Simple Framework of ZF Precoding Analysis for Full-Dimensional Massive MIMO Systems

In massive MIMO, replacing high-resolution ADCs/DACs with low-resolution ones has been deemed as a potential way to significantly reduce the power consumption and hardware costs of massive MIMO implementations. In this context, the challenge lies in how the quantization error effect can be suppressed under low-resolution ADCs/DACs. In this paper we study a spatial sigma-delta (ΣΔ) modulation approach for massive MIMO downlink precoding under one-bit DACs. ΣΔ modulation is a classical signal processing concept for coarse analog-to-digital/digital-to-analog conversion of temporal signals. Fundamentally its idea is to shape the quantization error as high-frequency noise and to avoid using the high-frequency region by oversampling. Assuming a uniform linear array at the base station (BS), we show how ΣΔ modulation can be adapted to the space, or MIMO, case. Essentially, by relating frequency in the temporal case and angle in the spatial case, we develop a spatial ΣΔ modulation solution. By considering sectored array operations we study how the quantization error effect can be reduced, and the effective SNR improved, for zero-forcing (ZF) precoding. Our simulation results show that ZF precoding under spatial ΣΔ modulation performs much better than ZF precoding under direct quantization.

<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, 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.

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.

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.

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.

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 orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Wireless network is one of the most important things in the development of telecommunication. However, the existing wireless technology has not been able to efficiently create a very high data rate because it was very sensitive to fading. Therefore, Orthogonal Frequency Division Multiplexing (OFDM) technology combined with MIMO (Multiple Input Multiple Output) transceiver system was used to gain more diversity and bandwidth efficiency. The propagation performed on the OFDM MIMO system was multipath propagation. To reduce Intersymbol Interference (ISI) was used Zero Forcing (ZF) equalizer which works by combining channel response and equalizer response itself to eliminate ISI. This study aims to determine the effect of Zero Forcing Equalizer on OFDM MIMO system using rayleigh fading channel and compared the result with OFDM MIMO STBC system. The research method used was simulation using MatLab R2015a. The simulation results showed that the performance of OFDM MIMO ZF system was worse than OFDM MIMO STBC system i.e BER vs EbNo simulation, eye diagram simulation, and constellation diagram simulation. The OFDM MIMO ZF system was required an Eb / No value more than 25 dB to achieve BER 10-4 while the OFDM MIMO STBC system only required an Eb / No value of 10.5 dB to achieve BER 10-4. The eye pattern generated by the OFDM MIMO ZF system was more closed and the dispersion of constellation signals away from the ideal point while OFDM MIMO STBC system displayed a more open eye pattern and the dispersion of its constellation signal closer to the ideal point. It indicated more ISI occurs in the OFDM MIMO ZF system than that in OFDM MIMO STBC system.

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.

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

In this paper, we develop the optimal relay design for multiple-input multiple-output (MIMO) multi wireless relaying networks, when we consider the problem of zero-forcing processing is studied for multi-input multi- output multi-relay communication system in which MIMO source-destination pairs communicate simultaneously. It is assumed that due to severe shadowing effects which communication links can be established only with the aid of relay node. The aim is to design the relay amplification matrix to maximize the achievable communication sum- rate through the relay, which in general amplifying-and- forward relaying mechanisms are considered. The zero forcing (ZF) algorithm has studied for a MIMO multi relay network by comparing its performance in terms of bit- error-rate (BER) at destination algorithm. In particular, we investigate its performance with and without using the ZF at the relay. Our results demonstrate that the system performance can be significantly improved by using the ZF algorithm at relay (optimal relay ZF algorithm)

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

In this paper we present a local channel correlation based zero-forcing (ZF) beamforming framework for the cell edge users. Without the instantaneous CSI (ICSI) assisting, we derive the exact expression of the averaged pairwise error probability (PEP) upper bounds at both of the receivers. According to the derived PEP bounds, an multi-objective optimization problem is formulated to get the elaborate power allocation and ZF beamforming design with the knowledge of local statistical channel state information (SCSI) at the transmitter side. By factorizing each beamforming matrix as the multiplication of two matrices, we can avoid inter-user interference through column orthogonal matrix design. Moreover, the original complicated optimization problem can be further decoupled into four simple sub-optimization problems. Then utilizing the Lagrange multiplying method, we finally achieve the feasible distributed statistical ZF beamforming design, which only involves the distributed computations based on the local channel correlations. Both theoretical analysis and simulation results confirm that the multi-cell spatial diversity gain can be fully exploited with only local SCSI. For comparison, the traditional perfect ICSI based ZF beamforming is analyzed and discussed. It is shown that in the high regime of signal-to-noise ratio (SNR), the diversity gain of the proposed statistical ZF beamforming is even better than that achieved by the conventional ICSI-aided ZF beamforming.