Properties of the beampattern of weight- and layout-optimizedsparse arrays

Theory for random arrays predicts a mean sidelobe level given by the inverse of the number of elements. In practice, however, the sidelobe level fluctuates much around this mean. In this paper two optimization methods for thinned arrays are given: one is for optimizing the weights of each element, and the other one optimizes both the layout and the weights. The weight optimization algorithm is based on linear programming and minimizes the peak sidelobe level for a given beamwidth. It is used to investigate the conditions for finding thinned arrays with peak sidelobe level at or below the inverse of the number of elements. With optimization of the weights of a randomly thinned array, it is possible to come quite close and even below this value, especially for 1D arrays. Even for 2D sparse arrays a large reduction in peak sidelobe level is achieved. Even better solutions are found when the thinning pattern is optimized also. This requires an algorithm that uses mixed integer linear programming. In this case solutions, with lower peak sidelobe level than the inverse number of elements can be found both in the 1D and the 2D cases     

一种旁瓣级可控的MVDR波束形成算法

针对传统的最小方差无畸变响应（Minimum Variance Distortionless Response,MVDR）波束形成方法存在的旁瓣较高且抑制干扰性能不稳健的情况,提出一种旁瓣级可控的自适应波束形成算法。该算法在MVDR基础上进行峰值搜索,将获得的峰值点从大到小进行排序,取次大值作为最高旁瓣的值,将得到的最高旁瓣值与期望旁瓣值比较,在其方位添加虚拟干扰加以抑制,从而得到新的波束图。再对新的波束图进行峰值搜索,不断重复上述过程,经过有限次迭代以达到期望旁瓣值。计算机仿真结果表明在均匀线阵基础上该算法能够将旁瓣控制到期望旁瓣级以下且比较稳健。     

Design and evaluation of a high data rate optical wireless system for the diffuse indoor channel using barker spreading codes and RAKE reception [optical wireless communications]

The performance of a high data rate optical wireless system (OWS) over the diffuse indoor infrared channel based on direct sequence spread spectrum (DSSS) techniques is highly sensitive to the properties of the aperiodic autocorrelation function and the spreading factor of the spreading sequence used. Ideally, the aperiodic autocorrelation function should have zero sidelobes in order to eliminate intersymbol interference caused by multipath propagation. In practice, such an ideal sequence does not exist in the binary field when data modulation is applied. For high data rates, a small spreading factor is desired in order to avoid an excessive system bandwidth. The family of Barker sequences is investigated in a DSSS-OWS. The Barker sequences are binary spreading sequences which exhibit small aperiodic autocorrelation values and short spreading factors. The system bit error rate (BER) performance is characterized on the diffuse indoor infrared channel when using RAKE reception. Results of BER against Eh/NQ are presented with data rate and spreading factor as parameters. The results demonstrate that of the seven Barker sequences existing, the length three Barker sequence {0 0 1} provides the best system design trade-off in respect of good BER performance and low implementation complexity.     

Thirty-two phase sequences design with good autocorrelation properties

Polyphase Barker Sequences are finite length, uniform complex sequences; the magnitude of their aperiodic autocorrelation sidelobes are bounded by 1. Such sequences have been used in numerous real-world applications such as channel estimation, radar and spread spectrum communication. In this paper, thirty-two phase Barker sequences up to length 24 with an alphabet size of only 32 are presented. The sequences from length 25 to 289 have autocorrelation properties better than well-known Frank codes. Because of the complex structure the sequences are very difficult to detect and analyse by an enemy’s electronic support measures (ESMs). The synthesized sequences are promising for practical application to radar and spread spectrum communication systems. These sequences are found using the Modified Simulated Annealing Algorithm (MSAA). The convergence rate of the algorithm is good.     

