The intelligent reflecting surface (IRS) consist of multiple passive elements which make it can passively reflect signals by setting phase angles. The design of IRS has been widely discussed due to its low power consumption and low-cost in recent years. In this article, IRS is used to improve the performance in a secrecy communication system which compose of multiple eavesdroppers equipped with multiple receive antennas and a legitimate user equipped with single antenna. It is assumed that only the imperfect channel state information of the eavesdroppers is available at the base station. To save power consumption, we aim to design the beamforming vector and IRS phase shift matrix by minimizing the transmission power while meeting the requirement of secrecy communication in the worst case of channel. Since the optimization problems have some non-convex constraints, we propose an alternative optimization algorithm to design the beamforming vector and IRS phase shift matrix by employing the semi-relaxation, S-procedure, and difference-of-convex algorithm. Finally, we verify the convergence of the proposed algorithm and reveal the effects of the channel uncertainty, the number of antennas at eavesdropper, and the number of elements at IRS on the transmission power.

In order to mitigate pilot contamination in massive multiple-input multiple-output (MIMO) systems and ensure that each user is uniformly provided with good communication quality, an optimization problem with max-min spectral efficiency as the objective function is constructed in this paper, which consists of pilot assignment and uplink power allocation. Unlike previous works, a scenario is considered here, where more resources occupied by pilot sequence but are not sufficient to allow all users in the system to use orthogonal pilots. So virtual users are needed to be introduced when solving pilot assignment. Based on the mutual interference ratio among users, the Hungarian algorithm can be adopted to solve pilot assignment. After the pilot assignment is completed, uplink power allocation is then performed. On the basis of keeping the result of the pilot assignment fixed, the geometric program (GP) method can be used to solve uplink power allocation. Our proposed scheme can be applied to fractional pilot reuse scenario, and also to integer pilot reuse scenario. The simulation results indicate that the proposed optimization scheme not only improves the minimum spectral efficiency, but also significantly outperforms some other existing schemes.

In order to overcome uplink pilot contamination，the technical bottleneck of massive MIMO,and different from the existing parallel parameter design strategy for blind pilot decontamination,a hierarchical parameter design method was proposed,which points out that different system parameters have different effects on the exact spectrum separation of the sample covariance matrix of the received signal.In other words,different parameters have different priority.Next,it was found that to achieve spectral separation,the power of the desired signal didn’t have to be higher than the interference,and the difference between the two was more important.Furthermore,in a more practical scenario where the pilot sequence length was less than the number of base station receiving antennas,a numerical algorithm was given for the first time to achieve the above-mentioned exact spectral separation.Since the hierarchical parament design ensures the exact separation of the asymptotic spectrum,the results show that the proposed scheme is more suitable for practical applications than the existing blind pilot decontamination.

We propose to use clustered interference alignment for the situation where the backhaul link capacity is limited and the base station is cache-enabled given MIMO interference channels, when the number of Tx-Rx pairs exceeds the feasibility constraint of interference alignment. We optimize clustering with the soft cluster size constraint algorithm by adding a cluster size balancing process. In addition, the CSI overhead is quantified as a system performance indicator along with the average throughput. Simulation results show that cluster size balancing algorithm generates clusters that are more balanced as well as attaining higher long-term throughput than the soft cluster size constraint algorithm. The long-term throughput is further improved under high SNR by reallocating the capacity of the backhaul links based on the clustering results.

With the rapid development of real-time applications in the Internet of Things, people have paid more and more attention on the traffic delay and power consumption. Cloud radio access networks (C-RANs) are seen as a novel network architecture with significant advantages in reducing latency and power consumption on control and data planes. In this paper, we aim to minimize the product of average delay and power consumption in a downlink C-RAN with a hierarchical structure of virtual controllers and high-speed but limited-capacity fronthaul links, by simultaneously considering edge caching and user association. We first study average delay model and power consumption model separately with fronthaul compression technique which is adopted to alleviate the capacity constraint of fronthaul links. Due to the NP-hardness of the user association problem, we propose a low-complexity heuristic algorithm according to the distance and caching of each RRH to find solutions. Meanwhile, the inefficient RRHs are turned into sleep mode to reduce power consumption. Simulation results reveal that the proposed algorithm achieves a better performance in terms of average delay and power consumption than three baseline algorithms.

