Linear Precoding Scheme Research Articles

Nonlinear-Precoded Multiuser Secure Transmission With Cooperative Jamming and Adaptive Limited Feedback

This paper studies secure transceiver design for multiuser multiantenna systems with an external passive eavesdropper and a cooperative jamming helper. Due to the finite-rate constraint of feedback channels, only quantized channel state information (CSI) of the legitimate users is available at the transmitter and the helper. A nonlinear-precoded secure transmission strategy is proposed using Tomlinson–Harashima precoding at the transmitter and null-space beamforming at the helper based on the quantized CSI. The accurate closed-form expression of an approximation for the ergodic rate of each legitimate user is obtained using quantization cell approximation for random vector quantization of the channels. Assuming the quantized CSI of the legitimate channels and the helper's channel at the eavesdropper, closed-form expression of an upper bound of the ergodic rate of each user's message at the eavesdropper is also derived. Then, a closed-form expression of an approximation for the worst-case ergodic secrecy sum rate follows. We also theoretically show that, besides the advantage in ergodic rate over the linear precoding scheme, when the quantized CSI is not available at the eavesdropper, Tomlinson–Harashima precoding is also more effective in degrading the received signal quality at the eavesdropper, and, thus, is more capable to enhance the secrecy of the systems compared with the linear precoding scheme. Given the total bandwidth constraint of CSI-feedback channels, an adaptive feedback bit allocation algorithm is proposed for each legitimate user to optimize the ergodic secrecy rate performance. Numerical results illustrate that the proposed nonlinear-precoded secure transmission strategy outperforms the corresponding linear precoding scheme, and significant advantage can be achieved by adaptively allocating the total available feedback bits.

Multiuser precoding scheme and achievable rate analysis for massive MIMO system

We analyze the downlink multiuser precoding of massive multiple input multiple output (MIMO) system, where the base station (BS) has ideal channel state information (CSI) and adopts three types of different linear precoding schemes, i.e., maximum ratio transmission (MRT), zero-forcing (ZF), and minimum mean squared error (MMSE). Under a Rayleigh fading channel, we attain the exact expressions on the achievable rate for these three precoding schemes. Moreover, we provide several insights on the achievable rates and reveal the relation of the number of BS antennas, the number of users, and the input signal-to-noise ratio (SNR) with the achievable rates respectively. It is found in general that the achievable rate increases with the number of BS antennas and the input SNR. To be more specific, the MRT precoding scheme is much inferior to the ZF and MMSE precoding schemes and tends to be at a fixed rate at the high SNR case. On the contrary, the MRT precoding scheme outperforms ZF precoding schemes at the low SNR case. Moreover, the total achievable rate always does not increase with the number of users and the optimal number of users always exists for the ZF and MMSE precoding schemes.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams -- crucial to the overall complexity -- while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme's constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Nested Precoding in MU-MIMO Channels: The Superposition Transmission of Space-Time Coding and Spatial-Division Multiplexing

Nonorthogonal multiple access (NOMA) can improve the spectrum efficiency through reusing the power-level space by different users. Although NOMA in single-input single-output channels has been thoroughly explored, it is still underexploited in multiple-input multiple-output (MIMO) channels. Precoding design in multiuser MIMO channels with nonorthogonal transmission is a multidimensional nesting problem, it is hard to compare two matrix channels if only their power levels are considered. In this paper, we first propose a method to compare the covariance matrices of two channel matrices, and then derive a channel condition under which the linear precoding scheme can achieve the sum capacity. Considering arbitrary realizations of multiuser channels, we provide a nested precoding algorithm that can work well in highly correlated multiuser channels. Based on this idea, a specialized superposition transmission scheme between signaling and data information is proposed, where plenty of resources beneath the signaling signal are utilized to transmit data information for dedicated users, and a large amount of extra rates are achieved. In addition, space-time coding is used for signaling information and spatial-division multiplexing is used for multiuser data information. Under the constraint that signaling information should be correctly decoded at any position in the cell, we seek to maximize the sum rate of the underneath multiuser data streams. To this end, the optimal and a low-complexity simplified precoding algorithms are developed. Finally, simulation results verify the throughput improvement and the correct decoding probability of the signaling information.

