Precoding Vectors Research Articles

Multi-Tag Backscattering to MIMO Reader: Channel Estimation and Throughput Fairness

Green low power networking with the least requirement of dedicated radio resources is need of the hour which has led to the upsurge of backscatter communication (BSC) technology. However, this inherent potential of BSC is challenged by hardware constraints of the underlying tags. We address this timely concern by investigating the practical efficacy of multiple-input-multiple-output (MIMO) technology in overcoming the fundamental limitations of BSC. Specifically, we first introduce a novel least-squares based channel estimation (CE) protocol for multi-tag BSC settings that takes care of both the unintended ambient reflections and the inability of tags in performing estimation by themselves. Then using it, a nontrivial low-complexity algorithm is proposed to obtain the optimal transceiver designs for the multiantenna reader to maximize the minimum value of the lower-bounded backscattered throughput among the single-antenna semi-passive tags. Additional analytical insights on both individually and jointly-optimal precoding vector and detector matrix at the reader are provided by exploring the asymptotically-optimal transceiver designs. Lastly detailed numerical investigation is carried out to validate the theoretical results and quantify the practically realizable throughput fairness. Specifically, more than seven-fold increase in the common-backscattered-throughput among tags as achieved by the proposed designs over the relevant benchmarks corroborates their practical significance.

Hybrid Precoding for an Adaptive Interference Decoding SWIPT System With Full-Duplex IoT Devices

In this article, a simultaneous wireless information and power transfer (SWIPT) system with full-duplex (FD) Internet of Things (IoT) nodes is considered and investigated. We induce the adaptive interference decoding (AID) strategy as well as the switch and inverter structure with antenna selection (SIAS)-based hybrid precoding scheme to the SWIPT system. A joint optimization of hybrid precoder, decoding rule, and power splitting (PS) ratio problem is formulated to minimize the total transmission power, while satisfying the data rate and harvested energy constraints. As it is a nonconvex problem, we propose a suboptimal solution with three stages. In the first stage, a search algorithm which can reduce the complexity of exhaustive search is proposed to decide the sending mode of each node. In the second stage, we utilize the semidefinite relaxation (SDR) approach to find the optimal digital precoder and PS ratios. In the last stage, we propose an alternate minimization algorithm to obtain the hybrid precoding vectors. The simulation results show that our proposed suboptimal solutions can achieve a better performance in terms of power consumption and outage probability compared with those for treating interference as noise (IAN) systems and the digital precoding schemes. Both AID strategy and SIAS-based hybrid precoding are beneficial to the FD SWIPT system. Moreover, the self-interference causes little effect on the system performance as long as it can be eliminated up to 30 dB, which can be easily achieved by the antenna separation technique.

Cache-Enabled MIMO Power Line Communications With Precoding Design in Smart Grid

Power line communication (PLC) is an attractive approach to provide information transfer services for the smart grid. A crucial issue in PLC networks is how to achieve reliable transmission for rural and remote users against severe fading and impulsive noise in an economic way. To address this problem, we propose a cache-enabled multiple-input and multiple-output (MIMO) PLC network to improve transmission reliability and minimize downloading cost for users. First, we deploy a local cache at each PLC access unit to store popular content requested by users according to a popularity-based data placement. As such, the proposed cache-enabled scheme can not only bring popular data close to users at the edge of PLC networks but also reduce the PLC backhaul burden. Second, in the data delivery stage, we propose a precoding design for each access unit and formulate average downloading price for each user. In particular, we solve optimal precoding vectors to simultaneously meet the target transmission rate and minimize the price of each user through an efficient algorithm. Numerical results corroborate that our cache-enabled MIMO PLC network can guarantee the transmission reliability whilst reducing the downloading price compared with the existing related works.

Multi-User Linear Precoding for Downlink Generalized Spatial Modulation Systems

In this letter, a linear precoding scheme is proposed for downlink (DL) multi-user (MU) generalized spatial modulation (GSM) systems. The proposed precoding scheme achieves, not only inter-user interference (IUI) free, but also maximum signal-to-noise ratio (SNR). The former achievement leads to higher multiplexing gain, while the later results in higher diversity gain. By formulating the precoder design as a constrained optimization problem, the optimal precoding vectors are derived by using singular value decomposition (SVD). Outage and ergodic capacities of the proposed scheme are then analyzed, and compared to that of the conventional GSM scheme and the MU zero-forcing (ZF) transmit beamforming scheme by simulations. Simulation results indicate that the proposed scheme can effectively eliminate the IUI, and achieve significant diversity gain.

