In this paper, the covert performance of the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided Terahertz (THz) communication systems with rate-splitting multiple access (RSMA) over the generalized α-μ fading channel is studied, where the discrete phase error and noise power uncertainty are considered. By means of the Gaussian approximation and Gamma distribution, the closed-form outage probability (OP) of the legitimate users is firstly derived. Then, the covert performance of the system is analyzed, and average detection error probability (ADEP) is deduced for the warden, and resultant closed-form ADEP is obtained. By minimizing the ADEP, the optimal detection threshold is derived with closed-form expression. With these results, subject to the constraints of covertness and reliability, the power allocation (PA) coefficients are optimized to minimize the OP of the covert user. Two adaptive PA schemes based on two-dimensional (2D) and one-dimensional (1D) search methods are respectively proposed to achieve the solutions, and resulting lower OP is attained. Simulation results indicate that the theoretical OP and ADEP can agree the corresponding simulations well, and randomizing the noise power of warden can improve the covert performance. Moreover, the warden with the optimized threshold can obtain lower ADEP than that with a fixed threshold, and the system with two PA schemes has a lower OP than that with a fixed PA, especially the scheme based on 1D search has lower complexity while maintaining the superior performance.

This paper investigates the performance bound of two-dimensional (2D) direction of arrival (DOA) estimation in reconfigurable intelligent surface (RIS) assisted wireless localization scenarios. While the Cramér-Rao lower bound (CRLB) is widely used as a low bound for mean square error of DOA estimation, it is only asymptotically tight. To this end, a tight error bound with closed-form solution for 2D DOA estimation is proposed adopting an information-theory approach. The theoretical framework is established by first deriving the joint a posteriori probability density function (PDF) of 2D DOA conditioned on received signals, followed by entropy power transformation to obtain closed-form 2D-DEE explicit expression. To gain further insights, the asymptotic expression of 2D-DEE is analyzed in high SNR region. Numerical results demonstrate that the derived 2D-DEE provides a tight bound over a wider range of SNR compared to the CRLB, thereby enabling a more accurate evaluation and prediction of the 2D DOA estimation performance.

Terahertz (THz) communication has received much attention recently for its large bandwidth availability, high data-rate transmission and alleviating the spectrum shortage, and it can meet the requirements of Internet of Things with large system capacity and networking capability. In this paper, the performance of multi-antenna THz communication systems with rate-splitting multiple access (RSMA) under the hardware impairments and imperfect successive interference cancelation (SIC) are investigated, where the THz channel is modeled as a composite fading channel including the molecular absorption effects, misalignment fading and small-scale α-μ fading. Taking the hardware impairments and imperfect SIC into account, the probability density function and cumulative distribution function of the effective channel gain are derived. A joint zero-forcing and maximum ratio transmission beamforming design is employed to eliminate the interference among devices. Then, with the performance analysis, the closed-form outage probability (OP) and diversity gain of the system are respectively deduced. By minimizing the OP, a closed-form power allocation (PA) scheme is proposed to adjust the PA coefficients between the common stream and private streams, and resultant lower OP is attained. Moreover, the closed-form expression of the ergodic sum rate (ESR) is derived by means of Fox-H function and the Meijer-G function. With this ESR expression, the asymptotic ESR at high signal to noise ratio (SNR) is also provided to gain further insights. Furthermore, a simple upper bound of the ESR is derived for performance evaluation based on the Jensen’s inequality. Simulation results show that the theoretical analysis is effective, and the proposed PA scheme can obtain lower OP. Besides, the impact of different system and fading parameters on the performance are also analyzed.

In this paper, the joint power allocation (PA), passive beamforming (BF) and hybrid BF (HBF) including digital and analogue BFs are designed for an intelligent reflecting surface (IRS)-assisted millimeter-Wave (mmWave) communication system with imperfect channel state information (CSI) and multiple mobile users to optimize the weighted sum rate (WSR) and energy efficiency (EE). The achievable WSR and EE of the IRS-mmWave system are first derived based on imperfect cascaded CSI for performance optimization. Then, the non-convex constrained problem is formulated to maximize the WSR, where the PA, HBF, phase and amplitude of IRS elements are jointly optimized. Given PA and passive BF (PBF), closed-form suboptimal HBF is obtained for each iteration. Also, given HBF and PBF, using the block coordinate descent (BCD) methods, closed-form PA is derived. Moreover, the phase and amplitude of IRS elements are derived for PBF design during each iteration. With the obtained HBF, the digital and analogue BFs are also derived. Based on this, joint schemes of PA, HBF and PBF are developed. Besides, an efficient iterative algorithm based upon the alternating optimization (AO), weighted minimum mean-square error (WMMSE) and Dinkelbach methods are presented for EE maximization and the suboptimal solution is obtained. Correspondingly, the energy-efficient design for joint PA, HBF and PBF is provided. Simulation results verify the proposed solutions.

