Channel Estimation Error Research Articles

Dual-Driven Learning-Based Multiple-Input Multiple-Output Signal Detection for Unmanned Aerial Vehicle Air-to-Ground Communications

Unmanned aerial vehicle (UAV) air-to-ground (AG) communication plays a critical role in the evolving space–air–ground integrated network of the upcoming sixth-generation cellular network (6G). The integration of massive multiple-input multiple-output (MIMO) systems has become essential for ensuring optimal performing communication technologies. This article presents a novel dual-driven learning-based network for millimeter-wave (mm-wave) massive MIMO symbol detection of UAV AG communications. Our main contribution is that the proposed approach combines a data-driven symbol-correction network with a model-driven orthogonal approximate message passing network (OAMP-Net). Through joint training, the dual-driven network reduces symbol detection errors propagated through each iteration of the model-driven OAMP-Net. The numerical results demonstrate the superiority of the dual-driven detector over the conventional minimum mean square error (MMSE), orthogonal approximate message passing (OAMP), and OAMP-Net detectors at various noise powers and channel estimation errors. The dual-driven MIMO detector exhibits a 2–3 dB lower signal-to-noise ratio (SNR) requirement compared to the MMSE and OAMP-Net detectors to achieve a bit error rate (BER) of 1×10−2 when the channel estimation error is −30 dB. Moreover, the dual-driven MIMO detector exhibits an increased tolerance to channel estimation errors by 2–3 dB to achieve a BER of 1×10−3.

Covert performance enhancement in NOMA enabled CoMP network with optimal RIS selection

In this paper, we consider the covert rate maximization problem for the cell edge user in a reconfigurable intelligent surface (RIS) aided downlink non-orthogonal multiple access (NOMA) network with coordinated multipoint (CoMP) transmission in the presence of channel estimation errors. We derive the analytical expression for the detection error probability (DEP) at the adversary (Willie) assuming the worst case scenario where they employ optimal detection threshold. With the derived analytical expression, we propose an optimal RIS selection scheme to boost the covert rate. To further improve the covert performance, we optimize the NOMA power allocation coefficients and phase shifts of the selected RIS subject to the target rate and covertness constraints. Simulation results demonstrate the improvement in covert rate and robustness offered by the proposed scheme in the presence of channel estimation errors over other benchmarks.

Robust Beamforming for Downlink Multi-Cell Systems: A Bilevel Optimization Perspective

Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming technique that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.

Non-orthogonal pilot pattern design and sparse channel estimation for underwater acoustic MIMO-OFDM systems

This paper proposes a novel non-orthogonal pilot pattern design method for underwater acoustic (UWA) multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems, leveraging compressive sensing (CS) channel estimation. This approach adopts the mutual incoherence property (MIP) and enhances pilot density without increasing pilot overhead. We conducted rigorous mathematical derivation to generate the explicit formula for the non-orthogonal pilot pattern with the mutual coherence of zero. In addition, we estimate multipath delay and amplitude by employing parallel orthogonal matching pursuit (OMP) channel estimation. The co-channel interference (CCI) is eliminated from the systems with the proposed non-orthogonal pilot pattern to estimate the channel coefficients from two transmitters without interference in a single iteration. Simulations and lake trial results demonstrate the superior performance of the proposed non-orthogonal pilot pattern over the orthogonal and existing non-orthogonal pilot patterns in terms of normalized mean square error (NMSE) of channel estimation and bit error rate (BER). The 2×8 UWA MIMO-OFDM system achieves a data rate of 78.11 kbps with a BER of 1.42×10−4 in the lake trial over the communication distance of 773 m.

