ZF Beamforming Research Articles

Orthogonal beamforming technique for massive MIMO systems

AbstractBeamforming represents a pivotal technology in massive multiple-input multiple-output (MIMO) systems, as it facilitates the regulation of transmission and reception operations. Beamforming techniques’ categorization is based either on their hardware architecture or implementation strategy. This paper proposes an orthogonal beamforming technology founded on a specific implementation method that utilizes predetermined orthogonal beams to serve users. The suggested approach incorporates numerous orthogonal beams relying on a substantial number of antennas at the base station. The primary objective of this approach is to enhance the performance of massive MIMO systems by augmenting spectral efficiency and accommodating more users. The proposed beamforming approach is well suited for millimeter frequency bands. The purpose of this paper is to explore the suggested orthogonal beamforming technology. The concept of this approach is described at first and then followed by an evaluation of its efficacy for a single user through the allocation of orthogonal beams. The suggested approach is also examined in the context of multiuser systems, and the results are compared with the adaptive ZF beamforming technique. Furthermore, the paper presents solutions to the issues that may arise in multiuser systems, for example, ensuring that each orthogonal beam is assigned to only one user. The simulations conducted in this study demonstrate that the suggested approach outperforms the ZF technique in terms of both the spectral efficiency and the number of serviced users. Specifically, the suggested approach can enhance SE by approximately 40.6% over the ZF technique, and it can support up to double the number of users when compared to the ZF approach.

Numerical Evaluation of the MU-MIMO Beamforming Performance with Channel Estimation

This paper presents the numerical evaluation of the ZF beamforming algorithm and DFT precoding using the LS channel estimation in the multiuser multiantenna (MU-MIMO) downlink system. The sum rate performance depending on a number of users are presented. The arising inter user correlation degrades the sum rate (spectral efficiency) performance of multiuser MIMO system especially in scenarios where the number of users is larger than the number of antennas at the BS. For MIMO channel simulation the QuaDRiGa channel model reflecting the real propagation conditions is used. The obtained performance of MU-MIMO ZF precoding in spatially correlated channel are compared with DFT precoding based on the empirical cumulative density function of the sum rate of multiple users. Numerical results show that the ZF precoder outperforms the DFT precoder in channel with less spatial correlation. The DFT precoder in spatially more correlated channel has advantage over ZF precoder.

Numerical Evaluation of the MU-MIMO Beamforming Performance with User Selection Algorithm

This paper presents the numerical evaluation of the ZF beamforming algorithm using the user selection in the multiuser multiantenna (MU-MIMO) downlink system. Two user selection algorithm – semiorthogonal user selection and greedy user selection are numerically evaluated based on the open source MIMO channel model. The sum rate performance depending on number of users are presented. The arising inter user correlation degrades the sum rate (spectral efficiency) performance of multiuser MIMO system especially in scenarios where the number of users is larger than the number of antennas at the BS. The selection of users is based on the orthogonality of the channels among selected users. For MIMO channel simulation the QUADRIGA channel model reflecting the real propagation conditions is used. The obtained performance of MU-MIMO ZF precoding in spatially correlated channel are compared based on the empirical cumulative density function of the sum rate of multiple users. Numerical results show that the ZF precoder using user selection (G ZF) outperforms the ZF precoder with random user selection in spectral efficiency. The greedy user selection in spatially correlated channel has advantage to semi-orthogonal user selection. It isobserved that as the increasing the number of served users used for selection the greedy user selection gives better performance than semi-orthogonal algorithm.

Performance Evaluation of the MU-MIMO Precoding Using the QuaDRiGa Channel Model

The article presents the analysis of characteristics of algorithms of signal precoding in a multi-antenna system with many users (MU-MIMO). This paper presents the numerical evaluation of the multiuser MIMO beamforming algorithms ZF and DFT codebook based on a QUADRIGA channel model, taking into account the real conditions of signal propagation. The generated channels are used to calculate SINR and the spectral efficiency values of each user using the conventional ZF and DFT beamforming codebook. The eigenvalues of the MIMO channel are important in evaluating the MU-MIMO transmission performance characteristics, such as the spectral efficiency of a precoded system. The obtained performance of MU-MIMO ZF and DFT codebook-based beamforming in spatially correlated channels are compared based on the empirical cumulative density function of the sum rate of multiple users. Spatial correlation degrades capacity performance, and in the channels, the DFT precoder has a more robust performance and outperforms the ZF precoder in spectral efficiency. Obtained results can be used by the algorithm evaluation in the system-level simulations.

