Ambiguity function of quadriphase coded radar pulse

Taylor's quadriphase coding (J.W. Taylor, Jr. and H.J. Blinchikoff, ibid., vol.23, no.2, p.156-70, Mar. 1988) is investigated for nonzero Doppler shifts. While the zero-Doppler cut of the ambiguity function (i.e. the autocorrelation) strongly resembles that of the corresponding biphase code, the remaining ambiguity function differs considerably. The ambiguity function of quadriphase code 13 is typified by a diagonal ridge as found in linear FM signals. The ambiguity function of quadriphase code 28A resembles the three parallel ridges of Frank code 16     

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.     

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     

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     

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     

The Effect of Limiting a Biphase or Quadriphase Signal Plus Interference

This paper analyzes the case of limiting an incoherent or coherent interference signal at the frequency of a biphase or quadriphase digital signal. The results give the IM products, interference, and attenuation of the digital signal, plus interference through a hard limiter.     

Design and analysis of new p(n,k) polyphase pulse compression codes

P(n,k) codes as a new class of polyphase pulse compression codes are introduced and analyzed in detail. The P(n,k) codes are conceptually derived by step approximation of the phase function of a nonlinear-frequency modulated (NLFM) Chirp signal with a favorable energy density spectrum. The significant advantages of P(n,k) codes over conventional polyphase codes are lower autocorrelation sidelobes and an improved tolerance of low Doppler shifts and precompression bandwidth limitations. The primary disadvantage of the P(n,k) codes over conventional codes is a loss in range resolution. The uniform P(n,k) codes are especially attractive for radars employing digital signal professing because their favorable correlation properties also remain when quantization effects are taken into account     

Spectral Energy Requirements and Adjacent-Channel Crosstalk in CAS

Four-frequency channels avoid the prior slot interference that handicaps single-frequency collision avoidance systems of equal message-slot capacity. Crosstalk between adjacent frequency channels is adequately limited If the receiver response to adjacent-channel signals is attenuated at least 52 dB. With 5-MHz channel separation, 48-dB crosstalk rejection was achieved in a test receiver by restricting the RF pulse rise time and decay time to 0.2 ?s minimum. Crosstalk resulting from biphase modulation can be effectively attenuated by limiting the minimum envelope transition time to 0.2 ?s. The effect of pulse rise time and decay time on the energy density spectrum is discussed.     

Doppler Properties of Polyphase Coded Pulse Compression Waveforms

Doppler properties of the Frank polyphase code and the recently derived P1, P2, P3, and P4 polyphase codes are investigated and compared. An approximate 4 dB cyclic variation of the peak compressed signal is shown to occur as the Doppler frequency increases. The troughs in the peak-signal response occur whenever the total phase shift across the uncompressed pulse, due to Doppler, is an odd multiple of ? radians. It is shown that while the P3 and P4 codes have larger zero-Doppler peak sidelobes than the other codes, the P3 and P4 codes degrade less as the Doppler frequency increases. Also, the effects of amplitude weighting and receiver bandlimiting for both zero and nonzero Doppler are investigated.     

扩频系统中伪码防错锁技术研究

针对扩频系统中出现的伪码错锁问题,分析了产生伪码错锁的原因,根据伪码自相关性和互相关性特点,从伪码捕获策略、错锁自动判决策略等角度研究了伪码防错锁措施：选择自相关性和互相关性尽可能好的码;合理设置捕获门限;减小多普勒捕获范围;采用并行伪码捕获方法,并在捕获过程中防止载波错捕现象发生;单独建立验证通道,进行相关值比较判决等。实践表明,采用文中方法可提高正确捕获概率,缩短捕获时间,从硬件设计上有效解决了伪码错锁问题。     

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.     

Range-time-sidelobe reduction technique for FM-derived polyphase PCcodes

A simple, easy to implement technique is presented that can significantly reduce the range-time-sidelobes of a class of polyphase pulse compression codes. This technique reduces the highest sidelobes to only one code element magnitude independent of effective pulse compression ratio. The codes considered are polyphase codes that are derived from the step-approximation-to-linear-frequency-modulation and linear-frequency-modulation waveforms such as the P1, P3, P4, and the Frank codes. The characteristics of these codes that make this possible are explained     

GPS多径信号的自适应滤波估计方法

 研究全球定位系统(GPS)多径信号估计的问题。通过分析自适应滤波器的原理,建立了数字中频信号处理的数学模型,提出一种用自适应滤波实现GPS多径幅度、码相位和载波相位估计的方法。该方法采用不同延迟的伪随机序列对信号进行解扩、解调和累加,得到了作为期望信号的系列自适应滤波相关值。对该方法与其他3种方法进行了理论上的分析比较,得出本方法具有信噪比高、自适应滤波性能好、带有码相位信息和不存在载波模糊度问题等优点。根据各种滤波器算法的特点和本应用的需求,给出了选用递归最小二乘算法实现的方法。通过计算机仿真,验证了提出的方法能够在14 dB的信噪比下,以1个采样间隔的时间延迟分辨率和0.005周的载波相位估计精度估计出GPS L1的多径信号。     

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     

A New Class of Polyphase Pulse Compression Codes and Techniques

A new class of symmetric radar pulse compression polyphase codes is introduced which is compatible with digital signal processing. These codes share many of the useful properties of the Frank polyphase code. In contrast with the Frank code, the new codes are not subject to mainlobe to sidelobe ratio degradation caused by bandlimiting prior to sampling and digital pulse compression. It is shown that bandlimiting the new codes prior to pulse compression acts as a waveform amplitude weighting which has the effect of increasing the mainlobe to sidelobe ratios.     

