Spatial Sigma-Delta Modulation for the Massive MIMO Downlink

We study co-primary spectrum sharing concept in small cell multiuser networks. Downlink transmission is considered with Rayleigh fading in interfering broadcast channel. Multiple-input-single-output (MISO) system is considered in two small cells. The sum rate maximization problem is studied in two cells having multiple users with multiple subcarriers. Zero-forcing (ZF) precoders are considered at both base stations. The problem becomes non-convex then and we factor the main objective problem into two subproblems. First subproblem is multiuser with subcarriers allocation where we assume that each subcarrier can be allocated to multiple users. Gale-Shapley algorithm is proposed for subcarrier allocation problem. Second subproblem is where ZF precoders are employed at both base stations for allocating power. It leads to water-filling based power allocation for both base stations.

Non-orthogonal multiple access (NOMA) is proposed as downlink precoding scheme in cellular wireless networks. Applying multiple antennas at the base station allows for spatial precoding and spatial multiplexing. In particular, the capacity region for multiple antenna downlink channels is achieved by dirty paper precoding (DPC) and time sharing. It cannot be achieved by linear superposition coding and successive interference cancellation (SIC). In this work, we investigate the performance of NOMA in multiple antenna downlink channels. We show that NOMA cannot achieve the sum capacity except for parallel channels. Furthermore, we propose an efficient algorithm to compute the minimum power for DPC with time sharing under rate constraint. The results are compared with NOMA and zero-forcing (ZF) precoding. The numerical experiments show that NOMA requires significantly more transmit power than DPC. Moreover, the performance gap between ZF precoding and NOMA highly depends on the SNR region, number of antennas, and minimum rate demands.

In this article, we investigate achievable sum-rates of a multiuser multiple-input multiple-output (MU-MIMO) network with maximal ratio transmission (MRT) and zero-forcing (ZF) precoders for downlink cellular scenarios. We use Gamma distribution to derive tight lower and upper bounds of the achievable sum-rates. From the analytical results, the sum-rates of the MRT and ZF precoders are increased with the number of the transmit antennas and transmit power, and there exists an optimal number of served users for the highest achievable sum-rates when using the ZF precoder.

Capacity maximizing in massive MIMO with linear precoding for SSF and LSF channel with perfect CSI

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.

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

General analysis of expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic per-cell sum spectral efficiency for a multi-cellular system with coordinated regularized zero-forcing (RZF) precoding is presented. An application to two-tier small-cell networks is considered, assuming independent and identically distributed (i.i.d.) and semi-correlated Rayleigh fading channels, with spatial correlation at the base station. Our analysis caters for equal and unequal correlation matrices for each terminal. For the i.i.d. case and when each terminal is assigned an equal correlation matrix, our expressions are averaged over the eigenvalue densities of the channel correlation matrices, which follow an uncorrelated and correlated complex central Wishart distribution. With unequal correlation matrices, we exploit the high signal-to-noise-ratio (SNR) convergence of RZF precoding to zero-forcing (ZF) precoding and use a second-order Neumann series expansion to derive closed-form approximations to the expected RZF SINR and ergodic sum spectral efficiency, via the expected ZF SNR and ergodic sum spectral efficiency. Our numerical results show the adverse effects of intercellular interference, along with the improvements in the above-mentioned performance metrics with network-wide coordination over cell-wide and macro-only coordination strategies. The derived expressions are robust to changes in system dimensions, operating SNRs, and correlation levels.