Effect of Oblique Projection Beamforming on the Achievable Rate in Massive MIMO System

The mitigation of interference is an ubiquitous problem in wireless communication systems for which a number of signal processing techniques have been developed. This problem is made more critical in the presence of an increased numbers of interfering cells, interfering users and antennas, as it is the case in massive MIMO systems. As a consequence, the conventional methods see their performance degrades. In this paper, we propose to incorporate Oblique Projection (OP) with conventional ZF beamforming in the downlink of a massive MIMO communication system and investigate the achievable data rate at the reception. Resulting beamformer uses oblique projection spaces to separate the received signal into two subspaces: the one pertaining to the desired user signal and the other to interference signals, thus achieving a high degree of interference suppression. It is shown that the OP beamforming performs better than Maximum Ratio Transmitting (MRT) and the transmit MMSE beamforming counterparts.

Analyzing Coverage Probability of Multitier Heterogeneous Networks Under Quantized Multiuser ZF Beamforming

In this paper, we analyze the coverage probability of a large-scale heterogenous cellular network (HetNet) where base stations (BSs) are equipped with multiantennas, serving a number of single-antenna user equipments (UEs) in the downlink—space division multiple access (SDMA). Adopting the tool of stochastic geometry, we analyze the coverage probability under the quantized zero-forcing beamforming (ZFBF). This analysis, however, intricate as a typical UE in a given cell experiences: i) a residual inter-user interference (IUI) rendered by the quantization error; ii) quantization-driven statistical correlation between its attending signal power and IUI; iii) Nakagami-type fading environment, induced by postprocessing ZFBF; and iv) intercell interference (ICI). Current related literature has not effectively accounted for issues (i), (ii), and (iv) and commonly resorted to simplifying scenarios of full SDMA (i.e., exponential fading), independency of IUI and attending signal power, approximating IUI via an exponential random variable, and the quantization cell approximation (QCA). Our analysis relaxes such limiting assumptions; it includes the more relevant random vector quantization (RVQ) method, and compared to the literature, does not resort to the evaluation of a higher order differentiation for the evaluation of the coverage probability by exploiting our previously developed method. We further introduce three novel approximations of the coverage probability: RVQ-M , RVG-G , and QCA , which the first two approximations are given in semi-closed-form formulas (requiring a simple integration step) and the last approximation is in a closed-form expression. All approximations are numerically affordable, and we confirm the RVG-G approximation is the most accurate one. Finally, we exploit our analysis to study several practically insightful issues to shed some lights on: 1) for given feedback capacity and number of UEs, when desification becomes beneficial; 2) how multitierness of HetNets can be exploited for substantially reducing feedback capacity; and 3) an adaptive share of feedback capacity for the purpose of CDI as well as channel quality information (CQI) feedbacks, when there is an uplink penalty subjected for the feedback procedure and the scheduled data rate at each BS is specified adaptively based on the quantized CQI.

Performance of Enhanced Massive Multiuser MIMO Systems Using Transmit Beamforming and Transmit Antenna Selection Techniques

In this paper, the performances of massive multiuser multiple input multiple output (MMU MIMO) system with different transmit beamforming (BF) techniques and different suboptimal transmit antenna selection (TAS) algorithms over Rayleigh fading channels are investigated. Three linear transmit BF types are considered, namely, maximum ratio transmission (MRT BF), zero forcing (ZF BF) and minimum mean square error (MMSE BF). Two TAS algorithms are considered, that are pairwise error probability minimization (PM) and the capacity maximization (CM). TAS techniques are used in order to reduce the number of radio frequency (RF) chains, system complexity, and cost. This makes MMU MIMO more applicable in beyond 4G communication systems. The simulation results show that TAS algorithms are capable of decreasing the complexity of the system while maintaining the same performance of the MMU MIMO system, complex TAS techniques are not needed at large number of RF chains, and the performance improvement due to the increase of this number is limited to a certain threshold. It also demonstrated that the MMSE BF and ZF BF bit error rate performance values are better than MRT BF values for both CM and PM TAS algorithms, but it is limited to the large number of users. On the other hand, the MRT BF technique performance is good at small Eb/N0 values for both PM and CM TAS but it is relatively less affected by increasing the number of users.

