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.     

Reciprocal radar waveforms

Digitally coded radar waveforms can be used to obtain large time-bandwidth products (pulse compression ratios). It is demonstrated that periodic radar waveforms with zero sidelobes or almost zero sidelobes can be defined. A perfect periodic code is a periodic code whose autocorrelation function has zero sidelobes and whose amplitude is uniform (maximum power efficiency=1). An asymptotically perfect periodic code has the property that as the number of elements in the code goes to infinity the autocorrelation function of the code has zero sidelobes and its power efficiency is one. The authors introduce a class of radar waveforms that are either perfect or asymptotically perfect codes. These are called reciprocal codes because they can be derived through a linear transformation of known codes. The aperiodic performance of the reciprocal code is examined     

Two-valued frequency-coded waveforms with favorable periodic autocorrelation

There are known phase-coded (two-valued or polyphase) CW radar signals that exhibit perfect periodic autocorrelation function (PACF). A PACF is perfect when all its out-of-phase autocorrelation values are identically equal to zero. This paper investigates periodic, two-valued, frequency-coded signals. While none could be found with perfect PACF, we present examples with nearly perfect PACF. Their relationship to binary phase-coded signals is also considered. These signals should be attractive for CW radars because of their simple implementation, clean spectrum, and the favorable range response of their matched receiver.     

Sequences and arrays with perfect periodic correlation

Properties and methods for synthesizing sequences with perfect periodic autocorrelation functions and good energy efficiency are discussed. The construction is extended to two-dimensional perfect arrays. The construction methods used are based mainly on a search in the frequency domain and on a multiplication theorem for periodic sequences and arrays     

Poly-phase codes and optimal filters for multiple user ranging

A technique is introduced to select poly-phase codes and optimal filters of a pulse compression system that have specific temporal and frequency characteristics. In the particular problem under study, multiple vehicles are assigned unique codes and receiver filters that have nearly orthogonal signatures. Narrowband users, that act as interference, are also present within the system. A code selection algorithm is used to select codes which have low autocorrelation sidelobes and low cross correlation peaks. Optimal mismatched filters are designed for these codes which minimize the peak values in the autocorrelation and the cross correlation functions. An adjustment to the filter design technique produces filters with nulls in their frequency response, in addition to having low correlation peaks. The method produces good codes and filters for a four-user system with length 34 four-phase codes. There is considerable improvement in cross and autocorrelation sidelobe levels over the matched filter case with only a slight decrease in the signal-to-noise ratio (SNR) of the system. The mismatched filter design also allows the design of frequency nulls at any frequency with arbitrary null attenuation, null width, and sidelobe level, at the cost of a slight decrease in processing gain     

Weight effects on the periodic ambiguity function

CW radar signals and processors are discussed. The use of the periodic ambiguity function (PAF) to analyze the delay-Doppler performance of CW signals and their corresponding correlation receivers, is extended to include weight function effects. This work provides tools which can predict the delay-Doppler response of almost any phase-coded CW radar. Examples demonstrate that a combination of CW signals having perfect periodic autocorrelation, a matched reference signal with a large number of modulation periods and a smooth weight function, can create a delay-Doppler response with extremely low sidelobes, strongly resembling the response of a coherent pulse train     

Low sidelobe radar waveforms derived from orthogonal matrices

Novel waveforms are described that have low sidelobes when individual or multiple waveforms are approximately processed. They are related to orthogonal matrices that may be associated with complementary sequences and also with periodic waveforms having autocorrelation functions with constant zero-amplitude sidelobes. Also described are sets of sequences whose cross-correlation functions sum to zero everywhere. A potential application is the elimination of ambiguous range stationary clutter     

Phase-Coded Interrupted CW Signals and Processors

High resolution radars require signals with large time-bandwidth product such as CW signal and coherent pulse train (CPT). We discuss a phase-coded interrupted CW (ICW) signal which is the combination of CW signal and CPT. Phase codes used here are with perfect periodic autocorrelation. The periodic ambiguity function of ICW signals is studied including single-carrier signal and multi-carrier signal. It is interesting that the gate function has different effects on two signals and contributes to a multi-carrier ICW signal which yields nearly perfect autocorrelation. Meanwhile we also suggest an efficient receiver approach to ICW signals, which can reduce the computational burden of the processor and utilize the good properties of P3 and P4 codes.     