Optimal Block Diagonalization precoding scheme for MU-MIMO Downlink channel Using Particle Swarm Optimization

As wireless communication turns out to be more common, the interest for higher rates of data transfer and continuous availability is expanding. Future wireless systems are provisioned to be very heterogeneous and interconnected. Higher data rates and Quality of Service (Qos) are two major expectations from any wireless technology. Fading is the main phenomenon which restricts the realization of Qos demand and higher data rates in wireless technologies. Fading is caused by obstacles in signal path which degrades the received signal’s quality. To mitigate the impact of fading on communication system the application of precoding techniques can be used. In this regard, this paper presents optimization of Block-Diagonalization (BD) based linear precoding scheme for multi-user multiple-input multiple output (MU-MIMO) systems. Simulation environment consists of a MIMO downlink scenario where a single base station (BS) with antennas transmits to K receivers each with antenna. The application of Particle Swarm Optimization (PSO) is used to find the optimal number of received antennas so as to reduce system complexity while maintaining Bit Error Rate (BER) performance of the system. MATLAB based simulation scenario is presented and evaluated over Rayleigh fading environment. Simulation results validate that the performance of Block– Diagonalization scheme can be improved up to 5dB with the application of Particle Swarm Optimization technique.

Robust MISO Beamforming With Cooperative Jamming for Secure Transmission From Perspectives of QoS and Secrecy Rate

Robust quality-of-service (QoS)-based and secrecy rate-based secure transmission designs are investigated for a multiple-input single-output system with multiple eavesdroppers and a cooperative jammer. Two scenarios are considered: (a) eavesdroppers’ channel state information (ECSI) is available and (b) ECSI is unavailable. In scenario (a), a QoS-based design is considered to minimize the worst case signal-to-interference-and-noise ratio at the eavesdroppers and to guarantee the QoS of the legitimate receiver. A secrecy rate-based design is also studied where the worst case secrecy rate is maximized. In scenario (b), a QoS-based design is considered to maximize the power of jamming signals under the QoS constraint of the legitimate receiver, and the secrecy rate-based design is not applicable. In all these designs, we jointly optimize the transmit beamforming vector and the covariance matrix of jamming signals under individual power constraints. As the optimization problems are non-convex, we propose an algorithm for each problem through semidefinite relaxation. Our analysis and simulation results show that, even though the linear precoding scheme in our designs is transmit beamforming rather than the general rank transmit covariance, this does not cause any loss of optimality.

Nonlinear Precoding for Multipair Relay Networks With One-Bit ADCs and DACs

We consider a multipair half-duplex relay communication network, where the relay is deployed with one-analog-to-digital converters and one-bit digital-to-analog converters. To suppress the interpair interference and quantization artifacts, we propose nonlinear precoding schemes to forward the quantized signals at the relay. We first present a technique based on gradient projection, and then show how to refine the solution using ordered quantization and perturbation methods. For the single-user case with BPSK symbols, we obtain a closed-form solution for the optimal transmit vector. Numerical results verify that the proposed precoding design significantly outperforms quantized linear precoding strategies.

Massive MIMO Performance With Imperfect Channel Reciprocity and Channel Estimation Error

Channel reciprocity in time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems can be exploited to reduce the overhead required for the acquisition of channel state information (CSI). However, perfect reciprocity is unrealistic in practical systems due to random radio-frequency (RF) circuit mismatches in uplink and downlink channels. This can result in a significant degradation in the performance of linear precoding schemes, which are sensitive to the accuracy of the CSI. In this paper, we model and analyse the impact of RF mismatches on the performance of linear precoding in a TDD multi-user massive MIMO system, by taking the channel estimation error into considerations. We use the truncated Gaussian distribution to model the RF mismatch, and derive closed-form expressions of the output signal-to-interference-plus-noise ratio for maximum ratio transmission and zero forcing precoders. We further investigate the asymptotic performance of the derived expressions, to provide valuable insights into the practical system designs, including useful guidelines for the selection of the effective precoding schemes. Simulation results are presented to demonstrate the validity and accuracy of the proposed analytical results.

