides with the experimental ergodic secrecy rate, and the achievable ergodic secrecy rate is not influenced by the number of eavesdropping antennas or the channel advantage of the eavesdropping link. Compared to the secure MBM scheme using the traditional artificial noise (AN) technique, the proposed SQCM scheme shows significant performance gain without consuming jamming power when the eavesdropper has more antennas than the legitimate receiver. Compared to the precoded MBM and probabilistic optimized MBM schemes exploiting the eavesdropper's CSI, the proposed SQCM scheme has better secrecy performance in all SNR region and medium-to-high SNR regions respectively without requiring the eavesdropper's CSI.

Multicell Massive MIMO Multicast Transmission With Finite-Alphabet Inputs

This paper investigates the precoding design for multicast transmission in multicell massive multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The users within each cell are interested in common information, and different cells provide distinct information. Focusing on the weighted max-min fairness (MMF) problem with only statistical channel state information at the base station, we provide the necessary conditions of the optimal precoding vectors to maximize the minimum weighted achievable ergodic rate, and an iterative algorithm is proposed to optimize the precoding vectors. To achieve lower computational complexity, we then derive a lower bound on the achievable ergodic rate for finite-alphabet inputs. Considering the problem of the minimum weighted rate lower bound maximization, we utilize the concave-convex procedure (CCCP) to develop a CCCP-based algorithm, which is proven to converge to a local optimum. Furthermore, exploiting the channel characteristic in massive MIMO systems, we prove that the optimal precoding vectors, maximizing the minimum weighted rate lower bound, are linear combinations of eigenvectors of transmit correlation matrices, and the original problem can be shifted into a lower dimensional space. Motivated by this insight, a relation-based algorithm is devised to obtain the optimal solution of the weighted MMF problem by using the duality between the MMF problem and the quality of service problem. Numerical results illustrate the tightness of the achievable ergodic rate lower bound and the significant performance of the devised algorithms.