Self-Clutter Cancellation and Ambiguity Properties of Subcomplementary Sequences

In radar signal design it is well known that a fixed volume under the ambiguity surface representing signal energy can only be shifted but not eliminated in the delay-Doppler plane because of the constraint imposed by Woodward's total volume invariance. Rihaczek has shown that periodic signal repetition, though appealing to increased energy, increases the time-bandwidth product at the expense of introducing pronounced ambiguities in the delay-Doppler plane, and thus self-clutter is generated when signals are repeated in the time domain to increase energy. The undesirable self-clutter has a masking effect on targets in different resolution cells thereby limiting performance. An analysis is presented to show that a class of waveforms described in an earlier paper as the subcomplementary set of sequences which are basically repetitive and Hadamard coded, exhibit the property of cancelling self-clutter completely in the delay-Doppler plane if their ambiguity functions are combined. By this technique it is possible to repeat contiguously a basic waveform N times in a prescribed manner to increase signal energy and to cancel totally the resulting self-clutter by combining the ambiguity functions of N different repetitive waveforms which are Hadamard coded. A convenient matrix method to combine the ambiguity functions of subcomplementary sequences, which is an extension of known methods to derive the ambiguity function of repetitive waveforms, is presented. Radar implementation considerations and comparison of performance with various forms of linear frequency modulation (FM) are also discussed.     

Direction-finding with sparse rectangular dual-size spatialinvariance array

A novel sparse array geometry embedding two sizes of spatial invariances is presented for use with a new ESPRIT-based (estimation of signal parameters via rotational invariance techniques) algorithm for aperture extension. The half-wavelength invariance yields unambiguous but high-variance direction cosine estimates to disambiguate low-variance but cyclically ambiguous estimates from the larger invariance. With larger invariance at 60 half-wavelengths, resolution threshold for two closely spaced emitters is reduced by 50 dB and estimation error by 100-fold. Array design formulas are also presented     

Angle measurement in the presence of mainbeam interference

The problem of reducing interference impinging on an antenna array when the sources lie in the main beam is addressed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed, based on the estimation procedure presented, to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N₀ and angular separation between the target and the interference sources     

True proportional navigation with maneuvering target

We analytically obtain the capture regions for the true proportional navigation (TPN) missile guidance law against an intelligently maneuvering target. Two versions of TPN are considered. The first is the original TPN which assumes the commanded lateral acceleration to be directly proportional to the line-of-sight (LOS) rate only, the proportionality factor being an arbitrary constant or dependent only on the initial closing velocity. The other, known as RTPN (realistic TPN), assumes the commanded lateral acceleration to be directly proportional to the LOS rate and also the current closing velocity. The target is assumed to maneuver in such a way as to increase the LOS rate and thus directly oppose the proportional navigation (PN) philosophy of annulling the LOS rate. A necessary and sufficient condition for capture is derived for the original TPN, and using it, the exact capture region is obtained. A sufficient condition for capture is derived for RTPN and is used to obtain its capture region partially. Some necessary conditions for capture are also derived for RTPN and are used to obtain an upper bound on its complete capture region. Using these conditions some important results on the existence of capture regions and a comparative study of capturability of TPN laws are also presented     

Direction finding for two-dimensional incoherently distributed sources with Hadamard shift invariance in non-uniform orthogonal arrays

This paper proposes a novel algorithm for Two-Dimensional (2D) central Direction-of-Arrival (DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays (NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold (GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.     

Angle of arrival estimation of coherent signals using an arraydoublet in motion

Shown here is how the estimation of signal parameters via relational invariance techniques (ESPRIT) algorithm may be used with a single pair of antennas in motion to estimate angles of arrival (AOA) for coherent signals. The approach exploits the Doppler frequency shifts caused by the doubler in motion. With this estimator, the number of signals that can be handled is not limited by the size of the array, as in the usual ESPRIT application, but by an adjustable parameter. A theoretical performance analysis of the estimator and typical examples showing the use of this estimator are given     

The Effect of Random Steering Vector Errors in the Applebaum Adaptive Array

The effect of random errors in the steering vector of an Applebaum adaptive array is examined. Each component of the steering vector is assumed to have a random error component uncorrelated between elements. The array output signal-to-interferenceplus-noise ratio (SINR) is computed as a function of the error variance. It is shown that the array output SINR becomes more sensitive to steering vector errors as more elements are added to the array and as the received desired signal power becomes larger. The variance of the steering vector error that may be tolerated depends on the required desired signal dynamic range. The larger the dynamic range that must be accommodated, the smaller the error variance must be.     

