Presence Of Imperfect Channel State Information Research Articles

Outage Performance of Underlay CR-NOMA-based D2D Communications under Imperfect CSI and SIC

Background: Non-orthogonal multiple access (NOMA) is a promising technique for improving wireless communication performance in the future. In addition to NOMA, cognitive radio (CR) is another technology that can address the issue of limited spectrum availability and meet the increasing demands for wireless connectivity. Methods: This paper focuses on investigating underlay CR-NOMA-based D2D communications. The study assumes a decode-and-forward (DF) mode used in the system, where nearby users (D1, D2) act as helper users to assist distant users (D3, D4). The paper derives the closed-form expressions for outage probability (OP) and throughput at the far users in three scenarios: (1) Perfect successive interference cancellation (SIC) and perfect channel state information (CSI), (2) Imperfect CSI, and (3) Imperfect SIC. Results: In CR-NOMA mode, the results indicate that the performance of user D4 was better than user D3. Additionally, the OP performance of distant users employing CR-NOMA mode surpasses that of users using CR-OMA mode. The optimal power allocation (PA) values are investigated. Conclusion: The presence of imperfect CSI and SIC has an unfavorable influence on the outage performance. Monte Carlo simulations are used to validate the derived analytical expressions.

A Cooperative Deception Strategy for Covert Communication in Presence of a Multi-Antenna Adversary

Covert transmission is investigated for a cooperative deception strategy, where a cooperative jammer (Jammer) tries to attract a multi-antenna adversary (Willie) and degrade the adversary’s reception ability for the signal from a transmitter (Alice). For this strategy, we formulate an optimization problem to maximize the covert rate when three different types of channel state information (CSI) are available. The total power is optimally allocated between Alice and Jammer subject to the Kullback-Leibler (KL) divergence constraint, which can be expressed analytically and be widely used as a covertness measurement. Different from the existing literature, in our proposed strategy, we also determine the optimal transmission power at the jammer when Alice is silent, while existing works always assume that the jammer’s power is fixed. Specifically, we apply the S-procedure to convert infinite constraints into linear-matrix-inequalities (LMI) constraints. When statistical CSI at Willie is available, we convert double integration to single integration using asymptotic approximation and substitution method. Finally, our simulation results show that for the proposed strategy, the covert rate is increased with the number of antennas at Willie. Moreover, compared to the benchmark, our proposed strategy is more robust in the presence of imperfect CSI.

Transmit Antenna Selection in NOMA-Based Integrated Satellite-HAP-Terrestrial Networks With Imperfect CSI and SIC

Integrated satellite-high altitude platform-terrestrial networks (IS-HAP-TNs) and non-orthogonal multiple access (NOMA) scheme are considered to be the key components of next generation networks, which can satisfy the demands of high-quality transmission, wide coverage and large-scale connections. In this letter, we analyze the performance of NOMA-based IS-HAP-TNs with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) and successive interference cancellation (SIC). Specifically, considering the requirements of different users for spectrum efficiency, two TAS schemes are proposed to balance the system performance and complexity. In addition, the closed-form expressions for the outage probability of the IS-HAP-TNs in the presence of imperfect CSI and SIC are derived to verify the performance of different schemes. Besides, the asymptotic outage behavior and diversity orders at high signal-to-noise ratios are also presented to get further insights. Finally, Monte Carlo simulations manifest the advantages and disadvantages characters of two schemes and reveal the impacts of key parameters on the system performance.

Robust MMSE Precoding and Power Allocation for Cell-Free Massive MIMO Systems

We consider the downlink of a cell-free massive multiple-input multiple-output (MIMO) system with single-antenna access points (APs) and single-antenna users. An iterative robust minimum mean-square error (RMMSE) precoder based on generalized loading is developed to mitigate interference in the presence of imperfect channel state information (CSI). An achievable rate analysis is carried out and optimal and uniform power allocation schemes are developed based on the signal-to-interference-plus-noise ratio. An analysis of the computational costs of the proposed RMMSE and existing schemes is also presented. Numerical results show the improvement provided by the proposed RMMSE precoder against linear minimum mean-square error, zero-forcing and conjugate beamforming precoders in the presence of imperfect CSI.

