DBF of Multiple Simultaneous Beams for Improved Target Search and Angle Estimation Performance of Radar System

YU Kai-bor

(Shanghai Key Laboratory of Intelligent Sensing and Recognition,Shanghai Jiao Tong University， Shanghai 200240, China)

·DBF在现代雷达中的应用·

DBF of Multiple Simultaneous Beams for Improved Target Search and Angle Estimation Performance of Radar System

YU Kai-bor

(Shanghai Key Laboratory of Intelligent Sensing and Recognition,Shanghai Jiao Tong University， Shanghai 200240, China)

This paper describes techniques for improving radar target search and angle estimation performance over the coventional monopulse processing in the elimination of beam-shape loss. Specifically, we have developed a scheme that uses multiple sets of monopulse beams. We also show how monopulse processing scheme and the maximum-likelihood scheme can be combined to balance the performance and processing requirement. These techniques make use of digital beamforming of multiple simultaneous received beams and processing using multiple algorithms. Simulation results are included to show the improvement in target search and angle estimation and the elimination of beam-shape loss.

digital beamforming; multiple simultaneous beams; monopulse; maximum-likelihood; target detection; angle estimation

0 Introduction

Conventional monopulse processing (Scheme 1) involves one beam in transmit and multiple simultaneous beams on receive. Typically a sum beam without any tapering is employed in the transmit array for full power operation. A uniform weighting will have transmit antenna pattern narrowest beamwidth but higher sidelobes. Beam-spoiling can also be applied to broaden the transmit antenna beamwidth[1]. On receive two or more beams are formed for target detection and angle estimation, i.e. the sum beam, the delta-azimuth and the delta-elevation beam. The sum beam is used for surveillance search and target detection. Once a target is detected, the ratio of delta-azimuth beam over the sum beam is used for azimuth angle estimation, and the ratio of delta-elevation beam over the sum beam is used for elevation angle estimation. This approach for angle estimation is computationally efficient as it requires only the computation of the monopulse ratios and a table look-up for the angles. Received beams are typically tapered for sidelobe control leading to wider received beamwidth. Taylor weighting is used for the sum beam and Bayliss weighting is used for the difference beams. A target at the peak of the beam has the highest signal-to-noise ratio (SNR) compared to the rest of the beam. Thus a target away from the center of beam suffers from beam-shape loss resulting to lower SNR and degradation in target detection and angle estimation performance. The beam-shape loss and degradation in target detection and angle estimation performance can be recovered if multiple simultaneously received beams are employed. A full digital array (i.e. an array digitized at element-level) supports different processing architectures with different processing performance and computational complexities. Furthermore, these processing schemes can be combined to balance the performance and the computational burden.

In Section 1, we discuss the processing architectures and algorithms using multiple simultaneously received beams. First, we review the processing architecture of the maximum-likelihood (ML) method[2-4]. This approach has been advocated for improved radar target search and track for its merits in the elimination of the beam-shape loss. Second, we discuss a new processing algorithm that uses multiple sets of monopulse beams. Third, we show how the monopulse processing scheme and the ML processing scheme can be combined to balance the performance and processing requirement. In section 2, some simulations are included to illustrate the performance of the processing schemes. Section 3 is the summary.

1 Algorithms Using Multiple Simultaneously Received Beams

The conventional monopulse scheme for radar detection and angle estimation (Scheme 1) is illustrated in Fig.1. In this section, we look into using multiple simultaneously received beams to reduce the beam-shape loss. Modern radar technology employs digital beamforming (DBF) at the sub-array level or at the element level. The digital degrees-of-freedom (DOFs) available provide flexibilities and capabilities compared to analog beamforming. These capabilities include improved dynamic range, improved interference suppression and clutter performance and forming of multiple simultaneously received beams. In this paper, we consider the benefits in the elimination of beam-shape loss and the extension of the coverage performance using multiple simultaneously received beams.

Fig.1 Conventional monopulse scheme for radar detection andangle estimation (Scheme 1)

Radar flexibilities and capabilities increase with the level of digitization. Element level digitization supports forming of arbitrary number of beams and types of beams where some approximations are required if we have only sub-array digitization. For example, it is not possible to form Taylor and Bayliss beams simultaneously from digital sub-array outputs unless multiple radio frequency (RF) sub-arrays are employed. The elements within the sub-arrays are typically tapered for the Taylor beam and a direct sum of the sub-array outputs will generate the desired Taylor sum beam. An approximation on the Bayliss difference beam can be generated by using an average Bayliss-on-Taylor taper for each sub-array. A similar kind of approximation is also required for forming a cluster of squinted sum beams from digital sub-arrays.

