Effect of Envelope Limiting in Adaptive Array Control Loops

The properties of an adaptive array antenna, including transient response rate and control loop noise, depend on the intensity of the external noise field. This dependence can be reduced by envelope hard limiting in the control loops, without degrading the performance of the adaptive array.     

Equivalent transformation for a partially adaptive array

A partially adaptive array is one in which elements of a phased array are controlled or adaptively weighted in groups or in which certain elements, called auxiliary elements, are made controllable. Mathematically, this type of array is formed by transforming all of the elements of an array by a nonsquare matrix such that the resulting output vector has a length less than the number of array elements. It is shown that there is an equivalent matrix transform that can effectively be utilized in analyzing the partially adaptive array's performance when a small number of external jammers are present. Processor implementation and convergence rate considerations lead to the desirability of reducing the dimensionality of the cancellation processor while maintaining good sidelobe interference protection. A meaningful measure of canceller performance is to compute the optimal output signal-to-noise ratio. This expression is a function of the jammer, direction-of-arrival vectors (DOAVs), jammer powers, the array steering vector, and internal noise. It is shown that if this expression is computed for the fully adaptive array then it is easily computed for the partially adaptive array by transforming the jammer DOAVs and the steering vector by the orthogonal projection matrix defined by the rows of the subarray transformation matrix and substituting these vectors back into the original expression for the fully adaptive array     

Effect of Single-Bit Digitization in Adaptive Array Control Loops

The properties of an adaptive array antenna, including transient response rate and control loop noise, depend on the intensity of the external noise field. The dependence can be reduced by 1-bit digitization of the real and imaginary parts of the signals from which the envelopes in the control loops are formed. This can be done without degrading the performance of the adaptive array.     

Control-Loop Noise in Adaptive Array Antennas

Adaptive array receiving antennas can be designed to sense the external noise field and to optimize the array illumination function. A substantial improvement in signal-to-noise ratio can be obtained with adaptive arrays when the external noise field is nonuniformly distributed in angle. The external noise process may be time varying and contain both discrete sources and continuously distributed sources. Two adaptive array implementations which maximize the signal-to-noise ratio are described in this paper. Expressions are derived for control-loop noise, i.e., the variance of the array element weights, and for the additional noise in the array output due to this element weight noise. It is shown that both the element weight noise and the array convergence rate are determined by the eigenvalues of the noise covariance matrix.     

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     

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.     

Adaptive array CFAR detection

Presented here is a large class of adaptive array detection algorithms with constant false alarm rate (CFAR), so that the false alarm rate can be set to any preassigned number without knowledge of the noise covariance matrix. This class map incorporate any usual method of cell averaging and any method for array weight vector synthesis. A sufficient condition for CFAR is derived, which is easy to satisfy in practice. Basic system parameters are discussed. An example of detection performance for a simple cell-averaging detector, in which the array weight vector is synthesized by the method of diagonal loading, is provided using Monte Carlo simulations     

Prediction of Adaptive Array Performance

A direct relationship between the conventional properties of an array and the array performance in an adaptive mode is given. Expressions are provided to obtain the output signal-to-interference-plus-noise ratio (SINR) of an adaptive array in terms of its conventinal pattern and the locations of the desired signal and jammers. These expressions permit one to evaluate the performance of an adaptive array without an exhaustive search for all possible scenarios and parametric values to ascertain that the required performance levels be met. In fact, one can predict the jammer locations for which the array will provide its best and worst performance by observing the conventional pattern. Several examples are provided to demonstrate the relationship between the conventional pattern and the adaptive array performance. The examples include both linear and planar arrays.     

Theory of Adaptive Radar

This paper reviews the principles of adaptive radar in which both the spatial (antenna pattern) and temporal (Doppler filter) responses of the system are controlled adaptively. An adaptive system senses the angular-Doppler distribution of the external noise field and adjusts a set of radar parameters for maximum signal-to-interference ratio and optimum detection performance. A gradient technique for control of the radar array/filter weights is described and shown to generate weights which asymptotically approach optimum values. Simulation results illustrate the convergence rate of adaptive systems and the performance improvement which can be achieved.     

An Lms Adaptive Array Using a Pilot Signal

A least mean square (LMS) adaptive array requires a reference signal. When the desired signal contains a pilot signal, it may be used as the reference signal. In this paper the steady-state performance of an LMS adaptive array in which the pilot signal is used as the reference signal is examined. It is shown that the LMS adaptive array occasionally suppresses the desired signal. The loop gain, which is an important parameter, is also considered.     

