Minimum Mean Square Error Beamforming Research Articles

Joint mode selection and resource allocation to flexibly guarantee quality of service for downlink MISO-NOMA systems

Non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC) detection, knownas SIC NOMA, enjoys higher spectral efficiency (SE), but suffers increased processing complexity and additional error propagation compared to Non-SIC NOMA,in whichthe receivers directly detect their own signalsfrom thesuperposed signalwithout SIC detection. We propose a joint Mode Selection and Power Allocation (MSPA) scheme that can flexibly realize different kinds of tradeoffs while guaranteeing minimum rate requirements (MRRs) for two-user MISO-NOMA downlink. Specifically, we first obtain rate region boundaries that guarantee two users’ MRRs for two candidatemodes: maximum-ratio transmission (MRT)/SIC NOMA and minimum mean square error beamforming (MMSE-BF)/Non-SIC NOMA. We then construct an expression of power allocation factors (transmit power factors) that can satisfy the two users’ MRRs for MRT/SIC NOMA (MMSE-BF/Non-SIC NOMA) by introducing a parameter λ. Finally, we achieve outer boundary of the union ofthe two modes' rate regionsby mode selection and derive expected users' rates on it. Numerical results demonstrate that the proposed MSPA can improve SE and flexibly achieve different kinds of tradeoffs by adjusting λ, while guaranteeing the two users’ MRRs simultaneously for high signal to noise ratio (SNR) scenario and alternately guaranteeing the two users’ MRRs for low SNR scenario.

Beamforming Design for In-Band Full-Duplex Multi-Cell Multi-User MIMO Networks With Global and Local CSI

This paper investigates beamforming techniques for in-band full-duplex multi-cell multi-user (IBFD-MCMU) wireless networks considering hardware impairments (HWIs), channel uncertainty, and limited channel state information (CSI). For the global CSI scenario, we first enhance zero-forcing (ZF), maximum ratio transmission and combining (MRTC), and minimum mean-squared error (MMSE) beamforming to be compatible with multi-antenna users and IBFD base stations. Then, we investigate beamforming schemes for the local CSI assumption where only intra-cell channel knowledge is fully available at the base stations, and inter-cell channels are known statistically due to the limited training resources. With these limitations, two MMSE-based methods are proposed, which regard unknown CSI as random instances (i.e., eMMSE-RI) and noise (i.e., eMMSE-N). We explore the self-interference cancellation (SIC) capability of beamformers and evaluate the performance of these methods in 3GPP scenarios. Numerical results reveal that the enhanced MMSE beamforming can achieve the desired IBFD with low analog SIC depth, inspiring a low-cost IBFD transceiver design. The practical imperfections (e.g., transceiver HWIs, channel uncertainty, limited CSI) decrease the achievable sum rate but do not reduce the IBFD gain. With CSI limitations, eMMSE-RI outperforms eMMSE-N for microcells, where the probability of the presence of LOS is high, whereas eMMSE-N performs better when cell size is enlarged.

A coherent signal beamforming technique based on sub-array cross correlation

In this paper, a new coherent signal beamforming technique based on sub-array cross correlation (SCC) is proposed for the signal cancellation caused by traditional adaptive beamforming in multipath environment. Firstly, the array is uniformly divided into two mutual non-overlapped sub-arrays, and the preprocess of blocking expected signal is performed inside every sub-array to remove the expected signal component from the received signal on the premise that the direction of expected signal is known in advance. Then, minimum variance distortionless response (MVDR) allows us to obtain the desired signal with noise. Afterwards, based on the fact that the noise between different elements is not correlated, the MVDR output of one sub-array can be taken as the expected signal of the other sub-array to perform the beamforming with minimum mean square error (MMSE) criterion. Finally, the weight for the full array is obtained by combining the MMSE beamforming weights of the two sub-arrays. The proposed method can effectively solve the above coherent beamforming problem. What's more, the SCC beamformer performs well in the case with small samples. Both theoretical derivation and simulation experiment verify the feasibility and validity of the proposed beamformer.

