Asymptotic Spectral Efficiency Research Articles

Performance Analysis of Cell-Free Massive MIMO Network With Large-Scale-Fading Decoding and Low-Resolution ADCs

Concentrating on cell-free massive multiple-input multiple-output (MIMO) networks with low-resolution analog-to-digital converters (ADCs), we derive the theoretical achievable uplink spectral efficiency (SE) for the minimum mean-squared error (MMSE)-based large-scale fading decoding (LSFD). Moreover, we investigate the bit allocation (BA) among access points (APs) to maximize the asymptotic sum SE under the constraint of total ADC quantization bits. Simulation results confirm that our theoretical analysis is accurate and validate that the proposed BA technique is preferable to the random and fixed counterparts.

Spatially Correlated Multi-Pair Massive MIMO Relaying With Rician Channel and Phase Shifts

Multi-pair two-way half-duplex massive multiple-input multiple-output (mMIMO) relaying with multiple user-pairs is being actively explored. Most of the existing mMIMO relaying investigations consider either spatially correlated Rayleigh fading or uncorrelated Rician fading channel and also ignore the impact of phase shifts in the line-of-sight (LoS) component due to change in user location and hardware effects. We consider a multi-pair mMIMO amplify-and-forward relay system with spatially correlated Rician channel along with phase shifts. We derive the asymptotic spectral efficiency expressions for different power scaling schemes considering phase aware and phase unaware minimum mean square based channel estimates. Numerical investigations reveal that the impact of LoS component varies with the power scaling schemes.

Analysis and Optimization of Spectral and Energy Efficiency in Underlaid D2D Multi-Cell Massive MISO Over Rician Fading

This paper investigates the uplink spectral efficiency (SE) characterization and energy efficiency (EE) optimization of device-to-device (D2D) communications underlying a multi-cell massive multiple-input single-output (m-MISO) network, assuming that the channels are modeled with Rician fading. First, an analytical expression for the lower-bound of the ergodic capacity of a typical cellular user (CU) is derived with imperfect channel state information in the presence of D2D links’ interference. Then, a closed-form approximate achievable SE expression for a typical D2D pair is derived considering Rician fading between D2D pairs. The asymptotic SE behavior is analyzed in strong line-of-sight (LOS) conditions for CU and D2D pairs. Also, simplified expressions are obtained for the special case of Rayleigh fading. Next, to optimize the total EE, a transmit data power allocation based on the derived rate expressions is formulated. Since the optimization problem has a non-linear and non-convex objective function, it is intractable to be solved straightforwardly. Therefore, we resort to utilizing an iterative algorithm relying on fractional programming. The numerical results show that a stronger LOS component (i.e., larger Rician K-factor) between a typical CU and its serving BS leads to a significant improvement in the system performance, while it has less effect on the D2D network.

Age-Limited Capacity of Massive MIMO

We investigate the age-limited capacity of the Gaussian many channel with total <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> users, out of which a random subset of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K_{a}$ </tex-math></inline-formula> users are active in any transmission period, and a large-scale antenna array at the base station (BS). In an uplink scenario where the transmission power is fixed among the users, we consider the setting in which both the number of users, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , and the number of antennas at the BS, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> , are allowed to grow large at a fixed ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\zeta = {M}/{N}$ </tex-math></inline-formula> . Assuming perfect channel state information (CSI) at the receiver, we derive the achievability bound under maximal ratio combining. As the number of active users, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K_{a}$ </tex-math></inline-formula> , increases, the achievable spectral efficiency is found to increase monotonically to a limit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log _{2}\left ({1+\frac {M}{K_{a}}}\right)$ </tex-math></inline-formula> . Further extensions of the analysis to the zero-forcing receiver as well as imperfect CSI are provided, demonstrating the channel estimation penalty in terms of the mean squared error in estimation. Using the age of information (AoI) metric, first coined by Kaul et al., as our measure of data timeliness or freshness, we investigate the trade-offs between the AoI and spectral efficiency in the context massive connectivity with large-scale receiving antenna arrays. As an extension of Liu and Yu, based on our large system analysis, we provide an accurate characterization of the asymptotic (finite system size) spectral efficiency as a function of the number of antennas and the number of users, the attempt probability, and the AoI. It is found that while the spectral efficiency can be made large, the penalty is an increase in the minimum AoI obtainable. The proposed achievability bound is further compared against recent massive MIMO-based massive unsourced random access (URA) schemes.