Two-State Feedback Loop Adaptive Arrays for Pulsed Interference Signals

A two-state feedback loop is presented which increases the effectiveness of an adaptive array in the presence of pulsed interference signals. In the case of the two-state feedback loop, one state permits the maximum adpative response, consistent with the loop stability, and is activated in the presence of an interfering pulse. During the other state, which is activated when the interfering pulse is off, the weights are frozen at the values reached at the end of the last interfering pulse and are maintained until the next disturbance occurs. It is shown that an adaptive array with the proposed two-state loops steers permanent minima in the direction of the interfering signals, irrespective of their duty cycle. The performance of a communication system protected by such an adaptive array improves significantly over one protected by a conventional adaptive array.     

The Power-Inversion Adaptive Array: Concept and Performance

The use of a power-inversion adaptive array to improve the signal-to-interference ratio in a communication system is described. "Power inversion" refers to the ability of an adaptive array to invert the power ratio of two received signals. The power-inversion ion technique is useful because it does not require detailed ledgeknow about desired-signal structure or arrival angle. The perform ance attainable with a power-inversion array is described and typical al design curves are presented.     

LINEAR PREDICTION APPROACH IN AIRBORNE ADAPTIVE ARRAYS

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机载相控阵雷达中抑制杂波的线性预测法

从一个多通道自回归过程拟合杂波信号的概念出发 ,提出了用线性预测法实现机载相控阵雷达的时空二维自适应信号处理。研究表明 ,杂波过程可以用一个低阶的多通道自回归过程很好地拟合 ,从而使用一个低阶的线性预测处理器以较低的代价实现准最优的处理。同时 ,这种低阶的线性预测处理器还具备冗余的自由度以对付除杂波外的其他有色噪声和干扰     

Performance of a Modified Applebaum Adaptive Array

The performance of a modified Applebaum adaptive array is studied. The new array is obtained by removing the desired signal component from the output signal fed back to the correlator of an Applebaum type adaptive array. Various signal scenarios, including single desired signals or multiple simultaneous desired signals are examined. The new array is less sensitive to beam pointing errors and does not cause power inversion of desired signals. In the case of multiple simultaneous desired signals, the new array does not degrade the SNRs of strong desired signals.     

The Performance of an LMS Adaptive Array with Frequency Hopped Signals

The performance of an LMS adaptive array with a frequency hopped, spread spectrum desired signal and a CW interference signal is examined. It is shown that frequency hopping has several effects on an adaptive array. It causes the array to modulate both the amplitude and the phase of the received signal. Also, it causes the array output SINR (signal-to-interference-plus-noise ratio) to vary with time and thus increases the bit error probability for the received signal. Typical curves of the desired signal modulation and the time-varying SINR at the array output are presented. It is shown how the array performance depends on hopping frequency, frequency jump size, interference frequency, signal arrival angles, and signal powers.     

Application of Gram-Schmidt algorithm to fully adaptive arrays

The Gram-Schmidt orthogonalization (GSO) algorithm has excellent numerical performance and is readily applicable to systolic implementations such as in a field of adaptive cancellation systems. A modified GSO algorithm for a fully adaptive array is proposed and computer simulations show that the proposed algorithm gives superior performance. A systolic implementation of the proposed GSO algorithm for fully adaptive array is presented. A feedback mode GSO algorithm for use with analog weights is also presented and has been shown to have excellent performance in the presence of weight errors     

Fast Algorithms for Time Domain Broadband Adaptive Array Processing

Recursive algorithms are presented for time domain, broadband, adaptive beamforming. The algorithms are rapidly converging and can be computationally efficient for a certain range of array processor parameters. The algorithms are presented for two forms of array processor. One form is a Frost-type structure in which explicit constraints are required for defining the array-look direction and also to control the sensitivity of the array processor to implementation errors. The other form is a partitioned array processor in which constraints are built into the processor and the adaptive weight control algorithm is therefore unconstrained. The two processors presented are both element-space processors but the algorithms can be applied also to beam-space processors.     

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.     

Weight Jitter Phenomena in Adaptive Array Control Loops

An analysis of weight jitter in adaptive array control loops is presented. lt is shown that steady state weight jitter and statistical dependence between input signal and weight processes are related factors. A Markov characterization for the first-order adaptive array loop is presented and Fokker-Planck techniques are used to obtain the steady state probability density of the weight process for the case of a one-loop array. From this density the mean and the variance of the weight process are obtained and the dependence of these statistics upon loop and input signal parameters is explored.