In massive multiple input multiple output systems, the nonlinear channel estimation method has been initially proved to completely eliminate pilot contamination, which is based on spectrum separation theory to remove interference through projecting it onto the subspace of the desired signal. However, in view of the existing system parameters design for ensuring exact spectrum separation being not accurate, a hierarchical system parameter design method is proposed in this letter. It clarifies the different functions of the different system parameters, so that the asymptotic spectrum of the covariance matrix of the received signal could be more accurately separated. Furthermore, according to the proposed numerical algorithm, in the presence of pilot interference, a better tradeoff between channel estimation quality and pilot overhead is given. It uses pilots as few as possible to obtain the most of the channel estimation quality gain, which is brought by projecting onto the subspace of the separable asymptotic spectrum described above. All of these make our approach more practical.

大规模MIMO系统中基站(BS)端天线数量很大,用于下行信道估计的导频开销将占用很多系统资源,尤其是在FDD模式下。为了减少导频开销,文中提出一种信道矩阵拆分方案,即利用多用户信道间的空间相关性将角域变换下的信道矩阵拆分为两个更加稀疏的信道矩阵,然后采用压缩感知(CS)技术分别恢复出这两部分信道,最后把两部分信道矩阵相加即得到完整的信道估计。不同于传统的信道估计方案,多个用户(UE)端接收到来自BS的导频信号后不在本地进行信道估计,而是把接收到的信号直接反馈给BS,在BS端进行信道的联合恢复。仿真结果表明,所提方案能够有效降低信道估计所需导频开销,同时保证良好的信道估计性能。

In multi-cell massive multiple-input multiple-output (MIMO) systems, the reasonable design of user uplink pilot power and data power is the key to improving system performance. This paper aims to maximize the target cell's sum achievable uplink rate, and users' uplink pilot-to-data power ratio (PDPR) in this cell is designed in the presence of pilot contamination (PC). The optimal uplink PDPR under the condition of the lower bound of the sum achievable uplink rate is calculated. Based on this optimal uplink PDPR, the user joint optimization algorithm (UJOA) is proposed to design uplink PDPR in the target cell. To achieving the purpose of jointly optimizing the uplink PDPR, we use the error factor controlling the uplink PDPR and gradually approach the optimal uplink PDPR of each user in the target cell. Numerical results show that the UJOA scheme is better than the same ratio (SR) scheme in the design of uplink PDPR. We can achieve the better sum achievable uplink rate in the target cell and have a large gain in the system performance when using the uplink PDPR which designed by UJOA.

Pilot contamination (PC) is one of the main obstacles that limit the performance of massive multiple-input multiple-output (MIMO) systems. In this paper, we propose the asynchronous scheduling which is based on the fractional pilot reuse so that the users can be free from the pilot contamination during the uplink transmission. According to the level of interference, the users are divided into two groups, which are referred as the center users, who suffer from the mild pilot contamination, and the edge users, who suffer from the severe pilot contamination. Based on this distinction, a cell-center pilot set is reused for all the center users in all cells, whereas a cell-edge pilot set is applied for the edge users in the adjacent cells. In this case, the pilots used by the cell-edge users are orthogonal to each other. So the edge users can transmit the pilots at any time. But the pilot set for the center users are reused for all the cells, the cell-center users send their pilots in the non-overlapped time periods in order to avoid the pilot contamination. With this scheduling, the cost of the orthogonal pilots for each cell is reduced obviously. And the base station (BS) can easily recover the estimation of the pilots as it knows there is no pilot contamination. Simulation results show that the proposed asynchronous fractional pilots scheduling (AFPS) outperforms the other conventional pilot assignment schemes.

This study investigates the spectral efficiency of multi-pair massive multiple-input multiple-output amplify-and-forward relay networks by considering the composite channel aging effect. The rational of this work is that the channel aging effect caused by phase noise and node movements is an inevitable practical channel impairment in time-varying fading channels and substantially degrades the performance. The proposed model comprises multiple sources and multiple destinations, each equipped with a single antenna, which communication via a relay equipped with a very large number of antennas by employing maximal-ratio combining/maximum-ratio transmission. Based on this model, the authors first derive a closed-form lower bound expression for the achievable rate of per source–destination pair. Then, by using the derived expression, they study how the transmitted powers of each source and the relay can be reduced without compromising the spectral efficiency when the number of relay antennas approaches infinity. They also discuss the effect of channel aging coefficients, including Doppler shift and phase noise increment variance, on the asymptotic spectral efficiency under different power scaling laws. Both theoretical analysis and Monte Carlo simulations disclose that the channel aging effect does not affect the power scaling laws but degrades the spectral efficiency.