In this paper, the covert performance of the non-orthogonal multiple access (NOMA) system with random transmit power under hardware impairments over the Nakagami fading channel is investigated, where the stronger user serves as a covert user (Bob) and receives the secure message from the transmitter (Alice) under the cover of the weaker user (Carl). The transmission is monitored by a warden (Willie). To improve the covert performance, we randomize the transmit power of Alice, which is subject to a uniform distribution. Based on this, considering the randomness of covert user’s position, we derive the closed-form expressions of the average detection error probability (ADEP) respectively for the warden with instantaneous and statistical channel information. Then, the optimal detection threshold based on one-dimensional (1D) search method is presented for minimizing the ADEP. To simplify the optimal threshold, the suboptimal threshold with low complexity is also derived. Besides, the outage probability (OP) of the system is deduced for performance analysis and optimization. Under the constraints of covertness and reliability, the power allocation (PA) coefficient is optimized to minimize the OP of the covert user, and the 1D search scheme is proposed to obtain the optimal solution. Also, a suboptimal scheme is presented to reduce the complexity of the optimal scheme. Numerical results are presented to validate our theoretical analysis, and show that randomizing the transmit power can effectively improve the covert performance. Moreover, the system with two optimized thresholds can obtain lower ADEP than that with a fixed threshold, and the system with two optimized PA coefficients has a lower OP than that with a fixed PA.

For millimeter wave (mmWave) or Terahertz (THz) communications, by leveraging the high spatial resolution offered by large antenna arrays and the multi-path sparsity of mmWave/THz channels, a novel inter-symbol interference (ISI) mitigation technique called delay alignment modulation (DAM) has been recently proposed. The key ideas of DAM aredelay pre-compensationandpath-based beamforming. However, existing research on DAM is mainly based on fully digital beamforming, which requires the number of radio frequency (RF) chains to be equal to the number of antennas. This paper proposes the hybrid analog/digital beamforming based DAM, including both fully and partially connected structures. The analog and digital beamforming matrices are designed to achieve performance close to DAM based on fully digital beamforming. While DAM was considered for the path-based channel model with integer delays in the previous work, this paper extends DAM to a more general tap-based model that accounts for fractional path delays. To further reduce the cost of channel estimation and improve the performance for wireless channels with fractional delays, DAM with codebook-based beam alignment and DAM-orthogonal frequency division multiplexing (DAM-OFDM) with hybrid beamforming are proposed. The effectiveness of the proposed techniques is verified by extensive simulation results.

In this paper, the energy consumption (EC) optimization of an aerial high altitude platform station (HAPS) aided mobile edge computing (MEC) network with non-orthogonal multiple access (NOMA) in the presence of imperfect successive interference cancellation is studied. Specifically, joint design schemes of the resource allocation (RA) and the two-dimensional (2D) horizontal position are proposed to minimize the sum EC subject to the different constraint conditions. In particular, we jointly optimize the receive beamforming (BF), the power allocation (PA), HAPS position, the local computation resource, the computation task offload coefficient, and the computation resource allocated for each user via the block coordinate descent method. Namely, given the other optimization parameters, we first optimize a 2D position of HAPS. Then, given the 2D position, by introducing the auxiliary variables, a joint design of BF, PA, offload coefficient and computation resource is solved by an efficient iteration algorithm based on the successive convex approximation method. Additionally, a suboptimal joint design scheme is also developed to lower the complexity. Simulation results show that the proposed two design schemes of the joint RA and position are effective in reducing the EC, and they have a lower EC when compared to benchmark schemes.