MMSE based beamformer in massive MIMO-IDMA downlink systems

Abstract Now-a-days Massive MIMO (mMIMO) become an attractive technology due to its spectral and energy efficiency by the means of simple signal processing. However, in overloaded scenario, wherein the number of users equipments (UEs) are larger than number of antennas, the spectral effciency (SE) suffers and hence error rate performance, it has been shown recently that use of code domain NOMA in mMIMO can improve the SE performance. Further, interleave division multiple access (IDMA) has been drawn much attention as a suitable code domain non-orthogonal multiple access (NOMA) for future communication standards. This paper proposes the work in two folds, first a massive multiple input and multiple output (MIMO) and IDMA communication system is jointly proposed in which antennas on the base station serves users simultaneously in the same frequency band. Both and are large in numbers. Secondly, the minimum mean square error (MMSE) based beamformer is suggested to combat the propagation loss and effect of multiple access interference (MAI), for massive MIMO-IDMA system under downlink communication constraints. With the help of simulation results, the performance of the proposed system with MMSE beamforming have been investigated in terms of BER vs SNR curve plot.

Hybrid and full-digital beamforming in mmWave Massive MIMO systems: A comparison considering low-resolution ADCs

In a millimeter-wave (mmWave) Massive multiple-input multiple-output (MIMO) systems, full-digital beamforming (i.e., connecting each antenna with a specific radio-frequency (RF) chain) becomes inefficient due to the hardware cost and power consumption. Therefore, hybrid analog and digital transceiver where the number of RF chains are much smaller than that of the antennas has drawn great research interest. In this work, we investigate the use of low-resolution analog-to-digital converters (ADCs) in the uplink of multi-user hybrid and full-digital mmWave Massive MIMO systems. To be specific, we compare the performance of full-digital minimum mean square error (MMSE) and hybrid MMSE beamforming in both sum rates and energy efficiency. Accurate approximations of sum rates and energy efficiency are provided for both schemes, which captures the dominant factors. The analytical results show that full-digital beamforming outperforms hybrid beamforming in terms of sum rates and requires only a small portion (γ) of antennas used by hybrid beamforming to achieve the same sum rates. We given sufficient condition for full-digital beamforming to outperform hybrid beamforming in terms of energy efficiency. Moreover, an algorithm is proposed to search for the optimal ADC resolution bits. Numerical results demonstrate the correctness of the analysis.

Massive Connectivity With Massive MIMO—Part II: Achievable Rate Characterization

This two-part paper aims to quantify the cost of device activity detection in an uplink massive connectivity scenario with a large number of devices but device activities are sporadic. Part I of this paper shows that in an asymptotic massive multiple-input multiple-output (MIMO) regime, device activity detection can always be made perfect. Part II of this paper subsequently shows that despite the perfect device activity detection, there is nevertheless significant cost due to device detection in terms of overall achievable rate, because of the fact that non-orthogonal pilot sequences have to be used in order to accommodate the large number of potential devices, resulting in significantly larger channel estimation error as compared to conventional massive MIMO systems with orthogonal pilots. Specifically, this paper characterizes each active user's achievable rate using random matrix theory under either maximal-ratio combining (MRC) or minimum mean-squared error (MMSE) receive beamforming at the base-station (BS), assuming the statistics of their estimated channels as derived in Part I. The characterization of user rate also allows the optimization of pilot sequences length. Moreover, in contrast to the conventional massive MIMO system, the MMSE beamforming is shown to achieve much higher rate than the MRC beamforming for the massive connectivity scenario under consideration. Finally, this paper illustrates the necessity of user scheduling for rate maximization when the number of active users is larger than the number of antennas at the BS.