基于二阶锥规划的稳健低旁瓣自适应波束形成

针对水下成像时圆弧阵常规波束旁瓣级较高,当存在强干扰时容易带来较多虚警的缺点,提出一种基于二阶锥规划的稳健低旁瓣自适应波束形成方法。该方法通过对波束旁瓣进行优化设计,可以将波束旁瓣级进行严格控制,并进一步结合协方差矩阵重构法,使波束形成器的稳健性得到提高,最后将该波束优化问题转化为二阶锥规划问题进行求解。计算机仿真结果表明,相较于其他算法来说,文中算法在波束旁瓣级得到严格控制的同时,可以在存在各类失配的情况下获得更高的输出信干噪比,稳健性更高。水池实验进一步验证了该方法的有效性,该研究成果可以在声呐成像领域应用。     

Birefringent filter design by use of a modified genetic algorithm

A modified genetic algorithm is proposed for the optimization of fiber birefringent filters. The orientation angles and the element lengths are determined by the genetic algorithm to minimize the sidelobe levels of the filters. Being different from the normal genetic algorithm, the algorithm proposed reduces the problem space of the birefringent filter design to achieve faster speed and better performance. The design of 4-, 8-, and 14-section birefringent filters with an improved sidelobe suppression ratio is realized. A 4-section birefringent filter designed with the algorithm is experimentally realized.     

Implementation of broadband low-sidelobe beamforming in time domain

In modern active and passive sonar systems, broadband beamforming for acoustic arrays is widely used to suppress unwanted interference and to detect target signals of interest. A broadband low sidelobe beamforming scheme in time domain is proposed in this paper. The first step of this scheme is to delay the outputs of each element in the acoustic array by a tapped-delay-line (TDL) to accomplish the integer part of the time delay need to form a beam. Then, finite impulse response (FIR) digital filters are used to implement the fractional part of the time delay. The weighting coefficients for all array elements at different frequencies to realize the low sidelobe beams are also implemented with the FIR digital filters. Finally, the outputs of the digital filters are summed up to yield the time domain beam output. The design of low sidelobe beam pattern and that of the FIR digital filters are two crucial technical issues in this beamforming procedure. The low sidelobe beams of each sub-band are designed using the optimized beam synthesis approach based on the principle of MVDR beamforming. An improved adaptive approach are used for the design of FIR digital filters, and the design requirements of these filters were specified by the weights of low sidelobe beams of each sub-band over the broad frequency band. Results of computer simulation for a twelve-element arc array show that the beamforming scheme is very effective in forming low sidelobe broadband beam.     

基于人工蜂群遗传算法的稀疏全聚集成像方法研究

稀疏阵列设计是一种可提高相控阵成像实时性的有效途径。遗传算法能较好解决线性阵列稀疏这种典型的约束优化问题。但此算法的局部搜寻能力较弱,且在后期搜寻效率较差。为此,论文通过构建人工蜂群-遗传算法的阵列稀疏方法,把蜂群寻找最优解的过程引入到传统遗传算法中,增加全局最优解的搜索能力。结果显示,人工蜂群-遗传算法优化后得到的稀疏阵列比遗传算法优化后得到的稀疏阵列具有更高的旁瓣抑制力,阵列的峰值旁瓣水平达到-11.40 dB。而在阈值为-6 dB时,两种算法优化得到的稀疏阵列主瓣宽度都等同于全阵列2.8°的主瓣宽度。最后,论文通过相控阵检测系统在钢轨试样上采集超声信号,利用人工蜂群-遗传算法设计得到的稀疏矩阵进行全聚焦成像。实验结果显示,当阵元数为32的线性阵列在稀疏率达到75%时,稀疏阵列的阵列性能指标分辨率、信噪比与满阵相差不大,但成像效率却提高了53.04%。     

Barker-coded ultrasound color flow imaging: theoretical and practical design considerations

Barker-coded excitation is applied to improve the sensitivity versus resolution tradeoff for ultrasound color flow imaging (CFI). Direct sequence encoding and complex baseband decoding methods that enable flexible combination of demodulation frequency and Barker-chip duration are proposed. Based on a general Wiener decoding filter formulation, three different conditions that pertain to the relationship between the Barker-chip duration and demodulation frequency are found, such that they result in real, complex symmetric and complex asymmetric decoding filter sequences, respectively. It is also shown that the matched filter and the inverse filter represent two extreme cases of the Wiener filter, and the latter is proposed for decoding Barker-coded CFI signals with maximum range sidelobe suppression. Some practical considerations such as coding gain, integrated sidelobe level (ISL) and peak sidelobe level (PSL) for various decoding filter lengths, and the influence of flow rate also are analyzed. Linear array imaging of steady flow in straight tubes is simulated based on a 4-cycle base pulse at 6.25 MHz, a 5-chip Barker code, a 32-tap decoding filter, and standard color flow data processing. The resultant color flow images demonstrate the expected improvements in penetration and axial resolution.     