In this article, energy efficiency (EE) is maximized for the reconfigurable intelligent surface (RIS) aided millimeter-Wave (mmWave) networks with non-orthogonal multiple access (NOMA) and multiple mobile devices. To this end, we first propose the EE optimization, under the constraints of maximum power, minimal rate of devices and constant modulus of beamforming (BF) vectors. Then, the joint resource allocation scheme of power allocation (PA) and BF is designed. Specifically, given PA, an effective iterative algorithm based on the majorization-minimization, concave-convex procedure and block coordinate descent (BCD) is presented to obtain closed-form solutions of suboptimal passive BF (PBF) and analog BF (ABF) for each iteration. Then, given PBF and ABF, an effective iterative algorithm based on the successive convex approximation, BCD and Dinkelbach methods is derived to achieve suboptimal closed-form PA for each iteration. By incorporating these two algorithms into the BCD method, a joint optimization algorithm for EE maximization is presented. As a result, joint resource allocation of PA, PBF and ABF is attained. Besides, the convergence and complexity of the algorithms are analyzed. For comparison, the benchmark scheme based on the multidimensional search method and artificial bee colony algorithm is also presented. Simulation results show that the proposed joint scheme is effective and higher EE can be obtained with lower complexity.

Cell-free massive multiple-input multiple-output (CF mMIMO) is known for its ability to provide ubiquitous connectivity. In this paper, we investigate the achievable spectral efficiency (SE) of a user-centric (UC) CF mMIMO system with both multi-antenna APs and users over joint-correlated Rayleigh fading channels. First, we provide a performance analytical framework for the system with the linear decorrelator and study the impact of hardware impairments (HIs) at transceivers on the uplink SE. Based on that, we discuss the local minimum mean-squared error (MMSE) and partial MMSE combining schemes and the partial large-scale fading decoding (LSFD) method from a scalable point of view. Besides, the exact closed-form SE expression is derived with maximum ratio combining (MRC). Then, we study the MMSE-based successive interference cancelation (MMSE-SIC) detector and give an approximate closed-form SE expression with MRC. In the simulations, we compare the linear decorrelator to the MMSE-SIC detector under different hardware-impaired scenarios. Numerical results correspond to the theoretical analyses and show that the impact of HIs can be mitigated by adding the number of receive antennas.

In Cell-Free Massive multi-input multi-output (CF mMIMO), it is challenging to assign regular pilots due to the pre-log pilot overhead on spectral efficiency (SE). This paper explores a superimposed-pilot-(SP)-assisted CF mMIMO system which avoids the separate pilot training duration by superimposing pilot symbols onto data symbols. We consider spatial-correlated Rician fading channels with and without random phase shifts, where linear minimum-mean-square-error (LMMSE) estimators are performed at each access point locally. Then, we derive the closed-form SE expressions with maximal-ratio (MR) combining. To fill the gap, we introduce novel expressions of MMSE combining vectors and compare their SE performance with approximate MMSE combining vectors. Next, a generic model is provided for the optimal large-scale fading decoding (LSFD), and we derive the closed-form suboptimal LSFD solutions with MR combining. A line-of-sight-based combining scheme is proposed based on the approximate analysis, where closed-form SE expressions are derived using MR and MMSE combining and corresponding optimal LSFD coefficients. Numerical results show that the combination of MMSE and optimal LSFD yields almost 200% enhancement over the combination of MR and simple centralized decoding in 95% likely per-user SE without phase shifts, and 111% enhancement when phase shifts exist.

Abstract Deep neural networks (DNN) based automatic modulation classification (AMC) has achieved high accuracy performance. However, DNNs are data‐hungry models, and training such a model requires a large volume of data. Insufficient training data will cause DNN models to experience overfitting and severe performance degradation. In practical AMC tasks, training the deep model with sufficient data is challenging due to the costly data collection. To this end, a novel probability density function (PDF) based data augmentation scheme and a method to determine the required minimum sampling size for data enlargement is proposed. Compared with the known image‐based augmentation scheme, the proposed waveform‐based PDF technique has low complexity and is easy to implement. Experimental results show that the required size of the training dataset is one order of magnitude smaller than the sufficient dataset in the additive white Gaussian noise channel, and effective recognition can be achieved using around 60% of the total examples under the Rayleigh channel. Moreover, the presented scheme can expand training data under frequency and phase offsets.