A Nonredundant SVD-based Precoding Matrix for Blind Channel Estimation in CP-OFDM Systems Over Channels with Memory

In this paper, we investigate blind channel estimation in cyclic, prefixed orthogonal frequency division multiplexing (OFDM) systems using precoding matrices. Many studies show how the performance of bit error rate (BER) and mean square error of channel estimation are impacted by using a circulant matrix as a precoding matrix. We investigate a new structure for the precoding matrix in which the first row is generated by an exponentially decreasing equation along with the Toeplitz function and deploying singular value decomposition (SVD) to generate the final precoder matrix. This type of SVD-based precoding matrix has been presented and simulated under various circumstances. The resulting precoding matrix is employed in two different OFDM systems to estimate the channel frequency response vector up to scalar ambiguity. The proof of the precoding matrix full rank property is presented, along with other criteria that help with the development of various precoding matrices.

Symbol-level precoding scheme robust to channel estimation errors in wireless fading channels

Most studies on symbol-level (SL) precoding have assumed that channel estimation is perfect. However, because interference signals or additive white Gaussian noise exist in the received signal for channel estimation, channel estimation errors always exist. In this paper, we propose an SL precoding scheme that is robust to channel estimation errors. First, using the characteristics of the channel estimation errors, we derive an equation for the worst-case mean squared error (MSE) which is the maximum of the MSE. Then by designing the SL precoding to minimize the worst-case MSE, it has robust characteristics against channel estimation errors.

Effective capacity of rate-splitting multiple access with channel estimation errors

In view of its advantages to adeptly reduce interference and low complexity, rate-splitting multiple access (RSMA) is emerging as an innovative framework for the next generation of the wireless communication networks. In this paper, we conduct the performance analysis of a two user RSMA network under delay constrains, taking channel estimation errors into account as well. Utilizing the effective capacity (EC) as our metric, we investigate the effects of delay on a pair of RSMA users. Specifically, we derive analytical expressions for the EC concerning both the near user (SRn) and the far user (SRf). Additionally, we offer asymptotic results under high signal-to-noise ratio (SNR) conditions. From our analysis, several noteworthy conclusions can be drawn and outlined below: (1) The effective capacities (ECs) of SRn and SRf exhibit improvement with SNR increasing, while at high SNR, the ECs of SRn and SRf converge to the constants. (2) Compared to the non-orthogonal multiple access, the considered RSMA network exhibits superior EC performance due to its inherent advantages in interference management. (3) The presence of channel estimation errors adversely affects EC performance of RSMA networks, with this impact being more pronounced in the high SNR regime.

Deep Learning-aided Channel Estimation Combined with Advanced Pilot Assignment Algorithm to Mitigate Pilot Contamination for Cell-Free Networks

Objectives: The performance of Cell-Free Massive Multiple Input Multiple Output (CFMM) is analyzed in this paper for its two bottlenecks i.e., Pilot Contamination (PC) and Channel Estimation Error (CEE). Methods: The CFMM network is strongly affected by PC which is one of the bottlenecks due to which quality of service and accuracy of channel estimation gets impacted. Therefore, we address this problem by presenting advanced pilot assignment algorithm to mitigate PC and deep learning aided channel estimation for reducing CEE for the CFMM systems to maximize spectral efficiency (SE). We derive achievable uplink and downlink SE expressions for the proposed system, and compare with Minimum Mean Square Error and Maximum Ratio combining techniques. As well, the performance is evaluated for different antenna configurations. The advanced pilot assignment algorithm is compared with greedy pilot assignment and random pilot assignment methods. The performance of cellular massive multiple input multiple output (MIMO) is derived for comparison. The performance of CFMM system is evaluated using MATLAB software. Findings: The UL and DL performance of the proposed system in terms of SE is 3.2 times higher than the conventional CFMM with MMSE and MR combining techniques. Average sum spectral efficiency of the proposed system increases with increase in number of access points (APs). Comparison with different antenna configurations reveals that, with 400 APs equipped with single antenna, only UE with good channel condition shows performance enhancement, but when each AP is equipped with 4 antennas, the UE with unfavourable channel condition also give better performance. Advanced pilot assignment scheme proves to be better than greedy and random pilot assignment techniques. For the same cellular set up, the proposed CFMM system achieves higher SE than the cellular massive MIMO. Novelty: Due to the advanced pilot assignment algorithm used in the proposed CFMM system, at a time, only one AP is selected and the selected AP with its full received power serves the desired UE, which suppresses interference resulting in improved SE performance. The serving AP is selected considering the distance between UE and AP, rather than using large scale fading coefficient which is the unique feature of pilot assignment algorithm. The proposed deep learning-aided channel estimation method, minimizes the mean square error (MSE) between the actual channel and the channel estimates obtained from the MMSE estimation resulting in reduction in channel estimation error. Thus, the use of the proposed advanced pilot assignment algorithm and deep learning-aided channel estimation method increase the SE performance of the CFMM system. Keywords: Cell­Free Massive Multiple Input Multiple Output, Pilot Contamination, Channel Estimation Error, Minimum Mean Square Error, Maximum Ratio