Omnidirectional Precoding for Massive MIMO With Uniform Rectangular Array—Part II: Numerical Optimization Based Schemes

In Part II of this two-part paper, we develop novel numerical optimization approaches to design omnidirectional precoding schemes for a massive multiple-input multiple-output system equipped with a uniform rectangular array (URA). To this end, we first formulate the omnidirectional precoding design as a semidefinite program (SDP) with rank constraint. An iterative rank-reduction algorithm is then proposed to produce omnidirectional transmission solution with a minimum number of precoding vectors. It is shown that the proposed algorithm can always obtain three precoding vectors (i.e., a rank-3 precoding matrix) to generate a perfectly omnidirectional power radiation pattern for any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P \times Q$</tex-math></inline-formula> URA with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\min \lbrace P, Q\rbrace &gt;2$</tex-math></inline-formula> , or yield an omnidirectional transmission solution with (theoretically minimum) two precoding vectors for any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P \times Q$</tex-math></inline-formula> URA with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\min \lbrace P, Q\rbrace \leq 2$</tex-math></inline-formula> . In addition, to facilitate analog precoding design, we further impose constant-modulus constraints for every entries of the precoding matrix. Through judicious (re-)formulation, we develop an efficient Newton's method, which can compute four constant-modulus precoding vectors to generate an omnidirectional power radiation pattern for any URA configuration. The numerical results demonstrate the merits of the proposed schemes.

Omnidirectional Precoding for Massive MIMO With Uniform Rectangular Array—Part I: Complementary Codes-Based Schemes

In the public channels, it is desirable to transmit the common signals omnidirectionally to ensure cell-wide coverage. In Part I of this two-part paper, we develop low-cost closed-form omnidirectional precoding designs for a massive multiple-input multiple-output (MIMO) system equipped with a uniform rectangular array (URA). By formulating the omnidirectional transmission design for a general URA as a feasibility optimization problem, we derive an optimal solution based on the complementary set (CS) or the complete complementary codes (CCC). We prove that the precoding vectors based on the CS or CCC sequences can generate a perfectly omnidirectional power radiation pattern. Since both CS and CCC sequences are binary and constant-modulus, the proposed schemes are well suited to be implemented in the radio frequency analog domain with low hardware cost and suppressed peak-to-average power ratio. The numerical results validate the superior performance of the proposed schemes over the existing alternatives.

Interference Subspace Alignment in Multiple-Multicast Networks

In the traditional interference channel (IC), each transmitter works in the mode of one-to-one. For serving more user terminals (UTs), a multiple-multicast network is proposed, in which there are multiple transmitters, and each transmitter works in the mode of one-to-many. Thus, each UT would suffer from both the intra-transmitter and inter-transmitter interference. Given the transmitting and receiving degrees of freedom, the desired signal would be more difficult to be separated from the numerous interference signals. For managing the interference, an interference subspace alignment (ISA) algorithm is proposed to decrease the dimension of the interference subspace. Different from the traditional iterative interference alignment (IA) algorithms, which iteratively calculate the precoding and receiving combining matrices to minimize the strength of interference, the ISA algorithm directly aligns the interference subspace spanned by the $T-N$ transmitters within that spanned by the residual $N$ transmitters, in which $T$ denotes the number of all the transmitters, and $N$ is the cardinality of the transmitter set used for IA. Now, the dimension of each UT's interference subspace is determined via $N$ transmitters ( $N ). During the subspace alignment, we, respectively, construct the composite IC state matrices for the $T-N$ and $N$ transmitters, and the composite precoding vector, which lies in the null space of the composite IC matrices. Thus, all the precoding matrices can be obtained once. After the subspace alignment, each UT's receiving combining matrix can be designed to lie in the null space of the aligned interference subspace. According to the simulation results, the proposed ISA algorithm can effectively suppress the interference and improve the system sum rate compared with the traditional interference management algorithms.