In this paper, the millimeter-wave (mmWave) communications and non-orthogonal multiple access (NOMA) are exploited for mobile edge computing (MEC) networks to improve the performance of task offloading. Aiming at improving the computation efficiency (CE) and ensuring the fairness among users, we study the CE optimization for mmWave-MEC with NOMA, where both the analog beamforming (ABF) and hybrid beamforming (HBF) architectures under the partial offloading mode are considered. First, according to the max-min fairness criterion, the CE optimization problem is formulated to jointly optimize the ABF at the base station and the local resource allocation of each user in mmWave-MEC with ABF. An efficient algorithm based on the penalized successive convex approximation is proposed to solve this non-convex problem. Then, the max-min CE optimization problem in mmWave-MEC with HBF is studied, where the joint design of the HBF at the BS and the local resource allocation of each user is carried out. By using the penalty function and the inexact block coordinate descent method, a feasible optimization algorithm is developed to tackle this challenging problem. Simulation results verify the convergence of the proposed algorithms and show that the proposed resource allocation schemes can improve the system CE effectively, and the mmWave-MEC with HBF scheme can obtain higher CE than that with ABF scheme. Besides, the NOMA scheme exhibits superior performance over the conventional orthogonal multiple access scheme in terms of CE.

Cell-free (CF) massive multi-input multi-output (mMIMO) is a potential key technology in future 6G wireless networks, which is in a position to service many users uniformly. In this paper, we aim to investigate the impact of multi-antenna access points (APs) and users on the channel estimation of CF mMIMO with two different linear minimum mean-squared error (LMMSE) estimators when low-quality hardware is applied. We firstly give the LMMSE estimator on multi-antenna users via vectorization operation with all radio frequency (RF) chains and the low-complexity LMMSE estimator with a single-RF chain, where the impact of transmit and receive spatial correlation, hardware impairment (HI) and different pilot assignment are considered. Then, we provide the comparison of the normalized MSE (NMSE) performance and computational complexity between the two schemes. Simulation results show that the single-RF scheme can significantly reduce the complexity as the number of antennas increases. Meanwhile, the loss of NMSE performance is relatively trivial, and the single-RF scheme may outperform the full-RF scheme with random pilot assignment and other schemes like element-wise MMSE and least-square estimators.

This article investigates energy efficiency (EE) maximization for an Internet of Things-based (IoT) distributed antenna system (DAS) with imperfect channel state information (CSI) subject to maximum transmit power and minimum data rate constraints. First, we derive achievable rates and corresponding EE expressions of the system for single and multiple IoT devices. Then, we formulate the EE maximization problem in the single-device IoT-DAS with imperfect CSI, and it has a special form of the difference of concave functions. To solve this problem, we develop a near-optimal power allocation (PA) scheme by using the concave–convex procedure (CCCP) and block coordinate descent (BCD) method. It can achieve an EE performance similar to that of the optimal exhaustive search scheme, but with lower complexity. Based on this result, we present a suboptimal PA scheme with a single-layer iteration to decrease the complexity and maintain a performance similar to that of the near-optimal scheme. Using the results above, the EE optimization for IoT-DAS with imperfect CSI for multiple devices is addressed. A near-optimal PA scheme based on the fractional programming (FP) theory as well as the CCCP and BCD methods for solving the optimization problem is presented. Also, a suboptimal PA scheme based on the FP theory and BCD method is developed to further decrease the complexity. Interestingly, these two schemes have the same performance for perfect CSI. Simulation results show the validity of the developed schemes and their superior performances over existing methods.

In this paper, the joint design of power allocation (PA), beamforming (BF) and positioning is studied for unmanned-aerial-vehicle (UAV) aided millimeter-Wave (UAV-mmWave) systems, with the objective of maximizing the energy efficiency (EE), under the constraints of maximum transmitting power, minimum data rate from the ground users and positioning range of the UAV. To address the above problem, we first obtain the positioning of the UAV, with the help of approximate beam pattern. Then, near-optimal BF and closed-form PA are derived given the obtained position, with the help of block coordinate descent method. To reduce the complexity, two suboptimal BF schemes with one-loop iteration and closed-form solutions are respectively derived. Furthermore, we propose the simplified algorithms for two special cases, i.e., only line-of-sight (LoS) path and Non-LoS (NLoS) path exist between the users and the UAV. Simulation results verify the effectiveness of the developed joint schemes and show the superior EE performance. Moreover, they can obtain almost the same performance as the existing benchmark schemes but with lower complexity.