Performance Analysis of TDD Reciprocity Calibration for Massive MU-MIMO Systems With ZF Beamforming

This study analyzes a two-way signaling method for time division duplex reciprocity calibration (RC) in multiuser beamforming systems. The system model of RC is established, and the estimation error of the RC coefficient is derived. The effect of this error is examined in terms of the user signal-to-interference-plus-noise ratio (SINR) and capacity. Results reveal the relationship between the user SINR and RC errors as well as the number of antennas and users. Moreover, the findings show that the colocated antenna array is less sensitive to calibration errors than the case of distributed antennas even if the calibration signal-to-noise ratio (SNR) is identical. The interference resulting from imperfect calibration becomes the determinant that constrains the performance, particularly when a high user SNR is required.

Sum Rate Analysis of MU-MISO Systems with ZF Beamforming over Composite Fading Channels

The performance of multiuser multiple-input single-output (MU-MISO) systems is not only affected by small-scale multipath fading but also by large-scale fading (i.e., shadowing) and path loss. In this paper, we concentrate on the sum rate distribution of MU-MISO systems employing linear zero-forcing beamforming, accounting for both multipath fading and shadowing effects, as well as spatial correlation at the transmit and receiver sides. In particular, we consider the classical spatially correlated lognormal model and propose closed-form bounds on the distribution of the achievable sum rates in MU-MISO systems. With the help of these bounds, we derive a relationship between the interuser distance and sum rate corresponding to 10% of the cumulative distribution function under different environmental conditions. A practical conclusion from our results based on the considered system is that the effect of spatially correlated shadowing can be considered to be independent when the interuser distance is approximately five times the shadowing correlation distance. Furthermore, a detailed analysis of the effects of composite channel attenuation consisting of multipath fading and shadowing is also provided.

Optimal number of users in zero-forcing based multiuser MIMO systems with large number of antennas

The optimal number of users achieving the maximum sum throughput is analyzed in zero-forcing (ZF) based multiuser multiple-input multiple-output (MIMO) systems with a large number of base station (BS) antennas. By utilizing deterministic ergodic sum rates for the ZF-beamforming (ZF-BF) and ZF-receiver (ZF-R) with a large number of BS antennas [1], [2], we can obtain the ergodic sum throughputs for the ZF-BF and ZF-R for the uplink and downlink frame structures, respectively. Then, we can also formulate and solve the optimization problems maximizing the ergodic sum throughputs with respect to the number of users. This paper shows that the approximate downlink sum throughput for the ZF-BF is a concave function and the approximate uplink sum throughput for the ZF-R is also a concave function in a feasible range with respect to the number of users. The simulation results verify the analyses and show that the derived numbersof users provide the maximum sum throughputs for the ZF-BF as well as ZF-R in multiuser MIMO systems with a large number of BS antennas.

하향링크 다중사용자 다중안테나 시스템을 지원하는 반복 가중치 최소평균자승오류 빔형성 기법

기존의 최소평균자승오류 빔형성 기법은 간섭제거나 정합필터 빔형성 기법보다 우수한 성능을 보여주지만, 전체 전송률의 증가를 목적으로 하지는 않는다. 본 논문은 전체 전송률을 가중된 평균자승오류로 표현하여 증가시키는 기법을 제안하였다. 제안 기법은 기존의 최소평균자승오류 기법에서 출발하여 반복적으로 가중치와 빔을 갱신함으로써 전체 전송률을 증가시킨다. 모의실험 결과를 통해 제안 기법이 기존 기법보다 전체 전송률 측면에서 뛰어나며, 기존 기법과 달리 사용자의 수가 높아질수록 전체 전송률이 증가하는 것을 확인하였다.

Increasing Security Degree of Freedom in Multiuser and Multieve Systems

Secure communication in the multiuser and multieavesdropper (MUME) scenario is considered in this paper. It has be shown that secrecy can be improved when the transmitter simultaneously transmits an information-bearing signal to the intended receivers and artificial noise to confuse the eavesdroppers. Several processing schemes have been proposed to limit the cochannel interference (CCI). In this paper, we propose the increasing security degree of freedom (ISDF) method, which takes an idea from dirty-paper coding (DPC) and ZF beam-forming. By means of known interference precancellation at the transmitter, we design each precoder according to the previously designed precoding matrices, rather than other users' channels, which in return provides extra freedom for the design of precoders. Simulations demonstrate that the proposed method achieves the better performance and relatively low complexity.

On the achievable rates of multiple antenna broadcast channels with feedback-link capacity constraint

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

A Note on the Bivariate Chi Distribution

A Note on the Bivariate Chi Distribution