Multi-cell Massive Multiple-input Multiple-output Systems Research Articles

User Grouping and Pilot Allocation for Spatially Correlated Massive MIMO Systems

This paper proposes a novel approach to deal with pilot contamination for spatially correlated massive multiple-input multiple-output (MIMO) systems with insufficient pilots. Specifically, a typical multi-cell multi-terminal time division duplex massive MIMO system is modeled first. To maximize the average achievable system capacity, a user grouping method which progressively merges the individual terminals with the largest angle of arrival similarity is proposed to mitigate the intra-cell interference. Furthermore, in order to alleviate the inter-cell interference, a pilot allocation method is proposed, including two algorithms, i.e., group matching algorithm and graph coloring-based pilot allocation algorithm. Compared with the existing pilot allocation schemes, the simulation results validate that the proposed approach can effectively improve the complexity-performance trade-off with a finite number of the base station antennas.

Antenna Tilt Adaptation for Multi-Cell Massive MIMO Systems

This letter proposes an antenna tilt adaptation approach for multi-cell massive multiple-input multiple-output systems. The asymptotic spectral efficiency of the system with pilot contamination in the limit of the antennas is first derived. The analysis demonstrates that the spectral efficiency is a concave function of the tilts with some specific requirements being satisfied. As a result, a gradient descent-based method is proposed to approach the optimal tilt. Numerical results verify that the proposed approach performs better than a traditional low-complexity approach.

Max–Min Multicell-Aware Precoding and Power Allocation for Downlink Massive MIMO Systems

We propose a max-min multi-cell aware regularized zero-forcing (Max-Min MCA-RZF) precoding and power allocation scheme for downlink multi-cell massive multiple-input multiple-output (MIMO) systems. A general correlated channel model is considered, and the adopted channel state information (CSI) acquisition model includes the effects of estimation errors and pilot contamination. We use results from random matrix theory to derive deterministic equivalents for the proposed Max-Min power allocation in the large system limit which solely depend on statistical CSI, but not on individual channel realizations. Our numerical results show that the proposed Max-Min MCA-RZF precoder achieves a substantially higher network-wide minimum rate than the MCA-RZF and the conventional RZF precoders with uniform power allocation, respectively, as well as the conventional RZF precoder with Max-Min power allocation.

Optimal pilot design in massive MIMO systems based on channel estimation

The performance of multicell massive multiple-input multiple-output (MIMO) systems is heavily affected by pilot contamination. This study considers the problem of pilot contamination and analytical expressions are presented on the normalised mean square error (NMSE) of the minimum mean square error channel estimation algorithm. Based on the NMSE of the massive MIMO systems, a pilot design criterion is proposed to design the optimal pilot sequences for mitigating the pilot contamination. Following this criterion, Chu sequence with perfect auto-correction and cross-correlation properties are employed to design the optimal pilot sequences. Then the performance of the proposed pilot design-based scheme is investigated, and the exact NMSE expressions are presented. The excellent performance of this pilot design scheme has been confirmed in the authors' simulations.

Low-Complexity Precoding for Sum Rate Maximization in Downlink Massive MIMO Systems

We propose a precoding scheme to improve the downlink sum rate for a multicell massive multiple-input multiple-output (MIMO) system. We first present a low-complexity approach based on dirty paper coding and zero-forcing that combines a reduced form of QR decomposition and an orthogonal projection. We formulate a downlink sum rate optimization problem that takes both intracell and intercell interference into account, and then we use the convex conjugate to transform the problem into an unconstrained dual problem to find an optimal solution by applying a quasi-Newton algorithm with low complexity per iteration. We prove that the proposed algorithm exhibits faster convergence than other methods, and the numerical results verify that the proposed precoding design outperforms conventional precoding methods in multicell massive MIMO systems.

Single branch search based pilot allocation for multi‐cell massive multiple‐input multiple‐output systems

The performance of multi-cell massive multiple-input multiple-output systems is constrained by inter-cell interference. In this study, a pilot allocation approach is proposed to mitigate interference in such systems. The asymptotic spectral efficiency in the limit of the number of antennas is derived first. By analysing the derivatives of the spectral efficiency with the pilot allocation, a single branch search algorithm for pilot allocation is formed. In contrast, the existing approaches allocate pilots for each cell separately or with brute-force search. The analysis and numerical results show that the proposed approach is of better compromise in mitigating the interference and reducing the computational complexity.