Performance analysis of OSSK-UWOC systems considering pointing errors and channel estimation errors.

In this paper, we present the bit error rate (BER) performance of the underwater wireless optical communication (UWOC) systems using the optical space shift keying (OSSK) on the gamma-gamma turbulent fading channel, which also considers pointing errors and channel estimation errors. Firstly, we develop the new expressions for the probability density function (PDF) based on the Gamma-Gamma distribution with error factors. Subsequently, we analyze the statistical characteristic of the difference in attenuation coefficients between two channels in the OSSK system, by which we provide analytical results for evaluating the average BER performance. The results show that the effective improvement of spectral efficiency (SE) and BER performance is achieved by rationally allocating the number of lasers and detectors in the system. The OSSK-UWOC system performs better when a narrow beam waist is used. Furthermore, the presence of channel estimation error brings the BER performance advantage to the system, and the system with a high channel estimation error (ρ = 0.7) shows a 4 dB improvement in signal-to-noise ratio (SNR) gain compared to the system with a low channel estimation error (ρ = 0.95). The findings in this paper can be used for the UWOC system design.

Performance analysis of inverse successive interference cancellation in NOMA-based communications

AbstractNon-orthogonal multiple access (NOMA) is a promising solution to enhance the spectral efficiency of sixth generation (6G) networks. NOMA enables multiple users to be concurrently served, relying on superposition coding at the transmitter and successive interference cancellation (SIC) at the receivers. However, in practice, hardware impairments and channel estimation errors will lead to incorrect signal ordering. This study analyses inverse successive interference cancellation (ISIC) in downlink power-domain NOMA networks. In the worst case, ISIC will inversely order the N received signals, compared to conventional SIC. First, ISIC will decode the signal with the minimum allocated power, while treating the other $$N-1$$ N - 1 signals as interference. This process is repeated $$N-1$$ N - 1 times and in the last step, the signal with the maximum allocated power will be decoded without interference. Various key performance metrics for ISIC are analytically derived, including the outage probability, throughput, error probability, ergodic rate, achievable sum-rate, energy and spectral efficiency. In order to provide further insights on ISIC, an asymptotic analysis is also provided. Comparisons with SIC reveal that for the signal with the second-lowest power allocation level, ISIC achieves better performance, while the performance of the information signal with the minimum allocated power is degraded. Overall, our findings shed light on the performance of NOMA in practical settings where SIC can not be correctly performed and focuses on the worst-case where the decoding order at the receiver is completely inversed.