Another consideration in the algorithm development is the processing complexity. The computational burden can be attributed to the forming of multiple simultaneous beams and the pulse compression and Doppler processing associated with each beam. Also, there is substantial computational cost associated with the angle search of the maximum-likelihood beam-space processing (MLBP) scheme. The ML approach to angle estimation requires a two-dimensional iterative or grid search over the entire beam.

Here we review the MLBP scheme (Scheme 2) as applied to the digital array radar system where digital inputs can be element-based or sub-array-based (Fig. 2).

Fig.2 MLE of multiple sum beams(Scheme 2)

These inputs are firstly digital beamformed to generate a number of beams. The cluster of sum beams includes a center beam surrounded by 4 squinted sum beams located on the 3 dB contour or the 6 dB contour on a 2×2-shape or diamond-shape configuration (Fig.3).

Fig.3 Cluster of 5 sum beams with center beam surrounded by 4 beams on a diamond-shame configuration (top)or squinted on a 2×2 grid (bottom)

The digital beamforming can be expressed as following

(1)

(2)

whereg(u,v),R,rare the beam patterns, covariance matrix of the noise data and the output beam data respectively. The maximum can be determined using iterative search or grid search. This method is computational intensive. It also requires memory storage for the set of antenna beam patterns. Onceuandvare searched to sufficient accuracy, the corresponding target magnitude can be used for target detection. The target amplitude estimate is given by the following

(3)

The ML approach in fact eliminates the beam-shape loss by pointing the beam at the desired angular direction. However, it requires a search for all angles at every range cell, thus its computation is very intensive. Some modifications are required for its use in practical radar search application. A detection before angle estimate approach can be developed similar to monopulse scheme where ML processing is invoked only after target detection using the center sum beam. The modified scheme using the center beam for detection followed by MLE angle estimation (Scheme 2A) achieves the benefits of the elimination of beam-shape loss in angle estimation but still suffers the beam-shape loss for the detection, as shown in Fig.4. Another modification can be derived to use all the sum beams for detection, and the ML processing can be invoked once a target is detected by one or more beams, as shown in Fig.5 (Scheme 2B). This approach eliminates the beam-shape loss and the requirement to search for the target angle for every range cell; it still requires an extensive angle search once a target is detected.

Fig.4 MLE with multiple sum beams, modified with detectionfirst with center sum beam (Scheme 2A)

Fig.5 MLE using multiple sum beams modified with detectionfirst using all sum beams (Scheme 2B)

Multiple simultaneous beams can be generated by using multiple sets of weighting coefficients. Suppose B0 is the transmit beam center. On receive 4 sets of monopulse beams are generated to provide target search and angle estimation processing. The squinted beams B1, B2, B3 and B4 are located at a distance of a 3 dB or 6 dB beamwidth away from B0 and can be in the configuration of 2×2-shaped or diamond-shape.

The deterministic beamforming for simultaneous beams followed by target detection and angle estimation (Scheme 3) is given by Fig. 6 and is described in the following steps:

Fig.6 Monopulse prcessing using 4 sets of monopulse beams(Scheme 3)

Step 1: The sub-array or element data are combined digitally to generate 4 sets of monopulse beams (Fig.7) given by

(4)

Fig.7 4 sets of monopulse beams

The weighting coefficients of the squinted beams can be constructed from those of the center beam by steering

(5)

(6)

Using these weights, the antenna patterns are given by

(7)

Step 2: Detection processing is accomplished by selecting the maximum of the magnitudes of all the sum beams and compared to a threshold, i.e.

(8)

wherei*beam gives the maximum detection performance. The sum beam and the delta beam measurements are then used for the monopulsei*angle estimation.

Step 3: The ratio of the corresponding delta-azimuth beam over theith sum beam is used to determine the azimuth angle and the ratio of the corresponding delta-elevation beam over theith sum beam is used to determine the elevation angle using look-up tables

(9)

Step 4: The directional-cosines are derived with respect to thei-th beam. These coefficients can be transformed back to the center beam reference

(10)

Employment of multiple simultaneous beams eliminates the beam-shape loss of conventional monopulse in target detection and angle estimation, thus enables search performance over larger area. This scheme eliminates the beam-shape loss and extends the coverage performance like the MLE approach at the expense of the computational cost as it is required to carry the computational load of forming 12 beams and the associated pulse compression and Doppler processing.