Analysis of One-Bit Quantized Precoding for the Multiuser Massive MIMO Downlink

We present a mathematical analysis of linear precoders for downlink massive MIMO multiuser systems that employ one-bit digital-to-analog converters at the basestation in order to reduce complexity and mitigate power usage. The analysis is based on the Bussgang theorem, and applies generally to any linear precoding scheme. We examine, in detail, the special case of the quantized zero-forcing (ZF) precoder, and derive a simple asymptotic expression for the resulting symbol error rate at each terminal. Our analysis illustrates that the performance of the quantized ZF precoder depends primarily on the ratio of the number of antennas to the number of users, and our simulations show that it achieves performance similar to a more complicated nonlinear least-squares encoder for low-to-moderate signal to noise ratios, where massive MIMO systems are presumed to operate. We also use the Bussgang theorem to derive a new linear precoder optimized for the case of one-bit quantization, and illustrate its improved performance.

Precoding and Power Optimization in Cell-Free Massive MIMO Systems

Cell-free Massive multiple-input multiple-output (MIMO) comprises a large number of distributed low-cost low-power single antenna access points (APs) connected to a network controller. The number of AP antennas is significantly larger than the number of users. The system is not partitioned into cells and each user is served by all APs simultaneously. The simplest linear precoding schemes are conjugate beamforming and zero-forcing. Max-min power control provides equal throughput to all users and is considered in this paper. Surprisingly, under max-min power control, most APs are found to transmit at less than full power. The zero-forcing precoder significantly outperforms conjugate beamforming. For zero-forcing, a near-optimal power control algorithm is developed that is considerably simpler than exact max-min power control. An alternative to cell-free systems is small-cell operation in which each user is served by only one AP for which power optimization algorithms are also developed. Cell-free Massive MIMO is shown to provide five- to ten-fold improvement in 95%-likely per-user throughput over small-cell operation.

On Integer-Forcing Precoding for the Gaussian MIMO Broadcast Channel

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach for communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally-scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.

Design of Low Complex Linear Precoding Scheme for MU-MIMO Systems

The block diagonalization (BD) is a linear precoding technique for multiuser interference elimination in multi-user multiple-input multiple-output (MU-MIMO) systems. Though various methods of block diagonalization have been identified, they are convoluted regarding the computations involved. In this paper we have modeled a new paradigm for the performance improvement and complexity reduction in BD based precoding algorithms. This is consummated using principal component analysis (PCA). The traditional highly complex singular value decomposition is replaced by QR decomposition in PCA (QR-PCA) for complexity reduction. The PCA along with QR decomposition and minimum mean squared error (MMSE) channel inversion technique parallelize the MU-MIMO channel into independent and proportionate single user MIMO channel. The simulation result shows that the proposed QR-PCA based precoding algorithm in comparison with the existing algorithm achieves comparatively better sum-rate, lower BER, and lower computational complexity. The PCA along with MMSE channel inversion avoids the decoder structure, which makes the receiver system simple.

Downlink Massive MIMO Systems: Achievable Sum Rates and Energy Efficiency Perspective for Future 5G Systems

To meet up with the ever increasing subscribers' demand for higher data rates and mobile data traffic growth in the telecommunication industry, the fifth generation (5G) systems is being considered for the next future cellular communication standards. The two principal design requirements being aimed at in 5G are robust data transmission rates in Gigabits and low power consumption systems. Massive multiple input multiple output (M-MIMO) technology is an evolving smart antenna technology which has some key promising potentials to boost 5G networks in meeting the aforementioned requirements. However, there is an emergent concern that increased number of antenna arrays in M-MIMO system could induce high power consumption and poor energy efficiency when deployed at the base stations (BSs). Also, inter-cellular interference which occurs as a result of pilot contamination, fast fading and uncorrelated noise effects in the radio channels are other open issues in M-MIMO system. This work investigates and compare the achievable sum rates and energy efficiency of a downlink single cell M-MIMO systems utilizing linear and nonlinear precoding schemes. First, we have shown how the increasing signal-to-noise ratio and M-antennas impact the achievable sum rates. Furthermore, the energy saving potentials of M-MIMO systems in macro, micro and pico cellular environments when linear and nonlinear precoding schemes are utilized at the BS have been demonstrated. Particularly, by means of power fairness index, the tradeoff among the energy efficiency, sum rate and the system users have also been presented and discussed. Results show that substantial energy efficiency improvements can be achieved in micro and pico cellular environments of downlink M-MIMO systems when non-linear successive interference cancellation precoding is applied compared to linear precoding schemes.

