The performance of a -steering beamformer in correlated Rayleigh fading

We consider the performance of a -steering adaptive beamformer in a distributed Rayleigh fading environment. To determine the beamformer coefficients, the signal and interference array response vectors must be estimated. An estimator that makes use of the knowledge of the spatial distribution of the signal is proposed and compared with other estimators that do not use this information. As the angular spread of the signal increases, the value of this information is reduced, until, for the case of isotropic scattering, the estimate that uses the spatial distribution is equivalent to the estimate that does not. Performance results are presented that compare the performance of the different estimators. We derive closed-form expressions for the signal-to-interference-plus-noise ratio (SINRO) and probability of error for the case where the training data are orthogonal.     

基于波束形成跳频系统抗干扰方法研究

本文研究利用波束形成技术与跳频技术相结合,在存在宽带阻塞干扰以及跟踪干扰时,将信号与干扰在空域进行分离,提高跳频系统的抗干扰性能。指出利用空间平滑不仅可以有效抑制相干跟踪干扰,而且提高了波束的收敛速度。仿真结果证明了该方法的有效性。     

基于稀疏约束和SRV约束的宽带自适应波束形成

针对传统的宽带MVDR自适应波束形成中,抑制干扰的同时会抬高旁瓣电平,且过多的线性约束会导致波束输出的SINR性能下降的问题,提出了一种基于SRV约束和稀疏约束的低旁瓣、高增益宽带自适应波束形成方法.该方法在窄带MVDR自适应波束形成基础上,通过增加波束图稀疏约束来降低波束的旁瓣电平,同时利用空间响应偏差(SRV)约束将窄带算法推广到宽带MVDR 自适应波束形成中,极大地降低了算法的复杂度,改善了波束输出的SINR 性能.与传统方法相比,该方法在降低宽带波束的旁瓣电平的同时,还具有良好的干扰抑制效果.数值仿真实验验证了该方法的有效性.     

A Novel Adaptive Antenna Array for DS/CDMA Code Acquisition

Equipped with an adaptive beamformer, existing adaptive array code acquisition still relies on the correlator structure. Due to the inherent property of the associated serial-search scheme, its mean acquisition time is large, especially in strong interference environments. In this paper, we propose a novel adaptive filtering scheme to solve the problem. The proposed scheme comprises two adaptive filters, an adaptive spatial and an adaptive temporal filter. With a specially designed structure, the spatial filter can act as a beamformer suppressing interference, while the temporal filter can act as a code-delay estimator. A mean squared error (MSE) criterion is proposed such that these filters can be simultaneously adjusted by a stochastic gradient descent method. The performance as well as the convergence behavior of the proposed algorithm are analyzed in detail. Closed-form expressions for optimum filter weights, optimum beamformer signal-to-interference-plus-noise ratio (SINR), steady-state MSE, and mean acquisition time are derived for the additive white Gaussian noise (AWGN) channel. Computer simulations show that the mean acquisition time of the proposed algorithm is much shorter than that of the correlator-based approach, and the derived theoretical expressions are accurate.     

Optimum beamforming performance degradation in the presence of imperfect spatial coherence of wavefronts

Optimum-adaptive beamforming is generally analyzed and used assuming perfectly known wavefronts. There are several applications involving propagation media that are neither isotropic, nor homogeneous, nor deterministic. There are also applications where the arrays may be nondeterministic and/or nonrigid or, more simply, are in motion. Typical examples of such applications are radar, sonar, underwater and satellite and, in general, wireless communication systems. In these cases, the resulting wavefronts can be randomly distorted. We analyze the performance of an optimum-adaptive beamformer when the desired signal component or the interference are not fully coherent over the array aperture. The effects of reduced spatial coherence, for both signal and interference cases, are evaluated in terms of output signal-to-interference-plus-noise ratio (SINR) degradation with respect to the ideal case where the reception of a fully coherent signal is only affected by the presence of a zero-mean additive white Gaussian noise. For this purpose, we provide a theoretical analysis, deriving analytical expressions for general models of spatial coherence loss, supported by numerical results.     

On the coherent interference suppression using a spatiallysmoothing adaptive array

The behavior of a spatially smoothing adaptive array is examined. An expression for the weight vector is first derived. Using the array gain on the desired signal and the coherent interference is obtained. Then the expression for output signal-to-noise (SNR) is derived. It shows that the performance of the spatially smoothing array depends on the number of the subarrays, the angle separation, relative power and initial phase difference between the desired signal and the coherent interference. For good interference suppression it is found that the magnitude of the phase difference of the incident and interference signals must be greater than the beamwidths of both the subarray and the equivalent array. There is also a tradeoff between increasing the groups of subarrays and decreasing the number of elements in the subarrays. Computer simulation results are given that validate the analysis     

Statistics of adaptive nulling and use of the generalizedeigenrelation (GER) for modeling inhomogeneities in adaptive processing