Analysis of worst-case phase quantization sidelobes in focused beamforming

The effect of phase quantization errors on the sidelobe level in a phased-array beamformer is considered. The theory of random and periodic phase errors is reviewed. Periodic phase errors occur for an unfocused array with uniform element distance and give rise to discrete sidelobes. The main result of the paper is an analysis of the periodic phase error in the case that the beamformer is focused. An estimate for the worst-case discrete sidelobe level as a function of focal depth is derived. The theory is illustrated and verified by simulations.     

Use of modulated excitation signals in medical ultrasound. Part II: Design and performance for medical imaging applications

In the first paper, the superiority of linear FM signals was shown in terms of signal-to-noise ratio and robustness to tissue attenuation. This second paper in the series of three papers on the application of coded excitation signals in medical ultrasound presents design methods of linear FM signals and mismatched filters, in order to meet the higher demands on resolution in ultrasound imaging. It is shown that for the small time-bandwidth (TB) products available in ultrasound, the rectangular spectrum approximation is not valid, which reduces the effectiveness of weighting. Additionally, the distant range sidelobes are associated with the ripples of the spectrum amplitude and, thus, cannot be removed by weighting. Ripple reduction is achieved through amplitude or phase predistortion of the transmitted signals. Mismatched filters are designed to efficiently use the available bandwidth and at the same time to be insensitive to the transducer's impulse response. With these techniques, temporal sidelobes are kept below 60 to 100 dB, image contrast is improved by reducing the energy within the sidelobe region, and axial resolution is preserved. The method is evaluated first for resolution performance and axial sidelobes through simulations with the program Field II. A coded excitation ultrasound imaging system based on a commercial scanner and a 4 MHz probe driven by coded sequences is presented and used for the clinical evaluation of the coded excitation/compression scheme. The clinical images show a significant improvement in penetration depth and contrast, while they preserve both axial and lateral resolution. At the maximum acquisition depth of 15 cm, there is an improvement of more than 10 dB in the signal-to-noise ratio of the images. The paper also presents acquired images, using complementary Golay codes, that show the deleterious effects of attenuation on binary codes when processed with a matched filter, also confirmed by presented simulated images.     

Sidelobeless multiple-object discriminant filters recorded as discrete-type computer-generated holograms

The computer generation of sidelobeless multiple-object discriminant correlation filters has been stressed. We propose to synthesize the filter functions by use of the simulated-annealing algorithm. By this method the filters can be obtained as discrete-type computer-generated holograms. The filters can suppress the sidelobes and provide sharp correlation peaks. A computer simulation and an optical experiment were performed, and the expected correlation responses were obtained.     

Finite impulse response utilizing the principle of superposition

A critical parameter in any finite impulse response (FIR) design is the impulse response length, which must be optimized for the given design specifications in order to reduce the size of the filter. To this end, many design algorithms have been introduced, such as Remez exchange, linear programming, and least mean squares. A new algorithm has been derived that is simple, efficient, and accurate for the design of arbitrary filter specifications and requires fewer computations than many other FIR approaches. This paper provides the definition of the basic functions used for the design process. An overview of the design process is given and the design technique used to design filters with tailored passband and stopband responses to yield a near-optimum time length is presented. This design can be very useful when compensating for the effects of a second transducer or other second order effects in surface acoustic wave (SAW) devices. The effects of monotonically increasing sidelobes on the impulse response length are discussed and illustrated. The addition of arbitrary phase response to the filter design process is discussed. The results of the current FIR approach are discussed and compared with other design techniques.     