One of the benefits of DBF is that it supports multiple processing schemes simultaneously. Furthermore these schemes can be combined to balance the computational complexity and performance. We here describe a scheme on combining the monopulse and the MLE schemes. The rational is that monopulse processing is computational most efficient and performs very well when the target is within the beam. The MLE scheme has optimal performance in the elimination of beam-shape loss and in the extension of the coverage at the cost of computational burden in the angle search. Multiple sets of monopulse beams eliminate beam-shape loss and extend coverage at the expense of computational requirement of beamforming of 12 channels and carry out the associated pulse compression and Doppler processing. Thus we combine the monopulse processing and MLE processing by constructing a scheme with 1 set of monopulse beams in the center and 4 additional sum beams at the 3 dB or 6 dB away from the center beam center as in the MLBP scheme. The 5 sum beams are used for detection as in Scheme 2B. Once a target is detected, we determine which sum beam generates the detection. If the detection is attributed to the center sum beam, we know the target is within the center beam, and monopulse processing is used for the target detection, otherwise, the target is on the edge or outside of the center beam, thus MLE processing using the 5 sum beams is invoked. In this approach (Scheme 4), the beam-shape loss is eliminated and the coverage is extended and monopulse processing is utilized when the target is within the beam. This scheme is illustrated in Fig. 8.

Fig.8 Combined monopulse and MLE processing (Scheme 4)

2 Simulation Results

In this section, we assess the beam-shape loss and the angle estimation performance of the discussed schemes using simulation. We consider a circular array with digital beamforming at the element level with half-wavelength spacing. For each processing scheme, the antenna gain performance and the angle estimation are generated by moving the target source over the 3 dB and 6 dB received beamwidth on a grid spacing of 2 msine along both theuaxis and thevaxis. The transmit beam is assumed to be spoiled uniformly over the entire 6 dB beamwidth and thus the effect is included in theSNRfor the performance evaluation. The antenna gain and the angle estimation performance are evaluated at each grid point and are averaged over the 3 dB and 6 dB beamwidth. For the angle estimation performance, theSNRis set to be 18 dB when the target is at the peak of the beam. A Monte-Carlo simulation of 100 times is used to determine the angle performance for each grid point. The beam-shape loss and the angle estimation performance are summarized in Table 1 and Table 2 respectively. The values averaged over 3 dB beamwidth serve as the basic performance parameters and the values averaged over the 6 dB beamwidth are used to evaluate the coverage performance extension. The performance of the monopulse processing is used as the benchmark for comparison. The beam-shape loss for monopulse processing is 1.1 dB and 2.6 dB over the 3 dB beamwidth and 6 dB beamwidth respectively (Fig.9) . TheRMSEfor angle estimation is 2.87 msine and 4.03 msine for the 3 dB beamwidth and 6 dB beamwidth respectively (Fig.10). The results show that the beam-shape loss can be recovered by ML processing or by employment of multiple simultaneously received beams. The beam-shape loss using 4 sets of monopulse beams (Scheme 3) is 0.7 dB over both the 3 dB and the 6 dB beamwidth (Fig.11), and the beam-shape loss using 5 sum beams (Scheme 2B) is 0.4 dB over both the 3 dB and 6 dB beamwidth (Fig.12). Angle estimation performance for scheme 2 is given by Fig.13. For angle estimation, Scheme 3 with multiple sets of monopulse beams has the best performance results (Fig.14) where Scheme 4 approaches the performance of the monopulse scheme within the 3 dB beamwidth and the performance of MLE scheme within the 6 dB beamwidth (Fig.15). The processing and computational costs of the schemes are summarized in Table 3.

Table 1 Summary of beam-shape loss performance dB

SchemeBeam-shapelossaverageover3dBbeamwidthBeam-shapelossaverageover6dBbeamwidthMonopulseprocessing(Scheme1)1.12.6MLBP(Scheme2)00MLBPwithcenterbeamfordetection(Scheme2A)1.12.6MLBPwithallbeamsfordetection(Scheme2B)0.40.4Multiplesetsofmonopulsebeams(Scheme3)0.70.7Combinedmonopulse&MLE(Scheme4)0.40.4

Table 2 Summary of RMSE angle estimation performance msine

SchemeTotalRMSEaverageover3dBbeamwidthTotalRMSEaverageover6dBbeamwidthMonopulseprocessing(Scheme1)2.874.03MLBP(Scheme2)3.153.45Multiplesetsofmonopulsebeams(Scheme3)2.602.62Combinedmonopulse&MLE(Scheme4)2.963.37

Fig.9 Sum beam gain average over the 3 dBcontour and 6 dB contour

Fig.10 Monopulse angle estimation error performance (Scheme 1)

