Applied Mechanics and Materials Online: 3-8-8 ISSN: 66-748, Vols. 347-35, pp -5 doi:.48/www.scientific.net/amm.347-35. 3 Trans Tech Publications, Switzerland Study on Imaging Algorithm for Stepped-frequency Chirp Train waveform Wang Liang, Shang Chaoxuan, He Qiang, Han Zhuangzhi, Ren Hongwei Department of Electronics and Optics Engineering, Ordnance Engineering College, Keywords: Stepped-frequency; Chirp; Imaging Shijiazhuang, 53, China email: kevin9@63.com Abstract. A range profile synthetic algorithm of the stepped-frequency chirp train waveform is designed to obtain HRRP (High Resolution Range Profile) in this paper. Based on waveform model, grating lobes restraining method is proposed with the help of autocorrelation function. Due to the matched filter operation, image energy spill over the close range bins, which causes ghost images. Set parameters of inner pulse bandwidth, stepped frequency and chirp compression envelop sampling frequency properly, and then carry the synthetic algorithm, the ghost images are restrained. All of the results are validated by simulation. Introduction For purposes of radar, it is desirable to emit waveforms with wide bandwidth in order to enhance range resolution. Such waveforms are not practical for some reasons, e.g., hardware limitations. Stepped-frequency waveform is used by modern radars to get HRRP with narrow instant bandwidth, it can get extremely wide overall bandwidth without usage of expensive hardware supporting wide instantaneous bandwidth. Chirp signal is used as sub-pulse to get higher transmitting power without losing range resolution at the same time. Stepped-frequency chirp waveform has better ambiguity function [] than stepped-frequency waveform when T f> because of the grating lobes effect, this issue is discussed in [, 3], and an approach is proposed to suppress grating lobes below a desired threshold level. Stepped-frequency chirp waveform is used in many kinds of radar system [4-6], a subaperture processing method is proposed in [7] for stepped-frequency chirp waveform compression,suitable for both linearly stepped and nonlinearly stepped case. Pulse compression makes energy spill-over and ghost images appear [8]. Based on the model of stepped-frequency chirp waveform, this paper proposes a range profile synthetic algorithm, with proper parameters setting, grating lobes and ghost image are got rid. Waveform model analysis f B f N f f T r T t Fig.. Time-frequency serials of transmitting waveform Time-frequency sequence of stepped-frequency chirp train transmitting waveform is shown in Figure, and its time domain model is expressed as: N Si( t) = u c( t itr)exp[ j πci ft]exp[ j π ft] () N All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 3.3.36.75, Pennsylvania State University, University Park, USA-9/4/6,7:9:9)
Instruments, Measurement, Electronics and Information Engineering where u ( t) = rect( )exp[ jπkt ] is a chirp pulse, k=b /T is the chirp rate, B is the bandwidth, c T t T T is the pulse duration, T r is the pulse repetition interval (PRI), C i f is the i-th hopping frequency, f is the fundamental frequency, and N is the transmitting pulse number. Based on the transmitting model, echo can be expressed as N t itr τ( t) Sr( t) = ρirect[ ] exp[ jπk( t itr τ( t)) + j πi f( t τ( t))+ j π f( t τ( t))] () T where ρ i is the amplitude of the i-th pulse, τ ( t) = ( R vt)/ c is the echo delay, where R is the range from radar to target, v is the target velocity, c is the light velocity. The basic waveform is N t-itr S( t) = rect( )exp( j πi ft)exp( j π ft) (3) T Echo is mixed with the fundamental waveform and got the video frequency signal: N t itr τ( t) Sh( t) = Airect[ ] exp[ jπk( t itr τ( t)) ]exp[ j πi fτ( t)] exp[ j π fτ( t)] (4) T When v=, τ(t)=τ=r/c, the video frequency signal is composed by two parts: the first is a chirp t itr τ signal rect[ ] exp[ jπk( t it τ) ] in [it r +τ-t /, it r +τ+t /], and the second one is the phase T r changes caused by frequency hopping, exp[-jπc n fτ] exp[-jπf τ]. So the signal will be processed by two steps: take chirp compression first, sample the compression result, and then carry IDFT. The compression result of chirp signal u c( t) is sin( πktt ) kt exp( jπkt ) exp( jπ /4) (5) πktt When v=, the compression of formula (4) is N t itr τ sin[ πkt( t itr τ)] Sc( t) = Ai kt rect[ ] T πkt ( t it τ) (6) exp[ jπk( t itr τ) ]exp( jπ/4) exp( j πi f τ) exp( j π f τ) Sample data at t=it r +τ,and the digital signal can be expressed as S () i = A kt exp( jπ/4) exp( j πi f τ) exp( j π f τ),, N- (7) c i Normalize the sampled data and carry IDFT, we get sin[ π( l N f R/ c)] y( l) = Nsin[ π( l/ N f R/ c)] The output of IDFT is a discrete sinc function and the range resolution is /N f. Imaging algorithm For stepped-frequency chirp waveform Parameters are set as: f =35 GHz, T = µs, T r =µs, N=36 in the following. Parameters such as f, B and sampling frequency f s are different in the actual discussion. A. Image grating lobes generation and restraining method To stepped-frequency pulse radar waveform, the ambiguity range should be farther than or equal to the range resolution of a single pulse, i.e. T f, and this is the tight constraint condition between T and f which can be applied in stepped-frequency chirp waveform also. When frequency hopping points N is determined, it needs to increase stepped frequency f to increase the total bandwidth of the waveform. The larger bandwidth is, the better the precision will be. Also, for farther detection, the time duration, T, needs to get wider to improve the transmitting energy. If T f >, there will be grating lobes make the range detection ambiguity. Set stepped frequency f = r (8)