Domain Selective Precoding in 3-D Massive MIMO Systems

Three-dimensional multiple input multiple output (3-D MIMO) with a large number of active antennas equipped in a uniformly rectangular antenna array has a significant potential in improving the system capacity. In this paper, we present an efficient two-dimensional (2-D) downlink precoding scheme for single-cell 3-D massive MIMO systems. Considering instantaneous channel state information at the base station, we show that either the elevation or azimuth domain can be used for interference cancellation. We divide the interference into two components, one of which is canceled in the elevation domain, while the other is canceled in the azimuth domain. Based on this domain selective (DS) strategy, two DS precoding algorithms are proposed for the single-path scenario based on the zero forcing and signal-to-leakage-plus-noise ratio criteria. Next, we extend our DS precoding scheme to a multi-path scenario. In the proposed algorithms, the precoding vectors of different users are determined in parallel, so as to reduce the computational complexity. Simulation results are provided to demonstrate that the proposed algorithms can achieve better spectral efficiency performance with a low computational complexity.

Secure Transmission via Beamforming Optimization for NOMA Networks

Owing to the eminent performance gain, non-orthogonal multiple access (NOMA) has been regarded as a promising approach to achieve high throughput and low latency for the next-generation networks. Nevertheless, potential adversaries can still pose a threat to secure transmission in NOMA systems. Hence, in this article, secure transmission schemes based on beamforming optimization are designed to combat both internal and external eavesdropping for downlink multi-input single-output NOMA networks. Using the transmit beamforming design, we first propose two schemes to protect the privacy of a specific NOMA user in the presence of untrusted users. Then, the sum secrecy rate optimization problem is studied to combat the external eavesdropper through optimizing the precoding vectors, when the channel state information (CSI) is available. In addition, two secure beamforming strategies with the help of artificial noise and inter-user interference are proposed without eavesdropping CSI, respectively. Simulation results are presented to demonstrate the effectiveness of the proposed schemes, and some open issues are discussed as well.

Secure Transmission via Joint Precoding Optimization for Downlink MISO NOMA

Non-orthogonal multiple access (NOMA) is a prospective technology for radio resource constrained future mobile networks. However, NOMA users far from a base station (BS) tend to be more susceptible to eavesdropping because they are allocated more transmit power. In this paper, we aim to jointly optimize the precoding vectors at the BS to ensure the legitimate security in a downlink multiple-input single-output (MISO) NOMA network. When the eavesdropping channel state information (CSI) is available at the BS, we can maximize the sum secrecy rate by joint precoding optimization. Owing to its non-convexity, the problem is converted into a convex one, which is solved by a second-order-cone-programming-based iterative algorithm. When the CSI of the eavesdropping channel is not available, we first consider the case that the secure user is not the farthest from the BS, and the transmit power of the farther users is maximized via joint precoding optimization to guarantee its security. Then, we consider the case when the farthest user from the BS requires secure transmission, and the modified successive interference cancellation order and joint precoding optimization can be adopted to ensure its security. A similar method can be exploited to solve the two non-convex problems when the CSI is unknown. Simulation results demonstrate that the proposed schemes can improve the security performance for MISO NOMA systems effectively, with and without eavesdropping CSI.

Precoding design of NOMA-enabled D2D communication system with low latency

This letter investigated a device-to-device (D2D) communication underlaying cellular system, where one wireless device (WD) can directly transmit information to two inner users under non-orthogonal multiple access (NOMA) protocol with low latency. Considering the user fairness and reliability, both users can adopt successive interference cancellation (SIC) to decode information by the given decoding order. Subject to predefined quality-of-service (QoS) requirement and the constraint of WD’s transmit power, the maximal rate of latter decoded information and the corresponding precoding vectors are obtained by applying the technique of semidefinite relaxation (SDR) and the Langrangian duality method. Then, the suboptimal scheme based on singular value decomposition (SVD) is also proposed with a lower computational complexity. Numerical simulation shows that with the design of proper precoding vectors D2D communication system assisted by NOMA has a better performance than orthogonal multiple access (OMA).