In this article, the adoption and performance of a constant envelope (CE) type spatial precoder is addressed in large-scale multiuser MIMO based cellular network. We first formulate an efficient computing solution to obtain the antenna samples of such CE precoder. We then evaluate the achievable CE precoder based multiuser downlink (DL) system performance and compare it with the corresponding performance of more ordinary zero-forcing (ZF) spatial precoder. We specifically also analyze how realistic highly nonlinear power amplifiers (PAs) affect the achievable DL performance, as the individual PA units in largearray or massive MIMO systems are expected to be small, cheap and operating close to saturation for increased energy-efficiency purposes. It is shown that the largely reduced peak-to-average power ratio (PAPR) of the PA input signals in the CE precoder based system allows for pushing the PA units harsher towards saturation, while allowing to reach higher signal-to-interference-plus-noise ratio (SINRs) at the intended receivers compared to the classical ZF precoder based system. The obtained results indicate that the CE precoder can outperform the ZF precoder by up to 5–6 dBs, in terms of the achievable SINRs, when the PA units are pushed towards their saturating region. Such large gains are a substantial benefit when seeking to improve the spectral and energy-efficiencies of the mobile cellular networks.

We provide a simple, yet general and accurate framework for analyzing zero-forcing (ZF) precoding performance for a full-dimensional massive multiple-input multiple-output system. Exploiting an order two Neumann series, our framework approximates the expected (average) ZF signal-to-noise ratio and ergodic sum spectral efficiency, while catering for a finite multipath propagation model, as well as correlated and uncorrelated user equipment (UE) positions in both azimuth and elevation domains. The analysis provides clear insights on the influence of propagation and system parameters on ZF performance. We identify how far UEs must lie in azimuth and elevation for the ZF precoder to approach uncorrelated channels. Our framework is useful for predicting the ZF performance degradation arising from channel correlation. For optimal performance, UEs could be separated by around 30° in azimuth and 15° in elevation - conditions which are difficult to meet in reality.

In paper the numerical investigation of the impact of delayed channel state information (CSI) due to user movement and caused channel aging on the performance of multiuser precoder in downlink MISO system. The time variant CSI is obtained by the least squares channel estimation. We consider Zero Forcing algorithm and numerical optimization based solution of calculating precoder vectors maximizimg sum rate of multiuser system. For numerical simulation the QuaDRiGa channel model reflecting the real propagation conditions for moving users is used. The obtained performance of multiuser Zero Forcing and optimization based beamforming in spatially correlated channel are compared based on the empirical cumulative density function of the sum rate of multiple users.

In wireless communications, massive multiple-input multiple-output (MIMO) systems in which the base station (BS) is equipped with a large number of antennas can provide significant spectral and energy efficiency by means of simple signal processing. Therefore, massive MIMO is an attractive technology for next-generation wireless communication systems and for green communications. However, phase noise (PN) introduced by the impairment of oscillators can cause a severe performance loss in wireless communication systems. Solving the PN problem for massive MIMO systems in both the downlink and uplink is challenging as it is a multivariate joint PN estimation and data detection problem. The optimal solution is difficult to derive and may lead to high complexity. In this paper, we propose a zero-forcing (ZF) based precoding scheme with PN suppression to solve the PN problem for massive MIMO downlink systems. By using the ideal PN free output signal-to-noise ratio (SNR) of the ZF precoding as a performance upper bound, analytical and numerical results show that when the required SNR is satisfied, the output SNR of the proposed scheme can approach the upper bound, except for very large PN variances. Moreover, the complexity of the proposed scheme is low on both the BS and the user sides, and the BS does not need any feedback information from the users.