Weighted-Graph-Coloring-Based Pilot Decontamination for Multicell Massive MIMO Systems

A multicell massive multiple-input multiple-output (MIMO) system, which utilizes a large number of base-station antennas to simultaneously serve a set of users, suffers from pilot contamination (PC) due to unavoidable reuse of pilots in adjacent cells. In this paper, a weighted-graph-coloring-based pilot decontamination (WGC-PD) scheme is proposed to mitigate PC for multicell massive MIMO systems. Specifically, based on limited cooperation among cells, an edge-weighted interference graph (EWIG) is first constructed to depict the potential PC relationship among users, whereby two users in different cells are connected by a weighted edge, indicating the strength of potential PC when they reuse the same pilot. Then, inspired by classical graph coloring algorithms, we develop the WGC-PD scheme by denoting each color as a pilot and each vertex as a user in the EWIG, which is able to mitigate PC by assigning different pilots to connected users with a large weight in a greedy way with insufficient pilot resource. Compared with exhaustive search among numerous pilot assignment solutions, the proposed WGC-PD scheme is able to mitigate PC with significantly reduced complexity, which is verified by numerical results.

Pilot Power Allocation Through User Grouping in Multi-Cell Massive MIMO Systems

In this paper, we propose a relative channel estimation error (RCEE) metric, and derive closed-form expressions for its expectation $\rm {Exp}_{rcee}$ and the achievable uplink rate holding for any number of base station antennas $M$, with the least squares (LS) and minimum mean squared error (MMSE) estimation methods. It is found that RCEE and $\rm {Exp}_{rcee}$ converge to the same constant value when $M\rightarrow\infty$, resulting in the pilot power allocation (PPA) is substantially simplified and a PPA algorithm is proposed to minimize the average $\rm {Exp}_{rcee}$ per user with a total pilot power budget $P$ in multi-cell massive multiple-input multiple-output systems. Numerical results show that the PPA algorithm brings considerable gains for the LS estimation compared with equal PPA (EPPA), while the gains are only significant with large frequency reuse factor (FRF) for the MMSE estimation. Moreover, for large FRF and large $P$, the performance of the LS approaches to the performance of the MMSE, which means that simple LS estimation method is a very viable when co-channel interference is small. For the achievable uplink rate, the PPA scheme delivers almost the same average achievable uplink rate and improves the minimum achievable uplink rate compared with the EPPA scheme.

Energy‐efficient dual‐layer coordinated beamforming scheme in multi‐cell massive multiple‐input–multiple‐output systems

To improve the energy efficiency of multi-cell massive multiple-input–multiple-output system while guaranteeing the information transmission quality, this study proposes a dual-layer coordinated beamforming scheme. In the proposed scheme, the beamformer at each evolved node B (eNB) is divided into a cell-layer beamformer and a user-layer beamformer. The cell-layer beamformer is used to mitigate inter-cell interference (ICI) by exchanging long-term channel state information (CSI) among eNBs. The user-layer beamformer serves user according to the local real-time CSI at each eNB. On the basis of the dual-layer structure, the cell-layer beamformers, the user-layer beamformers, and power allocation are jointly optimised in order to minimise the total transmit power across all the eNBs subject to the signal-to-interference-plus-noise ratio requirements and single-antenna power constraints. To make the original problem solvable, the ICI is replaced by its upper bound. Then, the problem is partitioned into two convex sub-problems, and two iterative algorithms are proposed in order to find the sub-optimal solution to the original optimisation problem. Simulation results show that the proposed scheme performs better than two reference schemes including the existing zero-forcing scheme and coordinative multiple point schemes.

Uplink training for multicell massive multiple‐input–multiple‐output systems: a combination of time‐shifted and time‐aligned pilot approaches

Pilot contamination reduction can improve the achievable uplink and downlink rates in a multicell massive multiple-input–multiple-output system. To this end, this study first proposes two schemes to mitigate the effect of pilot contamination by implementing uplink training with time-aligned and time-shifted pilot transmissions. Accordingly, these techniques enable the system not only to exploit the advantages of time-shifted training but also to benefit from the use of conventional systems that improve the achievable rates. The authors introduce channel estimation in matrix form by estimating from a near minimum mean square error method. Furthermore, linear detector and precoding methods are used for a base station with a finite number of antennas in order to derive the closed-form lower bounds of the achievable rates with two uplink training schemes for both uplink and downlink transmissions. Finally, numerical results are presented to verify the analysis.

