Time-frequency hop codes based upon extended quadratic congruences

Time-frequency hop codes are developed that can be used for coherent multiuser echolocation and asynchronous spread spectrum communication systems. They represent a compromise between Costas codes, which have nearly ideal autoambiguity but not so good cross-ambiguity properties, and linear congruential codes, which have nearly ideal cross-ambiguity but unattractive autoambiguity properties. Extended quadratic congruential code words are shown to have reasonably good autoambiguity and cross-ambiguity properties across the whole class of code sets considered. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the position and amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time/bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of the new codes     

Frequency hop multiple access codes based upon the theory of cubiccongruences

The need for families of frequency-hop codes which have mutually small auto-ambiguity and cross-ambiguity functions is discussed. Current coding methods are reviewed. A new family of frequency-hop codes based upon the number-theoretic concept of cubic congruences is introduced. It is shown that for about 50% of the prime numbers, families of full codes exist which have at most two coincidences for any time-frequency shift in their auto-ambiguity functions and at most three coincidences in the set of mutual cross-ambiguity functions     

Periodic ambiguity functions of EQC-based TFHC

The time-frequency hop codes based upon extended quadratic congruences (TFHC-EQC) were developed previously (1988, 1991). The known results about the ambiguity functions of the TFHC-EQC are extended from aperiodic cases to periodic cases. Precisely, the following new results are proved: (1) The tight upper bound for the periodic auto-ambiguity function of the TFHC-EQC is 6; (2) the periodic cross-ambiguity upper bound of the TFHC-EQC is at least (N-1)/2; (3) there exists a subset TFHC-EQC of volume (N-1)/2 such that its periodic cross-ambiguity is tightly upper bounded by 8     

On cross-ambiguity properties of Welch-Costas arrays

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar system, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers     

Time-Frequency HOP Signals Part I: Coding Based upon the Theory of Linear Congruences

Time-frequency hop codes are developed based upon the theory of linear congruences. These codes can be used for multiuser radar and asynchronous spread spectrum communications systems. A uniform upper bound is placed on the cross-correlation function between any two elements of the code set. The upper bound is minimized by choice of time-bandwidth product and is shown to diminish as 2/N, where N is the number of elements in the code set. The size and position of spurious peaks in the autocorrelation functions are discussed. The results are extended to narrowband ambiguity functions.     

Synthesis of Ambiguity Functions for Prescribed Responses

The synthesis of radar ambiguity functions is approached using burst-pulse time-frequency waveform coding. Noting that the parameters that define the central response of the ambiguity function for these code classes also define the waveform code, a statistical decision procedure based upon the central response is employed to obtain Bayes-type codes. The selection of the code parameters is subject to restrictions imposed by the noncentral response of the ambiguity function. Three classes of random time-frequency codes are treated: 1) uniform amplitude, uniform pulsewidth matched codes; 2) uniform amplitude, nonuniform pulsewidth matched codes; and 3) uniform amplitude, uniform pulsewidth with receiver amplitude mismatch.     

Ambiguity Functions for Quadratic Phase-Coded Pulse Trains

The matched filter ambiguity function is presented for a burst waveform composed of repeated subbursts, each one of which consists of N pulses in which the phase is varied quadratically from pulse to pulse. The resulting ambiguity function exhibits small residual ambiguities along the delay axis separated by the reciprocal of the pulse repetition frequency (PRF). A cross-ambiguity function is derived which reduces these ambiguities to zero amplitude. A third cross-ambiguity function is presented for a receiver matched to a generalized Hamming weighted repeated quadratic burst. The location in the delay/Doppler plane of the waveform ambiguities for these waveforms is compared with that of an uncoded pulse burst.     

Cross-correlation properties of algebraically constructed Costasarrays

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically constructed Costas arrays for a given construction and dimension. Finding two arrays that minimally correlate implies that the signals based on these arrays also minimally correlate. The properties of finite fields are reviewed, and the major algebraic constructions for Costas arrays are presented, i.e. the Welch construction and the Golomb construction. The discrete cross-correlation properties of the Costas arrays are derived for arrays of the same dimension derived from the same construction. The use of Costas arrays in the signal design problem is discussed, and examples are given to show the cross-correlation of the signals based on the algebraically constructed arrays     

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.     

Design Principles of MIMO Radar Detectors

This paper considers the problem of multiple-input multiple-output (MIMO) radars employing space-time coding (STC) to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the first is based on the classical Chernoff bound, the second is an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well-known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.     