Multicell Massive MIMO Multicast Transmission With Finite-Alphabet Inputs

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

An Efficient Algorithm for mmWave MIMO Systems

Efficient and Symmetry based precoding plays a key role in wireless communications. In order to improve the transmission performance of multi-user millimeter wave Multiple-Input Multiple-Output (MIMO) (MU-mmWave MIMO) systems, this paper proposes an analog precoding scheme for the receiver of mmWave MIMO with split sub-array hybrid analog and digital architecture. Then, we propose a hybrid analog and digital precoding algorithm based on channel reciprocity (APoCR) to maximize the spectral efficiency by utilizing the triple joint optimization problem, which can be divided into the analog and digital part. The analog combination vectors (ACVs) are obtained by the signal-to-interference-and-noise ratio (SINR) reception maximization of each downlink user and the analog precoding vectors (APVs) are obtained by the SINR reception maximization of each uplink antenna array. The digital precoder of the transmitter is designed after the analog part optimization to alleviate the interference between multiple data streams of the users. The simulation results show that the proposed precoding algorithm has a better sum rate, fast convergence, and improved SINR than the other state-of-the-art algorithms.

Joint Trajectory and Precoding Optimization for UAV-Assisted NOMA Networks

The explosive data traffic and connections in 5G networks require the use of non-orthogonal multiple access (NOMA) to accommodate more users. Unmanned aerial vehicle (UAV) can be exploited with NOMA to improve the situation further. In this paper, we propose a UAV-assisted NOMA network, in which the UAV and base station (BS) cooperate with each other to serve ground users simultaneously. The sum rate is maximized by jointly optimizing the UAV trajectory and the NOMA precoding. To solve the optimization, we decompose it into two steps. First, the sum rate of the UAV-served users is maximized via alternate user scheduling and UAV trajectory with its interference to the BS-served users below a threshold. Then, the optimal NOMA precoding vectors are obtained using two schemes with different constraints. The first scheme intends to cancel the interference from the BS to the UAV-served user, while the second one restricts the interference to a given threshold. In both schemes, the non-convex optimization problems are converted into tractable ones. An iterative algorithm is designed. Numerical results are provided to evaluate the effectiveness of the proposed algorithms for the hybrid NOMA and UAV network.

Efficient Constant Envelope Precoding With Quantized Phases for Massive MU-MIMO Downlink Systems

This study considers a generalized constant envelope-based precoding design problem in massive multiuser multiple-input multiple-output systems, in which the output signals of digital-to-analog converters are restricted to $M$ -ary phase-shift keying signaling to facilitate the use of low-cost and power-efficient power amplifiers at a base station. We aim to jointly optimize the precoding vector and the precoding factor to minimize the mean-squared error between the transmitted and the estimated symbols. However, the considered precoding problem is nonconvex and challenging to solve because the precoding vector and the precoding factor are coupled together. To address this problem, we apply the alternating minimization (AltMin) framework to decouple the considered problem into two problems: the precoding factor design problem and the precoding vector design problem. The former has an analytical solution, while the latter requires solving a difficult combinatorial problem, which we address by proposing a simple yet efficient gradient projection (GP)-based algorithm to find an approximate precoding vector. Simulation results demonstrate that the proposed GP-based AltMin algorithm achieves the same or higher BER performance than state-of-the-art algorithms while requiring lower complexity. In addition, when higher order modulations are employed, the error floor experienced by the existing algorithms can be substantially mitigated by the proposed GP-AltMin algorithm through increasing the number of phase bits.

Pricing user scheduling and precoding in relay‐assisted massive MIMO systems

A downlink user scheduling algorithm based on the pricing scheduling factor is proposed for the established relay-assisted massive multiple input multiple output (MIMO) model, which represents the typical remote cell with multiple relays and a massive MIMO base station. Different from the traditional scheduling algorithms, the authors' proposed scheduling algorithm simultaneously takes account of the strength of the desired signal and interference, in which the proposed scheduling factor takes interference strength as the price to select appropriate users. An analysis on the optimal precoding vector is given by assuming each relay adopts equal gain transmission (EGT). According to the analysis, a non-cooperative solution based on the phase difference of EGT is proposed to search the optimal transmission direction of EGT with low complexity. An analytical upper bound of system sum rate is also obtained. Simulation results indicate that the proposed scheduling algorithm has excellent sum rate performance and slight rate degradation compared with the brute-force search algorithm.