An LMS Adaptive Array for Multipath Fading Reduction

Multipath fading often poses a serious hindrance in radiocommunication. The application of a least-mean-square (LMS)adaptive array to the problem of multipath fading reduction is discussed. However, it is known that multipath components are in general correlated with one another. We examine the effect of the correlation on the performance of the LMS adaptive array. When the correlation coefficient does not equal or approximate 1, the LMS adaptive array suppresses the multipath signals significantly by nulling. On the other hand, when the correlation coefficient nearly equals 1, the LMS adaptive array prevents the output signalpower from decreasing. Therefore, the LMS adaptive array mayreduce the multipath fading effectively for any correlation coefficient value. A reference signal in the LMS adaptive array is also discussed. It is shown that synchronization in the referencesignal generation must be extremely accurate. Moreover, aprocessor configuration is proposed which may generate thereference signal with the required accuracy.     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters     

Adaptive Array Behavior with Periodic Phase Modulated Interference

We consider a least mean square (LMS) adaptive array [1] receiving a phase modulated interference signal. The phase modulation is assumed to be periodic and to have finite bandwidth. Under these assumptions, we determine the time-varying array weights, the modulation on the array output desired signal, and the time-varying output interference-to-noise ratio (INR) and SINR (signal-to-interference-plus-noise ratio). We present numerical results describing the behavior of a 2-element adaptive array that receives an interference signal with sinusoidal phase modulation. We show how each signal parameter (arrival angle, power, modulation index, and modulation frequency) affects the performance of the array.     

Monopulse Resolution of Interferometric Ambiguities

Ambiguities in interferometers with high angular accuracy must be resolved to achieve a practical system design. A new technique for ambiguity resolution is described and is based on monopulse circuitry used with the interferometric elements. The overall angular accuracy of the system is achieved by the interferometer; the angular accuracy of the monopulse subsystem is used to resolve interferometric ambiguities. An expression for the probability of correct ambiguity resolution is derived as a function of element size and monopulse accuracy which indicates that high probability of ambiguity resolution results when the size of the interferometric elements are a fraction of the interferometric baseline. Finally, a comparison between conventional monopulse and interferometric system designs is made for the three principal parameters, signal sensitivity, angular accuracy, and field of view, that dictate the appropriate choice for a particular application. Interferometric systems are more appropriate than monopulse systems for those applications in which angular accuracy and field of view are more important than signal sensitivity.     

一种基于协方差矩阵重构的相干信源DOA估计算法

针对空间相干信源的波达方向估计问题,提出了一种基于协方差矩阵重构的TSVD-ESPRIT算法。它利用包含所有信源信息的特征向量构造Toeplitz协方差矩阵,避免了阵列有效孔径的损失,分辨率高且稳定性好;并且利用ESPRIT算法代替MUSIC算法进行DOA估计,避免了谱峰搜索,大大降低了计算量。数据仿真和分析证明了该算法的正确性和有效性。     

Resolution and synthetic aperture characterization of sparse radar arrays

The concept of radar satellite constellations, or clusters, for synthetic aperture radar (SAR), moving target indicator (MTI), and other radar modes has been proposed and is currently under research. These constellations form an array that is sparsely populated and irregularly spaced; therefore, traditional matched filtering is inadequate for dealing with the constellation's radiation pattern. To aid in the design, analysis, and signal processing of radar satellite constellations and sparse arrays in general, the characterization of the resolution and ambiguity functions of such systems is investigated. We project the radar's received phase history versus five sensor parameters: time, frequency, and three-dimensional position, into a phase history in terms of two eigensensors that can be interpreted as the dimensions of a two-dimensional synthetic aperture. Then, the synthetic aperture expression is used to derive resolution and the ambiguity function. Simulations are presented to verify the theory.     

