Finite Number Of Antennas Research Articles

The Robustness of Favorable Propagation in Massive MIMO to Location and Phase Errors

The impact of random errors (implementation inaccuracies) in element locations and beamforming phases on favorable propagation (FP) in massive multiple-input multiple-output (MIMO) line-of-sight (LOS) channels is studied. For arbitrary array geometry and under independent (possibly non-Gaussian) errors, the FP property is shown to hold for the perturbed array as long as it holds for the unperturbed one. This means that small errors do not have catastrophic impact on the FP, even for a large number of antennas. The negative impact of random errors is to slow down the convergence to the asymptotic value so that more antennas are needed under random errors to achieve the same low inter-user interference as without errors. For large but finite number of antennas, the distribution and an analytically-tractable approximation of the inter-user interference power are obtained. Practical design guidelines are given that quantify the accuracy level needed to make the impact of random errors negligible. The analytical results are validated via numerical simulations and are in agreement with measurement-based studies.

Dynamic Antenna Selection for Colocated MIMO Radar

Antenna distribution plays an important role for the performance gain in multiple-input–multiple-output (MIMO) radar target tracking. Since to meet the requirements of the low probability of interception, especially in a hostile environment, only a finite number of antennas can be activated at each step. This naturally leads to a performance-driven resource management problem. In this paper, a dynamic antenna selection strategy is proposed for tracking targets in colocated MIMO radar. The derived posterior Cramér–Rao lower bound (PCRLB) of joint direction-of-arrival (DOA) and Doppler estimate were chosen as the optimization criteria. Furthermore, in the deviation, the target radar cross-section (RCS) as the determining variable and the random variable are both discussed. The objective function is related to the antenna allocation and non-convex, and an efficient fast discrete particle swarm optimization (FDPSO) algorithm is proposed for the solution exploration. Additionally, a closed-loop feedback system is established, where the main idea is that the tracking information from the current time epoch is utilized to predict the PCRLB and to guide the antenna adjustment for the next time epoch. The simulation results demonstrate the performance improvement compared with the three fixed-antenna configurations. Moreover, the FDPSO can provide close-to-optimal solutions while satisfying the real-time demand.

Reconfigurable Intelligent Surface-Assisted Massive MIMO: Favorable propagation, channel hardening, and rank deficiency [Lecture Notes

Massive multiple-input multiple-output (MIMO) and reconfigurable intelligent surface (RIS) are two promising technologies for 5G-and-beyond wireless networks, capable of providing large array gain and multiuser spatial multiplexing. Without requiring additional frequency bands, those technologies offer significant improvements in both spectral and energy efficiency by simultaneously serving many users. The performance analysis of an RIS-assisted massive MIMO system as a function of channel statistics relies heavily on fundamental properties, including favorable propagation, channel hardening, and rank deficiency. The coexistence of both direct and indirect links results in aggregated channels, whose properties are the main concerns of this “Lecture Notes” article. For practical systems with a finite number of antennas and engineered scattering elements of the RIS, we evaluate the corresponding deterministic metrics, with Rayleigh fading channels as a typical example.

Performance of Network-Assisted Full-Duplex for Cell-Free Massive MIMO

Network assisted full-duplex (NAFD) is a spatial-division duplex technique for future wireless networks with cell-free massive multiple-input multiple-output (CF massive MIMO) network, where a large number of remote antenna units (RAUs), either using half-duplex or full-duplex, jointly support truly flexible duplex including time-division duplex, frequency-division duplex and full duplex on demand of uplink and downlink traffic by using network MIMO methods. With NAFD, bi-directional data rates of the wireless network could be increased and end-to-end delay could be reduced. In this paper, the spectral efficiency of NAFD communications in CF massive MIMO network with imperfect channel state information (CSI) is investigated under spatial correlated channels. Based on large dimensional random matrix theory, the deterministic equivalents for the uplink sum-rate with minimum-mean-square-error (MMSE) receiver as well as the downlink sum-rate with zero-forcing (ZF) and regularized zero-forcing (RZF) beamforming are derived. Numerical results show that under various environmental settings, the deterministic equivalents are accurate in both a large-scale system and system with a finite number of antennas. It is also shown that with the downlink-to-uplink interference cancellation, the uplink spectral efficiency of CF massive MIMO with NAFD could be improved. The spectral efficiencies of NAFD with different duplex configurations such as in-band full-duplex, and half-duplex are compared. With the same total numbers of transmit and receive antennas, NAFD with half-duplex RAUs offers a higher spectral efficiency. To alleviate the uplink-to-downlink interference, a novel genetic algorithm based user scheduling strategy (GAS) is proposed. Simulation results show that the achievable downlink sum-rate by using the GAS is greatly improved compared to that by using the random user scheduling.

