A remark on the definition of Costas arrays

A weaker definition of Costas arrays is shown to be equivalent to the standard one. A Costas array is a diagram whose corresponding frequency-hopping pattern has good range-doppler ambiguity properties. Our result implies that even when we demand ostensibly less restrictive ambiguities in the doppler direction, the resulting waveform becomes a Costas waveform.     

基于System Generator的Costas锁相环设计实现

介绍了一种基于Xilinx公司FPGA开发工具System Generator进行全数字Costas锁相环的设计仿真方法。通过对Costas锁相环原理的分析,从离散域变换阐述了环路参数的计算及电路设计,基于对CORDIC算法设计DDS的讨论,利用FPGA实现了设计,最后全面分析了环路性能。     

QPSK扩频调制信号载波跟踪环路设计

扩频接收基带通常需要载波跟踪环来完成本地载波与接收信号载波的同步,科斯塔斯环是常用的非相干载波相位跟踪环,具有较好的鉴相特性。本文基于常规的单路单载波解调的科斯塔斯环原理,对科斯塔斯环做了改进,提出了对双通道平衡QPSK扩频基带所用载波跟踪环科斯塔斯环的改进方法,并推导出环路误差鉴相信号,用Matlab进行了仿真实验,结果证明利用本环路可实现载波稳定跟踪。     

数字Costas环的matlab仿真及其FPGA实现

基于锁相环的模型,研究了数字Costas环的结构和性能．首先介绍了Costas环的基本原理及数学模型,其次使用matlab编程的方法实现了软件上的仿真,最后在QuartusⅡ＋ModelSim环境中用VHDL语言实现了该算法．仿真和实验结果表明,该Costas环路具有十分优良的性能．     

Improving Frequency Acquisition of a Costas Loop

A Costas loop for tracking a BPSK signal does not acquire when the initial frequency error is comparable to the loop bandwidth. This paper describes methods for deriving control proportional to frequency error so as to improve the frequency acquisition capability by an AFC augmentation. A composite AFC/Costas loop is realized by combining the individual loops. Pull-in from a frequency error much greater than the Costas loop bandwidth is now feasible. The increase in phase error due to the AFC capability is evaluated by a linearized analysis. If the bandwidth of the AFC portion is sufficiently narrow, the degradation is negligible. Improved frequency acquisition can also be realized by a simple modification of the Costas loop to remove the low-pass filter on the quadrature phase detector channel, with negligible degradation to phase tracking.     

Tracking Performance of Costas Loops with Hard-Limited In-Phase Channel

It is becoming increasingly popular in the design of suppressed carrier receivers, which employ Costas loops for earrier reconstruction, to hard-limit the output of the in-phase channel. Doing so allows replacement of the analog multiplier, which forms the loop error signal, with a chopper-type device which typically exhibits much less dc offset. The false lock behavior of such a hard-limited loop was recently investigated and shown to be quite different from that of the conventional Costas loop without the hard limiter. This paper presents the companion, analysis of the tracking performance of the hard-limited loop and assesses the penalty, if indeed it is a penalty rather than an improvement, in this performance relative to the conventional Costas loop with an analog third multiplier. In particular, for the case ofRCarm filters and NRZ data, the squaring loss (or equivalently the linear loop tracking jitter) is evaluated and illustrated as a function of the ratio of arm filter bandwidth to data rate and data signal-to-noise ratio. Superimposed on these numerical results will be the corresponding ones for the conventional Costas loop. As a finale, the equivalence in operation of the Costas loop with hard-limited in-phase channel and a baseband modulation carrier reconstruction loop referred to as a demod/ remod loop is discussed.     

Interleavers for turbo codes using permutation polynomials over integer rings

A class of deterministic interleavers for turbo codes (TCs) based on permutation polynomials over /spl Zopf//sub N/ is introduced. The main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code. Moreover, since the interleaver can be generated by a few simple computations, storage of the interleaver tables can be avoided. By using the permutation polynomial-based interleavers, the design of the interleavers reduces to the selection of the coefficients of the polynomials. It is observed that the performance of the TCs using these permutation polynomial-based interleavers is usually dominated by a subset of input weight 2m error events. The minimum distance and its multiplicity (or the first few spectrum lines) of this subset are used as design criterion to select good permutation polynomials. A simple method to enumerate these error events for small m is presented. Searches for good interleavers are performed. The decoding performance of these interleavers is close to S-random interleavers for long frame sizes. For short frame sizes, the new interleavers outperform S-random interleavers.     

