Effect Of Channel Estimation Error Research Articles

Performance Analysis of Uplink Index-Modulated NOMA for 6G Wireless Communications

In this letter, we mathematically analyze the bit-error rate (BER) performance of a generalized uplink index-modulated non-orthogonal multiple access (IM-NOMA) system consisting of a base station (BS) with multiple antennas and an arbitrary number of devices with different modulation schemes. We focus on the case that a single subcarrier is activated among S(≥2) subcarriers according to index bits to reduce computational complexity. The optimal joint maximum-likelihood (JML) algorithm is assumed to be used for detecting a super-imposed symbol from multiple devices. The closed-form BER is shown to be matched well with simulation results. We also investigate the effect of channel estimation error on the BER. To the best of our knowledge, the mathematical characterization of BER of the generalized uplink IM-NOMA system with an arbitrary number of uplink devices with different modulation schemes and multiple receive antennas at the BS does not exist in the literature. Finally, we show that our analytical framework can be applied to analyze a cell-free massive MIMO NOMA system, which is expected to be one of the most promising techniques for 6G wireless communication systems.

Sum Rate Analysis for Massive MIMO-NOMA Uplink System With Group-Level Successive Interference Cancellation

The deep integration between non-orthogonal multiple access (NOMA) and massive multiple-input multiple-output (MIMO) technology is a promising way to achieve massive connectivity and high capacity in B5G/6G wireless communication system. In this letter, a novel signal processing framework for massive MIMO-NOMA data transmission is proposed based on group-level successive interference cancellation (GLSIC), in which the users are grouped according to the distances to the base station (BS) and NOMA is applied among different groups by employing GLSIC to reduce the inter-group interference. The uplink sum rate is derived for the proposed GLSIC-based massive MIMO-NOMA system with minimum mean square error channel estimator and maximal ratio combiner at BS, and the effects of channel estimation error, inter-group pilot contamination, and imperfect GLSIC are analytically quantified in the derivation. Theoretical analysis and simulation results show that, under the same conditions, the proposed GLSIC-based system achieves higher uplink rate than the existing cluster-based MIMO-NOMA system with user-level SIC.

Spectral Efficiency of Precoded 5G-NR in Single and Multi-User Scenarios under Imperfect Channel Knowledge: A Comprehensive Guide for Implementation

Digital precoding techniques have been widely applied in multiple-input multiple-output (MIMO) systems to enhance spectral efficiency (SE) which is crucial in 5G New Radio (NR). Therefore, the 3rd Generation Partnership Project (3GPP) has developed codebook-based MIMO precoding strategies to achieve a good trade-off between performance, complexity, and signal overhead. This paper aims to evaluate the performance bounds in SE achieved by the 5G-NR precoding matrices in single-user (SU) and multi-user (MU) MIMO systems, namely Type I and Type II, respectively. The implementation of these codebooks is covered providing a comprehensive guide with a detailed analysis. The performance of the 5G-NR precoder is compared with theoretical precoding techniques such as singular value decomposition (SVD) and block-diagonalization to quantify the margin of improvement of the standardized methods. Several configurations of antenna arrays, number of antenna ports, and parallel data streams are considered for simulations. Moreover, the effect of channel estimation errors on the system performance is analyzed in both SU and MU-MIMO cases. For a realistic framework, the SE values are obtained for a practical deployment based on a clustered delay line (CDL) channel model. These results provide valuable insights for system designers about the implementation and performance of the 5G-NR precoding matrices.

NOMA-Based Cognitive Satellite Terrestrial Relay Network: Secrecy Performance Under Channel Estimation Errors and Hardware Impairments

Nonorthogonal multiple access (NOMA) and cognitive integrated satellite terrestrial relay networks are the promising and key part for the next-generation wireless networks. This article researches the joint effects of channel estimation errors (CEEs) and hardware impairments on the secrecy performance of cognitive integrated satellite terrestrial relay networks. The noncolluding eavesdropping scheme is applied in the multiple eavesdroppers, where the eavesdropper with the highest eavesdropping capacity is selected to overhear the legitimate transmission signal. Moreover, the detailed analysis for the secrecy outage probability (SOP) is obtained based on the utilized partial terrestrial relay selection strategy. To obtain the insightful conclusions, the asymptotic analysis along with the secrecy coding gain and secrecy diversity order for the SOP are further derived, which gives the effective methods to valuate the impacts of CEEs and hardware impairments on the considered system with the NOMA scheme in high signal-to-noise ratio regime. Moreover, simulations are derived for the secrecy energy efficiency. Finally, Monte Carlo simulations are given to prove the correctness of the theoretical SOP analysis.