LI Cancellation and Power Allocation for Multipair FD Relay Systems With Massive Antenna Arrays

Massive antenna arrays are capable of canceling out the loop interference (LI) at the relay station in multipair full-duplex (FD) relay networks even without LI channel knowledge if the number of antennas is allowed to grow without a bound. For large but finite number of antennas, however, channel estimation-based LI cancelation is required. In this letter, we propose a pilot protocol for LI channel estimation by exploiting the channel coherence time difference between static and moving transceivers in a multipair FD relay system. To maximize the end-to-end achievable rate, we also design a novel power allocation scheme to adjust the transmit power of each link at the relay. The analytical and numerical results show that the proposed novel pilot protocol and power allocation scheme jointly improve spectral and energy efficiency significantly with realistic coherence time differences.

Low-Complexity Truncated Polynomial Expansion DL Precoders and UL Receivers for Massive MIMO in Correlated Channels

In Time Division Duplex reciprocity-based massive MIMO, it is essential to compute the downlink precoding matrix over all OFDM resource blocks within a small fraction of the uplink-downlink slot duration. Because of this harsh computation latency constraint, early implementations of massive MIMO considered the simple Conjugate Beamforming (ConjBF) precoding method. On the other hand, it is well-known that in the regime of a large but finite number of antennas, the Regularized Zero-Forcing (RZF) precoding is generally much more effective than ConjBF. In order to close the gap between ConjBF and RZF, while meeting the latency constraint, truncated polynomial expansion (TPE) methods have been proposed. In this paper, we present a novel TPE method that outperforms previously proposed methods in the non-symmetric case of users with different channel correlations, subject to the condition that the covariance matrices of the user channel vectors can be approximated, for a large number of antennas, by a family of matrices with common eigenvectors. This condition is met, for example, by uniform linear and uniform planar arrays in far-field conditions. The proposed method is computationally simple and lends itself to classical power allocation optimization such as min-sum power and max-min rate . We provide a detailed analysis of the computation latency vs computation resources, specifically targeted to a highly parallel FPGA hardware architecture. We conclude that the proposed TPE method can effectively close the performance gap between ConjBF and RZF with computation latency of less than one LTE OFDM symbol, as assumed in Marzetta’s work on massive MIMO.

Multicast Wirelessly Powered Network With Large Number of Antennas via First-Order Method

To prolong the lifetime of energy constrained devices in Internet of Things, devices can harvest wireless energy from the control signal multicast from the access point. Unfortunately, hampered by the path-loss, the efficiency of such multicast wirelessly powered network is low. While large-scale antennas at access point can be used to improve the efficiency, the beamforming design problem in multicast wirelessly powered network is known to be NP-hard, and the traditional difference of convex programming becomes prohibitively time consuming in large-scale settings. On the other extreme, by using the assumption of infinite number of antennas and applying the law of large numbers, simple beamforming solution is possible. However, when applied to scenarios with finite number of antennas, the performance of such asymptotic solution is far from that of difference of convex programming. To resolve this apparent complexity-performance dilemma, this paper develops an algorithm which reduces the computation time by orders of magnitude, while still guaranteeing the same performance compared with the difference of convex programming. In particular, the proposed algorithm consists of two fast-convergent iterative procedures and is guaranteed to obtain a Karush–Kuhn–Tucker solution. Furthermore, in each iteration, the algorithm only requires the computation of inner products between channel vectors and can be run in parallel for all the users. Thus, the complexity scales linearly with the number of antennas at access point. Finally, numerical results validate the performance and the speed of the proposed scheme.

Analytical Approximation of the Channel Rate for Massive MIMO System With Large But Finite Number of Antennas

In practical massive multiple-input–multiple-output (MIMO) system, limited transmitted antennas installed at the base station (BS) cannot guarantee the ideal orthogonality and the theoretical channel rate cannot thus be achieved. In this paper, we consider the approximation of channel rate for the configuration of large but finite number of antennas at BS in a massive MIMO system. A perturbation matrix is introduced to model the non-ideal orthogonality. And then, Taylor expansion of determinant is utilized to derive the closed form of the achievable channel rate. The convergence of the Taylor expansion is theoretically proved and simulated. Numerical results show that our calculation of channel rate can get a better approximation compared with the practical rate, especially in the case of high expansion order and large number of antennas.

Analytical Approximation for Capacity in Massive MIMO Systems

In most existing research on massive multiple-input multiple-output (MIMO) systems, theoretical analysis relies on the assumption that the number of antennas at the base station is infinite. Under this assumption, channel vectors for different users will be asymptotically orthogonal; therefore, the calculation of channel capacity can be greatly simplified. However, in practical systems, the number of antennas is always finite, and the channel vectors for different users cannot be completely orthogonal. In this paper, we propose an analytical approximation for the channel capacity of massive MIMO systems, with a finite number of antennas. Numerical results show that the derived closed-form expression is more accurate than the one assuming that the channel vectors are asymptotically orthogonal.