Power Allocation Schemes for Uplink Massive MIMO System in the Presence of Imperfect CSI

In this paper, spectrum efficiency (SE) and energy efficiency (EE) performances of uplink massive multiple-input multiple-output (MIMO) systems with continuous-rate adaptive modulation and imperfect channel state information (CSI) are investigated over Rayleigh fading channels. Given a target BER, closed-form SE and EE expressions are derived. With these results, a constrained non-concave optimization problem of power allocation (PA) to maximize the SE is firstly formulated subject to the maximum transmit power per user. A near-optimal PA scheme with the concave-convex procedure (CCCP) method is then developed, and it can offer nearly optimal performance close to that of the optimal scheme with exhaustive search, but require lower complexity. Since this scheme needs more iterations, we propose a suboptimal scheme with reduced complexity and slight performance loss, which utilizes the property of a large number of receive antennas to approximate the objective function as a concave one, thereby reducing the number of iterations. Secondly, the PA problem for EE maximization under the same constraints is addressed. Based on the CCCP method and fractional programming theory, we propose a near-optimal PA scheme to solve this problem, and it has the EE performance very close to the optimal exhaustive search scheme. However, multi-layer iterations make this scheme have relatively higher complexity. For this reason, we propose a low-complexity suboptimal scheme with small EE loss by using variable transformation and a large number of antennas. Based on the above results, we simultaneously optimize both EE and SE. A multi-objective optimization problem (MOP) subject to the maximum power constraint and proportional data rate constraint is formulated. By means of the weighted sum method, the complicated MOP is transformed into a simple single-objective optimization problem. Then a PA scheme is proposed by using the Lagrange multiplier method to balance the EE and SE effectively. Simulation results validate the effectiveness of the proposed PA schemes in term of high SE and EE, and illustrate the fundamental tradeoff between EE and SE for different parameter settings.

Robust Linear Beamforming in Wireless Sensor Networks

A typical wireless sensor network (WSN) has multiple sensors, each of which obtains noisy observation of one common physical event and sends the observation to a fusion center (FC) for post-processing. This paper provides a comprehensive research on robust linear transceiver design in the presence of imperfect channel-state information (CSI) in multi-input multi-output (MIMO) WSNs. For the CSI uncertainty, the classical ellipsoid model is assumed, where channel estimation errors live in an ellipsoid. Two robust beamforming problems are considered: 1) the worst-case mean-square-error (MSE) minimization with limited power and 2) sum-power minimization with guaranteed worst-case MSE. For both problems, centralized and decentralized solutions are developed. Moreover, an interesting fundamental relation between the metrics of signal-to-noise ratio (SNR) and MSE has been presented, which extends our proposed solutions to handle the transceiver design when SNR is considered. Extensive numerical results are presented to confirm our findings.

Low‐overhead constant envelope precoding in multi‐cell massive MIMO systems with pilot contamination

The authors consider downlink transmission in a multi-cell massive multiple-input and multiple-output (MIMO) system and focus on decreasing the feedback overhead caused by cell cooperation in constant envelope precoding (CEP). In the literature, the single-cell case for CEP with perfect channel state information (CSI) has been studied. Here, considering full cooperation among the cells, they develop CEP for the multi-cell case. They devise a low overhead centralised construction for CEP which employs limited cooperation among the cells, providing higher system throughput. To achieve the minimum feedback overhead, a distributed realisation of CEP is proposed where each cell locally performs CEP. Furthermore, a new optimisation problem is solved to compensate for the effects of pilot contamination. In addition, to reduce the computational complexity, a relaxed iterative form is presented for the limited cooperation and the distributed scenarios. Numerical results show that in the proposed structures, despite a tremendous decrease in the system overhead, the performance confronts merely an insignificant degradation, <10%, compared to the full-cooperation case. Moreover, in the presence of imperfect CSI, the performance of the distributed structure whose imperfect CSI is compensated for, approaches the performance of this structure in the perfect CSI scenario.

Full/Half Duplex Cooperative NOMA Under Imperfect Successive Interference Cancellation and Channel State Estimation Errors

This paper investigates the application of non-orthogonal multiple access (NOMA) in a coordinated direct and relay transmission (CDRT) system, where the base station (BS) directly communicates with the near (i.e., cell-centric) user, while it requires the help of a dedicated full duplex (FD) relay to communicate with the far (i.e., cell-edge) user. For the considered NOMA-FD-CDRT system, we derive closed-form expressions for the outage probabilities and ergodic rates experienced by the downlink users, under the realistic assumptions of imperfect channel state information (I-CSI) and imperfect successive interference cancellation (I-SIC). Expressions for system outage probability and ergodic sum rate are also presented. The links are assumed to experience independent, non-identically distributed Nakagami-m fading. The analysis of outage probabilities are carried out for both integer and non-integer values of the fading severity index. Extensive simulation results are described to validate the accuracy of analytical results, and to illustrate the performance gain of the considered system, as compared to NOMA-HD-CDRT system and the orthogonal multiple access (OMA) based CDRT system. Our results show that, both channel estimation error variance and I-SIC factor have significant impact on the performance of the considered NOMA-FD/HD-CDRT system. Further, to ensure fairness in terms of outage, we numerically determine the power allocation coefficient at the BS that provides equal outage performance for both the near and the far users in the presence of I-CSI and I-SIC. Furthermore, we derive closed-form expression for the optimal power allocation (OPA) coefficient at the BS that minimizes the system outage probability of the NOMA-FD/HD-CDRT network under I-CSI. With the help of numerical and simulation investigations, we establish that the proposed OPA significantly reduces the system outage probability, as compared to random (i.e., non-optimal) power allocation at the BS.