Cyclic code shift keying: a low probability of intercept communication technique

A low probability of intercept (LPI), or low probability of detection (LPD) communication technique known as cyclic code shift keying (CCSK) is described. We discuss the basic concepts of CCSK and describe a system based on the use of random or pseudorandom codes for biphase modulation. We use simulation to show that the bit error rate (BER) for CCSK can be closely estimated by using existing equations that apply to M-ary orthogonal signaling (MOS). Also, we show that significantly fewer computations are required for CCSK than for MOS when the number of bits per symbol is the same. We show that using biphase modulation results in waveforms that have a large time-bandwidth product and very low input signal-to-noise ratio (SNR) and thus inherently have an LPI by a radiometer. We evaluate detection by a radiometer and show that LPI can be achieved by using codes of lengths greater than about 2/sup 12/ (i.e., by transmitting more than about 12 bits per symbol). Results illustrate the effect that the CCSK symbol length and error probability, and the radiometer integration time and probability of false alarm (PFA), have on detection by a radiometer. We describe a variation of CCSK called truncated CCSK (TCCSK). In this system, the code of length 2/sup k/ is cyclically shifted, then truncated and transmitted. Although shortened, the truncated code still represents k bits of information, thus leading to an increased data rate. We evaluate radiometer detection of TCCSK and it is shown that the probability of detection is increased compared with the detection of CCSK.     

航空发动机中介轴承的故障特征与诊断方法

提出了转差域频谱和转差域包络谱的概念,建立了诊断航空发动机中介轴承故障的方法.利用发动机高、低压转差作为触发信号,对发动机振动信号进行等转差周期采集,并在转差域对振动信号进行频谱和包络谱分析.结果表明:不平衡响应、不对中响应以及外环静止的轴承故障响应等振动信号在转差域频谱和转差域包络谱上的位置随转速变化;而中介轴承的故障响应在转差域频谱上的边频成分间距不随转速变化,具有倍频“恒间距”特征;在转差域包络谱上的位置也不随转速变化,具有“恒频”特征.带外环故障的中介轴承实验表明:转速变化时,在转差域包络谱中,外环故障特征倍频成分位置不变;在转差域频谱中,出现间隔宽度恒定为外环故障特征倍频的频率成分.      

Generalized Feedback Decoding of Convolutional Codes

The use of convolutional codes with feedback decoding is a common error-correction technique in simple communication systems. A drawback of conventional feedback decoding is the limitation to a class of self-orthogonal codes which, in general, are nonoptimum. Based on distance properties of the utilized code and test-error pattern analysis, we propose generalized feedback decoding which does not have the abovementioned limitation. This is minimum distance decoding and can be applied to any convolutional code while still maintaining its simplicity. Therefore, it has the advantage of being easily adopted in existing systems. We can use the relatively complicated Viterbi or sequential decoders in larger terminals and, with the same code, use the proposed decoders in smaller terminals; otherwise, both large and small terminals must utilize the same type of decoder. The proposed decoding scheme could also be used to simplify and speed up sequential decoding. In addition, comparisons of the proposed decoder with other feedback decoders are presented.     

Ambiguity properties of quadratic congruential coding

The ambiguity characteristics of multiple access frequency hop codes based on standard quadratic congruences are investigated in the light of results obtained for codes based on Costas arrays and extended quadratic congruences. While the autoambiguity properties are found to be very similar to those of Costa codes, i.e. nearly ideal, the cross-ambiguity properties of quadratic congruential codes are much better. These results are valid across the whole class of code sets considered, but they are obtained at some expense in the pulse compression characteristics of the codes. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the 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 quadratic congruential coding with respect to Costas coding     

A neural network approach to pulse radar detection

A multilayer feedforward neural network is applied to pulse compression. The 13-element Barker code and the maximum-length sequences (m-sequences) with lengths 15, 31, and 63 b were used as the signal codes, and four networks were implemented, respectively. In each of these networks, the number of input units was the same as the signal length while the number of hidden units was three and the number of output units was one. In training each of these networks, backpropagation learning was used and the number of training epochs was 500. Using this approach, a more than 40 dB output peak signal-to-sidelobe ratio can be achieved. These fault-tolerant neural networks can provide a robust means for pulse radar detection