Angle-of-Arrival-Dependent Interference Modeling in Rician Massive MIMO

In this paper, we study the uplink in a single-cell massive multiple-input–multiple-output system. The base station (BS) is equipped with three antenna arrays, each covering one third of the cell area. Each antenna array comprises a large yet finite number of antennas. The single-antenna users are randomly and uniformly distributed in the cell, transmitting to the BS utilizing full channel inversion power control. All users experience Rician fading. Receiver maximum-ratio-combining is performed at the BS. Under such a setting, we focus on one cell sector and analyze the intrasector interference in a realistic situation where the number of BS antennas is not extremely large compared with the user number. In particular, we show that, due to the line-of-sight (LoS) component of the channel, the interference is partially determined by the angles of arrival of the signals. We approximate the LoS component interference by a Beta mixture. The interference in Rician fading is then modeled as a noncentral chi-square distribution with a random noncentrality parameter, corresponding to the LoS component. The approximate interference distribution can be used to compute signal-to-interference-ratio-dependent metrics such as outage probability and average throughput.

Spectral and energy efficiency of downlink MU-MIMO systems with MRT

This paper studies the achievable spectral efficiency (SE) of downlink multiuser multiple-input-multiple-output (MIMO) system, where the base station (BS) is deployed an arbitrary finite antenna number and communicates simultaneously with many users. We assume that the BS has accurate channel state information (CSI) and adopt maximum ratio transmission (MRT) precoding. An accurate analytical result for the achievable SE is obtained. Based on the analytical result on the achievable SE, we further study the achievable energy efficiency (EE) of multiuser MIMO system by considering an energy consumption model. Results indicate that the increasing number of BS antennas can boost the achievable SE of system, whilst the achievable SE tends to a saturated rate in the high signal-to-noise ratios (SNR) regime. Furthermore, an important conclusion is that the increasing number of users is beneficial for the achievable EE and there is an optimal antenna number to maximize the EE of system.

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.

From Loschmidt daemons to time-reversed waves.

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses 'time-reversal mirrors' with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that 'instantaneous time mirrors', mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

Original Symbol Phase Rotated Secure Transmission Against Powerful Massive MIMO Eavesdropper

Massive multiple-input multiple-output (MIMO) has been extensively studied and considered as a key enabling technology for the fifth generation (5G) wireless communication systems, due to its potential to achieve high energy efficiency and spectral efficiency. As the concept of massive MIMO becomes more popular, it is plausible that the eavesdroppers will also employ massive antennas, which may remarkably enhance their ability to intercept the information. In this paper, motivated by the need to protect against the eavesdroppers equipped with powerful large antenna arrays, which has received scarce attention in the literature, a physical layer security approach called original symbol phase rotated (OSPR) secure transmission scheme is proposed to defend against eavesdroppers armed with unlimited antennas. The basic idea of the proposed OSPR scheme is to randomly rotate the phase of original symbols at the base station (BS) before they are transmitted, so that the massive MIMO eavesdropper will be confused by the intercepted signals, which may not represent the true information symbols. However, the legitimate users are able to infer the correct phase rotations and take proper inverse operations to recover the original symbols. We show that when the BS has a large enough, but finite number of antennas, the proposed OSPR scheme can achieve a considerable security performance in that the eavesdropper is unable to recover most of the original symbols, even with unlimited antennas. The process and the security performance of the proposed OSPR scheme are presented in detail. Simulation results are provided to further corroborate that the proposed OSPR scheme is a potential green secure transmission candidate technique for the future wireless networks.

On achievable rate of massive MIMO multiple access channels via virtual representation

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) systems in correlated fading channels via virtual representation. The fast fading MIMO channel matrix is assumed to have a Rayleigh-distributed random component with variance profile. Under the minimum mean-squared error receiver employed, we first derive the first and second asymptotic moments of signal-to-interference-plus-noise ratio (SINR). Then, we propose that the probability distribution function of SINR, which can be well approximated by a Gamma distribution. Finally, we derive a lower bound on the SINR and approximation of achievable rate. Numerical results demonstrate that both the lower bound on the SINR and the approximated rate apply for a finite number of antennas and remain tight.

Nonasymptotic Analysis of Capacity in Massive MIMO Systems

In this letter, we analyze the capacity of a point-to-point massive MIMO system in the regime of a large (but finite) number of antennas. Different from previous works resorting to asymptotic random matrix theory, concentration inequalities are used in our nonasymptotic analysis for massive MIMO systems with a finite number of antennas. We first derive deterministic bounds on the ergodic capacity for massive MIMO systems. Furthermore, we obtain statistical bounds within which the instantaneous capacity falls with a falling-in probability . As the number of antennas increases, the statistical bounds on the instantaneous capacity become tighter and the corresponding falling-in probability increases, which reveals an interesting phenomenon that the instantaneous capacity has fewer random fluctuations as the number of antennas becomes larger. Simulations show that these theoretical bounds match well with our experimental results. Therefore, the bounds can be useful for the design and analysis of practical massive MIMO systems with a large but finite number of antennas.