The Effect of Channel Estimation Error on Secrecy Outage Capacity of Dual Selection in the Presence of Multiple Eavesdroppers

The Effect of Channel Estimation Error on Secrecy Outage Capacity of Dual Selection in the Presence of Multiple Eavesdroppers

Channel Estimation and Secret Key Rate Analysis of MIMO Terahertz Quantum Key Distribution

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

Effect of Channel Estimation Errors on the Asymptotic Secrecy Outage Performance for Space Shift Keying

This paper presents the derivation of exact and asymptotic closed-form formulas of the secrecy outage probability (SOP) for space shift keying (SSK) systems over Rayleigh fading channels, especially in the presence of imperfect channel state information (CSI) at a legitimate receiver. Comprehensive analyses of the achievable secrecy performance limit for the SSK systems were performed by judiciously exploiting the derived SOP expressions, which enable us to obtain explicit and useful insights into the effect of channel estimation errors on the secrecy performance for the considered systems. The exactness of our theoretical analyses was validated numerically.

On the Energy Efficiency Maximization of NOMA-Aided Downlink Networks With Dynamic User Pairing

This study investigates a combined system comprising non-orthogonal multiple access (NOMA) and beamforming in a downlink network. To fully exploit the advantages of NOMA, user (UE) pairing and beamforming design are jointly optimized via a generalized model for UE association, subject to energy efficiency maximization. Owing to the combination of binary variables and nonconvex constraints, the resulting optimization problem belongs to the class of mixed-integer nonconvex programming. An innovative algorithm, integrating the inner-approximation and Dinkelbach methods, is proposed herein to address a nonconvex fractional function. By introducing a pairing matrix and relaxing the binary variables into continuous ones, our approach is capable of reaching an optimal solution, where two arbitrary UEs are optimally paired regardless of geographical or spatial constraints. For practical scenarios, we further propose a robust design to manage the effect of channel estimation errors under settings involving channel uncertainty. Numerical results show that our proposed designs, even with the presence of the imperfect channel state information at the base station, significantly outperform the conventional beamforming and existing pairing schemes.

Performance analysis of angular diversity receiver based MIMO–VLC system for imperfect CSI

Visible light communication (VLC) has emerged as a promising technology for 5G and beyond communication networks in the last few years. In this paper, a multiple-input multiple-output (MIMO) VLC system using angular diversity receiver is proposed. In particular, the repetition coding is adopted at the transmitter and receiver diversity schemes, i.e. maximum-ratio combining (MRC), equal gain combining (EGC) and selection best combining (SBC), are adopted at the receiver for further performance enhancement. The closed-form expressions for average error probability of the proposed system are derived in the presence of imperfect channel state information (CSI). This research investigates that the increment in SNR is not sufficient to offset the effect of channel estimation error especially at high estimation error. The error performance analysis of the proposed MIMO–VLC system with and without estimation error is presented for different receiver locations and semi-half angles of the transmitting light emitting diodes (LEDs). Analytical results are verified with the simulation results.