In this paper, we present the computation-efficient resource allocation (RA) schemes for millimeter-wave mobile edge computing (mmWave-MEC) system with the aid of reconfigurable intelligent surface (RIS), which is used to assist the uplink communication from the users to the base station (BS). By means of the theoretical analysis, the achievable rate and computation efficiency (CE) are derived. Then, the optimization problem for the CE maximization under the constraints of the minimum rate, maximum power consumption and local CPU frequency is formulated, where the joint design of the hybrid beamforming at the BS and the passive beamforming at the RIS as well as the local resource allocation of each user is carried out. An effective iterative algorithm based on the penalized inexact block coordinate descent (BCD) method is proposed to obtain the computation-efficient RA scheme. Next, a low-complexity suboptimal RA scheme based on the BCD method is proposed, and corresponding algorithm is presented. Simulation results show that the proposed schemes are effective, and high CE can be attained. Moreover, the second scheme can achieve the CE performance close to the first scheme but with lower complexity. Besides, it is effective to deploy the RIS scheme in mmWave-MEC system, which can strike a balance between the CE and energy consumption when compared to the conventional relay schemes.

Energy efficiency (EE) optimization of joint power allocation (PA) and beamforming (BF) is studied for multiuser distributed multiple-input multiple-output (D-MIMO) systems with maximum ratio combining. Subject to power budget constraints, a non-convex constrained optimization problem is firstly formulated to maximize EE of single-user D-MIMO. We propose a near-optimal joint design scheme with the block coordinate descent method, which has an effective iterative algorithm to find optimal BF for fixed PA, and an iterative algorithm based on the Dinkelbach methods to find optimal PA for fixed BF. We also develop a low-complexity suboptimal joint scheme, which has closed-form BF and PA by maximizing an effective signal-to-noise ratio for fixed PA and a derived EE upper bound for fixed BF, respectively. It has lower complexity than the near-optimal scheme with slight performance loss. With these results, two joint design schemes are developed for multiuser D-MIMO. The first scheme can achieve the best performance, while the second one based on closed-form PA and BF has slight performance loss in comparing to that of the former, but with lower complexity. Simulation results verify the effectiveness of the developed schemes over some existing schemes.

Due to the requirement of low-power network devices for the proliferation of high data communication, enabling technologies for energy sustainable Internet of Things (IoT) are of great significance. In this article, we investigate the energy-efficiency (EE) optimization of IoT-distributed antenna (DA) system with simultaneous wireless information and power transfer (SWIPT) technique over fading channels, where the IoT device is equipped with power splitter to integrate the energy harvesting and information decoding processes via adjusting the transmit power of each DA port and power splitting (PS) ratio of IoT device. According to the analysis of EE, an optimization problem with the aim of maximizing the system EE is formulated under the constraints of maximum transmit power of each DA port as well as minimum harvested energy. Through analyzing the structure of the objective problem, it is found that the EE optimization problem, which combines transmit power allocation (PA) with PS problem, can be predigested to a PA problem. Then, the amount of valid DA ports and the corresponding PA are achieved by utilizing the Karush-Kuhn-Tucker conditions and Lambert function. Based on this, we propose an optimal resource allocation scheme without iteration to obtain the optimal PA and PS ratio, and the resulting closed-form expressions are provided. Considering that perfect channel state information (CSI) is hard to achieve, we also study the resource allocation scheme based on the imperfect CSI (i.e., statistical CSI with large-scale fading information), two suboptimal schemes are proposed. These two schemes have better robustness and lower complexity than the optimal scheme with perfect CSI because they only need partial channel information, but the performances are worse than the latter, as expected. Computer simulation indicates that proposed schemes are valid and can obtain superior EE performance with lower complexity.

In this paper, the error performance and spectrum efficiency (SE) of uplink massive multiuser spatial modulation (SM) MIMO systems with zero-forcing detection for perfect and imperfect channel state information (CSI) are investigated over composite Rayleigh fading channels. We firstly derive the error probabilities of transmit antenna index detection and transmitted symbol detection of each user. Using these results, the bit error rate (BER) performance of the system under perfect CSI is analyzed. Furthermore, a closed-form average BER of the system is derived. We generalize the analytical results of perfect CSI to those of imperfect CSI for practicality, and derive a closed-form BER for the system with imperfect CSI. Based on this, two asymptotic BER expressions are developed to characterize the error performance of the system for large-scale receive antennas and high SNR. By means of the asymptotic expressions, the diversity order of the system is attained. Besides, we derive a lower bound on the achievable SE of the system with imperfect CSI. With this lower bound, an approximate expression of the achievable SE is obtained in closed form. Simulation results indicate that our theoretical analysis is valid, and agrees with simulation results well.