Downlink User Capacity of Massive MIMO Under Pilot Contamination

Pilot contamination has been regarded as a main limiting factor of time division duplexing (TDD) massive multiple-input-multiple-output (Massive MIMO) systems, as it will make the signal-to-interference-plus-noise ratio (SINR) saturated. However, how pilot contamination will limit the user capacity of downlink Massive MIMO, i.e., the maximum number of users whose SINR targets can be achieved, has not been addressed. This paper provides an explicit expression of the Massive MIMO user capacity in the pilot-contaminated regime where the number of users is larger than the pilot sequence length. This capacity expression characterizes a region within which a set of SINR requirements can be jointly satisfied. The size of this region is fundamentally limited by the pilot sequence length. Furthermore, the scheme for achieving the user capacity, i.e., the uplink pilot training sequences and downlink power allocation, has been identified. Specifically, the generalized Welch bound equality sequences are exploited and it is shown that the power allocated to each user should be proportional to its SINR target. With this capacity-achieving scheme, the SINR requirement of each user can be satisfied and energy-efficient transmission is achieved in the large-antenna-size (LAS) regime. The comparison with two non-capacity-achieving schemes highlights the superiority of our proposed scheme in terms of achieving higher user capacity. Furthermore, for the practical scenario with a finite number of antennas, the actual antenna size required to achieve a significant percentage of the asymptotic performance has been analytically quantified.

Ergodic Rate Analysis for Multipair Massive MIMO Two-Way Relay Networks

This paper considers a multipair massive multiple-input-multiple-output two-way relay network, in which multiple pairs of users are served by a relay station with a large number of antennas, which uses maximum ratio combining/maximum ratio transmission and a fixed amplification factor for reception/ transmission. First, the users' ergodic rates are derived for the case with a finite number of antennas, and then, the rate gain is analyzed when the transmit power of the senders and the relay is sufficiently large. We show that the ergodic rates increase with the number of antennas at the relay, i.e., N, but decrease with the number of user pairs, i.e., K, both logarithmically. The energy efficiency for the network is also investigated when the number of antennas grows to infinity. It is further revealed that the ergodic sum-rate can be maintained while the users' transmit power is scaled down by a factor of 1/N or the relay power by a factor of 2K/N. This indicates that users obtain an energy efficiency gain of N, but the relay has an energy efficiency gain of N divided by the number of users, i.e., 2K.

Massive MIMO Multicasting in Noncooperative Cellular Networks

We study the massive multiple-input multiple-output (MIMO) multicast transmission in cellular networks where each base station (BS) is equipped with a large-scale antenna array and transmits a common message using a single beamformer to multiple mobile users. We first show that when each BS knows the perfect channel state information (CSI) of its own served users, the asymptotically optimal beamformer at each BS is a linear combination of the channel vectors of its multicast users. Moreover, the optimal combining coefficients are obtained in closed form. Then we consider the imperfect CSI scenario where the CSI is obtained through uplink channel estimation in timedivision duplex systems. We propose a new pilot scheme that estimates the composite channel which is a linear combination of the individual channels of multicast users in each cell. This scheme is able to completely eliminate pilot contamination. The pilot power control for optimizing the multicast beamformer at each BS is also derived. Numerical results show that the asymptotic performance of the proposed scheme is close to the ideal case with perfect CSI. Simulation also verifies the effectiveness of the proposed scheme with finite number of antennas at each BS.

Performance Analysis of Multi-Source Multi-Relay with Multiple Antennas Cooperative Networks with Best Relay Selection

In this paper we analyze the system performance of multi-source multi-relay with multiple antennas cooperative networks. We present an amplify and forward (AF) multiple-input multiple-output relay scenario, where finite number of sources communicate with single destination via multiple relay access points equipped with finite number of antennas. In this network a relay selection scheme is adopted, where the best relay is chosen using the instantaneous channel state information (CSI). Maximal ration combiner (MRC) and maximal ratio transmitter (MRT) are used at the relay to obtain maximum achievable received signal-to-noise ratio (SNR). We derive closed-form and analytical bound expressions for the outage probability and symbol error rate (SER) with joint multiple-sources and cooperative diversity. Further high SNR asymptotic analysis on the outage probability and average SER are performed to characterize the diversity gain. Then, the analytical expressions are validated with Monte Carlo simulations. The results reveal that the diversity gain is determined by the number of the sources, the number of access points in the system and the number of the antennas in each access point. ©2014 Engineering and Technology Publishing.