In this paper, we propose a reduced-rank space-time adaptive processing (STAP) technique for airborne phased array radar applications. The proposed STAP method performs dimensionality reduction by using a reduced-rank switched joint interpolation, decimation and filtering algorithm (RR-SJIDF). In this scheme, a multiple-processing-branch (MPB) framework, which contains a set of jointly optimized interpolation, decimation and filtering units, is proposed to adaptively process the observations and suppress jammers and clutter. The output is switched to the branch with the best performance according to the minimum variance criterion. In order to design the decimation unit, we present an optimal decimation scheme and a low-complexity decimation scheme. We also develop two adaptive implementations for the proposed scheme, one based on a recursive least squares (RLS) algorithm and the other on a constrained conjugate gradient (CCG) algorithm. The proposed adaptive algorithms are tested with simulated radar data. The simulation results show that the proposed RR-SJIDF STAP schemes with both the RLS and the CCG algorithms converge at a very fast speed and provide a considerable SINR improvement over the state-of-the-art reduced-rank schemes.

/pdf/reduced-rank-stap-schemes-for-airborne-radar-based-on-4i84lgnoun.pdf

Reduced-Rank STAP Schemes for Airborne Radar Based on Switched Joint Interpolation, Decimation and Filtering Algorithm

Critical government and industry sectors (such as law enforcement, transportation, communication, and finance) are growing increasingly dependent on Global Navigation Satellite Systems (GNSS) for positioning, navigation, and timing. At the same time, the availability of low-cost GNSS jamming devices are presenting a serious threat to GNSS and increasing the likelihood of outages to infrastructures relying on GNSS. The attacks range from malicious parties intentionally jamming GNSS signals within a targeted geographical region to uninformed users causing accidental interference. This paper is an overview of different approaches adopted to date to mitigate GNSS disruption caused by intentional and unintentional jamming. The first approach outlined in this paper is the use of inertial systems to aid GNSS. The second and third approaches are the filtering of jamming/interference in the spatial and time-frequency domains, respectively. The fourth approach is vector tracking of GNSS signals in the receiver.

Protecting GNSS Receivers From Jamming and Interference

This paper addresses the estimation of the code-phase (pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. The signal is received by an antenna array in a scenario with interference and multipath propagation. These two effects are generally the limiting error sources in most high-precision positioning applications. A new estimator of the code- and carrier-phases is derived by using a simplified signal model and the maximum likelihood (ML) principle. The simplified model consists essentially of gathering all signals, except for the direct one, in a component with unknown spatial correlation. The estimator exploits the knowledge of the direction-of-arrival of the direct signal and is much simpler than other estimators derived under more detailed signal models. Moreover, we present an iterative algorithm, that is adequate for a practical implementation and explores an interesting link between the ML estimator and a hybrid beamformer. The mean squared error and bias of the new estimator are computed for a number of scenarios and compared with those of other methods. The presented estimator and the hybrid beamforming outperform the existing techniques of comparable complexity and attains, in many situations, the Crame/spl acute/r-Rao lower bound of the problem at hand.

/pdf/ml-estimator-and-hybrid-beamformer-for-multipath-and-16xcy6l9s8.pdf

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper establishes the role of sparse arrays and sparse sampling in antijam global navigation satellite systems (GNSS). We show that both jammer direction of arrival estimation methods and mitigation techniques benefit from the design flexibility of sparse arrays and their extended virtual apertures or coarrays. Taking advantage of information redundancy, significant reduction in hardware and computational cost materializes when selecting a subset of array antennas without sacrificing jammer nulling or localization capabilities. In addition to the spatial array sparsity, antijam can utilize sparsity of jammers in the spatio–temporal frequency domains. By virtue of their finite number, jammers in the field of view are sparse in the azimuth and elevation directions. For the class of frequency modulated jammers, sparsity is also exhibited in the joint time-frequency signal representation. These spatial and signal characteristics have called for the development of sparsity-aware antijam techniques for the accurate estimation of jammer space-time-frequency signature, enabling its effective sensing and excision. Both theory and simulation examples demonstrate the utility of coarrays, sparse reconstructions, and antenna selection techniques for antijam GNSS.