The energy‐efficient power allocation (PA) of distributed antenna system using multiple receive antennas is studied over spatially correlated Rayleigh channels. A new energy efficiency (EE) defined as the ratio of the average transmission rate to the consumed total power is presented. According to this definition, subject to the maximum power constraint, an optimal PA scheme is developed by maximising the EE. It is shown that the solution of PA in the constrained EE optimisation does exist and is unique. A Newton method with iterative algorithm is proposed to attain the PA. To avoid iterative calculation of the optimal scheme, a suboptimal PA scheme is derived by means of the Lambert function. As a result, closed‐form PA is obtained. The developed schemes only need the statistical channel information and large scale information, and thus they have lower overhead and better robustness. Moreover, they may include the ones over spatially independent channel as special cases. The theoretical EE is further derived for performance evaluation, and the resultant closed‐form expression is obtained. Computer simulation indicates that the theoretical EE agrees well the simulation result, and the suboptimal PA scheme can achieve the EE value near to the optimal one with lower complexity.

Energy efficiency (EE) plays an indispensable role in the battery constrained systems. In this study, the EE optimisation problem for asymmetric analogue network coding (ANC) protocol is analysed in a two‐way relaying network, where the two sources have different transmission rate requirements. A generalised power consumption model is applied consisting of not only the transmit power and fixed circuit power, but also the most general rate‐dependent dynamic circuit power, with which a power allocation problem is formulated to achieve the maximal EE constrained by the rate requirements as well as the total transmit power budget. By exploiting the two‐layer optimisation method and non‐linear fractional programming theorem, the original EE maximisation problem is solved in an efficient way. Specially, when the rate‐dependent circuit power is modelled as the linear function of transmission rate, a closed‐form solution is obtained. Through simulations, the proposed power allocation algorithm is verified and the impacts of some system parameters such as relay location, transmit power and transmission rate asymmetry are also provided to gain useful insights, which facilitates the energy‐efficient design for the practical asymmetric ANC protocol.

In this paper, we develop an optimal precoder and a suboptimal precoder for uplink distributed antenna systems with transmit correlation over Rician channels. The objective is to minimize a pairwise error probability (PEP) with constrained transmit power. The optimal scheme uses an efficient projection-based steepest descent algorithm to obtain the Gram matrix of the precoder, while the suboptimal scheme exploits the eigen-structure of the Gram matrix to obtain its unitary matrix (beamforming) and eigenvalues (power control). For a given beamforming (BF), an efficient power adaptation based on a fuzzy signal-to-noise ratio (SNR) is developed. The PEP analysis at low SNR is used to obtain a suboptimal BF. The derived BF and the fuzzy power adaptation have closed-form expressions that make the suboptimal scheme computationally efficient in comparison with existing methods. The BF can be re-optimized via the Riemannian steepest descent method to further reduce the PEP. Simulation results show that the proposed optimal scheme not only gives the performance the same as the existing optimal scheme when the latter can converge, but it also has lower computational complexity and faster convergence. Moreover, the suboptimal scheme can give a nearly optimal error rate.

Interference coupling in heterogeneous networks introduces the inherent non-convexity to the network resource optimization problem, hindering the development of effective solutions. A new framework based on multi-pattern formulation has been proposed in this paper to study the energy efficient strategy for joint cell activation, user association and multicell multiuser channel allocation. One key feature of this interference pattern formulation is that the patterns remain fixed and independent of the optimization process. This creates a favorable opportunity for a linear programming formulation while still taking interference coupling into account. A tailored algorithm is developed to solve the formulated network energy saving problem in the dual domain by exploiting the problem structure, which gives a significant complexity saving compared to using standard solvers. Numerical results show a huge improvement in energy saving achieved by the proposed scheme.