Proactive Jamming Toward Interference Alignment Networks: Beneficial and Adversarial Aspects

Interference alignment (IA) is a prospective method to achieve interference management in wireless networks. On the other hand, jamming can be deemed either as a potential threat to degrade the performance of wireless networks, or as a helper to combat the eavesdropping for the legitimate networks. In this paper, we consider these two opposite scenarios, beneficial and adversarial jamming, toward IA networks, and based on which two proactive jamming schemes are proposed. In the first scheme, the jammer utilizes its precoding vector to constrain the jamming signal into the same subspace as the interference at each IA receiver, which will disrupt the potential eavesdropping significantly without affecting the transmission of IA users. Specifically, secure transmission can be guaranteed through the jamming without any additional cooperation with the IA users. In the second scheme, the jammer utilizes its precoding vector to project the jamming signal into the same subspace as that of the desired signal at each IA receiver secretly. Thus, the IA users cannot detect the concealed jamming signal, which will result in the performance degradation of the IA network. Extensive simulation results are presented to show the effectiveness of the two proposed jamming schemes toward IA networks.

Multicast Precoding for Multigateway Multibeam Satellite Systems With Feeder Link Interference

This paper studies the multigroup multicast precoding problem in frame-based multigateway multibeam satellite communications with feeder link interference. We formulate a sum rate maximization problem that incorporates the minimum signal-to-interference-and-noise-ratio requirement for each user, the sum power constraint at each gateway, as well as the per feed power constraints at the satellite. Both transparent payload and payload with on-board processing are considered. In the former case, we propose a centralized algorithm by employing the successive convex approximation (SCA) approach, which iteratively approximates the original nonconvex problem to a second-order cone program. Moreover, in order, for each gateway, to compute its precoding vector locally with local channel state information, we devise a decentralized algorithm by incorporating consensus alternating direction method of multipliers (ADMM) into the SCA framework. For the latter case, we devise a two-stage precoding scheme where, in the first stage, a leakage-based minimum mean-square-error scheme is employed to control the feeder link interference efficiently. In the subsequent second stage, we use the SCA-ADMM approach to deal with the user link interference while maximizing the sum rate. Finally, numerical results are presented to demonstrate the performance of the proposed schemes.

Givens rotation based column-wise hybrid precoding for millimeter wave MIMO systems

Hybrid precoding is a promising technique for millimeter wave (mmWave) large-scale multiple-input multiple-output (MIMO) systems. This paper considers a hybrid precoding architecture which is composed of a reductive digital precoder and a phase-only control radio frequency (RF) precoder, and proposes a Givens rotation based column-wise hybrid precoding algorithm. In the proposed algorithm, the digital precoding matrix and the RF precoding matrix are alternatively optimized column by column. For the optimization of the constant modulus RF precoding vector, it is interesting that the optimal solution can be expressed as a product of an arbitrary constant modulus vector and a series of Givens rotation matrices. Accordingly, the original problem is transformed into an unconstrained problem of the Givens rotations, which is easy to be solved. After obtaining the optimal RF precoding vector, the optimal digital precoding vector can be given through the least squares method. Simulation results show that the proposed algorithm can approach the performance of the fully digital precoder effectively and enjoy a higher spectral efficiency than previous works under various channel environments and different system settings.

A Secure Receive Spatial Modulation Scheme Based on Random Precoding

With the rapid growing demand for transmission rate, transmission security is becoming increasingly important. This paper proposes a novel scheme aiming at transmission security enhancement on the basis of the spatial modulation technology. In the proposed scheme, the transmitter maps the information bits to the index of a receive antenna, then a precoding vector is randomly selected in the null space of the targeted antenna. Due to the randomness of the precoding vector, it's difficult for the eavesdropper in unknown locations to detect the index of the targeted antenna using maximum-likelihood detection, hence its receiving performance can be greatly degraded compared with the legitimate receiver. Both theoretical analysis and simulation results verified the secure enhancement performance of the proposed scheme. Moreover, unlike most of the existing schemes which require that the transmitter should equip more antenna than the receiver, our scheme works well even if the transmitter has less antennas than the receiver.