An extended chirp scaling algorithm for spaceborne sliding spotlight synthetic aperture radar imaging

A system impulse response with low sidelobes is critical in synthetic aperture radar（SAR） images because sidelobes contribute to noise and interfere with nearby scatterers. However,the conventional tricks of sidelobe suppression are unable to be exactly applied to the case of spaceborne sliding spotlight SAR due to great azimuth shifts in both time and frequency domains. In this paper, an extended chirp scaling algorithm is presented for spaceborne sliding spotlight SAR data imaging. The proposed algorithm firstly uses the spectral analysis（SPECAN） technique to avoid the azimuth spectrum folding effect and then employs the chirp scaling（CS） algorithm to achieve data focusing, i.e., the so-called two-step approach. To suppress the sidelobe level, an efficient strategy for the azimuth spectral weighting which only involves matrix multiplications and short fast Fourier transformations（FFTs） is proposed, which is a post-process executed on the focused SAR image and particularly simple to be implemented. The SAR image processed by the proposed extended CS algorithm is very precise and perfectly phase-preserving. In the end, computer simulation results verify the analysis and confirm the validity of the proposed algorithm.     

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.     

Efficient exhaustive search for optimal-peak-sidelobe binary codes

The work presented here describes an exhaustive search for minimum peak sidelobe level (PSL) binary codes, combining several devices for efficiency. These include combinatoric tree search techniques, the use of PSL-preserving symmetries to reduce search space, data representations and operations for fast sidelobe computation, and a partitioning scheme for parallelism. All balanced 64-bit minimum PSL codes are presented, and the upper limit on known consecutive lengths to have PSL = 4 codes is extended to 70. In addition, a technique for determining balance properties of a code for given PSL-preserving transformations is developed.     

Adaptive array transient sidelobe levels and remedies

The transient sidelobe level of a sidelobe canceler (SLC) is a function of the external noise environment, the number of adaptive auxiliary antennas, the adaptive algorithm used, auxiliary antenna gain margins, and the number of samples used to calculate the adaptive weights. An analytical result for the adaptive sidelobe level is formulated for the case when the adaptive algorithm is the open-loop, sampled matrix inversion (SMI) algorithm. The result is independent of whether concurrent or nonconcurrent data processing is used in the SMI algorithm's implementation. It is shown that the transient sidelobe level is eigenvalue dependent and increases proportionally to the gain margin of the auxiliary antenna elements with respect to the quiescent main antenna sidelobe level. Techniques that reduce this transient sidelobe level are discussed, and it is theoretically shown that injection independent noise into the auxiliary channels significantly reduces the transient sidelobe level. It is demonstrated that using this same technique reduces the SMI noise power residue settling time     

Properties of Dolph-Chebyshev Weighting Functions

Dolph-Chebyshev amplitude weighting is used with FFT signal processors and array antennas when a low sidelobe response is required. This particular weighting minimizes the width of the mainlobe response while forcing all of the sidelobes to a specified sidelobe level. As the specified sidelobe level is reduced, the mainlobe width increases, as does the loss in signal-to-noise ratio. This correspondence describes how the Dolph-Chebyshev weights may be easily calculated, and gives design data showing how signal-to-noise loss and mainlobe width vary with the specified sidelobe level.     

Computationally Efficient Bank of Rectangular Digital Filters

A computationally efficient scheme for forming a bank of identical contiguous rectangular digital filters is described. The data processing is organized in a sequential form allowing use of the FFT algorithm as the first stage. An example is given in which a bank of 256 rectangular filters is formed using only a few percent of the number of complex multiplies required by straightforward procedures. The steepness of cutoff is unaltered and the inband ripple is only slightly affected, but the sidelobe level suffers some degradation.     

A multiobjective optimization approach to determine the parameters of stepped frequency pulse train

Frequency stepping techniques are commonly used in modern radar system to get high range resolution with the disadvantage that its autocorrelation function (ACF) yield undesirable “grating lobes”. Wider mainlobe deteriorates the range resolution capability of the waveform and higher peak sidelobe either hides the small targets or causes the false target detection. Several techniques have been used to choose the parameters of linear frequency modulated (LFM) pulse train to suppress the grating lobes without paying much attention to the mainlobe width and peak sidelobe level. In this paper a multiobjective optimization (Nondominated Sorting Genetic Algorithm-II (NSGA-II)) approach is proposed to optimize the parameters of the LFM pulse train to achieve reduced grating lobes, low peak sidelobe level and narrow mainlobe width. The optimization problem has been studied in two different ways: first one is associated with the reduction of grating lobes and the minimization of peak sidelobe level of the ACF with constraints and second one is related to the minimization of the peak sidelobe level and mainlobe width of the ACF with constraints. Simulation studies have been carried out to justify the potentiality of the proposed approach.     