The downlink capacity performance of distributed antenna systems (DAS) with antennas selection is investigated in a composite fading channel which takes path loss, Rayleigh fading and lognormal shadowing into account. According to the performance analysis, and using log-normal distribution approximation, the tightly approximate closed-form expressions of cumulative distribution function (CDF) and probability density function (PDF) of the effective SNR are obtained, respectively. Based on these results, the outage capacity performance of DAS is analyzed. By utilizing the Gaussian distribution approximation, a simple approximate outage capacity is derived. As a result, the closed-form expression is achieved. All these expressions will provide good theoretical performance evaluation for DAS. Simulation results show that the derived outage capacity is effective, and can match the corresponding simulation well.

Based on the asymptotic analysis in spatially correlated Rician fading channel, the precoders for space‐time block‐coded multiple‐input multiple‐output system at high and low signal‐to‐noise ratios (SNRs) are, respectively, designed to minimise the system bit error rate (BER). The precoding for high SNR provides closed‐form positive power allocation by using the Langrage optimisation method, and has the BER performance close to that of the optimal scheme, especially at high SNR. The Langrage multiplier does exist and is unique, and practical Newton's method is proposed to find its optimal value. Moreover, it has a closed‐form solution for some special cases. Thus, it avoids the iterative calculation of some existing precoding schemes. The precoding for low SNR has a closed‐form solution similar to onedirectional (1‐D) beamforming, and can obtain the performance very close to that of the optimal scheme at low SNR. By combining the above two schemes, a simple and effective suboptimal precoding scheme can be achieved for different SNRs. Simulation results show that the proposed scheme derived from the integration of high and low SNR can provide BER lower than the equal power precoding, and obtain the BER performance close to that of the existing optimal scheme with low complexity.

In this paper, unified BER performance and outage probability analyses of downlink multiuser scheduling for multiple-input multiple-output (MUS-MIMO) transmission/combining (transceiving) systems with imperfect channel state information (CSI) caused by feedback over Rayleigh fading channels is presented. The unified analysis is applicable to MIMO transceiving systems whose received signal-to-noise ratio (SNR) is given as largest order statistic of chi-square distribution. The performance of MUS-MIMO employing selective transmission/selective combining (ST/SC), ST/maximum ratio combining (MRC) and space-time block codes (STBC) can be analyzed by this general framework. Accurate and approximate unified closed-form BER and outage probability expressions of the MUS-MIMO transceiving system with normalized SNR-based scheduling in heterogeneous networks are derived. Based on the approximate BER and outage probability expressions, diversity gains are analyzed at high SNR. The results indicate that the MUS-MIMO for using the three transceiving schemes can achieve full diversity order for perfect CSI, while the diversity gain is degraded differently for the three transceiving schemes under imperfect CSI. Computer simulation shows that the theoretical analysis is in good agreement with simulation results, and the approximate BER expressions are very close to the accurate ones but with lower computational complexity.

In this paper, a statistically robust precoder design is presented for space-time coded multiple-input, multiple-output (MIMO) relay networks over double correlated Rician channels. We assume both the source and destination terminals are equipped with multiple-antenna, while a single antenna is used in distributed non-regenerative relay nodes for reducing feedback overhead and processing burden on relays. The precoding matrix at the source terminal and amplifying parameters of relay nodes are optimized to maximize the total signal-to-noise ratio (SNR) at the destination assuming only statistical channel state information (CSI) available at the transmission sides. The optimization problem can be efficiently solved by an iterative method, resulting in a single-beam mode source precoder and diagonal precoding matrix for relay nodes. Numerical results demonstrate that the proposed scheme outperforms the equal power allocation scheme and existing method with single antenna nodes.

The performance analysis of a space‐time coded multiple‐input multiple‐output (MIMO) system with variable‐rate adaptive modulation over flat Rayleigh fading channels for both perfect and imperfect channel state information (CSI) is presented. In this study, the optimum fading gain switching thresholds for attaining maximum spectrum efficiency (SE) subject to an average bit error rate (BER) constraint are derived. The existence and uniqueness of the Lagrange multiplier in the constrained SE optimisation is studied. It is shown that the Lagrange multiplier does exist and is unique for imperfect CSI. On the other hand, the Lagrange multiplier will be unique if the existence condition for MIMO under perfect CSI is satisfied. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. By the switching thresholds, closed‐form expressions of the SE and average BER are obtained. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that the space‐time block coded MIMO system using adaptive modulation (AM‐STBC‐MIMO) with average BER constraint provides SE better than AM‐STBC‐MIMO with fixed thresholds, and AM‐STBC‐MIMO using a BER upper bound, but it has performance degradation in SE for imperfect CSI.

