Beamforming Weights Research Articles

Robust Cooperative Relay Beamforming Design for Security

In this paper, we investigate a security transmission scheme at the physical layer for cooperative wireless relay networks in the presence of a passive eavesdropper. While the security scheme has been previously investigated with perfect channel state information(CSI) in the presence of a passive eavesdropper, this paper focuses on researching the robust cooperative relay beamforming mechanism for wireless relay networks which makes use of artificial noise (AN) to confuse the eavesdropper and increase its uncertainty about the source message. The transmit power used for AN is maximized to degrade the signal-to-interference-plus-noise-ratio (SINR) level at the eavesdropper, while satisfying the individual power constraint of each relay node and worst-case SINR constraint at the desired receiver under a bounded spherical region for the norm of the CSI error vector from the relays to the destination. Cooperative beamforming weight vector in the security scheme can be obtained by using S-Procedure and rank relaxation techniques. The benefit of the proposed scheme is showed in simulation results.

Optimal design of modal beamformers for circular arrays.

An approach to optimal design of circular harmonics based modal beamformers for circular arrays is presented. Theoretical analysis shows the equivalence between the element-space and circular-harmonics-domain beamformers. By deriving the expression for the signal and noise covariance matrices, array manifold, and the array response in terms of the circular-harmonics-domain beamforming weights, the weights design problem is formulated as one of minimum variance distortionless response beamforming in the circular harmonics domain. It is found that the well-known phase-mode beamformer for circular arrays can be viewed as an ideal minimum variance distortionless response beamformer against the planarly isotropic noise in the circular harmonics domain. This interesting result is useful for analyzing and evaluating the performance of the phase-mode circular arrays. In this circular-harmonics-domain beamformer, additional constraints can be imposed to improve its robustness and control the sidelobes, which is important in practical applications. The developed approach can include both the delay-and-sum and phase-mode beamformers as special cases, which leads to very flexible designs. Simulation and experimental results show excellent performance of the proposed beamforming approach.

Modifying MVDR Beamformer for Reducing Direction-of-Arrival Estimation Mismatch

The minimum variance distortionless response (MVDR) beamforming algorithm is used in smart antenna design for wireless communication. The operation of MVDR is based on finding the optimum weight to direct the main lobe beam to the desired user location with a unity gain. MVDR is very sensitive to signature vector mismatch. This mismatch occurs due to waveform deformation, local scattering, imperfect array element calibration and element shape distortion, which leads to errors in finding the direction of arrival (DOA) of the signal. In this paper, a new technique to modify the MVDR is presented, modelled and evaluated. The proposed algorithm is named modified MVDR (MMVDR) and is dependent on reconstructing the signature vector (steering vector) and the covariance matrix to introduce accurate beamformer weight by re-localization the reference element to be in the middle of ULA, rather than at one end side. The new reference position partitions the array’s elements into two groups around this reference, which leads to treat received signals with identical phase along the array’s elements, as well as increasing the degree of freedom to deals with different types of uniform arrays. The evaluation results show that MMVDR outperforms MVDR with respect to beamformer accuracy, system cost, processing time and signal classification to overcome the errors in DOA estimation which occur due to fabrication and calibration errors.

Iterative beamforming algorithm for improved throughput in multi‐cell multi‐antenna wireless systems

Mitigating the effects of inter-cell interference in a multi-cell wireless network is essential to improve the achieved performance. In this study, the authors develop an iterative distributed beamforming scheme that addresses the effect of inter-cell interference problem on the downlink of a multi-cell multi-antenna wireless system with linear beamformers. The proposed scheme attempts at improving the overall system performance by exploiting network duality principle to jointly compute the optimal transmit and receive beamforming weights such that the desired received power is maximised while minimising the caused interference to other users. Network duality allows the serving base stations and the intended users to jointly compute the beamforming weights of the transmit/receive antenna elements, which improve network performance. The proposed scheme considers variable levels of channel information feedback and different transmit–receive antenna configurations. Simulation results show that a significant performance improvement is achieved through the joint optimisation of the transmit/receive beamforming vectors. Results also indicate that compared with reference schemes, their scheme improves the achieved sum-rate by up to 50%.

Probability distribution of multiple-target data snapshots applied to large-aperture array processing

We consider sonar array target detection and azimuth estimation in experimental scenarios consisting of large-aperture horizontal line arrays of hydrophones in the water column. In such scenarios, successful distinction of quiet targets from the background noise strongly depends on having sufficient independent data snapshots available for computation of adaptive beamforming weights. In this work, the discrete Fourier transform matrix is used for projecting the array data into a sparse domain, from which the theoretical probability density function of each (sparse-domain) datum can be obtained. It is shown that the sparse data exhibits a scaled chi-squared distributed magnitude, with a scale factor that depends on signal-to-background noise ratio and array size. Using this theoretical distribution and Monte Carlo simulations, minimum experimental requirements for target detection are quantified and highlight the tradeoff between data sample size, array aperture, and signal-to-noise ratio. In addition, a s...