A Time Sidelobe Reduction Technique for Small Time-Bandwidth Chirp

A filtering technique is described which permits time sidelobe suppression of small time-bandwidth product shirp. Signal-to-noise loss and time sidelobe level sensitivity to Doppler shift are presented for a filtered chirp waveform whose time-bandwidth product is 10.     

Biphase Sequence Generation with Low Sidelobe Autocorrelation Function

Since Barker-like sequences could not be found for sequence lengths greater than 13, radar system designers have been searching for biphase sequences with discrimination (ratio of the magnitude of the mainlobe to the magnitude of the peak sidelobe of the autocorrelation function of the sequence) greater than 13. We present new results on biphase Legendre sequences for all prime lengths. The results of the paper are as follows. 1) Two lemmas on the symmetric properties of the Legendre sequences are stated and using these lemmas and simple rules of modulo arithmetic, a method is suggested for generating long sequences which does not require multiplications and divisions. 2) From the properties of autocorrelation function of the cyclically shifted Legendre sequence (LS) for prime lengths, a computationally efficient method is evolved for carrying out systematic search for sequences with discrimination greater than 13. The proposed method reduces the computational load by a factor of approximately 16. Using these techniques, we generated codes up to length 1019. In each case we searched for the code which gives the maximum discrimination for that length.     

Coherent Doppler tomography-a technique for narrow band SAR

Some concerns regarding a technique of narrowband synthetic aperture radar (N-SAR) imaging called coherent Doppler tomography (CDT), which may be a good candidate for spaceborne applications, are addressed. Using a single-frequency signal, are addressed. Using a single-frequency signal, resolution of two tenths of a wavelength can be achieved in the point spread function if the radar platform circles the ground path to be imaged. However, the high sidelobe level of -8-dB in the point spread function results in an unacceptable dynamic range. To reduce the sidelobe level, two approaches are presented: coherent processing using multiple discrete frequencies and noncoherent subaperture processing. Simulation results demonstrate that the sidelobe level is substantially reduced by both methods. However, the resolution is degraded and the computational overhead is greatly increased for noncoherent subaperture processing. Also presented is a possible satellite geometry configuration that could utilize N-SAR processing to provide high-resolution global mapping capability     

一种改进的Dolph—Chebyshev方法在阵列天线方向图综合中的应用

通过对传统Chebyshev多项式增加修正因子得到一种修正的Chebyshev多项式，并以此为基础提出了一种新的阵列天线方向图综合方法。与传统Chebyshev综合法相比，该方法可以在保持副瓣电平不变的情况下对主瓣进行任意展宽，待求参数少，综合过程简单，有很强的实用性。     

Active phased array design for high reliability

We discuss strategies for designing: active phased array antennas with high reliability. We show how to consider fault-tolerance in the design of the antenna architecture, so that replacement of failed components can be avoided for an extended period of time. First, we address the dependence of antenna life cycle cost on component failure rates. Then we discuss the design of active phased array architecture for maximizing antenna mean-time-between-failures (MTBF). The antenna MTBF is defined in terms of a specified degradation in peak sidelobe level. We present simulated data showing the effect of random, single, and clustered element failures on the peak sidelobe level of a low sidelobe antenna aperture. We use these data as a basis for analyzing various phased array architectures in terms of their antenna MTBF     

大多普勒容限巴克码脉压

 本文介绍用补偿式非相干型旁瓣抑制滤波器(SSF)实现13位巴克码脉冲压缩旁瓣抑制的理论计算及实验结果。补偿式非相干型SSF采用最小二乘近似逆滤波方法设计,若子脉冲宽度为0.7μs,峰值旁瓣电平不超过-30dB,这种SSF的多普勒容限能达到-40kHz～+40kHz。理论计算及实验结果都表明,所设计的补偿式非相干型SSF的多普勒容限比具有同样长度冲激响应序列的R-G-ISSF有显著改善。     

Comments on "on Probability of Error in Decision Feedback Equalizer"

The above-mentioned paper [1] derives bounds on the error probability of a decision feedback equalizer (DFE) which are claimed to be significantly tighter than the earlier upper bound of [2]. Unfortunately, [1] makes an unsupportable assumption which reddars the conclusions incorrect. We show that valid bounds can be obtained by the methods of [1], but that for the numerical example of [2] , the resulting upper bound is never tighter than, and sometimes significantly weaker than, that derived in [2]. Similarly, a lower bound derived by the method of [1] is shown for the same numerical example to be very close to the error-free past lower bound previously known.     