Uplink Power Control in Massive MIMO With Double Scattering Channels

Massive multiple-input multiple-output (MIMO) is a key technology for improving the spectral and energy efficiency in 5G-and-beyond wireless networks. For a tractable analysis, most of the previous works on Massive MIMO have been focused on the system performance with complex Gaussian channel impulse responses under rich-scattering environments. In contrast, this paper investigates the uplink ergodic spectral efficiency (SE) of each user under the double scattering channel model. We derive a closed-form expression of the uplink ergodic SE by exploiting the maximum ratio (MR) combining technique based on imperfect channel state information. We further study the asymptotic SE behaviors as a function of the number of antennas at each base station (BS) and the number of scatterers available at each radio channel. We then formulate and solve a total energy optimization problem for the uplink data transmission that aims at simultaneously satisfying the required SEs from all the users with limited data power resource. Notably, our proposed algorithms can cope with the congestion issue appearing when at least one user is served by lower SE than requested. Numerical results illustrate the effectiveness of the closed-form ergodic SE over Monte-Carlo simulations. Besides, the system can still provide the required SEs to many users even under congestion.

Power Scaling of Full-Duplex Two-Way Millimeter-Wave Relay With Massive MIMO

In this paper, the asymptotic performance of a full-duplex (FD) millimeter wave (mmWave) two-way relay (TWR) system with a massive multiple-input multiple-output (MIMO) structure is analyzed. After applying conjugate array response vector-based precoding to a hybrid analog and digital MIMO structure in the mmWave band, the asymptotic spectral efficiency of the system as the number of antennas approaches infinity is derived. Based on the asymptotic performance and different system configurations, power scaling schemes are investigated. Considering different power scaling strategies at each node, eight power scaling cases are discussed, and the corresponding asymptotic spectral efficiencies are derived. The results show that interference and noise can be fully eliminated by increasing the number of antennas. A high spectral efficiency can be achieved in a system wherein all the nodes are equipped with large antenna arrays. If the numbers of antennas of node A and node B are both limited, then the system can achieve considerable spectral efficiency and energy efficiency. For both configurations, the power of node A and node B can be scaled down without spectral efficiency loss. However, if only one node is equipped with limited antennas, only the node with a massive array can achieve a higher spectral efficiency. Moreover, we analyze the effect of the FD self-interference (SI) levels. We show that the spectral efficiency decreases rapidly as the SI intensity increases, which is related to the capability of SI cancellation. Under ideal conditions, the FD system can achieve twice the spectral efficiency of its conventional half-duplex (HD) counterpart. However, the FD SI and the finite number of antennas degrade the spectral efficiency of the FD system.

Low Complexity Optimization of the Asymptotic Spectral Efficiency in Massive MIMO NOMA

Massive multiple-input multiple-output (MIMO) technology facilitates huge increases in the capacity of wireless channels, while non-orthogonal multiple access (NOMA) addresses the problem of limited resources in traditional orthogonal multiple access (OMA) techniques, promising enhanced spectral efficiency. This work uses asymptotic capacity computation results to reduce the complexity of a power allocation algorithm for small-scale MIMO-NOMA, so that it may be applied for systems with massive MIMO arrays. The proposed method maximizes the sum-capacity of the considered system, subject to power and performance constraints, and demonstrates greater accuracy than alternative approaches despite remaining low-complexity for arbitrarily large antenna arrays.

Hybrid Massive MIMO Two-Way Relaying With Users and Relay Hardware Impairments

Most of the existing spectral efficiency (SE) investigations for massive multi-input multi-output (MIMO) relaying assume that each antenna has a dedicated radio-frequency (RF) chain with high-quality user and relay hardware. We consider a hybrid massive MIMO multi-pair two-way half-duplex relay, wherein each RF chain steers multiple antennas and assume that both users and relay have hardware impairments. We derive i) a novel closed-form SE expression using large-scale approximation; and ii) asymptotic SE expressions for two different power scaling schemes. We numerically demonstrate that i) a hardware-impaired hybrid relay has measurably degraded SE than a hardware-impaired conventional full-RF chain relay; and ii) the impact of hardware impairments do not vanish asymptotically as $N\rightarrow \infty$ , mainly due to users hardware impairments.

Spectral efficiency analysis for massive MIMO systems in Ricean fading channels

This study focuses on the spectral efficiency of massive multiple-input–multiple-output (MIMO) systems over Ricean fading channels. Assuming the channel reciprocity of uplink and downlink transmissions, the channels are estimated through uplink pilot sequence with least minimum mean square error (MMSE) estimator, which facilitates the investigation of equivalent channel model. With the equivalent channel model, adopting joint MMSE receiver, the uplilnk achievable sum-rate is studied, and finally, the asymptotic expression of spectral efficiency is obtained. Based on the proposed asymptotic spectral efficiency, numerical results give some guidelines about system parameters design: the authors should choose a proper length of the block fading channels to reduce the effect of pilot overhead, and an optimal length of pilot sequence always exists to guarantee a satisfying system performance in terms of spectral efficiency. Furthermore, the simulation results show that when fixing the number of users, shrinking the cell serving area and increasing the number of antennas can improve the system performance.