基于纠删码的遥测链路丢帧恢复技术

针对遥测系统在恶劣天气条件、航天器姿态调整、天线指向偏离、脉冲干扰等各种因素影响下出现的遥测信号闪断以至接收机丢帧问题,提出一种适用于闪断信道的纠删码技术,用于恢复丢失的数据帧.首先介绍LDPC（低密度奇偶校验）纠删码的编译码算法,然后构造一种以短码长的随机码为外码、IRA（不规则重复累积）LDPC码为内码的级联纠删码,最后给出纠删码的应用策略和实现纠删码所需的CCSDS（空间数据系统咨询委员会）协议扩展.通过仿真实验和分析,得到了LDPC纠删码和级联纠删码的纠删性能,得出级联纠删码与LDPC纠删码均可获得接近理想的纠删性能的结论,且级联纠删码的构造更为灵活,可适应不同的应用环境,对CCSDS协议进行适当扩展后即可支持纠删码在CCSDS遥测链路中的应用.     

Radar/Sonar Signal Design for Bounded Doppler Shifts

In many detection and estimation problems, Doppler frequency shifts are bounded. For clutter or multipath that is uniformly distributed in range and symmetrically distributed in Doppler shift relative to the signal, detectability of a point target or a communication signal is improved by minimizing the weighted volume of the magnitude-squared autoambiguity function. When clutter Doppler shifts are bounded, this volume is in a strip containing the range axis on the range-Doppler plane. For scattering function estimation, e.g., for weather radar, Doppler flow meters, and distributed target classifiers, it is again relevant to minimize ambiguity volume in a strip. Strip volume is minimized by using a pulse train, but such a signal has unacceptably large range sidelobes for most applications. Other waveforms that have relatively small sidelobe level within a strip on the range-Doppler plane, as well as small ambiguity volume in the strip, are obtained. The waveforms are composed of pulse pairs that are phase modulated with Golay complementary codes.     

Costas array generation and search methodology

Costas arrays are permutation matrices that provide sequencing schemes for frequency hop in FSK waveforms. Such frequency-shift keying (FSK) waveforms can be designed to have nearly ideal ambiguity function properties in both the time and frequency directions: the Costas property permits at most one coincident tone in autocorrelations in both time and frequency. Costas arrays are found by number-theoretic generators and their extensions, and by exhaustive search methods. Two new extensions of number-theoretic methods are introduced here that find two new Costas arrays. All Costas arrays for orders 24, 25, and 26 are disclosed here, including previously unknown examples.     

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.     

Staggered Costas Signals

A radar signal, based on coherent processing of a train of staggered Costas bursts, is suggested and investigated. The selection of sequences of each burst is based on a minimum number of collocation of their individual ambiguity function sidelobe peaks. The resulting ambiguity function combines qualities of both "thumbtack" and "bed of nails" signals. Comparison with linear-FM, V-FM, and complementary phase coded (CPC) signals is given, as well as comparison with hybrid signals consisting of both phase and frequency coding.     

Group-Complementary Array Coding for Radar Clutter Rejection

A radar waveform design technique which utilizes Lagrange's method of multipliers to control temporal sidelobes and to reduce Doppler sidelobes is described. This classical method of constrained optimization is applied to the problem of synthesizing a radar wave-form where mismatch loss is the objective function to be minimized. The associated constraints are taken from expressions for the composite temporal sidelobes of the cross-correlation response and the peak correlation response where sets of code words are used to modulate a series of radar pulses. The resulting code sets and receiver reference sets are called group-complementary and produce a trench parallel to or on the range axis of the cross-ambiguity surface.     

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     

基于二相编码的探测干扰一体化信号波形设计与仿真

如今,在信号处理技术飞速发展的背景下,针对传统的雷达信号设计暴露出的功能单一、低截获性能差以及距离速度分辨力较低等问题,构建了 1种基于十三位巴克码的探测干扰一体化信号波形。文中对其调制原理进行了分析,对其中的二相编码序列分量、伪随机码序列分量进行自相关函数特征分析,并分别从模糊函数、功率谱角度分析其探测特性和干扰特性。仿真实验证明,探测干扰一体化信号样式相较于单一调制的十三位巴克码信号具有较好的模糊函数和功率谱特性,在保持二相编码信号良好的多普勒敏感特性基础上,具有更好的距离分辨力以及更 大的干扰带宽。     

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