The purpose of this paper is to minimize total of the consumed power while making sure users can reach desired achievable rates in multi cell multi user massive multiple input multiple output (MIMO) system. The setting of CoBF (the coordinated beamforming scheme) in which each user receives useful signal from its own cell but treat signal from other cells as interference is considered. First, expressions of the downlink (DL) achievable user rates by taking maximum ratio transmission (MRT) precoding and zero-forcing (ZF) precoding into consideration are derived. Based on those expressions, the DL power minimization problem is presented, to solve this problem, linear programming is used. Further, the problem of finding appropriate achievable rate target by using max-min achievable rate algorithm is solved. Numerical results show effectiveness of our proposed method.

Pilot symbols are used to estimate channel state information (CSI) in Massive Multiple-input Multiple-output (MIMO) systems, the pilot-to-data power ratio (PDPR) is known to have an impact on estimation result. However, the works before only consider the one cell model which has no pilot contamination. This paper focus on the impact of imperfect CSI and pilot contamination on pilot-to-data power ratio. It investigates the impact of PDPR to minimize mean square error (MSE) of uplink data transmission of Massive MIMO systems. First, the MSE expressions of uplink data transmission of Massive MIMO system is derived, then a method to estimate channel covariance matrix and reduce the impact of pilot contamination is introduced, finally we compare the result to show the impact of PDPR on minimize MSE. The result shows PDPR has a impact on the uplink received data MSE of Massive MIMO system.

In this paper, we investigate the performance of a multi-pair massive MIMO AF relay network, where multiple source users communicate with multiple destination users through a relay equipped with a very large number of antennas, when zero-forcing (ZF) reception/transmission is utilized at the relay. In contrast to prior works, we derive new exact analytical closed-form expressions of the outage probability and the ergodic achievable rate, and these results are valid for any finite number of relay antennas. In particular, the asymptotic performance and power-scaling laws are further analyzed and compared under two different asymptotic cases for the number of relay antennas going to infinity with a fixed and large number of user pairs, respectively. Both analytical results and Mont-Carlo simulations have consistently shown the effects of the number of relay antennas and the number of user pairs on the outage probability, the achievable rate, and power-scaling laws.

The fundamental limit of massive multiple-input-multiple-output (MIMO) system's performance is pilot contamination due to the reuse of the same set of pilot sequences by users in adjacent cells, which can be alleviated by assign the pilot sequences to the users appropriately, power control and many other ways. In this paper, the network model considers stochastic geometry that users are distributed according to a homogeneous Poisson point process (PPP) to simulate the real user distribution. The signal-to-interference-plus-noise (SINR) of uplink can be analytically derived, and combined with the flexible pilot reuse to simulate the reality of the pilot allocation strategy. The users suffer from severe pilot contamination use orthogonal pilot and the others with light contamination can reuse a same set of pilot sequence, ultimately get the optimal pilot reusing factor and achieve a reasonable pilot allocation.

Very large multiple-input multiple-output (MIMO) technology has a potential of significantly improving the system performance of multi-cell time-division duplexing (TDD) networks, but in practice it is limited by pilot contamination. Different from the traditional channel estimation mean square error (MSE) expressions, the expressions that we derived have algebraic form, which no longer need hard matrix inversion as M, the number of the base station (BS) antennas, increasing. From them, we also found that the average transmitted power and length of training sequence almost does not help in enhancing the performance of MSE as \(M\rightarrow \infty \). Based on this, two pilot contamination reduction methods for the very large MIMO multi-cell TDD system were proposed. One is realized by grouping all the cells into two categories, using orthogonal pilots between these two types of cells or aligning the uplink pilot time slot of the cells in one category with the downlink data time slot of those cells in the neighboring categories. The other is to find the optimal division of pilot sequence length and the set of all users’s pilot transmission slots allocation through BSs’s coordination. The effectiveness of our proposed methods are verified via both theoretical analysis and numerical results.