Feedback beamforming technique for receiving multipath coherent signals

A novel feedback beamformer is proposed for receiving multipath coherent signals. First, a subtraction-based minimum variance distortionless response beamformer is utilized to obtain an estimation of the desired signal. Then its output is fed back to the original full aperture array where a minimum mean square error (MMSE) beamformer is applied. Due to multipath-matched feature of the MMSE beamformer, the novel feedback beamformer can combine multipath signals without aperture loss. Two feedback schemes are proposed and their effectiveness is verified via simulation.

Nonnegative Mixture for Underdetermined Blind Source Separation Based on a Tensor Algorithm

In this study, a tensor algorithm is proposed to blindly separate an instantaneous linear underdetermined mixture with non-stationary sources and nonnegative mixing matrix. It proceeds in two steps: 1) estimating the mixing matrix and 2) recovering the source signals. First, a canonical tensor model is constructed using a fourth-order cumulant tensor of the observed signals to estimate the mixing matrix. Then, an improved hierarchical alternating least squares algorithm is used to decompose the canonical tensor model, which ensures that all elements of the mixing matrix are positive. Finally, the sources are recovered using a minimum mean-squared error beamformer approach without any hypothetical limitation. We apply two classes of data (speech signals and biomedical signals) to substantiate the effectiveness of the proposed algorithm for underdetermined blind source separation.

A Beamforming Approach to Smart Grid Systems Based on Cloud Cognitive Radio

In this paper, we desire to use cognitive radio (CR) channels for communication among a wireless network of smart meters. However, self-interference critically limits the performance of CR systems. This is due to the coexistence of many unplanned systems simultaneously accessing the same signaling bands in an uncoordinated manner. To solve this problem, we show a beamforming approach that effectively mitigates the self-interference effects of the smart meter channel. The beamforming approach is based on minimum mean squared error (MMSE) method in smart meter systems. The MMSE beamformer usually requires accurate channel estimates and noise-plus-interference power estimates for effective mitigation of self-interference in CR systems. In this paper, we propose novel channel estimation and noise-plus-interference power estimation methodologies that efficiently exploit the preamble feature of the IEEE802.22 wireless regional area network (WRAN). Our framework is premised upon the utilization of a cloud computing smart grid infrastructure that hosts the IEEE 802.22 WRAN CR standard. The simulation results for a smart grid system with the MMSE beamformer illustrate significant improvements in system capacity and BER.

Generalized MMSE beamforming for multicell MIMO systems with random user geometry and channel feedback latency

Abstract In this paper, we propose a generalized minimum mean square error (MMSE) beamforming for downlink multicell multiple-input multiple-output (MIMO) systems with local BS cooperations. Unlike the previous beamforming strategies which have been designed for an idealized multicell MIMO system model, we consider a complicated but realistic multicell MIMO system model. Our realistic multicell MIMO system model captures (i) different average SNRs of users due to random geometrical distribution of users within cells, (ii) channel feedback latency due to air propagation time and signal processing time, and (iii) different channel aging effects for intracell channel information and intercell channel information due to an additional backhaul latency during the exchange of information between pairs of neighboring cells. The key novelty of this paper is that we derive the closed-form beamforming expressions of the generalized MMSE beamforming using convex optimization technique. The closed-form beamforming expression gives insights on how the geometry of users and channel feedback latency affect the construction of optimal beamforming vectors. Numerical results verify that the proposed generalized MMSE beamforming outperforms previous beamforming strategies in both BER and average throughput performances.