Spectral decomposition-based optimization for MMSE receiver design in an uplink MU-MIMO cooperative communication system with imperfect CSI

The receiver’s architecture is always a critical issue in multiple-input multiple-output (MIMO) systems, as it has a great impact on the system’s performance and complexity. Accordingly, in this paper, a spectral decomposition-based minimum mean squared error (MMSE) receiver is proposed in an uplink multi-user MIMO (MU-MIMO) system with a full-duplex decode and forward relay. Imperfect channel state information is assumed at the relay and base station where, least-squares channel estimation technique is applied due to its simplicity and low complexity. An equivalent relay is applied for self-interference cancellation. While, multi-user interference is mitigated by using the block diagonalization concept. A closed-form expression for the mean squared error (MSE) of the estimated data symbol is derived in the presence of channel estimation error. Moreover, an optimization problem is solved to derive an expression for the proposed MMSE receiver’s matrix. Finally, the performance of the proposed receiver is compared to that of the conventional receiver and Zero-forcing (ZF) receiver. Results show the superiority of the proposed receiver over both receivers.

Outage constrained transmission design for NOMA-based integrated sensing and communication systems

This paper investigates a framework for integrated sensing and communication (ISAC) based on non-orthogonal multiple access (NOMA). In this framework, a dual-function base station (BS) utilizes NOMA technology to send superimposed signals to various users, and this superimposed signal also acts on target sensing simultaneously. Considering the channel estimation error, ensuring the communication performance, and sensing performance requirements, a transmit power optimization problem of ISAC system using NOMA is studied. Specifically, in the statistical channel state information (CSI) error model, the total system communicate power is minimized while ensuring all single users' rate outage probability (OP) constraints and the requirements for the beampattern gains of all single radar targets. Unfortunately, the proposed problem is challenging to solve and non-convex. But we have devised a feasible way to deal with this problem. First, we use Bernstein inequality to transform the rate OP constraint, and this challenging non-convex problem is then successfully solved using a method based on semi-definite relaxation (SDR). The numerical outcomes demonstrate that the system's overall transmission power will increase due to the channel estimation error. The numerical findings also show that the ISAC system performs better with NOMA assistance than with OMA when comparing the NOMA and OMA schemes.

Machine learning assisted adaptive LDPC coded system design and analysis

AbstractThis paper proposes a novel machine learning (ML) assisted low‐latency low density parity check (LDPC) coded adaptive modulation (AM) system, where short block‐length LDPC codes are used. Conventional adaptive modulation and coding (AMC) system includes fixed look‐up table method, which is also called inner loop link adaptation (ILLA) and outer loop link adaptation (OLLA). For ILLA, the adaptive capability is achieved by switching the modulation and coding modes based on a look‐up table using signal‐to‐noise ratio (SNR) thresholds at the target bit error rate (BER), while OLLA builds upon the ILLA method by dynamically adjusting the SNR thresholds to further optimize the system performance. Although both improve the system overall throughput by switching between different transmission modes, there is still a gap to optimal performance as the BER is comparatively far away from the target BER. Machine learning (ML) is a promising solution in solving various classification problems. In this work, the supervised learning based k‐nearest neighbours (KNN) algorithm is invoked for choosing the optimum transmission mode based on the training data and the instantaneous SNR. This work focuses on the low‐latency communications scenarios, where short block‐length LDPC codes are utilized. On the other hand, given the short block‐length constraint, we propose to artificially generate the training data to train our ML assisted AMC scheme. The simulation results show that the proposed ML‐LDPC‐AMC scheme can achieve a higher throughput than the ILLA system while maintaining the target BER. Compared with OLLA, the proposed scheme can maintain the target BER while the OLLA fails to maintain the target BER when the block length is short. In addition, when considering the channel estimation errors, the performance of the proposed ML‐LDPC‐AMC maintains the target BER, while the ILLA system's BER performance can be higher than the target BER.

Two-Timescale Transmission Design and RIS Optimization for Integrated Localization and Communications

Reconfigurable intelligent surfaces (RISs) have tremendous potential to boost communication performance, especially when the line-of-sight (LOS) path between the user equipment (UE) and base station (BS) is blocked. To control the RIS, channel state information (CSI) is needed, which entails significant pilot overhead. To reduce this overhead and the need for frequent RIS reconfiguration, we propose a novel framework for integrated localization and communications, where RIS configurations are fixed during location coherence intervals, while BS precoders are optimized every channel coherence interval. This framework leverages accurate location information obtained with the aid of several RISs as well as novel RIS optimization and channel estimation methods. Performance in terms of localization accuracy, channel estimation error, and achievable rate demonstrates the effectiveness of the proposed approach.