Double zero minimum variance distortionless response beamformer

Adaptive beamformers (ABFs) place deep beampattern notches near interferers to suppress the interferers' power in the ABF output. The common sample matrix inversion (SMI) Minimum Variance Distortionless Response (MVDR) ABF computes the beamformer weights by substituting the sample covariance matrix (SCM) for the unknown ensemble covariance matrix in the MVDR expression. Errors in the SCM estimate of interferer direction due to limited sample support or interferer motion degrade the ABFs ability to suppress the interferer. This presentation exploits array polynomial properties to design a robust ABF. The array polynomial for a uniform linear array beamformer is the z-transform of the array weights. The array polynomial zeros on the unit circle correspond to the beampattern nulls. The proposed double zero (DZ) MVDR ABF solves for the MVDR weights using the SCM for a half-aperture subarray, then convolves the half-aperture weights with themselves to obtain the full aperture ABF weights. The resulting array polynomial for the DZ MVDR ABF has second-order zeros, producing broader and deeper notches in the interferer direction. The DZ MVDR ABF outperforms the SMI MVDR and covariance matrix tapered ABFs in simulations with stationary and moving interferers. [Work supported by ONR 321US.]

Sum-Rate Optimal Network Beamforming and Subcarrier Power Allocation for Multi-Carrier Asynchronous Two-Way Relay Networks

In this paper, we consider a multicarrier asynchronous bidirectional relay network, where different relay-transceiver links can cause different delays in the signals they convey, thereby producing inter-symbol-interference at the two transceivers. Such a two-way relay link can be modeled as a frequency selective channel with multiple taps, and thus, it can be equalized using orthogonal frequency division multiplexing (OFDM) transmission and reception schemes at the two transceivers, while the relays use simple amplify-and-forward relaying protocol. We prove rigorously that maximizing the sum-rate under a total power budget, through jointly optimal network beamforming at the relays and subcarrier power loading at the two transceivers, leads to a relay selection scheme, where only those relays which contribute to one tap of the end-to-end channel impulse response, have to be active and the remainder of the relays have to be switched off. The optimal tap can then be obtained using a simple search method. Moreover, we present semi-closed-form solutions for the optimal value of transceivers' subcarrier powers as well as for the relay beamforming weights.

Minimum variance beamformer weights revisited

Adaptive minimum variance beamformers are widely used analysis tools in MEG and EEG. When the target brain activity presents in the form of spatially localized responses, the procedure usually involves two steps. First, positions and orientations of the sources of interest are determined. Second, the filter weights are calculated and source time courses reconstructed. This last step is the object of the current study. Despite different approaches utilized at the source localization stage, basic expressions for the weights have the same form, dictated by the minimum variance condition. These classic expressions involve covariance matrix of the measured field, which includes contributions from both the sources of interest and the noise background. We show analytically that the same weights can alternatively be obtained, if the full field covariance is replaced with that of the noise, provided the beamformer points to the true sources precisely. In practice, however, a certain mismatch is always inevitable. We show that such mismatch results in partial suppression of the true sources if the traditional weights are used. To avoid this effect, the “alternative” weights based on properly estimated noise covariance should be applied at the second, source time course reconstruction step. We demonstrate mathematically and using simulated and real data that in many situations the alternative weights provide significantly better time course reconstruction quality than the traditional ones. In particular, they a) improve source-level SNR and yield more accurately reconstructed waveforms; b) provide more accurate estimates of inter-source correlations; and c) reduce the adverse influence of the source correlations on the performance of single-source beamformers, which are used most often. Importantly, the alternative weights come at no additional computational cost, as the structure of the expressions remains the same.

Dealing With Uncertainties on Phase Weighting of Linear Antenna Arrays by Means of Interval-Based Tolerance Analysis

The analysis of the tolerances on the power patterns radiated by linear antenna arrays whose excitations are affected by phase errors is carried out by means of an approach based on the interval analysis ( IA ). The rules and the features of the arithmetic of intervals, already effectively applied to analyze the effects of errors on the amplification levels, are exploited here to derive a suitable set of analytical relationships predicting the maximum deviations (i.e., upper and lower bounds) with respect to the nominal power pattern once the phase errors are defined as belonging to intervals of values. Representative numerical examples are reported and discussed to assess potentialities and limitations of the IA -based approach. Toward this end, different configurations of the beamforming weights affording low-sidelobes and steered beam patterns are analyzed.