时间分辨力约束下目标检测的波形优化设计

以最大化检测概率为优化准则，采用基于凸优化和随机化方法的具有相似性约束的相位编码算法（Phase Coding Algorithm with Similarity Constrain，PCA-SC）来设计发射波形，解决了主动声呐系统增大探测目标发射功率却不能提高检测概率的问题。同时，为有效降低PCA-SC算法所设计编码自相关函数的整体旁瓣级，提高其检测微弱目标的能力，在PCA-SC算法的基础上，结合新循环算法（Cyclic Algorithm-New，CAN）多相编码技术，提出了基于CAN的PCA-SC波形优化方法（Cyclic algorithm-new Phase Coding Algorithm with Similarity Constrain，CAN-PCA-SC）。仿真实验结果表明，PCA-SC和CAN-PCA-SC两种波形优化方法获得的发射信号均能够在满足系统所需时域分辨能力的要求下，实现检测概率的最大化，提高了目标检测性能，将时域分辨能力和检测性能有效地统一起来。相比PCA-SC波形设计方法，CAN-PCA-SC波形设计方法在保证获得的发射信号的检测概率优化效果一致的情况下，具有更低的积累旁瓣水平和更好的检测微弱目标的能力。     

Binary arrays with perfect odd-periodic autocorrelation

Arrays with good autocorrelation functions are required for coded aperture imaging. A generalized folding procedure is derived that permits the construction of arrays with good correlation properties from well correlating sequences for many array sizes. This synthesis method is applied to the construction of approximately square binary arrays with a single zero element and perfect odd-periodic autocorrelation functions. In addition, new binary arrays with constant sidelobes of their periodic autocorrelation functions (uniformly redundant arrays) can be generated with the generalized folding method.     

Scale and translation invariant minimum average correlation energy filter

A new type, to our knowledge, of scale and translation invariant correlation filter is described. Its form in polar coordinates generalizes the forms of the one-decomposition-term filters. That is combined with the minimum-average-correlation-energy optimization method to suppress the sidelobes and achieve correlation peaks. A theoretical analysis as well as a detailed explanation of the computational procedure is provided. The concept is tested on five interferometric images of 256 gray levels without preprocessing. The computed filter gives correlation peaks for reference image scales in the range of 0.3/4.0 (minimal scale: maximal scale = 1:13). The discrimination ability of the filter is investigated-no false peak occurred. The filter works in the background so that there is no need for input image segmentation. A method for extension is described to calculate a filter for more than one reference image.     

Design theories and performance limits of diffractive superresolution elements with the highest sidelobe suppressed

For the application of optical data storage, theories that we present can be used to design a diffractive super-resolution element (DSE) with the highest sidelobe suppressed. A globally optimal solution among general hybrid-type filters can be solved through linear programming. The obtained globally optimal performances set the exact performance limits of a general hybrid-type DSE with the highest sidelobe suppressed. A comparison of our design theories and the previous design methods shows the advantages of the former.     

Range sidelobes blanking by comparing outputs of contrasting mismatched filters

Range sidelobes, a major shortcoming of radar pulse compression, are often reduced through the use of mismatched filters. The authors propose to blank the remaining sidelobes by using two or more mismatched filters, whose sidelobes are designed to peak at different delays. The authors show how to design such filters and present promising simulation results with two or more mismatched filters.     

The estimation of the power spectrum of a signal

An algorithm is considered which enables the power spectrum to be estimated for a discrete sample of N values of the signal in a time interval of [−T/2, +T/2] using a filter which has the narrow spectral band as a rectangular time window, but with a sidelobe level of less than 4.3 dB. Examples of several “power” filters are presented. Translated from Izmeritel'naya No. 9, pp. 65–66, September, 2008.     

Real-time defect detection of steel wire rods using wavelet filters optimized by univariate dynamic encoding algorithm for searches

We propose a new defect detection algorithm for scale-covered steel wire rods. The algorithm incorporates an adaptive wavelet filter that is designed on the basis of lattice parameterization of orthogonal wavelet bases. This approach offers the opportunity to design orthogonal wavelet filters via optimization methods. To improve the performance and the flexibility of wavelet design, we propose the use of the undecimated discrete wavelet transform, and separate design of column and row wavelet filters but with a common cost function. The coefficients of the wavelet filters are optimized by the so-called univariate dynamic encoding algorithm for searches (uDEAS), which searches the minimum value of a cost function designed to maximize the energy difference between defects and background noise. Moreover, for improved detection accuracy, we propose an enhanced double-threshold method. Experimental results for steel wire rod surface images obtained from actual steel production lines show that the proposed algorithm is effective.