Guest Editorial

Guest Editorial

DOA-based beamforming for multi-cell massive MIMO systems

This paper proposes a direction-of-arrival (DOA)-based beamforming approach for multi-cell massive multiple-input multiple-output systems with uniform rectangular arrays (URAs). The proposed approach utilizes the steering vectors of the URA to form a basis of the spatial space and selects the partial space for beamforming according to the DOA information. As a result, the proposed approach is of lower computational complexity than the existing methods which utilize the channel covariance matrices. Moreover, the analysis demonstrates that the proposed approach can eliminate the interference in the limit of infinite number of the URA antennas. Since the proposed approach utilizes the multipaths to enhance the signal rather than discarding them, the proposed approach is of better performance than the existing low-complexity method, which is verified by the simulation results.

I/Q Imbalance Aware Widely-Linear Receiver for Uplink Multi-Cell Massive MIMO Systems: Design and Sum Rate Analysis

In-phase/quadrature-phase imbalance (IQI) is one of the most important hardware impairments in communication systems. It arises in the analogue parts of direct conversion transceivers and can cause severe performance losses. In this paper, IQI aware widely-linear (WL) channel estimation and data detection schemes for uplink multicell massive multiple-input multiple-output (MIMO) systems are proposed. The resulting receiver is a WL extension of the minimum mean-square-error (MMSE) receiver and jointly mitigates multiuser interference and IQI by processing the real and the imaginary parts of the received signal separately. Thereby, the IQI arising at both the base station and the user terminals is taken into account. The considered channel state information acquisition model includes the effect of pilot contamination, which is caused by the reuse of the same training sequences in neighbouring cells. We apply results from random matrix theory to derive analytical expressions for the asymptotic achievable sum rates of the proposed IQI aware and conventional IQI unaware (IQU) receivers in the large system limit. Our simulation and analytical results show that the performance of the proposed IQI aware WLMMSE (IQA-WLMMSE) receiver in a system with IQI is close to that of the MMSE receiver in an ideal system without IQI.

Asymptotic Equivalent Performance of Multicell Massive MIMO With Spatial–Temporal Correlation

In this letter, we derive some asymptotic equivalent (AE) sum rates of a multicell downlink massive multiple-input multiple-output (MIMO) system with different beamforming schemes. Due to insufficient antenna spacing and user mobility, we take spatial and temporal correlation into consideration and obtain a correlated channel state information (CSI) model. Under the correlated CSI model, the AE sum rates with matched filter (MF), zero-forcing (ZF) and regularized zero-forcing (RZF) beamforming are obtained in closed-form expression based on random matrix theory. These AE sum rates provide a key insight into theoretically evaluating the effect of correlated CSI on the performance. We find that the spatial correlation has a negative effect on the sum rate and the three beamformings are all sensitive to the temporal correlation. Furthermore, RZF and ZF beamforming are more robust to the spatial correlation compared with MF beamforming.

Statistical Beamforming for Interference Mitigation in Multi-cell Massive MIMO Systems

AbstractThis paper proposes a statistical beamforming approach to mitigate interference in multi-cell massive multiple-input multiple-output systems. The proposed approach projects the signal subspace onto the null space of the interference to form the weight vector with the statistical channel state information. In contrast to the existing methods which only utilize the partial null space of the interference, the proposed approach can collect more signal when mitigating the interference. In addition, the large system analysis demonstrates that the interference is eliminated with uniform rectangular arrays. Numerical results show that the proposed approach can achieve higher sum rate than the existing methods and verify the performance analysis.

On error rate performance of multi-cell massive MIMO systems with linear receivers

For an uplink of multi-cell multiuser (MU) Multiple-Input, Multiple-Output (MIMO) system, where each cell has a Base Station (BS) with M antennas and K users with single antenna, the Zero-Forcing (ZF) decoder and the Minimal Mean-Square Error (MMSE) decoder are considered. Upper bounds, lower bounds on Pair-wise Error Probability (PEP) of these decoders are derived. Moreover, analytic expressions of approximations on PEP are given. These show that, if the BS knows Channel State Information (CSI) in its own cell only and does not have CSI in other cells, error floors will occur even when Signal-to-Noise Ratio (SNR) goes to infinity for both the ZF decoder and the MMSE decoder, while these error floors disappear when M goes to large. All theoretical results above are confirmed by simulations. Especially, the approximations of PEP match up with simulation results very well.