Cooperative beamforming of full‐duplex relays for improving physical layer security

SummaryIn this paper, we consider secure communications of one source‐destination pair in the presence of one eavesdropper, when full‐duplex decode‐and‐forward cooperative relays operate to enhance physical layer security. While the conventional half‐duplex relay receives the signal from the source and forwards the re‐encoded signal to the destination in two separated time slots, the full‐duplex relay (FDR) performs the transmission and reception at the same time, which can ideally double the secrecy capacity. However, because of the simultaneous transmission and reception, each FDR suffers from both its own self‐interference and the interference from the other cooperative FDRs. When the conventional cooperative relaying schemes are used in full‐duplex relaying, it is obviously expected that the self‐interference signals cause severe degradation of the secrecy capacity. Here, we propose an iterative transmit power allocation and relay beamforming weight design scheme for cooperative FDRs to enhance the secrecy rate as well as suppress the self‐interference signals. Numerical results present that the FDRs with the proposed scheme significantly improve the secrecy rate compared with the conventional half‐duplex relays. Copyright © 2015 John Wiley & Sons, Ltd.

On Achievable SNR Region for Multi-User Multi-Carrier Asynchronous Bidirectional Relay Networks

We study the problem of obtaining achievable signal-to-noise ratio (SNR) region and the corresponding rate region for an asynchronous bidirectional multi-carrier relay network which consists of two transceivers and multiple relays. We assume that each relaying path, corresponding to each relay, causes a delay in the signal transmitted by one of the transceivers when this signal goes through that relay and arrives at the other transceiver. This delay depends on the distance traveled by the signal. Hence, different relaying paths incur different delays in the signal time of arrival at each of the two transceivers. In our data model, we take into account that these delays are different for different relaying paths. Assuming distributed beamforming at the relays and power control at the transceivers, we characterize the achievable SNR region and the corresponding rate region for this network. Such a characterization is performed when each subcarrier is used to enable bidirectional communication between several outer transceivers. To do so, we present our optimization framework and examine its structure, thereby showing how it can be solved. We prove that for the case where the rates over different subcarriers at each transceiver are constrained to be equal, our approach leads to semi-closed-form solutions for the relay beamforming weights and transceivers' subcarrier powers and for the boundaries of the SNR region.

Joint Spectrum Sharing and Power Allocation for OFDM-Based Two-Way Relaying

Considering a bidirectional amplify-and-forward based multi-carrier multi-relay network, we formulate two different joint power allocation and network beamforming problems. In the first formulation, we aim to minimize the total transmit power of the network, subject to two constraints on the transceiver rates. In the second problem, our goal is to maximize the sum-rate of the two transceivers subject to a constraint on the total network transmit power. In both problems, the design parameters include the relay beamforming weights and the transceiver power allocations over all subcarriers. We propose a two-step iterative method to tackle each problem and show that each method leads to (at least) a locally optimum solution. Each iterative method alternates between solving the underlying problem for one set of variables while the other set is fixed and vice versa. Each subproblem is shown to be amenable to a computationally efficient solution. Our simulation results show the efficiency of the proposed techniques.

Joint Beamforming and Power Allocation for Secrecy in Peer-to-Peer Relay Networks

This paper investigates the physical-layer security of a multiuser peer-to-peer (MUP2P) relay network for amplify-and-forward (AF) protocol, where a secure user and other unclassified users coexist with a multi-antenna eavesdropper and the eavesdropper can wiretap the confidential information in both two cooperative phases. Our goal is to optimize the transmit power of the source and the beamforming weights of the relays jointly for secrecy rate maximization subject to the minimum signal-to-interference-noise-ratio (SINR) constraint at each user, and the individual and total power constraints. Mathematically, the optimization problem is non-linear and non-convex, which does not facilitate an efficient resource allocation algorithm design. As an alternative, a null space beamforming scheme is adopted at the relays for simplifying the joint optimization and eliminating the confidential information leakage in the second cooperative phase, where the relay beamforming vector lies in the null space of the equivalent channel of the relay to eavesdropper links. Although the null space beamforming scheme simplifies the design of resource allocation algorithm, the considered problem is still non-convex and obtaining the global optimum is very difficult, if not impossible. Employing a sequential parametric convex approximation (SPCA) method, we propose an iterative algorithm to obtain an efficient solution of the non-convex problem. Besides, the proposed joint design algorithm requires a feasible starting point, we also propose a low complexity feasible initial points searching algorithm. Simulations demonstrate the validity of the proposed strategy.

Robust amplify‐and‐forward relay beamforming for security with mean square error constraint

In this study, security schemes at the physical layer are proposed for an amplify-and-forward relay system in the presence of a passive eavesdropper. We focus on maximising the transmit power of the artificial noise (AN) to degrade the minimum mean square error (MMSE) level at the eavesdropper, while achieving MMSE constraint for the desired receiver. Assuming that the desired receiver and the passive eavesdropper possess perfect channel state information (CSI), AN is designed to lie in the null space of legitimate channels. However, the available CSI is impossible to be perfect in practice. Therefore the authors present a robust beamforming scheme which maximises the worst-case transmit power of the AN under the condition of imperfect CSI and recovers a large fraction of the performance in the perfect CSI case. A classical alternating optimisation algorithm is proposed to obtain the relay beamforming weights, and simulation results show the benefit of proposed schemes.