BER performance of an MRT‐HQAM system over Rayleigh fading channels with channel estimation errors and feedback delay

In this study, the bit error rate (BER) performance of multiple-input-multiple-output (MIMO) hierarchical quadrature amplitude modulation systems employing maximum ratio transmission (MRT-HQAM) is investigated under the effects of imperfect channel state information (ICSI) due to the channel estimation error and feedback delay. Theoretical expressions for the BER performance of the MRT-HQAM systems are derived using the two common ICSI models that exist in the current literature, specifically when studying the MIMO beam-forming systems with ICSI, where the error term due to the ICSI is assumed to contribute to either the noise component or to the signal component. The BER results for the two ICSI models are presented and then compared. In addition, various antenna configurations are studied to illustrate the performance gains achievable with additional antennas, and to identify the ideal antenna configuration for a given number of antennas. Moreover, the hierarchical modulation parameter is varied to determine the varying levels of sensitivity of the hierarchical layers in the presence of ICSI. The theoretical BER expressions provided for both ICSI models are verified by simulation results.

Performance analysis of cross layer design with imperfect channel information in distributed antenna systems

In this paper, based on the imperfect channel state information (CSI), a cross layer design (CLD) scheme is developed for distributed antenna system (DAS) by combining adaptive modulation (AM) at the physical layer and automatic repeat request (ARQ) at the data link layer. The performance of DAS with CLD is investigated over composite fading channel which considers large-scale path loss and small-scale Rayleigh fading. With the performance analysis, the probability density function of the estimated signal-to-noise ratio (SNR) is derived, and then, the switching thresholds under a target packet error rate constraint are further derived. According to these results, and using numerical calculation, the closed form analytical expressions of average packet error rate and spectrum efficiency of DAS with CLD are, respectively, achieved, which will provide better evaluation way for the DAS performance. To decrease the performance loss caused by the conventional single estimation in the presence of imperfect CSI, the multi-estimation method is proposed to increase the system performance by exploiting previous channel estimation information. Numerical results corroborate our theoretical analysis, and the simulation is in consistence with the theoretical result. Moreover, the system performance can be increased by decreasing the estimation error and/or path loss. Especially, the multi-estimation method can enhance the performance effectively and enable the system to tolerate large estimation errors.

Secrecy Performance Analysis of Artificial-Noise-Aided Spatial Modulation in the Presence of Imperfect CSI

The security of information over wireless channels has always been an important aspect of wireless communication research. In this paper, the secrecy performance of a spatial modulated system with an artificial noise is investigated over the Rayleigh channel, and the corresponding secrecy rate is analyzed in the presence of imperfect channel state information (CSI). Based on the secrecy performance analysis, the ergodic rates and the corresponding lower bounds of the legitimate receiver and eavesdropper are, respectively, derived. As a result, the closed-form lower bound of ergodic rate of the legitimate receiver is obtained, and the lower bound of ergodic rate of the eavesdropper and the corresponding ergodic secrecy rate (ESR) can be achieved by calculating the mean values. To avoid the mean operation and reduce the complexity, the closed-form approximated expression of ESR is also derived. This theoretical ESR can include the one under perfect CSI as a special case and has the value close to the corresponding simulation. Thus, it can provide good performance evaluation for the artificial-noise-aided spatial modulation system with imperfect CSI. Simulation results verify the effectiveness of the theoretical analysis. The system with imperfect CSI is found to have low ESR as compared to the one with perfect CSI due to the estimation error. Moreover, initially, the ESR increases with increasing power of artificial noise, but then, due to the total power constraint, it starts decreasing.

Impact of estimation error on two-way relaying with relay antenna selection

Abstract This paper presents the performance analysis of two-time-slot two-way relaying while considering dual antennas at the relay and imperfect channel state information (CSI) at the receivers. We consider the Max–Min antenna selection scheme at the relay. For this scheme, we show the analytical symbol error probability in the presence of imperfect CSI and observe a close match between the analytical and numerical results. We also find that Max–Min antenna selection scheme is robust against CSI error and performs better than the maximum ratio transmission (MRT) based beamforming scheme in the presence of CSI error.