Mismatched-filter design for periodic binary phased signals

A mismatched filter design is introduced whereby the receiver filter coefficients are optimized with the property that all sidelobes of the cross-correlation function (CCF) are zero. Some results are given for binary sequences and the associated mismatched filters. For each length N>2 there exist at least one sequence and an associated mismatched filter with an ideal impulselike CCF, which means that there are no sidelobes at all in the receiver output signal     

Periodic ambiguity function of CW signals with perfect periodicautocorrelation

A periodic ambiguity function (PAF) is discussed which describes the response of a correlation receiver to a CW signal modulated by a periodic waveform, when the reference signal in the receiver is constructed from an integral number N, of periods T, of the transmitted signal. The PAF is a generalization of the periodic autocorrelation function, to the case of non-zero Doppler shift. It is shown that the PAF of N periods is obtained by multiplying the PAF of a single period by the universal function sin(Nπν T)/N sin(πνT), where ν is the Doppler shift, to phase-modulated signals which exhibit perfect periodic autocorrelation when there is no Doppler shift. The PAF of these signals exhibits universal cuts along the delay and Doppler axes. These cuts are functions only of t, N and the number M, the modulation bits in one period     

Synthesis of binary sequences with good autocorrelation andcrosscorrelation properties by simulated annealing

Simulated annealing is a statistical computational technique for obtaining approximate solutions to combinatorial optimization problems. An efficient simulated annealing algorithm is used to design binary sequence sets which have good autocorrelation and crosscorrelation properties. Some of the synthesized results are presented, and their properties are better than any other known in the literature. The synthesized binary sequence sets promise to be practically applicable     

Effect of Vertical Deflections and Ocean Currents on a Maneuvering Ship

Vertical deflections and ocean currents introduce errors into ship's inertial navigation systems (SINS). In the absence of exact knowledge, these quantities may be treated as distance-dependent stationary random processes. However, these distance-dependent random processes enter SINS as time-dependent error sources. The autocorrelation functions of these time functions depend on the manner in which the ship maneuvers. An equation relating the time-dependent autocorrelation function to the distance-dependent autocorrelation function is derived. The time-dependent autocorrelation function is obtained for four different situations. The first two examples are ships steaming at constant heading and constant, but not necessarily known, velocity. The third example involves a ship tracking back and forth over the same path. The last example describes a ship that steams at a constant speed but changes heading in a random manner.     

The autocorrelation of m-sequences over nonprime finitefields

Nonbinary m-sequences (maximal length sequences) for spread-spectrum communication systems that have a two-level autocorrelation are presented. The autocorrelation function of an m -sequence over the Galois field of q elements GF(q), where q=p^k, for p a prime and k an integer greater than 1, is developed and shown to be bilevel when the elements of GF(q) are expressed as elements of a vector space over the pth roots of unity     

On Clutter Modeling and the Spectra of Two-Dimensional Gauss-Markov Random Signals

The spectral properties of two-dimensional isotropic clutter signals are examined for the cases in which 1) the clutter has an exponential spatial autocorrelation function, and 2) the clutter is a two-dimensional Gauss-Markov random signal. The one- and twodimensional power spectral densities before and after antenna filtering are obtained, and some of the differences and similarities between these two models are discussed in the context of spectral analysis.     