This paper examines the integrity of the generalized eigenrelation (GER), which is an approach to assessing performance in an adaptive processing context involving covariance estimation when the adaptive processors are subject to undernulled interference. The GER is a mathematical relation, which if satisfied, often facilitates closed-form analysis of adaptive processors employing estimated covariances subject to inhomogeneities. The goal of this paper is to determine what impact this constraint has on the integrity of the adaptive nulling process. In order to examine the impact of the GER constraint on adaptive nulling, we establish fundamental statistical convergence properties of an adaptive null for the sample covariance-based (SCB) minimum variance distortionless response (MVDR) beamformer. Novel exact expressions relating the mean and variance of an adaptive null of a homogeneously trained beamformer to the mean and variance of a nonhomogeneous trained beamformer are derived. In addition, it is shown that the Reed et al. (1974) result for required sample support can be highly inaccurate under nonhomogeneous conditions. Indeed, the required sample support can at times depend directly on the power of the undernulled interference     

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.     

Broadband Interference Suppression Performance of Minimum Redundancy Arrays

The broadband interference suppression performance of the minimum redundancy array (MRA) used in the linearly constrained minimum variance (LCMV) beamformer is studied in this paper. The ideal continuous-time, infinite-length filter instead of the realistic finite-order digital filter is assumed in the array processor. The expressions of the power spectrum of the beamformer output in different scenarios are derived to compute the mean output power. Several original properties of the performance of the MRA compared with that of the uniform linear array (ULA) are obtained by mathematical proofs and numerical studies.     

Improved adaptive ing of coherent interference without spatial smoothing

A new scheme for adaptive ing in the presence of coherent interference is proposed that finds the weight vector using a nonsquare correlation matrix without spatial smoothing. Conventional schemes, which use square matrices, correspond to specific cases of the new method. It allows us to increase the dimension of the weight vector such that the ing capability is enhanced. Theoretic performance analysis is made, showing that the output signal-to-interference ratio (SINR) of such a beamformer is proportional to the weight dimension for sidelobe interference. Simulation results confirm this.     

A Nulling Performance Comparison Between a Single- and Multiple-Aperture Multiple-Beam Antenna

Discussed in this paper is the nulling performance of a single- and a multiple-aperture multiple-beam antenna (MBA). A linearly constrained minimum power algorithm incorporating both main beam and derivative constraints is formulated and simulated. The nulling resolution of the multiple-aperture MBA is shown to be superior to that of the single-aperture MBA. In addition, a method for illuminating a region in space with constant gain while simultaneously nulling interfering signals within a fractional single element beamwidth of this constant gain region is illustrated. A flat gain pattern is achieved by spacing derivative constraints over the spatial region where the desired signals are known to be transmitting. Derivative constraints are particularly useful when the precise directions of arrival for the desired signals are not available to the beamformer     

Performance of DMI and eigenspace-based beamformers

The performance of the direct matrix inversion (DMI) method for antenna arrays of arbitrary geometry is analyzed by asymptotic statistical techniques. The effects of eigenspace disturbance caused by finite samples on the output interference and noise powers are examined under the unit gain constraint in the direction of the desired signal. The results show that the performance of the DMI method is degraded mostly by the disturbed noise subspace. That suggests the use of an eigenspace-based beamformer in which the weight vector is computed by using the signal-plus-interference subspace component of the sample correlation matrix. Convergence properties of the eigenspace-based beamformer are evaluated for the cases in which the source number is known and in which it is overestimated. Theoretical analyses validated by computer simulations indicate that the eigenspace-based beamformer has faster convergence rate than the DMI method     

Adaptive nulling beamformer for rejection of coherent and noncoherent interferences

An adaptive beamforming method is presented which rejects coherent and noncoherent interferences by using an interference subspace, which is efficiently obtained from a submatrix of the covariance matrix of received signals. The use of the submatrix enables an increase in the effective array aperture size, as compared with the existing correlation-vector-based beamformer (CVB). As a result, the proposed beamformer can provide superior performance than conventional methods such as CVB and the weighted spatial smoothing (WSS).     

Transmit Subaperturing for MIMO Radars With Co-Located Antennas

We present a transmit subaperturing (TS) approach for multiple-input multiple-output (MIMO) radars with co-located antennas. The proposed scheme divides the transmit array elements into multiple groups, each group forms a directional beam and modulates a distinct waveform, and all beams are steerable and point to the same direction. The resulting system is referred to as a TS-MIMO radar. A TS-MIMO radar is a tunable system that offers a continuum of operating modes from the phased-array radar, which achieves the maximum directional gain but the least interference rejection ability, to the omnidirectional transmission based MIMO radar, which can handle the largest number of interference sources but offers no directional gain. Tuning of the TS-MIMO system can be easily made by changing the configuration of the transmit subapertures, which provides a direct tradeoff between the directional gain and interference rejection power of the system. The performance of the TS-MIMO radar is examined in terms of the output signal-to-interference-plus-noise ratio (SINR) of an adaptive beamformer in an interference and training limited environment, where we show analytically how the output SINR is affected by several key design parameters, including the size/number of the subapertures and the number of training signals. Our results are verified by computer simulation and comparisons are made among various operating modes of the proposed TS-MIMO system.      