Large-scale multiple-input-multiple-output ( MIMO) networks, together with relay technology, have received considerable attention due to their remarkable capacity potential. Nevertheless, the majority of recent research studies on the asymptotic capacity of large-scale MIMO amplify-and-forward ( AF) relay networks are limited to a fundamental assumption of small-scale fading, where the effect of large-scale fading, including shadow fading and path loss, is ignored. Motivated by this observation, in this paper, we present an extended model for the asymptotic capacity analysis in a composite fading environment, where Rayleigh fading, shadow fading, and path loss effect are incorporated altogether. Moreover, a realistic relay distribution is considered for real-world application of our capacity analysis. The proposed model consists of one source and one destination that are both equipped with M antennas, which communicate through K relays, each having N antennas. We first employ random matrix theory to derive the empirical cumulative distribution of the channel covariance matrix and analyze the asymptotic capacity per source-destination antenna pair as both M and NK tend to infinity, but their ratio remains as a constant. We then consider the asymptotic capacity under two asymptotic cases for a finite and an infinite number of relays, respectively. It is shown through both theoretical analysis and Monte Carlo simulations that increasing the shadowing standard deviation can improve asymptotic capacity, whereas increasing the path loss exponent would lead to a capacity reduction. Our simulation results also reveal the effects of the relay distribution, as well as the source and relay transmission powers, on the asymptotic capacity.

The problem of compressed sensing (CS) is considered in two-dimensional (2D) sparse decomposition measurement model. Correspondingly, a novel recovery algorithm - modified 2D subspace pursuit (M-2DSP) algorithm is proposed with the available prior support and chunk sparse structure. The massive multi-input multi-out (MIMO) system show a concealed sparse structure and temporal correlation in the user (UE) channel matrix in virtue of the shared local scatterers in the physical propagation environment. Thereby the proposed scheme can be applied to sparse channel estimation in massive MIMO systems with temporal correlation. Furthermore its effectiveness is proved, both theoretical analysis and experiment simulations testify the usefulness and advantages of the new algorithm in recovery performance, especially in smaller overhead training pilot quantity and lower transmit signal noise ratio (SNR).

Pilot contamination caused by non-orthogonal pilot sequences reuse in adjacent cells has become one of the main impairments for massive multiple-input multiple-output (MIMO) systems. A scheme named flexible pilot reuse is proposed in this paper to reduce the effect. The main idea is that users suffered from mild pilot contamination (PC) are allocated the same set of orthogonal pilots, while the users suffered from severe PC in adjacent cells all use orthogonal pilots. That is users in a cell have different reuse factors according to the severity of PC. We derive closed-form approximate expressions of uplink achievable rate for both mild and severe PC groups, then analyze the optimal reuse factor and obtain the suitable scope of cell users for the design of flexible pilot reuse. Simulation results show that the uplink sum rate is improved significantly with the proposed scheme compared to existing integer reuse.

This paper studies the downlink sum-rate and energy efficiency (EE) of massive multiple-input multiple-output (MIMO) systems under the effect of channel aging caused by the movements of users. First, a closed-form expression of the downlink sum-rate where zero-forcing (ZF) precoder is adopted at the base station (BS) is derived. Based on the expression, the power-scaling law that when the number of BS antennas M approaches to infinity, the transmit power of BS can be reduced proportionally to 1/√M is still satisfied in the massive MIMO downlink system. Second, we utilize a general power consumption model to analyze the EE of the system. Both theoretical analysis and Monte-Carlo simulations show that the emergence of channel aging could degrade the sum-rate and the EE of the system.

We investigate channel estimation mean square error (MSE) performance in Massive multiple-input multiple-output (MIMO) system with pilot contamination. Different from the traditional MSE expressions, the expressions that we derived have algebraic form, which no longer need hard matrix inversion as M, the number of the base station antennas, increasing. From them, we also found that the average transmitted power and length of training sequence almost does not help in enhancing the performance of MSE as M → ∞. Based on this, a scheme to reduce pilot contamination in time division duplexing (TDD) cellular networks is proposed with simple cooperation among base stations. Numerical results finally verify our derivations and the proposed scheme.