Spectral efficiency analysis and optimal power allocation for uplink multi-user cell-free massive MIMO networks employing STBCs

Massive MIMO is a key technique in the fifth generation (5G) of wireless networks. This technique, by increasing base station (BS) antennas and exploiting spatial diversity, improves system performance in terms of common criteria such as spectral efficiency. Cell free massive MIMO is considered for 6G mobile communications to overcome the shortcomings associated with the cellular design. In this system, BS antennas are distributed across the system environment and provide uniform service to all users. Also, space time block codes (STBCs) can be used to improve the diversity gain and reliability of the system. In this paper, a cell free massive MIMO system is investigated in the uplink considering effects of channel estimation errors. Users are equipped with two antennas and employ STBC. Lower bound of spectral efficiency is derived for the zero forcing (ZF) and maximal ratio combining (MRC) decoders. Furthermore, spectral efficiency is compared for dual and single antenna users. Moreover, two power control problems are defined based on minimizing the total transmit power and maximizing the minimum rate of the users. Also, an algorithm is proposed for removing the inefficient BSs in the network. The proposed theoretical ideas are evaluated via numerical simulations.

Energy efficiency optimization for amplify and forward relay networks with channel estimation errors

Due to the rapidly increasing energy consumption of the wireless communication systems, designing an energy-efficient system has become an important challenge. One can consider cooperative communication as a promising solution to reduce energy consumed by wireless networks. Hence, in this paper, we study the problem of maximizing energy efficiency by optimally allocating power in three cooperative channel scenarios. Unlike the previous works, imperfect channel state information is considered for all channels. Therefore, energy efficiency functions are derived considering channel estimation errors, and the following optimization problems are formulated to maximize the energy efficiency under the maximum transmission power and the minimum spectral efficiency constraints. Regarding the energy efficiency function behavior, an alternating optimization algorithm is used to find pilot and data transmission power at the source node. It also optimizes the power amplification gain of pilot and data at the relay node. Simulation results demonstrate that the imperfect channel state information condition can degrade the energy efficiency performance significantly. However, using the proposed power allocation method can improve the performance and compensate for the negative effect of channel estimation error. Moreover, the effect of circuit power on the optimal energy efficiency is investigated. It is shown that for a lower range of spectral efficiency, the negative effect of circuit power is greater than the channel estimation error’s negative effect, while for the higher values, the estimation error dominates the circuit power. We also observe that the results obtained from the proposed power allocation algorithms are close to the results of the global search method.

Interference management for D2D‐enabled HetNets with imperfect channel estimation

Device-to-device (D2D) and heterogeneous networks (HetNets) are two promising technologies to be introduced in the upcoming 5G network, for improving spectral efficiency and decreasing latency. However, sharing the same spectrum resources among different tiers of HetNet raised the interference challenge. In this paper, cross-tier interference management for underlay D2D users is studied in a heterogeneous macro-small cell network assuming imperfect channel state information (CSI). The network consists of one macro-cell with a centered macro-base Station (MBS) and several small-cell base stations (SCBS). Two types cellular users are considered; macro-cell cellular user equipment (MUE) associated with the MBS, and small-cell cellular user equipment (SUE) linked to SCBS. While two types of D2D users are considered; macrocell D2D (MD) located outside the range of the small cells and cross-tier D2D user equipment (CD), where each user of the D2D pair belongs to different network tier. Closed form expressions for the D2D optimal power that aim to maximize the coverage probability and the signal-to-interference-noise ratio (SINR) of both links are derived, while guaranteeing the quality of service (QoS) requirements for the cellular user. The effect of channel estimation error on the performance of both D2D and cellular users is evaluated.

Energy Efficiency of the Cell-Free Massive MIMO Uplink With Optimal Uniform Quantization

A cell-free Massive multiple-input multiple-output (MIMO) uplink is considered, where the access points (APs) are connected to a central processing unit (CPU) through limited-capacity wireless microwave links. The quantized version of the weighted signals are available at the CPU, by exploiting the Bussgang decomposition to model the effect of quantization. A closed-form expression for spectral efficiency is derived taking into account the effects of channel estimation error and quantization distortion. The energy efficiency maximization problem is considered with per-user power, backhaul capacity and throughput requirement constraints. To solve this non-convex problem, we decouple the original problem into two sub-problems, namely, receiver filter coefficient design, and power allocation. The receiver filter coefficient design is formulated as a generalized eigenvalue problem whereas a successive convex approximation (SCA) and a heuristic sub-optimal scheme are exploited to convert the power allocation problem into a standard geometric programming (GP) problem. An iterative algorithm is proposed to alternately solve each sub-problem. Complexity analysis and convergence of the proposed schemes are investigated. Numerical results indicate the superiority of the proposed algorithms over the case of equal power allocation.