Analysis of Energy Efficiency and Area Throughput in Large Scale MIMO Systems with MRT and ZF Precoding

The large-scale multiple input multiple output (LS-MIMO) systems are equipped with a large number of antennas at the base station. These systems are capable of serving a larger number of user terminals, with massive gains in the form of energy and bandwidth efficiency. The energy efficiency of LS-MIMO system depends on the overall power consumption and data rate. In this paper, we have improved the energy efficiency of the LS-MIMO system by using maximum ratio transmission/combining and zero forced linear pre-coding schemes in single and multi-cell scenarios. We have jointly considered the uplink and downlink communications to propose an improved, more practical and more realistic power consumption model. The proposed model deliberates the power required for the power amplifier, linear processing and the circuit components at the base stations and user terminals. The outcome of this work provides a significant improvement in terms of energy efficiency and area throughput. The analytical results illustrate that the LS-MIMO systems achieve the maximum energy efficiency and area throughput wherein larger number of transmit antennas are installed at the base station to serve comparatively greater number of users terminals. The mathematical results depict the similar performance for imperfect channel state information in multi-cell setups. All aspects of power consumption during bidirectional communication are considered to provide precise results. Hence, the improvements in simulations results support the accuracy of the proposed model.

Parametrization and Applications of Precoding Reuse and Downlink Interference Alignment

In this paper, we consider the downlink communication of an arbitrary number of transmitters over broadcast interference channels. In order to suppress interference, we investigate a network-level linear precoding scheme dubbed precoding reuse. Such a technique is leveraged on the interference alignment (IA) principle, where the undesired signals overlap in a reduced-dimension subspace at the receivers. Precoding reuse relies on two cascaded precoders to suppress intra- and inter-cell interference and requires feedback only within a cell. We designed precoding reuse schemes for which interference suppression can be attained in a coordinated or uncoordinated fashion over a fixed number of quasi-static channel uses. We provide expressions for the parametrization of the precoders and investigate the advantages, limitations, suitable scenarios, and applications of the proposed IA scheme. Finally, we pointed out the open problems, where the proposed IA scheme and parametrization can be implemented with little effort, demanding minimum changes to an existing cellular system supporting multi-user MIMO.

Degrees of Freedom of the MIMO $2 \times 2$ Interference Network with General Message Sets

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmitter, and two-receiver ( $2 \times 2$ ) interference network with a general message set consisting of nine messages, one for each pair of a subset of transmitters at which that message is known and a subset of receivers where that message is desired. An outer bound on the general nine-message $2 \times 2$ interference network is obtained and it is shown to be tight, thereby establishing the DoF region for the most general antenna setting wherein the four nodes have an arbitrary number of antennas each. The DoF-optimal scheme is applicable to the MIMO $2 \times 2$ interference network with constant channel coefficients, and hence, a fortiori , to time/frequency varying channel scenarios. In particular, a linear precoding scheme is proposed that can achieve all the DoF tuples in the DoF region. In it, the precise roles played by transmit zero-forcing, interference alignment, random beamforming, symbol extensions, and asymmetric complex signaling (ACS) are delineated. For instance, we identify a class of antenna settings, in which ACS is required to achieve the fractional-valued corner points. Evidently, the DoF regions of all previously unknown cases of the $2 \times 2$ interference network with a subset of the nine-messages are newly established as special cases of the general result of this paper. For instance, the DoF region of the well-known four-message (and even three-message) MIMO $X$ channel is newly established. This problem had remained open despite previous studies, which had found inner and outer bounds that were not tight in general. Hence, the DoF regions of all special cases obtained from the general DoF region of the nine-message $2\times 2$ interference network of this paper that include at least three of the four $X$ channel messages are new, among many others. This paper sheds light on how the same physical $2 \times 2$ interference network could be used by a suitable choice of message sets to take most advantage of the channel resource in a flexible and efficient manner.