Two-Dimensional Adaptive Array Beamforming With Multiple Beam Constraints Using a Generalized Sidelobe Canceller

This paper deals with the problem of two-dimensional (2-D) adaptive array beamforming with multiple beam constraints (MBC) using a generalized sidelobe canceller (GSC). We present a method for the construction of signal blocking matrix required by the 2-D GSC. The resulting 2-D adaptive beamformer can provide almost the same performance as conventional 2-D adaptive beamformers based on a linearly constrained minimum variance (LCMV) criterion. The effectiveness of the proposed GSC is that the construction of the required signal blocking matrix requires only the computation of a few entries from analytical formulas. In comparison with conventional methods, the proposed technique gets rid of the computational complexity due to the eigendecomposition required for finding the 2-D signal blocking matrix. For dealing with the performance degradation due to coherent interference, we present a 2-D weighted spatial smoothing scheme to effectively alleviate the coherent jamming effect. Several simulation examples are provided for illustration and comparison.     

On Diagonal Loading for Robust Adaptive Beamforming Based on Worst‐Case Performance Optimization

Robust adaptive beamforming based on worst‐case performance optimization is investigated in this paper. It improves robustness against steering vector mismatches by the approach of diagonal loading. A closed‐form solution to optimal loading is derived after some approximations. Besides reducing the computational complexity, it shows how different factors affect the optimal loading. Based on this solution, a performance analysis of the beamformer is carried out. As a consequence, approximated closed‐form expressions of the source‐of‐interest power estimation and the output signal‐to‐interference‐plus‐noise ratio are presented in order to predict its performance. Numerical examples show that the proposed closed‐form expressions are very close to their actual values.     

Performance analysis of an opportunistic multi‐user cognitive network with multiple primary users

Consider a multi‐user underlay cognitive network where multiple cognitive users concurrently share the spectrum with a primary network with multiple users. The channel between the secondary network is assumed to have independent but not identical Nakagami‐m fading. The interference channel between the secondary users (SUs) and the primary users is assumed to have Rayleigh fading. A power allocation based on the instantaneous channel state information is derived when a peak interference power constraint is imposed on the secondary network in addition to the limited peak transmit power of each SU. The uplink scenario is considered where a single SU is selected for transmission. This opportunistic selection depends on the transmission channel power gain and the interference channel power gain as well as the power allocation policy adopted at the users. Exact closed form expressions for the moment‐generating function, outage performance, symbol error rate performance, and the ergodic capacity are derived. Numerical results corroborate the derived analytical results. The performance is also studied in the asymptotic regimes, and the generalized diversity gain of this scheduling scheme is derived. It is shown that when the interference channel is deeply faded and the peak transmit power constraint is relaxed, the scheduling scheme achieves full diversity and that increasing the number of primary users does not impact the diversity order. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of beamformer configurations for DS-CDMA systems

Two different beamformer configurations for the base station receiver in direct-sequence code-division multiple access (DS-CDMA) systems, namely, a chip-based and a symbol-based configuration, are studied. In the chip-based configuration, different interfering components are rejected based on the spatial distribution of their power. In the symbol-based configuration, spatial diversity is exploited after despreading and different interfering components are rejected based on their interfering strength, which depends on both their power and code correlation with the signal of interest. For the symbol-based configuration, more effort is applied to rejecting the interfering components with higher interfering strength, and thus, a more selective and efficient system is achieved. Detailed performance analysis and simulations show that in the presence of multiple-access interference, the symbol-based configuration can lead to a significant improvement in the signal-to-interference-plus-noise ratio relative to that achieved with the chip-based configuration for both asynchronous and synchronous DS-CDMA systems.     

Adaptive array utilising multimode antennas for correlated non-circular arrivals

A regularised Capon beamformer under multipath or smart jamming environments is designed wherein the desired signal and correlated interferences are decorrelated by a modal smoothing operation. Unlike conventional spatial smoothing, modal smoothing is not limited to the arrays of spatially-coupled subarrays, and does not decrease the array aperture. By incorporating a soft subspace projection, this beamformer is still robust to the look direction error even in the presence of unknown non-uniform noise.     

Quadratically constrained adaptive beamforming for coherent signalsand interference

Severe signal cancellation often occurs in conventional adaptive beamforming if coherent interferers are present. The paper proposes adding quadratic constraints to a linearly constrained minimum variance (LCMV) adaptive beamformer to prevent signal cancellation in coherent interference environments. The additional constraint limits the beamformer output mean squared error to be less than a specified level. It is shown that if the quadratic constraint is properly chosen, then the original linearly constrained beamformer's signal cancellation is reduced to an arbitrarily small level while the interference cancellation is unchanged. In practice, the quadratic constraint is constructed based on estimates of the interference parameters. Sensitivity analyses show the performance of the resulting beamformer is robust with respect to this approximate constraint. The effectiveness of the quadratically constrained adaptive beamformer is further illustrated through simulations