Robust Transmission for Massive MIMO Downlink With Imperfect CSI

In this paper, the design of robust linear precoders for the massive multi-input-multi-output (MIMO) downlink with imperfect channel state information (CSI) is investigated. The imperfect CSI for each UE obtained at the BS is modeled as statistical CSI under a jointly correlated channel model with both channel mean and channel variance information, which includes the effects of channel estimation error, channel aging, and spatial correlation. The design objective is to maximize the expected weighted sum-rate. By combining the minorize–maximize (MM) algorithm with the deterministic equivalent method, an algorithm for robust linear precoder design is derived. The proposed algorithm achieves a stationary point of the expected weighted sum-rate maximization problem. To reduce the computational complexity, two low-complexity algorithms are then derived. One for the general case, and the other for the case when all the channel means are zeros. For the later case, it is proved that the beam domain transmission is optimal, and thus the precoder design reduces to the power allocation optimization in the beam domain. Simulation results show that the proposed robust linear precoder designs apply to various mobile scenarios and achieve high spectral efficiency.

Opportunistic source‐pair selection method with imperfect channel state information for multiuser bi‐directional relaying networks

This study investigates the impact of imperfect channel state information that is caused by feedback delay with time-variant channels and also by channel estimation errors with an opportunistic source-pair selection strategy. The investigation considers multi-user bi-directional wireless relaying networks. The opportunistic source-pair selection strategy selects the appropriate source-pair node among N available nodes. The selection strategy is based on each source pair's maximum sum-rate in each time slot. According to analytical, asymptotic, and Monte–Carlo simulation results, the opportunistic source-pair selection strategy, besides achieving a near-optimal solution for inter-cell interference that is caused by other user-pairs in the system model, also achieves diversity order in high signal-to-noise regimes. Moreover, the opportunistic source-pair selection strategy outperforms the max–min-based selection strategy in such a system model. Results also show that feedback delay degrades the achievable diversity order from N to 0 while affecting coding gain. The results also show that the channel estimation error case does not affect the achievable diversity order, but it does affect the system coding gain in low-signal-to-noise regimes. Moreover, the channel estimation error effects upon system coding gain become negligible at high-signal-to-noise regimes.

Performance Analysis of Nonlinear SFBC OFDM Systems Over TWDP Fading Channel

In this paper, the practical performance of space-frequency block code (SFBC)-based multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the presence of nonlinear power amplifier with imperfect channel state information (CSI) over two-wave with diffuse power (TWDP) channel is analyzed. In the performance analysis, we first introduce the equivalent single-input single-output (SISO) scalar model with nonlinear power amplifier and then the SISO model is used to construct a model for the nonlinear MIMO-OFDM system. Considering the channel estimation error at the receiver, we study the effects of MMSE channel estimation error on the channel capacity. What is more, based on inter modulation product (IMP) analysis, we study the BER performance of nonlinear SFBC MIMO-OFDM systems, considering M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM). And the effects of channel estimation error on the BER performance are studied. Finally, this paper also derives the closed-form expressions of the system optimal operating point. The numerical results and comparisons are provided for several forms of SFBC MIMO-OFDM. From these analysis results, it is found that the analytical interpretation of the observed behavior in the simulation can be advanced, and the actual analysis of the performance optimization of the nonlinear MIMO-OFDM system is also provided.