Fig.11 Sum beam gain by combining all 4 sum beams(Scheme 3)

Fig.12 Sum beam combining all 5 beams (Scheme 2B)

Fig.13 Angle estimation error by using MLE on 5 beams(Scheme 2)

Fig.14 Monopulse angle error using all 4 sets of beams(Scheme 3)

Fig.15 Angle error by combining monopulse and MLE(Scheme 4)

Table 3 Summary of processing and computational cost

Scheme#ofBeamsAngleestimatecomputationalcostMonopulseprocessing(Scheme1)3beamsLeastMLBP(Scheme2)5beamsMostMultiplesetsofmonopulsebeams(Scheme3)12beamsLeastCombinedmonopulse&MLE(Scheme4)7beamsModerate

3 Summary

Conventional monopulse processing suffers beam-shape loss in target detection and angle estimation. MLBP eliminates beam-shape loss at the expense of computational cost. The computational burden is on the implementation of the 2-dimensional angle search. DBF of multiple sets of monopulse beams eliminates beam-shape loss and extends detection and angle estimation coverage at the expense of computational cost. The computational burden is due to the digital beamforming of 12 beams and the associated pulse compression and Doppler processing. DBF provides flexibility in the processing schemes and these schemes can be combined to improve the performance and computational complexity. A scheme is developed where monopulse processing is employed if target is in the center beam and a 5 beam MLE is employed if the target is on the edge of the center beam or in the outer beams. In this manner, computational complexity is controlled, beam-shape loss is eliminated and the coverage performance is extended.

[1] KERCE J C, BROWN G C, MITCHELL M A. Phase-only transmit beam broadening for improved radar search performance[C]// Proceedings of 2007 IEEE Radar Conference. Boston, MA: IEEE Press, 2007: 451-456.

[2] DAVIES R M, FANTE R L. A maximum-likelihood beamspace processor for improved search and track[J]. IEEE Transactions of Antennas and Propagation, 2001, 49(7): 1043-1053.

[3] LIU Y, WONG C G, KENNEDY W. Computationally efficient angle estimation using maximum likelihood in a digital beam-forming radar[C]// Proceedings of 2007 IEEE Radar Conference. Boston, MA: IEEE Press, 2007: 337-342.

[4] BARANOSKI E, WARD J. Source localization using adaptive subspace beamformer outputs[C]// 1997 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP-97).[S.l.]: IEEE Press, 1997: 3773-3776.

专家介绍

余啟波 余啟波博士1977年毕业于耶鲁大学，获电子工程与应用数学学士学位；1979年毕业于布朗大学，获电子工程硕士学位； 1982年毕业于普渡大学，获电子工程专业博士学位。博士毕业后，在弗吉尼亚理工学院执教6年；在随后的二十五年中，先后在通用电气公司、雷声、洛克希德马丁和波音公司等著名企业里担任高级系统工程师职位。2015年，余博士以特聘教授身份受聘于上海交通大学。

余博士的主要研究领域包括：相控阵雷达系统设计、雷达系统建模与仿真技术、雷达信号处理、雷达电子战技术等。余博士在美国雷达工业界和国际学术界均享有盛名，他是早期雷达数字波束形成技术的主要倡导者之一，曾经参与了多部相控阵雷达系统的设计，目前是IEEE高级会员，拥有30多项美国发明专利，发表过60多篇学术论文，并且合作撰写过两部专著。曾于2012年～2015年担任IEEE宇航电子系统协会加利福尼亚分部的主席，多次担任IEEE雷达会议、SPIE高级信号处理等会议的技术程序委员会成员。

国家自然科学基金资助项目(61571294)；航空科学基金资助项目(2015ZD07006)

余啟波 Email：kbyu77@yahoo.com

2016-09-18

2016-11-20

TN957.51

A

1004-7859(2016)12-0009-07

同时数字多波束对改善相控阵雷达搜索和测角精度的分析

余啟波

(上海交通大学 上海市智能探测与识别重点实验室， 上海 200240)

文中基于数字波束合成体制的相控阵雷达，研究改善传统单脉冲体制雷达性能的方法。提出了一种基于一组同时数字多波束处理的新方法。文中证明该方法可以将单脉冲测角方法和极大似然估计测角算法进行性能的平衡。该方法利用了基于同时数字多波束形成技术以及多种处理算法。计算机仿真试验证明该方法可以在提升雷达目标检测和测角性能的同时有效的改善波束形状损失。

数字波束形成；同时多波束；单脉冲；极大似然估计；目标检测；角度估计

10.16592/ j.cnki.1004-7859.2016.12.002