/pdf/sparse-arrays-and-sampling-for-interference-mitigation-and-4t6o23sdxh.pdf

Sparse Arrays and Sampling for Interference Mitigation and DOA Estimation in GNSS

This article proposes constrained adaptive algorithms based on the conjugate gradient (CG) method for adaptive beamforming. The proposed algorithms are derived for the implementation of the beamformer according to the minimum variance and constant modulus criteria subject to a constraint on the array response. A CG-based weight vector strategy is created for enforcing the constraint and computing the weight expressions. The devised algorithms avoid the covariance matrix inversion and exhibit fast convergence with low complexity. A complexity analysis compares the proposed algorithms with the existing ones. The convergence properties of the CCM criterion are studied, conditions for convexity are established and a convergence analysis for the proposed algorithms is derived. Simulation results are conducted for both stationary and non-stationary scenarios, showing the convergence and tracking ability of the proposed algorithms.

/pdf/constrained-adaptive-filtering-algorithms-based-on-conjugate-3mhxnlcfdb.pdf

Constrained adaptive filtering algorithms based on conjugate gradient techniques for beamforming

This paper investigates the performance of reduced rank spacetime processors in the context of anti-jam mitigation for an M-code based GPS receiver utilizing a circular array. Several adaptive processing algorithms are discussed utilizing power minimization techniques. It is assumed an INS (inertial navigation system) or direction finding algorithm is incorporated into the receiver for satellite look direction based algorithms. Reduced rank space-time processing is accomplished via the innovative multistage Wiener filter (MSWF). It is demonstrated that the MSWF does not require matrix inversion, thereby reducing computational complexity. The processing algorithms are compared in terms of available degrees of freedom and distortion of the GPS cross correlation function (CCF).

Low complexity anti-jam space-time processing for GPS

This paper demonstrates that, under certain conditions, the method of conjugate gradients (CG) and the multistage Wiener filter (MWF) produce equivalent solutions. Equivalence follows from the fact that both algorithms minimize the same cost function in the same subspace, namely a Krylov subspace. Motivation for Krylov subspaces and their properties are developed herein. New insights into both algorithms follow from the equivalence including previously unpublished results on the convergence of the multistage Wiener filter as a function of rank. Furthermore a new perspective on CG is developed where CG can now be viewed as a reduced rank algorithm for the solution of the Wiener-Hopf equations.

http://ieeexplore.ieee.org/iel5/8442/26597/01191067.pdf

Insights from the relationship between the multistage Wiener filter and the method of conjugate gradients

Space-time power minimization pre-processing can exhibit a significant improvement in GPS receiver performance by exploiting spatial and temporal processing techniques. This type of preprocessing however, will require significant computations due to the large dimensionality of the complex valued space-time correlation matrix and will cause some distortion of the PN codes due to temporal processing. To reduce the computational complexity and distortion effects simultaneously, a conjugate symmetry space-time pre-processor has been proposed. It is demonstrated that this pre-processor enhances smoothness across angle and frequency and facilitates the use of real valued space-time correlation matrices in a reduced dimension utilizing the multi-stage nested Wiener filter (MSNWF).

Exploiting conjugate symmetry in power minimization based pre-processing for GPS: reduced complexity and smoothness

This paper investigates the performance of a reduced rank MMSE correlator for a RAKE receiver in the context of CDMA in frequency selective multipath. The MMSE correlator based on the correlations subtractive architecture (CSA) is derived for frequency selective multipath. It is demonstrated that the standard multiuser limited RAKE receiver can achieve BER performance close to the MMSE receiver spanning multiple symbols by replacing its conventional correlator with an MMSE correlator. The CSA generates an MMSE correlator without requiring matrix inversion (thereby reducing computational complexity) and facilitates direct replacement of the standard RAKE correlator.

MMSE correlator based RAKE receiver for DS-CDMA

This paper examines the impact of steering vector mismatch on the multistage Wiener filter (MWF). Since the NWF centrally features the steering vector in its formulation it is important to assess the impact of steering vector mismatch. Furthermore, since the MWF converges to the full rank MVDR solution, we would expect that steering vector mismatch would lead to signal cancellation (as with full rank MVDR) when the signal is present in the training data. We examine several standard techniques for increasing robustness and show how they apply to the MWE These include derivative constraints, quiescent pattern control (QPC) techniques, and covariance matrix tapers (CMT). We show that a combination of CMT and QPC, denoted CMTQ, is very effective at mitigating the impact of steering vector mismatch. Use of the CMTQ augmentation provides the steering vector mismatch robustness that we desire while retaining the reduced rank and reduced sample support characteristics of the MWE.

J.S. Goldstein

Papers

Low complexity anti-jam space-time processing for GPS

Insights from the relationship between the multistage Wiener filter and the method of conjugate gradients

Exploiting conjugate symmetry in power minimization based pre-processing for GPS: reduced complexity and smoothness

MMSE correlator based RAKE receiver for DS-CDMA

Robust steering vector mismatch technique for the multistage Wiener filter