Secrecy Rate Analysis of Opportunistic User Scheduling in Uplink Networks With Potential Eavesdroppers

In this paper, we investigate two user scheduling algorithms (optimal user and threshold-based user scheduling algorithms) when we consider potential eavesdroppers in an uplink wiretap network. The optimal user scheduling (OUS) algorithm selects the user who has the maximum secrecy rate, based on channel feedback from all users. On the other hand, the threshold-based user scheduling (TUS) algorithm first considers the information leakage from the users to potential eavesdroppers and then selects the user among candidates who satisfy a threshold criterion on the information leakage. The OUS algorithm shows an optimal performance in terms of secrecy rate, but the TUS algorithm can achieve secrecy rate comparable with the OUS algorithm with reduced feedback overhead. For main contributions, we mathematically analyze the asymptotic behavior of the achievable secrecy rate of two scheduling algorithms when the signal-to-noise ratio (SNR) approaches to infinity. Further, we derive the approximated secrecy rate of the TUS algorithm and propose criteria to determine threshold values which maximize the achievable secrecy rate of the TUS algorithm. We verify our analytical results through simulations. We perform an extra simulation to investigate the effect of channel estimation error in the wiretap links on the average secrecy rate. Due to different scheduling principles in OUS and TUS schemes, the TUS scheme yields robustness against the channel estimation error in the wiretap links, compared with the OUS schemes.

Multi-Cell Massive MIMO Uplink With Underlay Spectrum Sharing

The achievable rates are investigated for multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with underlay spectrum sharing. A general pilot sharing scheme and two pilot sequence designs (PSDs) are investigated via fully shared (PSD-1) and partially shared (PSD-2) uplink pilots. The number of simultaneously served primary users and secondary users (SUs) in the same time-frequency resource block by the PSD-1 is higher than that of PSD-2. The transmit power constraints for the SUs are derived to mitigate the secondary co-channel interference (CCI) inflicted at the primary base-station (PBS) subject to a predefined primary interference temperature (PIT). The optimal transmit power control coefficients for the SUs with max–min fairness and the common achievable rates are derived. The cumulative detrimental effects of channel estimation errors, CCI and intra-cell/inter-cell pilot contamination are investigated. The secondary transmit power constraint and the achievable rates for the perfect channel state information (CSI) case become independent of the PIT when the number of PBS antennas grows unbounded. Therefore, the primary and secondary systems can be operated independent of each other as both intra-cell and inter-cell interference can be asymptotically mitigated at the massive MIMO PBS and secondary base-station. Nevertheless, the achievable rates and secondary power constraints for the imperfect CSI case with PSD-1 are severely degraded due to the presence of intra-cell and inter-cell pilot contamination. These performance metrics depend on the PIT even in the asymptotic PBS antenna regime. Hence, the primary and secondary systems can no longer be operated independently for imperfect CSI with PSD-1. However, PSD-2 provides an achievable rate gain over PSD-1 despite the requirement of lengthier pilot sequences of the former than that of the latter.

Approximation for the ML detector in decode and forward relay networks and the effect of channel estimation error

The cooperative maximum ratio combiner (C-MRC) is able to collect the maximum available diversity in decode and forward (DF) relay networks, and is simple to be implemented relative to the maximum likelihood (ML) detector. In this study, the authors provide some approximations for the ML detector, and they prove that the well-known C-MRC detector which was considered to be an intuitive method is, indeed, a linear approximation for the ML detector in DF relay networks. They also study the performance of the approximated ML detector in the presence of channel estimation error. This study determines the sensitivity of the diversity gain achieved by the approximated ML detector to the channel estimation error. Simulation results are also presented to corroborate the derived analytical results.

Massive MIMO Configurations for Multi-Cell Multi-User Relay Networks

The performance of massive multiple-input multiple-output (MIMO) configurations for multi-cell multi-user amplify-and-forward relay networks is investigated. Two massive MIMO signal processing techniques (SPT-1 and SPT-2) are proposed, and their computational complexity and performance gains are compared with multi-pair massive MIMO relaying (SPT-3) by deriving the partial and full achievable asymptotic sum rates for perfect and imperfect channel state information. Thereby, the cumulative effects of channel estimation errors, co-channel interference (CCI), and pilot contamination are investigated. The best relay selection for the multi-branch relaying is investigated. An optimal user power control algorithm based on max–min fairness is formulated, and thereby, the power allocation co-efficients and optimal common achievable user rate are derived in closed-form. Our analysis reveals that the effects of pilot contamination for the multi-cell massive MIMO relaying become more severe than that for the single-hop counterpart due to the multiple sources of CCI and propagation of residual interference in dual-hop transmissions.