Optimum Mismatched Filters for Sidelobe Suppression

This paper discusses the application of least-mean-squares approximate inverse filtering techniques to radar range sidelobe reduction. The method is illustrated by application to the 13-element Barker code. The performance of the least-mean-square inverse filter is compared with the matched filter and with the simplified sidelobereducing filters of Rihaczek and Golden. A filter which completely suppresses the range sidelobes of a 13-element Barker sequence is only 0.2 dB worse than a matched filter in noise.     

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。     

Concatenated Sequences for Spread Spectrum Systems

Concatenated sequences are suggested and developed for use in spread spectrum (SS) systems. Special receiver realization is discussed and it is shown that the concatenated sequences offer great advantage in reducing the size of the matched filter correlators (MFC) in the SS receiver. Experimental systems have been built using concatenated sequences and their performance is reported here. It has been shown that a processing gain of 60 is obtainable with a 15 × 4 concatenated sequence which requires three tapped delay lines (TDL), two of length 15 and one of 4. Thus a total of only 34 delay units (with a nonlinear interface network, only 19 delay units) are required. Teleprinter signals can be transmitted over telephone channels using a bandwidth (BW) expansion of 60 with an input signal-to-noise ratio (SNR) of only -5.1 dB, resulting in a character- error-rate of 1 in 103. Techniques have been developed to reduce the sidelobe levels in the aperiodic autocorrelation functions (ACF) of the pseudonoise (PN) codes. For 15 length and 7 length PN sequences, sidelobes are reduced by 9 dB and 9.4 dB, respectively, using transversal filters. Application of the SS systems to the problem of multiaccessing and antijamming are discussed.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Strapdown inertial measurement units for motion compensation forsynthetic aperture radars

It is shown that synthetic-aperture radar (SAR) motion can be compensated by using an antenna-mounted strapdown inertial measurement unit (IMU) as the motion sensing system, but sensor and system errors affect SAR image quality. A strapdown IMU consists of three accelerator channels and three gyro channels. Strapdown IMU errors include gyro-scale and accelerometer-scale factor and bias errors, velocity error, platform tilt, and errors induced by limited inertial sensor bandwidth. The effects of these errors on the SAR image quality are presented in terms of the SAR impulse response. IMU errors that cause low-frequency phase errors (less than one cycle per array time) are categorized in terms of quadratic and cubic phase errors. IMU errors that cause high-frequency phase errors (greater than one cycle per array time) are categorized in terms of the integrated sidelobe ratio and peak sidelobe ratio. A motion compensation system conceptualization is described wherein a strapdown IMU is attached to an antenna and transfer-aligns to the aircraft's master navigator     

A new algorithm to optimize Barker code sidelobe suppressionfilters

The authors suggest a new algorithm for binary coding waveform sidelobe reduction after matched filtering and present a general method by which optimized sidelobe suppression filters for Barker codes can be obtained with a peak output sidelobe 2.62 dB lower than the results found in the literature (for 13-b Barker code). This optimization algorithm is also promising for other binary coding waveforms, such as truncated pseudonoise (PN) sequences and concatenated codes. This new approach can readily be applied to sidelobe-reduction filter design for other binary coding waveforms, such as truncated PN sequences, concatenated codes, etc., which often find their applications in radar systems and spread spectrum communication systems     

Creating complex signal samples from a band-limited real signal

A very efficient method of creating complex signal samples from a band-limited real signal is presented. Because the method employs a simple mixer followed by one analog-to-digital (A/D) converter, plus a finite-duration impulse response (FIR) filter for image band rejection, there is no phase distortion in the resulting sampled signal. The method is more efficient than competing methods based on infinite-duration impulse response (IIR) filters     

Filtering of moving targets using SBIR sequential frames

In this paper three-dimensional (3-D) finite-impulse response (FIR) filters are proposed for moving target detection and tracking from multiframe space-based infrared (SBIR) data. An optimal, in the l_p sense, 3-D FIR filter design technique is proposed which is suitable for the above application. This technique is the first 3-D FIR design of its kind presented in the open literature. Directional, matched, and adaptive 3-D filtering techniques are proposed. Prior to the filtering, clutter mean estimation and mean subtraction are required. Real time implementation of directional and/or matched filters for processing maneuvering targets is discussed and filter design methods are proposed. Finally, performance comparisons of the proposed and other available 3-D FIR and infinite-impulse response (IIR) filters, on real SBIR data, are presented in which the advantages of the proposed 3-D filters are shown     

A New Sampling Procedure for the Synthesis of Linear Transversal Filters

In linear transversal filters for signal processing, the impulse response of the filter is syntheszed in a sampled form by means of a tapped delay line with weighted and summed taps. The synthesis procedure consists of sampling the specified impulse response at appropriate intervals and using the sample values as the tap weights. A nonuniform sampling procedure for the synthesis of the impulse response is introduced, which can produce results more conveniently than the classical Shannon sampling procedure because of the simplicity of the transversal filter implementation. According to the new procedure, in the time domain the samples are taken at points where the instantaneous phase of the impulse response is a multiple of ir radians. The spectral distribution which ensues in the frequency domain consists of a series of spectra all having the same fractional bandwidth. The transversal filters synthesized by this sampling criterion are referred to as phase-sampled impulse response (PSIR) filters. An important application of PSI R filters is to the generation and matched filtering of a large class of AM and FM waveforms.     