The performance analysis of a space–time block coded multiple input multiple output system with variable-power (VP) adaptive modulation (AM) over Rician fading channels for imperfect channel state information is presented. The optimum switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. In the derivation, a very tight BER expression of quadrature amplitude modulation (QAM) is used to develop a new power adaptation scheme that can fulfil the target BER even at low signal-to-noise ratio (SNR) and achieve higher SE than the scheme using the BER upper bound commonly adopted in the literature. The existence and uniqueness of the Lagrange multiplier used in the constrained optimisation are investigated. It is shown that the Lagrange multiplier is unique when it exists. By using the switching thresholds, the authors obtain closed-form expressions of SE and average BER of the system. Computer simulation shows that the theoretical analysis is in good agreement with simulation. The results show that the proposed VP-AM scheme provides better SE than the constant-power counterparts and the VP-AM scheme using the commonly used BER bound.

In this study, a precoding scheme for minimising bit error rate (BER) subject to a power constraint for space-time-coded multiple-input–multiple-output systems over flat Rayleigh fading channel in the presence of channel estimation error and feedback delay is presented, it includes the precoding with estimation error or feedback delay only as its special cases. With this scheme, an algorithm for attaining the optimal power allocation across multiple beams is developed. It is shown that the Lagrange multiplier for the constrained optimisation does exist and is unique. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. Generally, the optimal power control may result in negative power allocation to some beams. A necessary and sufficient condition for the beams having positive power control is developed that simplifies the optimisation procedure. Simulation results show that the developed precoding scheme can provide BER lower than the equal power allocation scheme and the existing precoding scheme, but has performance degradation when compared with the precoding scheme with estimation error or feedback delay only.

We propose a novel adaptive transmission scheme for space-time coded multiple-input multiple-output beamforming systems with imperfect channel state information at the transmitter, of which the signal constellation, total transmit power (temporal power), and power allocation among eigen-beams (spatial power) are jointly adapted to maximize the average spectral efficiency, subject to a target bit-error-rate and an average power constraint. The power allocation over the spatial and temporal domains makes the traditional approach of partitioning the received signal-to-noise ratio (SNR) inapplicable to the above design problem. By introducing a new variable, called as effective signal-to-noise-to-modulation ratio (ESNMR), we derive a rate-selection policy by partitioning the range of the ESNMR with an optimal set of thresholds. A closed-form temporal power control policy and a simple spatial power allocation algorithm are also obtained. Numerical results demonstrate that the new adaptive transmission scheme yields a significant performance gain over existing adaptation systems.

This paper presents a strategy to allocate power both in space and time for beamforming orthogonal space-time block coded multi antenna systems with imperfect channel state information at the transmitter. Most of the existing schemes focus on spatial-only power allocation, while the temporal dimension is not well exploited. The proposed space-time strategy is developed by decoupling the temporal and spatial power calculation through asymptotic analysis, resulting in efficient computation. Numerical results demonstrate that the proposed scheme has considerable performance gains over the existing power adaptation schemes.

The performance of multi-input multi-output (MIMO) systems with variable-power (VP) adaptive modulation (AM) and antenna selection (AS) over Rayleigh fading channels for both perfect and imperfect channel state information (CSI) is presented. In this study, the optimum fading gain switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. It is shown that the Lagrange multiplier in the constrained SE optimisation is unique if the existence conditions for MIMO systems with transmit AS and receive maximal-ratio combining under perfect or imperfect CSI are satisfied. By using the switching thresholds, we obtain closed-form expressions of the SE and average BER for VP and constant-power (CP) systems. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that the VP-AM system using AS with the derived VP control scheme provides better SE than the CP counterpart and the VP-AM system with space-time coding and can fulfil the target BER for different signal-to-noise ratios (SNRs).

This paper presents a closed-form power allocation scheme for space-time coded multiple-antenna systems with imperfect channel state information at the transmitter. The proposed scheme is based on a so-called compressed signal-to-noise ratio (CSNR) criterion, where a single compression factor is used to minimize the bit-error-rate (BER). The obtained closed-form solution is computational efficient and achieves almost the same performance as the existing optimal approach which requires numerical search, and outperforms the existing suboptimal closed-form algorithm.