Achievable Rates of UAV-Relayed Cooperative Cognitive Radio MIMO Systems

We study the achievable rate of an uplink MIMO cognitive radio system where the primary user (PU) and the secondary user (SU) aim to communicate to the closest primary base station (BS) via a multi-access channel through the same unmanned aerial vehicle (UAV) relay. The SU message is then forwarded from the primary BS to the secondary network with a certain incentive reward as a part of the cooperation protocol between both the networks. A special linear precoding scheme is proposed to enable the SU to exploit the PU free eigenmodes. We analyze two scenarios in which the UAV relay gain matrix is either fixed or optimized. We derive the optimal power allocation that maximizes the achievable rate of the SU respecting power budget, interference, and relay power constraints. Numerical results highlight the cognitive rate gain of our proposed scheme with respect to various problem parameters. We also highlight the effect of UAV altitude on the SU and PU rates. Finally, when the relay matrix is optimized, we show that the PU rate is remarkably enhanced and that the SU rate is only improved at high-power regime.

Linear Precoding Scheme Design for MIMO Two-Way Relay Systems with Imperfect Channel State Information

The aim of this paper is to investigate a linear precoding scheme design for a multiple-input multiple-output two-way relay system with imperfect channel state information. The scheme design is simplified as an optimal problem with precoding matrix variables, which is deduced with the maximum power constraint at the relay station based on the minimum mean square error criterion. With channel feedback delay at both ends of the channel and the channel estimation errors being taken into account, we propose a matrix decomposition scheme and a joint iterative scheme to minimize the average sum mean square error. The matrix decomposition method is used to derive the closed form of the relay matrix, and the joint iterative algorithm is used to optimize the precoding matrix and the processing matrix. According to numerical simulation results, the matrix decomposition scheme reduces the system bit error rate (BER) effectively and the joint iterative scheme achieves the best performance of BER against existing methods.

Achievable DoF-Delay Trade-Offs for the $K$ -user MIMO Interference Channel With Delayed CSIT

The degrees of freedom (DoF) of the $K$-user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes that achieve increasing DoF values, but at the cost of long communication delays. This work proposes three linear precoding strategies, formulated in such a way that the achievable DoF can be derived as a function of the transmission delay, thus elucidating its achievable DoF-delay trade-off. All strategies are based on the concept of interference alignment, and built upon three main ingredients: delayed CSIT precoding, user scheduling, and redundancy transmission. In this respect, the interference alignment is realized by exploiting delayed CSIT in order to align the interference at the non-intended receivers along the space-time domain. Finally, the latter part of this work settles that all the proposed strategies work also for constant channels, except for SISO. In such a case, the schemes can be made feasible by resorting to asymmetric complex signaling concepts. This conclusion removes the time-varying channels assumption unnecessarily common along all the literature on delayed CSIT.

Performance Analysis of Multi-User Massive MIMO Downlink Under Channel Non-Reciprocity and Imperfect CSI

This paper analyzes the performance of linearly precoded time division duplex based multi-user massive MIMO downlink system under joint impacts of channel non-reciprocity (NRC) and imperfect channel state information (CSI). We consider a generic and realistic NRC model that accounts for transceiver frequency-response as well as mutual coupling mismatches at both user equipment (UE) and base station (BS) sides. The analysis covers two most prominent forms of linear precoding schemes, namely, zero-forcing (ZF) and maximum-ratio transmission (MRT), and assumes that only the statistical properties of the beamformed channel are used at the UE side to decode the received signal. Under the approximation of i.i.d. Gaussian channels, closed-form analytical expressions are derived for the effective signal to interference and noise ratios (SINRs) and the corresponding capacity lower bounds. The expressions show that, in moderate to high SNR, the additional interference caused by imperfect NRC calibration can degrade the performance of both precoders significantly. Moreover, ZF is shown to be more sensitive to NRC than MRT. Numerical evaluations with practical NRC levels indicate that this performance loss in the spectral efficiency can be as high as 42% for ZF, whereas it is typically less than 13% for MRT. It is also shown that due to the NRC, the asymptotic large-antenna performance of both precoders saturate to an identical finite level. The derived analytical expressions provide useful tools and valuable technical insight, e.g., into calculating the NRC calibration requirements in BSs and UEs for any given specific performance targets in terms of effective SINR or the system capacity bound.