Properties, performance and practical interest of the widely linear MMSE beamformer for nonrectilinear signals

Widely Linear (WL) Minimum Mean Square Error (MMSE) estimation has received a great interest these last 20 years for second order (SO) noncircular signals. In the context of radio communications networks, it has been shown in particular that WL MMSE receivers allow to implement Single Antenna Interference Cancellation (SAIC) of one rectilinear interference, such as Binary Phase Shift Keying (BPSK) or Amplitude Shift Keying (ASK) interference, or of quasi-rectilinear interference, such as Minimum Shift keying (MSK), Gaussian MSK (GMSK) or Offset Quadrature Amplitude Modulation (OQAM) interference, hence their great interest for Global System for Mobile Communications (GSM) cellular networks in particular. However, one may wonder whether WL MMSE receivers remain attractive for SO noncircular nonrectilinear interferences, not so scarce in practice. The purpose of this paper is mainly to answer to this important question by giving, in a self-contained and unified way, some new insights into the behavior, properties and performance of the WL MMSE beamformer in the presence of arbitrary noncircular signals and interference which are not necessarily rectilinear. It is shown in particular that, surprisingly, WL MMSE receivers lose their practical interest for strong interferences which are not rectilinear. This breakthrough thus generates a new open problem for the choice between linear and WL MMSE receiver corresponding to the detection of rectilinearity (and/or quasi-rectilinearity), instead of noncircularity, in a given noisy observation. Although this question is out of the scope of this paper, we finally propose preliminary tools based on blind source separation methods to solve this problem.

Sum Rate Optimization in Multiuser Cognitive Radio Networks

In multiuser cognitive radio (CR) networks, we address the problem of joint transmit beamforming (BF) and power control (PC) for secondary users (SUs) when they are allowed to transmit simultaneously with primary users (PUs). The objective is to optimize the network sum rate under the interference constraints of PUs, which is a nonconvex problem. Iterative dual subgradient (IDuSuG) algorithm is proposed by iteratively performing BF and PC to optimize the sum rate, among which minimum mean square error (MMSE) or virtual power-weighed projection (VIP2) is used to design beamformers and subgradient method is used to control the power. VIP2 algorithm is devised for the case in which the interference caused by MMSE beamformer exceeds the threshold. Moreover, channel uncertainty due to lack of cooperation is considered. A closed-form worst-case expression is derived, with which the uncertainty optimization problem is transformed into a certain one. A robust algorithm based on IDuSuG is provided by modifying updates in iterative process. Furthermore, second-order cone programming approximation (SOCPA) method is proposed as another robust algorithm. Typical network models are approximated to SOCP problems and solved by interior-point method. Finally the network sum rates for different PU and SU numbers are assessed for both certainty and uncertainty channel models by simulation.

An optimized unitary beamforming technique for MIMO broadcast channels

This paper addresses the problem of linear beamforming design in MIMO broadcast channels. An iterative optimization method for unitary beamforming is proposed, based on successive optimization of Givens rotations. Under the assumption of perfect channel state information at the transmitter (CSIT) and for practical average signal-to-noise ratios (SNR), the proposed technique provides higher sum rates than zero-forcing (ZF) beamforming while performing close to minimum-mean- squared-error (MMSE) beamforming when the number of transmit antennas equals the number of scheduled users. Moreover, it is shown to achieve linear sum-rate growth with the number of transmit antennas. Interestingly, the proposed unitary beamforming approach proves to be very robust to channel estimation errors. In the simulated scenarios, it provides better sum rates than ZF beamforming and even MMSE beamforming as the variance of the estimation error increases. When combined with simple vector quantization techniques for CSIT feedback in systems with multiuser scheduling, the proposed technique proves to be well suited for limited feedback scenarios with practical number of users, exhibiting performance gains over existing techniques.

Robust Linear Beamforming for MIMO Relay Broadcast Channel With Limited Feedback

This letter considers the relay-assisted multiuser downlink transmission with limited feedback in a wireless cellular network. Taking into account the channel quantization errors, we propose two robust linear beamforming schemes at the relay station based on zero forcing (ZF) criterion and minimum mean square error (MMSE) criterion, respectively. It is noted that the channel direction information (CDI) feedback is sufficient for determining the beamforming vectors in our proposed schemes, which reduces the feedback load. Simulation results show that compared with the conventional ZF beamforming and MMSE beamforming in limited feedback systems, the proposed precoding schemes achieve an improvement in the average bit error rate (BER) performance of the system.