Energy-Efficient Green Wireless Communication Systems With Imperfect CSI and Data Outage

Modern applications involve green communication technologies motivating well optimization in the power-limited regime. In comparison with most of the existing related work that assumes perfect channel state information (CSI) is always available, which is unfortunately not true in reality, this paper focuses on an optimal energy-efficient solution for resource allocation in multiuser orthogonal frequency division multiple access networks in the presence of imperfect CSI and data outage conditions. In particular, in view that wireless channel conditions, circuit power consumptions, and users’ quality-of-service (QoS) requirements are heterogeneous in nature, we enable attractive tuning options by letting energy efficiency optimization objective to assign weights to each allocation link. In addition, we interpret the effects of data outage due to imperfect CSI using a profound insight on the monotonicity of noncentral chi-squared inverse distribution function, which reveals that our design complies with expected physics and mechanics of conventional energy efficiency approach and that it can be successfully degenerated to the energy-efficiency model with perfect CSI. Furthermore, we formulate a mixed combinatorial problem toward maximizing the energy efficiency subject to a minimum QoS requirement, channel interference, and transmitting power constraints. The problem is transformed into an equivalent quasi-concave problem with respect to power, and concave problem with respect to the subcarrier indexing coefficients using the concept of subcarrier time sharing. We optimize through a simple and versatile methodology, which uses standard-Lagrangian optimization technique to obtain joint dynamic subcarrier and adaptive power allocations by means of final formulas. We also examine key properties of the introduced optimal solution in terms of implementation convergence and complexity, level of optimality, and impact of imperfect CSI coefficients and circuit power on network performance. The simulation results demonstrate the effectiveness of our allocation scheme for achieving higher energy efficiency performance with the guaranteed QoS support and lower complexity than the existing approaches especially when perfect CSI is not available.

Adaptive coding and modulation using imperfect CSI in cognitive BIC-OFDM systems

This work investigates adaptive coding and modulation (ACM) algorithms under the realistic assumption that the available channel state information (CSI) at the transmitter is imperfect due to estimation errors and/or feedback delays. First, we introduce an optimal performance metric for the secondary user (SU) bit-interleaved coded orthogonal frequency division multiplexing (BIC-OFDM) system, called the expected goodput (EGP). By using an accurate modeling approximation, we succeed in deriving a tractable and very accurate approximation for the EGP. This approximate EGP (AEGP) is then used for the derivation of several ACM algorithms which optimize the code rate and bit and energy allocation under a constraint on the interference caused to the PU network. In the numerical results, we show that the AEGP is far more accurate than previous attempts to model the GP in the presence of imperfect CSI. Further, we verify that, in spite of the imperfect nature of the available CSI, the derived ACM algorithms significantly increase the goodput of the SU network, compared to a non-adaptive selection of the transmission parameters.

Performance of heterogeneous multiuser MIMO system with cross-layer design and multiple outdated estimations in Rayleigh fading channel

By combining adaptive modulation and automatic repeat request protocol as well as user scheduling, a cross-layer design (CLD) scheme for multiuser MIMO system with the normalized signal-to-noise ratio (SNR)-based scheduling under heterogeneous case is developed, where perfect and imperfect channel state information (CSI) are both considered. Based on this, by exploiting previous channel estimation information, the multiple outdated estimates method is presented to improve the system performance under imperfect CSI. According to the performance analysis and the normalized-SNR based scheduling scheme, the average spectral efficiency (SE) and packet error rate (PER) of the system are derived, respectively. As a result, closed-form SE and PER expressions are attained. These expressions include the ones with conventional single outdated estimate as special cases, and can provide good performance evaluation for the multiuser CLD system under heterogeneous case. Simulation results show that the derived theoretical SE and PER are in consistent with the corresponding simulations. Moreover, the presented CLD scheme with multiple estimates can provide higher SE and lower PER than that with conventional single estimate in the presence of imperfect CSI. Besides, multiuser MIMO-CLD has superior performance over the conventional single user counterpart due to the multiuser diversity.