Efficient Solutions to Distributed Beamforming for Two-Way Relay Networks Under Individual Relay Power Constraints

This paper investigates distributed beamforming (DBF) designs for two-way relay networks (TWRNs), where two terminal nodes exchange information through a set of amplify-and-forward (AF) relays. We assume individual relay power constraints and study two important design problems, namely, the max–min fairness (MMF) problem and the weighted sum-rate maximization (WSRM) problem. For the MMF problem, unlike the existing works that usually solve the problem by a bisection method, we propose an efficient optimal solution by solving one convex second-order cone program (SOCP) only. For the WSRM problem, we develop an efficient iterative algorithm based on SOCP reformulation and the successive convex approximation (SCA) technique. For both the MMF and WSRM designs, we further propose a distributed implementation framework where each of the relays can independently compute its beamforming weight using its local channel state information (CSI) and some common parameters broadcasted by a control center. Simulation results are presented to demonstrate the performance advantages of the proposed solutions.

Optimal Beamforming and Performance Analysis of Wireless Relay Networks with Unmanned Aerial Vehicle

AbstractIn this paper, we investigate a wireless communication system employing a multi-antenna unmanned aerial vehicle (UAV) as the relay to improve the connectivity between the base station (BS) and the receive node (RN), where the BS–UAV link undergoes the correlated Rician fading while the UAV–RN link follows the correlated Rayleigh fading with large scale path loss. By assuming that the amplify-and-forward (AF) protocol is adopted at UAV, we first propose an optimal beamforming (BF) scheme to maximize the mutual information of the UAV-assisted dual-hop relay network, by calculating the BF weight vectors and the power allocation coefficient. Then, we derive the analytical expressions for the outage probability (OP) and the ergodic capacity (EC) of the relay network to evaluate the system performance conveniently. Finally, computer simulation results are provided to demonstrate the validity and efficiency of the proposed scheme as well as the performance analysis.

Sum Rate Maximization Based on Joint Power Control and Beamforming in MIMO One Way AF Relay Networks

Aims: Joint Power control and beamforming in MIMO one way AF relay networks by obtaining beamforming weights on relay nodes through maximizing sum rate while the total power consumed in all relay nodes are not greater than the certain predefined threshold. Study Design: Comparative study by simulation in MATLAB software.

The Application of JDL to Suppress Sea Clutter for Shipborne HFSWR

This paper deals with the problem of sea clutter suppression for shipborne high frequency surface wave radar (HFSWR) based on the joint domain localized (JDL) adaptive processing algorithm. The performance of the novel method is compared with 2D FFT plus digital beamforming (FFT-DBF) and orthogonal weight in different azimuths. The results based on simulated and real data show that the novel method provides higher detection performance than others.

General Rank Multiuser Downlink Beamforming With Shaping Constraints Using Real-Valued OSTBC

In this paper we consider optimal multiuser downlink beamforming in the presence of a massive number of arbitrary quadratic shaping constraints. We combine beamforming with full-rate high dimensional real-valued orthogonal space time block coding (OSTBC) to increase the number of beamforming weight vectors and associated degrees of freedom in the beamformer design. The original multi-constraint beamforming problem is converted into a convex optimization problem using semidefinite relaxation (SDR) which can be solved efficiently. In contrast to conventional (rank-one) beamforming approaches in which an optimal beamforming solution can be obtained only when the SDR solution (after rank reduction) exhibits the rank-one property, in our approach optimality is guaranteed when a rank of eight is not exceeded. We show that our approach can incorporate up to 79 additional shaping constraints for which an optimal beamforming solution is guaranteed as compared to a maximum of two additional constraints that bound the conventional rank-one downlink beamforming designs. Simulation results demonstrate the flexibility of our proposed beamformer design.

Interference Rejection Degradation in Function of the DOA in a Beamforming System

This paper analyzes the interference rejection degradation in a narrowband beamforming system formed by a Uniform Linear Array (ULA), as a function of the Direction of Arrival (DOA) of the desired signal. To calculate the beamforming weights, the Recursive Least Squares (RLS) algorithm was used. For each DOA of the desired signal, the Signal to Noise plus Interference Ratio (SINR) is estimated. When the DOA of the desired signal is near to the sector edge, the SINR is significantly degraded because of less effectiveness in the interference mitigation algorithm. A quantitative estimation of this degradation is provided in this work. Some possible solutions to cope with this situation are discussed, and also some design criteria are provided.