Costas序列在雷达信号设计中的应用研究

阐述了Costas序列的代数结构及其特点,分析了常用雷达信号,如线性调频脉冲信号、非线性调频脉冲信号等的模糊函数,文中指出当雷达信号使用Costas序列的构成方法形成跳频扩频的信号时,将获得理想的模糊函数性能,即同时获得极好的距离分辨率和速度分辨率。文中建立了多目标散射、多径衰落和加性高斯白噪声信道的数学模型,并介绍了多目标散射、多径衰落和加性高斯白噪声信道的雷达信号设计方法,最后给出了计算机仿真结果。     

Permutation filters: a class of nonlinear filters based on setpermutations

Introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory. The authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters (𝒫 filters). In particular, rank-order filters, weighted rank-order filters, and stack filters embody limited permutation transformations of a set. Indeed, by using the full potential of a permutation group transformation, one can design very efficient estimation algorithms. Permutation groups inherently utilize both rank-order and temporal-order information; thus, the estimation of nonstationary processes in Gaussian/nonGaussian environments with frequency selection can be effectively addressed. An adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion. Simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters     

On the Calculation of Squaring Loss in Costas Loops with Arbitrary Arm Filters

The calculation of the optimum performance of suppressed carrier receivers with Costas loop tracking is directly related to evaluating the loop's so-called squaring loss. Recent work by the author and others presented specific numerical results for this loss when the input data were biphase-L(Manchester coded) and the Costas loop arm filters were of then-pole Butterworth type. These results were largely obtained by numerical integration on a digital computer. This paper presents a partial fraction expansion technique for arriving at closed form expressions for squaring loss for Costas loops with arbitary arm filters and NRZ as well as Manchester coded data. Specific closed form results are given for one and two pole Butterworth filters as examples.     

基于软件无线电的载波跟踪环研究及仿真

载波跟踪是扩频通信中的一项关键技术，直接影响解调指标。文中介绍了Costas环的工作原理及数学模型，并分析了NCO和环路滤波器，对Costas环进行了改进．通过Matlab仿真，结果表明：在相同环路参数下，改进的Costas环比模拟的Costas环的跟踪性能有所改善．     

Constructions and properties of Costas arrays

A Costas array is an n × n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that n × n Costas arrays exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n = p - 1, n = q - 2, n = q - 3, and sometimes when n = q - 4 and n = q - 5, where p is a prime number, and q is any power of a prime number. All known Costas array constructions are listed for 271 values of n up to 360. The first eight gaps in this table occur at n = 32, 33, 43, 48, 49, 53, 54, 63. (The examples for n = 19 and n = 31 were obtained by augmenting Welch's construction.) Let C(n) denote the total number of n × n Costas arrays. Costas calculated C(n) for n ≤ 12. Recently, John Robbins found C(13) = 12828. We exhibit all the arrays for n ≤ 8. From Welch's construction, C(n) ≥ 2n for infinitely many n. Some Costas arrays can be sheared into "honeycomb arrays." All known honeycomb arrays are exhibited, corresponding to n = 1, 3, 7, 9, 15, 21, 27, 45. Ten unsolved problems are listed.     

全数字Costas环在FPGA上的设计与实现

Costas环是一种闭环自动调整系统,常用于抑制载波的相位调制系统中提取参考载波信号。文中在FPGA(现场可编程门阵列)平台上实现了全数字化的Costas环载波恢复电路,介绍了Costas环的基本原理,详细阐述了环路各部件的参数及电路设计,给出了实现后的RTL(寄存器传输逻辑)原理图及仿真测试数据,仿真结果表明,该Costas环路具有十分优良的性能。     

脉间Costas FH讷发辨毫米波雷达信号的DDS实现

介绍了一种高分辨率雷达信号（脉间Costas FH信号）和直接数字合成（DDS）技术,给出了脉间Costas FH信号与步进频率脉冲雷达信号的统一表达形式,以及用“频率挑选矩阵”从DDS所产生的信号集合中产生脉间跳频信号的方法,使用该种方法,可以增加雷达系统软硬件实现的灵活性。     