Family of multicarrier bi-phase radar signals represented by ternary arrays

A K times L ternary array, comprised of the elements {0, 1, - 1}, with some unique features, represents a multicarrier radar signal with favorable autocorrelation and ambiguity functions. Constructing such an array using Galois fields is described. As in a Costas binary array, only one frequency is transmitted at any time slot, but in our array the same frequency is repeated in several time slots, yielding a signal with considerably larger pulse compression than a Costas signal that uses the same number of frequencies     

Sampling Bandpass Signals

In a recent paper [1], Brown examined the sampling of a real finiteenergy bandpass signal having an (angular) bandwidth ? (in radians per second) at the theoretically minimum (average) rate of ?/? samples per second. Following Grace and Pitt's [2] quadrature sampling, a particular case of Kohlenberg's second-order sampling [3, 4], Brown has proved the feasibility of a separate interpolation of the in-phase and quadrature components of the signal when ?o = k?/2 (Brown's condition), where ?o is the center (angular) frequency of the signal and k is an arbitrary positive integer. Here the problem is reconsidered from a general point of view, introducing, under Brown's condition, an interpolation formula which includes that of Grace and Pitt and which extends a theorem of Populis [5-7]. We indicate the necessary and sufficient conditions to obtain a separate interpolation, offering closed formulas to obtain the interpolation functions. We also discuss the minimum oversampling rate needed whenBrown's condition is not verified.     

Finite data performance of MUSIC and minimum norm methods

In the direction of arrival (DOA) estimation problem, we encounter both finite data and insufficient knowledge of array characterization. It is therefore important to study how subspace-based methods perform in such conditions. We analyze the finite data performance of the multiple signal classification (MUSIC) and minimum norm (min. norm) methods in the presence of sensor gain and phase errors, and derive expressions for the mean square error (MSE) in the DOA estimates. These expressions are first derived assuming an arbitrary array and then simplified for the special case of an uniform linear array with isotropic sensors. When they are further simplified for the case of finite data only and sensor errors only, they reduce to the recent results given previously (1989, 1991). Computer simulations are used to verify the closeness between the predicted and simulated values of the MSE     

On radar detection and direction finding using sparse arrays

The potential performance of radar systems employing sparse arrays is investigated. Different sparse array geometries are evaluated with respect to detection and estimation performance. We present appropriate tools for analytical computation of the detection and estimation performance of the likelihood ratio test (LRT) and the maximum likelihood estimator (MLE), respectively. Particular attention is paid to the effect of ambiguity errors on system performance. The results show that sparse arrays have several advantages over nonsparse arrays, but that ambiguities deteriorate performance when sidelobe interference is present. Some ways to mitigate the ambiguity effects on system performance are briefly discussed.     

广义系统H∞控制的GARI方法

本文在[1]的基础上给出了广义系统在一般情况下H∞动态控制器存在的充要条件并在一定条件下将充分条件归结为两个代数Riccati不等式满足广义约束（CARI）的解，给出广义系统在该条件下的H∞次优控制器，并给出了数值实例说明本文的结果。     

Further study of the Pencil-MUSIC algorithm

For finding 2-D angles and polarizations of waves arriving at a rectangular array of crossed dipoles, the Pencil-MUSIC method can achieve the near optimum performance with much less computational burden than the MUSIC (multiple signal classification). Following an angle-only ESPRIT (estimation of signal parameters via rotational invariance techniques) method, an angle-only Pencil-MUSIC can be easily formulated which is far more accurate than the former especially in the coherent case. The angle-only Pencil-MUSIC is analyzed and compared with the original Pencil-MUSIC. The new version sacrifices the polarization estimation to achieve about 8 times more efficient computation The accuracy of the new version seems no more than 4 times worse in terms of estimation deviation