Robust Integrated Data and Energy Transfer Aided by Intelligent Reflecting Surfaces: Successive Target Migration Optimization Toward Energy Sustainability

Intelligent reflecting surfaces (IRSs) can actively adjust the wireless environment. However, accurate channel estimation on IRS-aided communication systems is difficult to obtain. Therefore, we study a robust beamforming design for an IRS-aided integrated data and energy transfer (IDET) with imperfect channel state information (CSI). Against the uncertain channel estimation error, we robustly design the transmit beamformers of the transmitter and the passive reflecting beamformer of the IRS to minimize the transmit power by satisfying both the wireless data transfer (WDT) and wireless energy transfer (WET) requirements for realising energy-sustainability in 6G. A successive target migration optimization (STMO) algorithm is proposed to obtain a robust design. The transmit covariance matrices are optimized by relaxing rank-one constraints, when a passive reflecting beamformer is given. Then, the target to minimize the transmit power is migrated to maximize the QoS requirements of energy users due to the fixed transmit power. A local optimal reflecting beamformer is obtained for improving the attainable WET performance, when the transmit covariance matrices are given. Finally, we prove that the rank-one transmit beamformers can always be found, which have the same WET and WDT performance as the transmit covariance matrices. The numerical results demonstrate the advantage of our design.

Bayesian Channel Estimation for Intelligent Reflecting Surface-Aided mmWave Massive MIMO Systems With Semi-Passive Elements

In this paper, we propose a Bayesian channel estimator for intelligent reflecting surface-aided (IRS-aided) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with semi-passive elements that can receive the signal in the active sensing mode. Ultimately, our goal is to minimize the channel estimation error using the received signal at the base station and additional information acquired from a small number of active sensors at the IRS. Unlike recent works on channel estimation with semi-passive elements that require both uplink and downlink training signals to estimate the UE-IRS and IRS-BS links, we only use uplink training signals to estimate all the links. To compute the minimum mean squared error (MMSE) estimates of all the links, we propose a novel variational inference-sparse Bayesian learning (VI-SBL) channel estimator that performs approximate posterior inference on the channel using VI with the mean-field approximation under the SBL framework. The simulation results show that VI-SBL outperforms the state-of-the-art baselines for IRS with passive reflecting elements in terms of the channel estimation accuracy and training overhead. Furthermore, VI-SBL with semi-passive elements is shown to be more spectral- and energy-efficient than the baselines with passive reflecting elements.

Preset Conditional Generative Adversarial Network for Massive MIMO Detection

In recent years, extensive research has been conducted to obtain better detection performance by combining massive multiple-input multiple-output (MIMO) signal detection with deep neural network (DNN). However, spatial correlation and channel estimation errors significantly affect the performance of DNN-based detection methods. In this study, we consider applying conditional generation adversarial network (CGAN) model to massive MIMO signal detection. First, we propose a preset conditional generative adversarial network (PC-GAN). We construct the dataset with the channel state information (CSI) as a condition preset in the received signal, and train the detector without direct involvement of CSI, which effectively resists the impact of imperfect CSI on the detection performance. Then, we propose a noise removal and preset conditional generative adversarial network (NR-PC-GAN) suitable for low-signal-to-noise ratio (SNR) communication scenarios. The noise in the received signal is removed to improve the detection performance of the detector. The numerical results show that PC-GAN performs well in spatially correlated and imperfect channels. The detection performance of NR-PC-GAN is far superior to the other algorithms in low-SNR scenarios.