Spectral Efficiency Optimization of Spatially-Correlated Multi-Pair Full-Duplex Massive MIMO Relaying

We consider a multi-pair two-way full-duplex (FD) amplify-and-forward relaying, where multiple FD multi-input multi-output (MIMO) users exchange information via a shared FD massive MIMO relay. We derive a closed-form spectral efficiency (SE) lower-bound for maximal-ratio combining/maximal-ratio transmission relay processing considering spatially correlated relay and user antennas, which most of the existing works have ignored. The derived SE lower-bound is applicable for arbitrary number of relay antennas, and simplifies to the following results available in the literature i) the asymptotic SE for number of relay antennas tending to infinity; and ii) the SE lower-bound with independent relay antennas and single-antenna users. We use this SE lower-bound to maximize the non-convex SE, which is of matrix fractional form. We optimize SE by approximating it as concave-convex function, and then by applying matrix quadratic transformation. We numerically validate the SE lower-bound for various system configurations and also characterize their performance for different spatial correlation and interference values. We investigate the gains achieved by the optimal SE over equal power allocation.

Scaling Analysis of Hardware-Impaired Two-Way Full-Duplex Massive MIMO Relay

We consider a multipair two-way full-duplex massive multiple-input multiple-output (mMIMO) hardwareimpaired relay, and derive a novel closed-form spectral efficiency (SE) expression for the zero-forcing (ZF) relay processing. We scale the hardware impairments for an N-antenna relay as N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</sup> with z ≥ 0, and analyze the asymptotic SE limits for three relay power scaling schemes. This current letter provides valuable insights in deciding favorable z values for the ZF relay processing, using which the hardware impairments can be scaled for the three relay power scaling schemes considered herein while maintaining a high SE.

Massive MIMO With Spatially Correlated Rician Fading Channels

This paper considers multi-cell Massive MIMO (multiple-input multiple-output) systems where the channels are spatially correlated Rician fading. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight (NLoS) component describing a practical spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE), element-wise MMSE (EW-MMSE), and least-square (LS) channel estimates for this model. Using these estimates for maximum ratio (MR) combining and precoding, rigorous closed-form uplink (UL) and downlink (DL) spectral efficiency (SE) expressions are derived and analyzed. The asymptotic SE behavior when using the different channel estimators are also analyzed. Numerical results show that the SE is higher when using the MMSE estimator than the other estimators, and the performance gap increases with the number of antennas.

Spectral- and Energy-Efficiency of Massive MIMO Two-Way Half-Duplex Hybrid Processing AF Relay

Multi-pair two-way massive multiple-input multiple-output (MIMO) relaying is being actively explored. Most of the massive MIMO relaying literature analyzes the spectral efficiency (SE) and energy efficiency (EE) of full radio-frequency (RF) chain relaying systems. We consider a multi-pair hybrid massive MIMO amplify-and-forward relay, with lesser RF chains than antennas. We consider zero-forcing processing at the relay, and analytically derive its asymptotic SE and EE expressions, with the number of relay antennas approaching infinity. We numerically demonstrate that for certain power scaling schemes, a hybrid relay has only marginally inferior SE and EE than a full-RF relay.

Performance analysis of multi‐pair two‐way amplify‐and‐forward relaying with imperfect CSI over Ricean fading channels

This study investigates the spectral efficiency (SE) and energy efficiency (EE) of a multipair two-way massive multiple-input multiple-output amplify-and-forward relaying system over Ricean fading channels. Both maximum-ratio combining/maximum ratio transmission and zero-forcing transmission/zero-forcing reception beamforming matrices are considered at the relay with imperfect channel state information (CSI). The asymptotic signal-to-interference-plus-noise ratio expressions (in the number of relay antennas M) are derived. Moreover, four power scaling schemes are proposed and the asymptotic SE and EE based on the proposed power scaling schemes are obtained analytically. Theoretical analyses and simulation results show that with imperfect CSI when M tends to infinity, the transmit power should be scaled down to different proportions for the Ricean channel with and without line-of-sight components to maintain a desirable rate. However, when M tends to infinity, SE is independent of the Ricean K-factor with perfect CSI.

Performance Analysis of Millimeter Wave Massive MIMO Systems in Centralized and Distributed Schemes

This paper considers downlink multi-user millimeter-wave massive multiple-input multiple-output (MIMO) systems in both centralized and distributed configurations, referred to as C-MIMO and D-MIMO, respectively. Assuming the fading channel is composite and comprised of both large-scale fading and small-scale fading, a hybrid precoding algorithm leveraging antenna array response vectors is applied into both the C-MIMO system with fully connected structure and the D-MIMO system with partially connected structure. First, the asymptotic spectral efficiency (SE) of an arbitrary user and the asymptotic average SE of the cell for the C-MIMO system are analyzed. Then, two radio access unit (RAU) selection algorithms are proposed for the D-MIMO system, based on minimal distance (D-based) and maximal signal-to-interference-plus-noise-ratio (SINR) (SINR-based), respectively. For the D-MIMO system with circular layout and D-based RAU selection algorithm, the upper bounds on the asymptotic SE of an arbitrary user and the asymptotic average SE of the cell are also investigated. Finally, numerical results are provided to assess the analytical results and evaluate the effects of the numbers of total transmit antennas and users on system performance. It is shown that, from the perspective of the cell, the D-MIMO system with D-based scheme outperforms the C-MIMO system and achieves almost alike performance compared with the SINR-based solution while requiring less complexity.