Robust MMSE Beamforming for Multiuser MISO Systems With Limited Feedback

This letter considers minimum mean square error beamforming (MMSEBF) for the downlink of a multiuser multiple-input single-output (MISO) system with limited feedback, where the transmitter only has quantized information regarding the direction of the channel. We present an improved approach which is robust to the channel uncertainties arising from the quantization errors and the lack of channel magnitude information. Simulation results show that the proposed robust MMSEBF scheme provides improved performance over the conventional beamforming schemes in limited feedback systems.

Analytical BER Evaluation of ZF Transmit Beamformer with Channel Estimation Error

The minimum mean square error (MMSE) multiple antenna transmission scheme for a code division multiple access (CDMA) system was recently developed by Choi and Perreau [1]. In this paper, we first show that the zero-forcing (ZF) transmit beamformer for multiple antenna CDMA system has the same form as the MMSE beamformer given by Choi and Perreau. We then develop an analytical method to obtain a closed-form expression of the bit error rate (BER) of the ZF transmit beamformer when there are channel estimation errors. The analytical and simulation results show good agreement, and confirm the importance of accurate channel state information (CSI) at the transmitter when using the ZF transmit beamformer.

A Bayesian Robust Adaptive Beamforming Based on Phase-Invariant MMSE Criterion

The Bayesian beamformer under minimum mean square error (MMSE) criterion has been reported to perform well against uncertainty in source direction of arrival (DOA), but its performance depends on the location of phase reference. This letter proposes a phase-invariant MMSE criterion under which the Bayesian beamformer is independent of the location of phase reference. An iterative algorithm is developed for designing such a new Bayesian beamformer. Numerical examples demonstrate that the new Bayesian beamformer can provide better performance than the existing Bayesian MMSE beamformer for either uniform or non-uniform linear array.

Sparse Bayesian Learning Approach to Adaptive Beamforming Assisted Receivers

In this letter, a new adaptive beamforming assisted receiver based on sparse Bayesian learning is proposed. We consider a general probabilistic Bayesian learning framework for obtaining sparse solutions to adaptive beamforming assisted receivers to improve the performance of an adaptive beamforming assisted receiver based on the minimum mean squared error (MMSE) scheme. Simulation experiments show that the bit error rate (BER) performance of the sparse Bayesian beamforming receiver shows an outstanding BER performance compared to MMSE beamforming receivers

Adaptive minimum bit-error rate beamforming

An adaptive beamforming technique is proposed based on directly minimizing the bit-error rate (BER). It is demonstrated that this minimum BER (MBER) approach utilizes the antenna array elements more intelligently than the standard minimum mean square error (MMSE) approach. Consequently, MBER beamforming is capable of providing significant performance gains in terms of a reduced BER over MMSE beamforming. A block-data adaptive implementation of the MBER beamforming solution is developed based on the Parzen window estimate of probability density function. Furthermore, a sample-by-sample adaptive implementation is considered, and a stochastic gradient algorithm, referred to as the least bit error rate, is derived. The proposed adaptive MBER beamforming technique provides an extension to the existing work for adaptive MBER equalization and multiuser detection.

Super-Exponential Blind Adaptive Beamforming

The objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions, suppress the noises and the interfering signals from other directions, and/or simultaneously provide the localization of the associated sources. In this paper, we present a higher order cumulant-based beamforming algorithm, namely, the super-exponential blind adaptive beamforming algorithm, which is extended from the super-exponential algorithm (SEA) and the inverse filter criteria (IFC). While both SEA and IFC assume noise-free conditions, this requirement is no longer needed, and all the noise components are taken into account in the proposed algorithm. Two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error (MMSE). Simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors; its performance with the use of the fourth-order cumulants is close to that of the nonblind optimal MMSE beamformer.