Massive multiple‐input multiple‐output (MIMO) systems with hundreds of correlated antennas at base station are capable of offering abundant spatial resources. When spatial‐domain modulation is applied to these systems, the spatial modulation (SM) using only one radiofrequency chain benefits practical implementation, but suffers from significantly reduced multiplexing gain offered by the massive number of antennas. By contrast, the generalised SM (GSM) allows to simultaneously activate multiple transmit antennas, which improves spatial multiplexing gain, but degrades the achievable error performance, as its design pays no attention to the antenna correlation. The authors propose an antenna grouped SM (GrSM) scheme, which is capable of circumventing the shortcomings of both the SM and GSM schemes suffered in massive MIMO scenarios. In the proposed GrSM scheme, transmit antennas are partitioned into multiple groups, where the relatively strongly correlated antennas within individual groups are used to implement component SM schemes, while the relatively weakly correlated antennas in different groups are beneficial to obtain multiplexing gain. In order to further improve the spectral efficiency, adaptive modulation is integrated with GrSM to form the adaptive GrSM (AGrSM). The achievable error and spectral efficiency performance of GrSM and AGrSM systems are investigated based on both mathematical analysis and Monte‐Carlo simulations, which are also compared with that of the conventional SM and GSM schemes, when massive MIMO communication scenarios are considered. Their studies and performance results show that GrSM is a promising transmit scheme for massive MIMO, which can outperform both the SM and GSM schemes.

High cost of millimeter wave (mmWave) hardware precludes the possibility to support each antenna element with a dedicated radio frequency (RF) chain in large-scale mmWave systems. It thus makes conventional baseband precoding, such as zero-forcing (ZF) which is deemed virtually optimal in the large array regime, impractical. In this paper, we consider the RF chain limitations present in large mmWave multiuser systems and propose to approach the desirable yet infeasible baseband ZF precoding by essentially steering the beam towards each user's strongest path, termed MUBS, through analog processing at the RF domain. Rates achieved by both baseband ZF and the proposed MUBS precoding are then derived in a closed form. We further study the rate loss of MUBS relative to the upper bound imposed by ZF precoding and find that the gap converges to a finite limit as the transmit antenna number N t goes large. Since the achievable rate of ZF grows without limit as N t increases, the proposed MUBS scheme thus promises to achieve most of ZF rates at large N t . Numerical results are also provided to validate the desirable performance of the proposed MUBS scheme.

Cell-free massive MIMO technology holds significant promise as a pivotal enhancement for next-generation 5G and 6G networks. This technology features a network architecture where a single central processing unit oversees multiple access points, thereby enhancing wireless communication capacity and efficacy. By enabling broader connectivity beyond the confines of standard cellular networks, it minimizes signal interruptions and improves spectral efficiency. Despite these advancements, further research is necessary to define a comprehensive implementation strategy for deploying cell-free massive MIMO systems under real-world conditions. The Signal-to-Interference-plus-Noise Ratio (SINR) plays a crucial role in wireless communications. In this paper, the problem of power allocation is addressed under the assumption of pilot contamination. Pilot contamination occurs when multiple users share the same pilot signal. Specifically, two users were assumed to have the same pilot signal, which significantly decreased the SINR and increased the interference among these users. This reduction in SINR leads to potential degradation in achievable data rates and overall system performance. The proposed algorithm aims to reduce the pilot contamination by solving a max-min optimization problem that insure a fairness among all users. The proposed algorithm obtained the optimal power coefficient associated with each user by taking the advantage of uplink-downlink duality and considering all interference terms in the calculations. The proposed algorithm find out the optimal solution in an iterative manner until the feasible solution is achieved. The methodology introduced calculation of achievable rates based on SINR, which is essential for evaluating power allocation in cell-free massive MIMO systems. Specifically, we focus on downlink sum-rate maximization and compare the effectiveness of Zero-Forcing (ZF) precoder against Conjugate Beamforming (CB) precoder.

We present a mathematical analysis of linear precoders for downlink multiuser massive MIMO. In the scenario we consider, one-bit digital-to-analog converters are employed at the basestation antennas for mitigating power consumption and hardware complexity. Using the Bussgang theorem, a probability-of-error analysis for a general precoder is presented. The special case of zero-forcing (ZF) precoders is considered and simplified error expressions are derived for asymptotic scenarios. Our analysis illustrates that the probability of error for the quantized ZF precoder depends primarily on the ratio of the number of antennas to the number of users. Our simulations also show that the quantized ZF precoder outperforms the high complexity ML encoder for low-to medium-SNRs.