11位巴克码的LP滤波器及其在多普勒频移下的性能

本文介绍使最大旁瓣值最小的11位巴克码滤波器（LP滤波器）的计算结果。并介绍多普勒频移对这种滤波器性能影响。LP滤波器长度为53时,旁瓣电平降到—39.5dB,比匹配滤波器改善18.7dB。对加权序列长度L为41、45、49和53的11位巴克码的LP滤波器计算结果表明,其性能受多普勒频移的影响表现为:它们的主瓣电平下降、主瓣展宽、最小旁瓣电平上升、旁瓣电平平方和上升和信噪比损失增大。在较小的多普勒频移（f_d）时,L大的LP滤波器其性能优于L小的LP滤波器,在多普勒频移交大时,这种优势逐渐消失,不同长度LP滤波器性能大体一致。     

Optimal Resolution of Rectangular Pulses in Noise

Optimal detection of rectangular pulses in noise is considered, subject to a sidelobe constraint which ensures adequate resolution capabilities, and a new sidelobe reduction filter is derived. Tests in the laboratory and on a Westinghouse AN/TPS-27 search radar system em indicate that use of the new filter substantially improves both resolution and clutter performance over such standard techniques as fast time constant (FTC), delay line differentiator (DLD), and pulse length discriminator (PLD).     

一种基于数字综合算法的MTD滤波器设计方法

利用空间阵列方向图合成中的数字综合算法 ,提出了一种新的MTD滤波器设计方法。该方法通过在滤波器频率响应的副瓣区放置大量的干扰信号 ,改变干扰信号的功率强度 ,从而自适应地控制滤波器频率响应的副瓣电平。这种方法所设计的MTD滤波器 ,其频率响应不仅在零频附近有宽而深的零陷 ,而且在其他副瓣区域可以为任意形状 ,具有较好的实用性。设计实例证实了这种方法的有效性。     

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.     

A sampling-based approach to wideband interference cancellation

Classical adaptive array schemes which use only complex spatial weights are inherently narrowband and consequently perform poorly when attempting to suppress wideband interference. The common solution to this problem is the use of tapped delay line filters in each spatial channel to facilitate space-time adaptive processing (STAP). The higher performance provided by the STAP architecture comes at the cost of a considerable increase in complexity. This paper presents a simpler technique based on programmable time adjustable sampling (TAS) that provides a limited number of wideband degrees of freedom. Two TAS methods are introduced: TAS-sidelobe canceler (TAS-SLC) is based on the sidelobe canceler, while TAS-minimum variance beamformer (TAS-MVB) is derived from the minimum variance beamformer. TAS is implemented by adjusting the sampling instant at selected array channels. TAS-SLC consists of controlling the sampling in the main channel of the sidelobe canceler With TAS-MVB array complex weights are substituted with TAS time delays. The performance of TAS methods with wideband interference is compared to the conventional sidelobe canceler and minimum variance beamformers. It is shown that TAS-SLC provides better performance than the sidelobe canceler, while TAS-MVB outperforms the minimum variance beamformer     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

Optimal FIR filters for time-varying state-space models

An optimal FIR (finite impulse response) filter and smoother is introduced for the time-varying state-space model. The suggested filter has an FIR structure and utilizes finite observation. It is shown that the impulse response of the optimal FIR filter can be obtained by a simple Riccati-type matrix differential equation. Especially for time-invariant systems, this FIR filter reduces to previously known simple forms. For implementation, a recursive form of the optimal FIR filter and smoother is derived by using adjoint variables, and computational algorithms are suggested. It is also shown by sensitivity analysis that the proposed optimal FIR filter alleviates potential divergence characteristics of the standard Kalman filter     

Range sidelobe reduction for the quadriphase codes

Filters that reduce the sidelobes of the quadriphase-coded waveform are realized by applying the biphase-to-quadriphase transformation to the filter designs that reduce the sidelobes of the prototype biphase code. The mismatch loss is invariant under this transformation, but the resulting peak-to-sidelobe ratio (PSR) can decrease 1.5 dB maximum. An example illustrates the procedure for a compressor composed of a sidelobe reducing filter cascaded with the matched filter and a compressor realized as one mismatched filter     

Remarks on ?Comments on 'Signal Resolution via Digital Inverse Filtering'?

Published comments on a recent paper criticized the use of inverse filtering as applied to resolution of overlapping radar signal returns. It is shown that an inadequate model of the inverse filter was assumed by the critic, which lead him to predict excessive time sidelobes at the filter output. It is demonstrated, by computer simulation, that the time sidelobes at the output of the true inverse filter are down 30 dB or more.     

低通滤波器的阶跃响应及其对动态校准的影响

动态测试系统在利用阶跃信号进行动态校准时,系统中的低通滤波器环节所产生的衰减振荡可能会误导测试人员,特别是对于带传压管道的动态压力测试系统。仿真与测试结果表明,各种模拟低通滤波器和IIR数字低通滤波器的阶跃响应都会出现一定的衰减振荡。针对带低通滤波器的系统以及其他系统的阶跃激励校准,通过对简单FFT频响分析方法、矩形单脉冲法、冲激响应法三种方法的比较,发现矩形单脉冲法能更正确地对阶跃校准数据进行频响分析。     

A Computationally Efficient Approximation to a Discrete-Time Matched Filter

When the number of filter coefficients is large, the solution of the discrete-time matched filter equation can be computationally difficult. In this paper several techniques are presented for approximating the impulse response of a matched filter without actually solving the matched filter equation. The performance of these approximating filters is analyzed and compared with the performance of the matched filter. It is also shown that an approximation which is best in a mean-squared-error sense is not necessarily best in terms of output signal-to-noise ratio.