Coupled AGC-Costas Loops with AM/PM Conversion

Costas loops are invariably designed in conjunction with an automatic gain control (AGC) loop for stabilizing performance. In such systems an inherent coupling between the AGC and Costas loops develops, complicating the standard phase referencing analysis. This coupling is further emphasized if the gain control amplifier introduces an AM/PM conversion, which causes power variations to enter the Costas loop as phase variations. In this paper the coupling effect between AGC and Costas loops is developed, leading to a pair of joint, interconnected dynamical tracking loops. Some degree of solution is attainable by assuming a first order AGC loop, and resorting to quasi-stationary analysis for evaluating the phase referencing generation. Results with and without AM/PM are presented, and illustrate how an improper AGC may in fact degrade the phase referencing from the expected performance.     

Costas序列在多用户雷达系统中的应用研究

讨论了跳频码的构造与性能,着重介绍了Costas序列的结构,用Costas序列设计跳频码能获得理想的自模糊和较好的互模糊性能.建立了跳频扩频信号的数学模型,给出了子脉冲正交的条件.论述了Costas序列的自(互)相关特性,给出了置换序列互相关函数的实用性质及模糊函数的求取算法,并进行了性能仿真,研究了Costas序列互模糊函数的特性,阐述了多用户系统中减小用户间相互干扰的方法.     

Introduction to "Synchronous Communications"

The paper "Synchronous Communications," originally published in this journal in December 1956 by John P. Costas, has had a profound effect on modem digital communications. At the time of its publication, virtually all communications were analog in nature and, in fact, the stated goal of the paper was to demonstrate an amplitude-modulated (AM) system that could provide significantly improved performance for analog signaling and to dispel the notion that single sideband (SSB) had inherent performance advantages over properly constructed AM signaling systems. This paper is particularly significant because it was the first to demonstrate that carrier phase could be reliably recovered from the received signal using a structure that has come to be known as the Costas Loop.     

Golomb Costas序列的结构及其在OFDM系统中的应用

研究了用循环移位法获得的Golomb Costas序列族的特性,建立了含有一个间隙行和一个间隙列的Golomb Costas序列的结构理论,深入研究了含有一个间隙行和一个间隙列的Golomb Costas序列的代数结构、构造方法和自（互）相关特性,并证明了相关的定理。探索了用含有一个间隙行和一个间隙列的Golomb Costas序列设计OFDM 系统中跳频图样的方法,举例说明了如何设计跳频码和怎样将跳频码分配给 OFDM 系统中的用户。用含有一个间隙行和一个间隙列的Golomb Costas序列设计跳频码能获得理想的自相关特性,并且当无线通信系统中多普勒频移受限时能获得极佳的互相关性能。     

Any two N × N costas signals must have at least one common ambiguity sidelobe if N > 3—A proof

Costas signals have an ambiguity function that approaches the ideal "Thumbtack" configuration. To increase the main lobe/side-lobe ratio without increasing the number of frequencies (signal dimension, N) it may be possible to stagger Costas signal pulses whose ambiguity sidelobe patterns do not coincide. We prove here that Costas signals of the same dimension, with completely different ambiguity sidelobe patterns, do not exist for N > 3.     

A simple method to determine the number of true different quadratic and cubic permutation polynomial based interleavers for turbo codes

Interleavers are important blocks of the turbo codes, their types and dimensions having a significant influence on the performances of the mentioned codes. If appropriately chosen, the permutation polynomial (PP) based interleavers lead to remarkable performances of these codes. The most used interleavers from this category are quadratic permutation polynomial (QPP) and cubic permutation polynomial (CPP) based ones. In this paper, we determine the number of different QPPs and CPPs that cannot be reduced to linear permutation polynomials (LPPs) or to QPPs or LPPs, respectively. They are named true QPPs and true CPPs, respectively. Our analysis is based on the necessary and sufficient conditions for the coefficients of second and third degree polynomials to be QPPs and CPPs, respectively, and on the Chinese remainder theorem. This is of particular interest when we need to find QPP or CPP based interleavers for turbo codes.