Power Allocation Schemes for Multicell Massive MIMO Systems

This paper investigates the sum-rate gains brought by power allocation strategies in multicell massive multipleinput multiple-output systems, assuming time-division duplex transmission. For both uplink and downlink, we derive tractable expressions for the achievable rate with zero-forcing receivers and precoders respectively. To avoid high complexity joint optimization across the network, we propose a scheduling mechanism for power allocation, where in a single time slot, only cells that do not interfere with each other adjust their transmit powers. Based on this, corresponding transmit power allocation strategies are derived, aimed at maximizing the sum rate per-cell. These schemes are shown to bring considerable gains over equal power allocation for practical antenna configurations (e.g., up to a few hundred). However, with fixed number of users (N), these gains diminish as M turns to infinity, and equal power allocation becomes optimal. A different conclusion is drawn for the case where both M and N grow large together, in which case: (i) improved rates are achieved as M grows with fixed M/N ratio, and (ii) the relative gains over the equal power allocation diminish as M/N grows. Moreover, we also provide applicable values of M/N under an acceptable power allocation gain threshold, which can be used as to determine when the proposed power allocation schemes yield appreciable gains, and when they do not. From the network point of view, the proposed scheduling approach can achieve almost the same performance as the joint power allocation after one scheduling round, with much reduced complexity.

Estimation accuracy of multi‐cell massive multiple‐input multiple‐output systems in correlated Rician fading channel

The performance analysis of a multi-user multi-cell massive multiple-input multiple-output system that applies a conventional channel estimation technique, namely the linear minimum mean square error over correlated Rician fading is investigated. Based on the analysis, it is found that increasing the line-of-sight component can enhance the estimation accuracy.

Linear Precoding of Data and Artificial Noise in Secure Massive MIMO Systems

In this paper, we consider secure downlink transmission in a multi-cell massive multiple-input multiple-output (MIMO) system where the numbers of base station (BS) antennas, mobile terminals, and eavesdropper antennas are asymptotically large. The channel state information of the eavesdropper is assumed to be unavailable at the BS and hence, linear precoding of data and artificial noise (AN) are employed for secrecy enhancement. Four different data precoders (i.e., selfish zero-forcing (ZF)/regularized channel inversion (RCI) and collaborative ZF/RCI precoders) and three different AN precoders (i.e., random, selfish/collaborative null-space based precoders) are investigated and the corresponding achievable ergodic secrecy rates are analyzed. Our analysis includes the effects of uplink channel estimation, pilot contamination, multi-cell interference, and path-loss. Furthermore, to strike a balance between complexity and performance, linear precoders that are based on matrix polynomials are proposed for both data and AN precoding. The polynomial coefficients of the data and AN precoders are optimized respectively for minimization of the sum mean squared error of and the AN leakage to the mobile terminals in the cell of interest using tools from free probability and random matrix theory. Our analytical and simulation results provide interesting insights for the design of secure multi-cell massive MIMO systems and reveal that the proposed polynomial data and AN precoders closely approach the performance of selfish RCI data and null-space based AN precoders, respectively.

Secure Transmission in Multicell Massive MIMO Systems

In this paper, we consider physical layer security provisioning in multicell massive multiple-input-multiple-output (MIMO) systems. Specifically, we consider secure downlink transmission in a multicell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) in the presence of a passive multiantenna eavesdropper. We investigate the resulting achievable ergodic secrecy rate and the secrecy outage probability for the cases of perfect training and pilot contamination. Thereby, we consider two different AN shaping matrices, namely, the conventional AN shaping matrix, where the AN is transmitted in the null space of the matrix formed by all user channels, and a random AN shaping matrix, which avoids the complexity associated with finding the null space of a large matrix. Our analytical and numerical results reveal the following, in multicell massive MIMO systems employing matched-filter precoding: 1) AN generation is required to achieve a positive ergodic secrecy rate if the user and the eavesdropper experience the same path loss; 2) even with AN generation, secure transmission may not be possible if the number of eavesdropper antennas is too large and not enough power is allocated to channel estimation; 3) for a given fraction of power allocated to AN and a given number of users, in case of pilot contamination, the ergodic secrecy rate is not a monotonically increasing function of the number of BS antennas; and 4) random AN shaping matrices provide a favorable performance/complexity tradeoff and are an attractive alternative to conventional AN shaping matrices.