具有（N-1）/2次乘法的快速傅里叶变换

 本文提出递归傅里叶变换的一种快速实现方法。对于一个质数长度的离散傅里叶变换,仅需用一个复数系数就可以递归算出全部N个（N=P）频率分量。恰当地选用这个系数,使其为2^-m形式,就可以用（m-1）次移位代替乘法,免去了递归结构内部的乘法,大大提高运算速度。这种方法结构简单,总共需用（N-1）/2次实数常数乘法,尤其适于硬件实现。文中给出快速运算的系数表、硬件实现的方案及乘法次数的比较,讨论了系数误差的影响,并提出了高精度实现的方案。     

Adaptive canceler and pulse compressor interactions

Performance results for the sidelobe level of a compressed pulse that has been preprocessed through an adaptive canceler are obtained. The adaptive canceler is implemented using the sampled matrix inversion algorithm. Because of finite sampling, the quiescent compressed pulse sidelobe levels are degraded due to the preprocessing of the main channel input data stream (the uncompressed pulse) through an adaptive canceler. It is shown that if N is the number of input canceler channels (main and auxiliaries) and K is the number of independent samples per channel, then K/N can be significantly greater than one in order to retain sidelobes that are close to the original quiescent sidelobe level (with no adaptive canceler). Also it is shown that the maximum level of degradation is independent of whether pulse compression occurs before or after the adaptive canceler if the uncompressed pulse is completely contained within the K samples that are used to calculate the canceler weights. This same analysis can be used to predict the canceler noise power level that is induced by having the desired signal present in the canceler weight calculation     

Performance of phased-array antennas with mechanical errors

The performance of planar phase-array antennas with mechanical errors is investigated. Errors in array element positions as a result of structural distortions are considered as deterministic and predictable. Detailed calculations for two assumed modes of distortion reveal that their effects on antenna performance are the loss of peak response in the scan direction and the broadening of the mainlobe, while the far-out sidelobe structure remains relatively intact. For large antennas, performance improvement can be expected by suitable phase compensation. Performance of antennas with random errors in their element positions must be treated statistically. Expressions of average directivity and sidelobe level corresponding to arbitrary error magnitudes in element position, amplitude and phase of excitation as well as finite rate of failure of element modules were derived and verified by direct numerical calculations from the antenna directivity patterns. For a planar phased-array antenna typical for space-based radars, the standard deviation of element position errors must not exceed 1% of the operating wavelength in order to maintain a -10 dBi sidelobe level     

Radar Performance Review in Clear and Jamming Environments

The performance of electronically scanned radar systems is evaluated for clear and barrage jamming environments. Radar figures of merit in jamming are derived for search and track modes and are directly related to antenna pattern relative sidelobe levels. A random sidelobe model is analyzed with various numbers of independent jammers. Probability distributions of detection probability are derived to determine detection performance versus average jamming level and number of jammers.     

Time jitter analysis for quadrature sampling

Time jitter in the quadrature sampling processes is modeled and the performance of an adaptive cancellation system in the presence of such time jitter is analyzed. It is shown that the decorrelation due to time jitter depends on the magnitude of the jitter, the sampling scheme used, the bandwidth of the signal and the intermediate frequency (IF) preceding the analog-to-digital (A/D) conversion stages. The performance of a sidelobe cancellation system in the presence of time jitter, for several sampling approaches, is evaluated numerically as well as simulated. The results show that the direct quadrature sampling scheme with a lower IF provides superior performance for an adaptive cancellation system     

Performance of Doppler Radar in the Presence of Random Fading

This paper deals with the performance of pulse Doppler radar in the presence of random fading. The behavior of this radar is studied as a statistical problem to bring out the limiting bounds of the ambiguity diagram and the nature of variance with respect to the Doppler frequency. The performance of the radar insofar as the first sidelobe is concerned, is shown to be better in the presence of fading than in the normal case. In a particular case where 75 pulses out of an aggregate of 250 pulses are missing, the first sidelobe level is 20.0 dB down from the main lobe with a probability of 23 percent.