Energy‐efficiency resource allocation for cognitive heterogeneous networks with imperfect channel state information

In this study, the authors focus on the downlink resource allocation to optimise energy-efficiency (EE) of orthogonal frequency division multiplexing-based cognitive heterogeneous network (HetNet), where network service providers operate multi-radio access technologies. A more practical case is considered, in which imperfect channel state information (CSI) is available for wireless channels between secondary base stations and secondary users (SUs), primary users (PUs). Since imperfect CSI may result in outage in secondary networks and make collision occur in primary networks, a joint subcarrier and power allocation scheme for the cognitive HetNet is proposed to guarantee quality of service requirements for both SUs and PUs in probabilistic manners. Then the probabilistic EE optimisation scheme is approximated into a deterministic convex form, and the optimal solutions for the scheme are derived by double-loop iteration method. Afterwards, the authors develop a low-complexity algorithm in the presence of imperfect CSI with a small reduction of system performance. Simulation results are provided to show the impact of channel estimation error on the EE optimisation problem and to highlight the performance improvement from considering channel estimation error in the joint subcarrier and power allocation scheme for the cognitive HetNet system.

Performance analysis of MIMO systems with arbitrary number transmit antenna selection and OSTBC in the presence of imperfect CSI

In this paper, the performance analysis of MIMO systems with arbitrary number transmit antenna selection (TAS) and orthogonal space-time block coding (STBC) in Rayleigh fading channels for imperfect channel state information (CSI) is presented. For the performance analysis, the moment generating function of the system effective SNR as well as its upper and lower bounds are derived. Then, accurate and approximate expressions of bit error rate (BER) of MIMO-TAS-STBC with MPSK and MQAM are further derived. Using the approximate BER formula and imperfect CSI, an adaptive antenna selection scheme is developed for minimizing the BER. The diversity gain and coding gain are analyzed at high SNR. The results indicate that the MIMO-TAS-STBC for imperfect CSI can only achieve partial diversity order $KN$ and the coding gain is affected by $K$, $N$, code rate, modulation pattern, and channel correlation coefficients, when $K$ transmit antennas are selected and $N$ receive antennas are used. Simulation results show that the theoretical analysis matches the simulation result well, and the approximate expressions are close to the accurate ones but have a lower complexity.

Unitary Beamformer Designs for MIMO Interference Broadcast Channels

Interference broadcast channel (IBC) is a generalized scenario for interference channel (IC) where each base station (BS) transmits to multiple users in its own cell while sharing same time-frequency resources with other adjacent BSs. In this case, it has been shown that by using interference alignment (IA) and under the availability of perfect channel state information (CSI), the achievable degrees of freedom (DoFs) can be linearly scaled up with the number of users. However, in the presence of imperfect CSI, the sum rate becomes degraded, and the achievability of full DoF can not be guaranteed. In this paper, considering a multiple-input-multiple-output (MIMO) IBC with constant channel coefficients, we propose IA algorithms that result in unitary beamformers. First, we consider two improved beamformer designs based on minimizing the weighted-leakage interference (Min-WLI) and maximizing the signal-to-interference-plus-noise ratio (Max-SINR). Second, we propose a novel minimum-mean-square-error (MMSE)-based IA algorithm. Both the improved Max-SINR and the MMSE-based IA schemes are optimized upon the knowledge of the channel estimation error variance so as to achieve better performance under CSI mismatch. We then demonstrate that these two schemes outperform Min-WLI and the conventional Max-SINR IA under perfect and imperfect CSI. Furthermore, it is shown that the MMSE-based IA achieves the same performance trend as the improved Max-SINR IA does; however, the former needs less CSI to be available and has less computational complexity compared to the latter. Moreover, it is established that the MMSE-based IA can result in diagonalized, decoupled subchannels under perfect CSI. The superiority of the proposed algorithms over the conventional schemes is corroborated by numerical simulations.

Adaptive LS- and MMSE-Based Beamformer Design for Multiuser MIMO Interference Channels

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

High Mobility Wireless Communications With Doppler Diversity: Fundamental Performance Limits

The objective of this paper is to quantify the fundamental tradeoff between Doppler diversity and channel estimation errors in high mobility systems. Fast fading variation in high mobility systems introduces Doppler diversity that can benefit system performance. On the other hand, it is more difficult to estimate and track a fast changing channel, thus channel estimation errors are non-negligible and they may seriously degrade system performance. Such a tradeoff relationship is studied by identifying the exact analytical expressions of two performance metrics: the maximum Doppler diversity order achievable with imperfect channel state information (CSI), and the loss in signal-to-noise ratio (SNR) caused by channel estimation errors. The analytical study is enabled by a simple repetition code at the transmitter, and a new optimum diversity receiver developed by analyzing the statistical properties of channel estimation errors. With the analytical results, the optimum allocation of transmission energy between pilot symbols and data symbols are obtained to simultaneously maximize the Doppler diversity order and minimize the SNR loss, thus achieve the optimum tradeoff between the two. The results reveal the fundamental performance limits of Doppler diversity systems operating in the presence of imperfect CSI, and they can be used to guide the design of practical systems.