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.

Effect of composite channel aging on the spectral efficiency of multi‐pair massive multiple‐input multiple‐output amplify‐and‐forward relay networks

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.

A Spectral-Efficient Transmission Scheme for Dimmable Visible Light Communication Systems

Dimming control is of vital importance for visible light communication (VLC) systems. Conventional dimmable transmission schemes based on compensation are spectrally inefficient. In this paper, we propose the use of two techniques, i.e., time-sharing and superposition, to construct spectral-efficient dimmable transmission schemes. For VLC systems with on–off keying (OOK) signaling, we present a general framework to construct dimmable transmission scheme by time-sharing among different dimming control codes. Arbitrary dimming target is achieved by adjusting the proportion of each dimming control code. We, then, give a practical construction of dimming control codes with semi-constant weight codes. We obtain optimal proportions of the semi-constant weight codes, which maximize the asymptotic spectral efficiency using linear programming. We also compute achievable rates of the proposed scheme under different dimming targets and different signal-intensity-to-noise-amplitude ratios. To achieve higher spectral efficiency ( $>$ 1.0 (b/s)/Hz), we present a dimmable multilevel transmission scheme based on superposition. In the proposed scheme, the first $\ell$ $-1$ levels adopt traditional OOK modulation, whereas the $\ell$ th level adopts the dimmable transmission scheme for OOK modulation. The transmitted signal is formed by superimposing modulated signals of the $\ell$ levels. Analysis shows that the proposed scheme achieves a higher spectral efficiency than the state-of-the-art schemes. Hence, it provides an attractive candidate for dimmable VLC systems with demanding spectral efficiency.

Spectral Efficiency of Distributed Large-Scale MIMO Systems With ZF Receivers

Distributed multiple-input multiple-output (D-MIMO) is a promising technique for next-generation wireless networks, which offers a remarkable spectral efficiency gain over the conventional colocated MIMO (C-MIMO). In contrast to C-MIMO, which can be regarded as a special case of D-MIMO, performance analysis of D-MIMO is a challenging problem. This is because radio channels between a user and the distributed radio ports (RPs) are characterized by nonidentical path-loss and shadowing effects that render the classical analytical methods nontractable. In this paper, new accurate expressions for the uplink spectral efficiency of D-MIMO and C-MIMO systems are presented and compared for given large-scale coefficients. We further consider the uplink spectral efficiency for a single-cell distributed large-scale MIMO (D-LMIMO) system with linear zero-forcing (ZF) receivers that account for path loss along with shadow fading and multipath fading effects. Exact expressions for the average spectral efficiency over shadow fading in the asymptotically very large number of RPs antenna regime is explicitly derived, and a tight closed-form lower bound on the asymptotic spectral efficiency is presented. We demonstrate that, the transmit power of each user in D-LMIMO can be scaled down proportionally to the inverse of the number of RP antennas with no performance reduction. Moreover, we study the spectral efficiency of a D-MIMO in a multicell environment taking into account accurate cochannel interference (CCI) models. These expressions provide meaningful insights into the impact of signal-to-noise ratio (SNR), RPs and user positions, number of RPs antennas, shadow fading, and out-of-cell interference on the spectral efficiency of D-MIMO over practical scenarios. Finally, numerical results are validated by simulation to confirm our analysis.

Spectral and energy efficiency analysis for massive MIMO multi-pair two-way relaying networks under generalized power scaling

In this work, we investigate the spectral efficiency (SE) and energy efficiency (EE) for a massive multiple-input multiple-output multi-pair two-way amplify-and-forward relaying system, where multi-pair users exchange information via a relay station equipped with large scale antennas. We assume that imperfect channel state information is available and maximum-ratio combining/maximum-ratio transmission beamforming is adopted at the relay station. Considering constant or scaled transmit power of pilot sequences, we quantify the asymptotic SE and EE under general power scaling schemes, in which the transmit power at each user and relay station can both be scaled down, as the number of relay antennas tends to infinity. In addition, a closed-form expression of the SE has been obtained approximately. Our results show that by using massive relay antennas, the transmit power at each user and the relay station can be scaled down, with a non-vanishing signal to interference and noise ratio (SINR). Finally, simulation results confirm the validity of our analysis.