弹道中段目标进动周期估计的改进自相关法

自相关法可用于估计弹道中段雷达目标的进动周期,它需要预先给出进动周期的上下限。进动周期下限可能远小于真实进动周期,此时自相关法的估计性能将严重下降。定义了自相关函数(ACF)的凸包,在此基础上提出了一种改进的自相关法。首先求出ACF和其凸包的差函数,然后搜索差函数的最大值,从而得到进动周期的估计值。理论分析和仿真结果表明:当进动周期下限和真实进动周期相差不大时,该方法的估计性能接近自相关法;当进动周期下限远小于真实进动周期时,该方法仍然具有良好的估计性能;由于进动周期的上下限之比通常大于2,因此该方法的计算量比自相关法增大的倍数小于1.4;同时它对先验信息的要求非常宽松。因此该方法具有广泛的适用性。     

Robust adaptive fault-tolerant control of a tandem coaxial ducted fan aircraft with actuator saturation

This paper is concerned with the robust adaptive fault-tolerant control of a tandem coaxial ducted fan aircraft under system uncertainty, mismatched disturbance, and actuator saturation. For the proposed aircraft, comprehensive controllability analysis is performed to evaluate the controllability of each state as well as the margin to reject mismatched disturbance without any knowledge of the controller. Mismatched disturbance attenuation is ensured through a structured H-infinity controller tuned by a non-smooth optimization algorithm. Embedded with the H-infinity controller, an adaptive control law is proposed in order to mitigate matched system uncertainty and actuator fault. Input saturation is also considered by the modified reference model. Numerical simulation of the novel ducted fan aircraft is provided to illustrate the effectiveness of the proposed method. The simulation results reveal that the proposed adaptive controller achieves better transient response and more robust performance than classic Model Reference Adaptive Control (MRAC) method, even with serious actuator saturation.     

一种MED最优滤波长度选择新方法及其应用

最小熵解卷积（MED）是旋转机械故障诊断领域广泛应用的有效方法，它可以从噪声中提取微弱的故障冲击成分。然而它的有效性依赖于滤波长度的选取，目前，针对MED滤波长度的自动选取并没有明确有效的方法，往往需要人为经验选择。因此，在MED的算法基础上，通过结合自相关函数，提出了一种MED最优滤波长度选择的新方法，该方法构建了一个能量判定标准来衡量输出信号的周期性，从而自适应地确定MED的最优的滤波长度以提升微弱故障信号中的周期脉冲成分，避免MED方法容易出现最大化单一随机脉冲现象的发生。该方法应用于滚动轴承故障微弱冲击特征提取，并利用两个实例进行了有效性验证：基于辛辛那提试验中心的滚动轴承全寿命疲劳加速试验；带机匣的航空发动机转子试验器模拟远离轴承振动源的故障试验。结果表明，所提方法可以消除传递路径影响，提升微弱冲击周期性特征，并且与最大相关峭度解卷积（MCKD）方法相比，诊断结果更具优势。     

难加工材料切削状态的识别——模式识别技术的应用

本文介绍模式识别技术在难加工材料切削状态识别中的应用,这是实现适应性控制的第一步。根据切削试验中切削力随机信号处理的结果,可以看出在自相关图和自功率谱图与切削现象之间存在着内在联系。在此基础上分别建立了有无积屑瘤以及将切屑分成三类的判别函数。利用这些判别函数来识别切削状态的结果表明,模式识别技术在切削加工中的应用是成功的。     

Noise Injected into Coherent Carrier Signals by Random Phase Changes

The autocorrelation and power spectrum of spurii arising from periodic random phase injections into a coherent backscatter signal are found. Design considerations of appropriate filters to eliminate spurii noise is discussed.     

New Autocorrelation and Prediction Techniques for the Demodulation of Binary Signals

The classic problem of detecting a narrowband signal received in a wideband noise is treated via new techniques, namely, autocorrelation computation and linear adaptive filtering. It is shown by analysis and simulation that the proposed techniques yield probility of bit errors cimparable to those provided by coding techniques. Expressions are derived for the detectability parameter of the new test statistics, and it is shown that these statistics are very close to the Gaussian approximation. The improvements obtained in the signal-to-noise ratio and the Gaussian nature of the new statistic implies an improvement in the capacity of the channel by the nonlinear and storage processes involved in the new techniques, something not achievable by linear filtering and/or memoryless detection techniques.