Performance evaluation of L‐maximal ratio combining diversity with estimation error for Shadowed Beaulieu‐Xie fading channels

SummaryTo provide the increasing demand for wireless technologies, high capacity with lower latency is vital. New emerging technologies like 5G, millimeter wave, THz, and so forth are able to characterize such complex fading and shadowed environments. Spatial diversity is one of the techniques to minimize fading in the wireless communication channel. The performance of the wireless communication system can be further optimized by using estimators at the receivers. The influence of imperfect channel estimation on the performance over shadowed Beaulieu‐Xie (SBX) fading channels with L‐maximal ratio combining (MRC) diversity is studied. The probability density function (PDF) of the received output signal‐to‐noise ratio (SNR) with L‐MRC over SBX fading channels is derived. Further PDF of the received output SNR, outage probability, and average bit error rate (ABER) using the derived PDF is evaluated for L‐MRC diversity with channel estimation error over SBX fading channels. ABER expression for Gray‐coded rectangular quadrature amplitude modulation over the SBX channel is also evaluated. The study also includes how the system performs under the effect of different shadowing and fading parameters.

Analysis of Coded Slotted ALOHA With Energy Harvesting Nodes for Perfect and Imperfect Packet Recovery Scenarios

We analyze the performance of Coded Slotted ALOHA (CSA) protocols in scenarios where users are equipped with limited batteries that are recharged through Energy Harvesting (EH). First, we assume a Perfect Packet Recovery Scenario (PPRS) for which the received packets are decoded with no errors when there is no interference. We introduce Battery Outage Probability (BOP) as an extra performance metric; and, we derive the optimal EH-CSA transmission policies, which offer the maximum attainable traffic load while maintaining an asymptotically negligible Packet Loss Ratio (PLR), under specific rate and BOP constraints. We extend our study to Imperfect Packet Recovery Scenario (IPRS) where impairments at the physical layer, including channel estimation and channel decoding errors, will distort messages being passed through the iterative Successive Interference Cancellation (SIC) process. The distorted messages being passed through the SIC process potentially lead to error propagation. In order to track the error propagation process, we define the concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Accumulated Noise plus Interference Power</i> (ANIP), and analytically track the evolution of its probability distribution. We employ our results to evaluate the bit error rates for different transmission policies for the case of IPRS. We also demonstrate the advantages of the optimal transmission policies through numerical examples for both PPRS and IPRS. Our results show that the optimal EH-CSA policies outperform the policies optimized for standard CSA without EH considerations, and the schemes that are optimal for PPRS are not necessarily optimal for the IPRS case. Furthermore, the EH-CSA optimal policies strictly outperform standard CRDSA when the system is required to support higher traffic loads.

Detecting Abrupt Change in Channel Covariance Matrix for MIMO Communication

The acquisition of the channel covariance matrix is of paramount importance to many strategies in multiple-input-multiple-output (MIMO) communications, such as the minimum mean-square error (MMSE) channel estimation. Therefore, plenty of efficient channel covariance matrix estimation schemes have been proposed in the literature. However, an abrupt change in the channel covariance matrix may happen occasionally in practice due to the change in the scattering environment and the user location. Our paper aims to adopt the classic change detection theory to detect the change in the channel covariance matrix as accurately and quickly as possible such that the new covariance matrix can be re-estimated in time. Specifically, this paper first considers the technique of on-line change detection (also known as quickest/sequential change detection), where we need to detect whether a change in the channel covariance matrix occurs at each channel coherence time interval. Next, because the complexity of detecting the change in a high-dimension covariance matrix at each coherence time interval is too high, we devise a low-complexity off-line strategy in massive MIMO systems, where change detection is merely performed at the last channel coherence time interval of a given time period. Numerical results show that our proposed on-line and off-line schemes can detect the channel covariance change with a small delay and a low false alarm rate. Therefore, our paper theoretically and numerically verifies the feasibility of detecting the channel covariance change accurately and quickly in practice.