Applied Mechanics and Materials Vols. 347-35 3 3 MHz, chirp bandwidth B = 3 MHz to detect target which is at 3 m, and we get Figure (a). From Figure (a), we can see that there are five other peaks except the real target peak at 3 m, and the five peaks make the ambiguity appear..8.6.4..8.6.4. 5 3 35 4 45 5 5 3 35 4 45 5 55 (a) Grating lobes restraining effect (b) Range ambiguity caused by grating lobes Fig.. Grating lobes and restraining effect Zero-Doppler cut of ambiguity function which is called autocorrelation also is used to analyze the grating lobes, when τ T, the autocorrelation function stepped-frequency waveform is τ τ sin( Nπτ f) R( τ) = sinc Bτ, τ T T T N f It has two parts, the first part is determined by chirp pulse sin( πτ ) τ τ R( τ) = sinc Bτ, τ T () T T And the second part determined by stepped frequencies has a relationship with the grating lobes sin( Nπτ f) R( τ) =, τ T () Nsin( πτ f) We get the peaks position of R ( ) τ following its expression g τlobes =, g =, ±, ±,, T f, τ < T () f Where x is the nearest integer less than or equal to x. When the production of waveform pulse width and stepped frequency is larger than, choosing appropriate value of T, f and B, make sure the value of R( τ ) are zeros when there are peaks in R( τ ), and the grating lobes will be removed. According to the formula, set f = 3 MHz, the chirp bandwidth will be B =4.5 MHz. Based on these parameters, the target profile at 3 m is shown in Figure (b), Compared with Figure (a), the range ambiguity peaks do not exist at all. B. Range profile synthetic algorithm M data arranged as [S n, S n, S nm ] are sampled at the n-th frequency, M range bins are composed based on the sampling data. After a transmitting cycle is accomplished, all the sampled data need to be reordered according to the frequency train. The refined range profile of the m-th range bin is got from the IDFT output of the N data [S m, S m, S Nm ] sampled at the same frequency point m. The detail signal processing is shown in Figure 3(a). Sampled points inner pulse duration f S S S 3 S M (9) f S S S 3 S M f S 3 S 3 S 33 S 3M n i-th range cell c/ f f N- S N S N S N3 S NM c/f s IDFT IDFT n i +-th range cell Range profile synthetic (a) Range profile synthetic algorithm (b) Signal processing algorithm Fig.3. Signal processing algorithm
4 Instruments, Measurement, Electronics and Information Engineering Due to parameters setting and other reasons, the refined range profiles are redundant, and the range profiles need to synthetic to get the exact range information. To a chirp signal whose bandwidth is B, the range resolution is c/b after compression, the minimum envelope sampling rate is /B, so f B (3) s The IDFT output resolution at some range bin is c/n f, and the range scope corresponding to the IDFT output is [(N-)c/ f]+ac/ f, where a is an integer, and a> means the range is larger than c/ f, and it is undersampling in this case. The range bin between two points is c/f s, and the refined range profile needs to cover a range bin, so it requires that f B f (4) s If f s > f, redundant is generated in every refined range scope, the usable profile part is determined by the sampling point. Some profile shown in Figure 3(b) need to be shifted because of undersampling influence, and the final result is got after the range profile synthetic algorithm. Ghost Images generation and restraining method The sampled data do not imply the real RCS information as the compression output is sinc function and it is impossible to sample the peak position of the envelope rightly every time. If there are some scattering targets in a range bin at the same time, the sampling output are not weighted linearly by every scattering point, but the summation after a non-uniform weighted by sinc function. Modulated by sinc function, each range bin have only one scattering point obtaining the maximum SNR (Signal to Noise Ratio) output mostly, and the other ones will be attenuated in some certain degree. Attenuation caused by sampling point is related to the range between sampling points and targets actual location. The more the attenuation is, the more energy will spill over the nearby range bins, causing ghost images there. Set simulation parameters as stepped frequency f = MHz, pulse modulation bandwidth B = MHz, sampling frequency fs= MHz, the range profile of two targets at 8 m and 3 m whose RCS are the same is shown in Figure 4. In Figure 4(a), the round point denotes the sampling position during the pulse compression, and the asterisk point is the targets real position. There is only one point that is sampled, and the RCS information reflected in the Figure 4(b) is no longer uniform due to non-uniform weighting by sinc function, also the leaking energy causes ghost images at 49 m and 47 m there..8.6.4. Compression sampling points 5 3 35 4 45 5 (a).8.6.4. Range profile synthetic result X: 49. Y:.4 X: 47.8 Y:.959 5 3 35 4 45 5 55 (b) Fig.4. Ghost images when f = MHz, B = MHz If the modulation bandwidth B is improved, the compression resolution will get better, and targets energy spill-over the nearby bins will decrease. In order to sample the amplitude information before sinc function decays 4dB, the sampling frequency needs to be /B at least..8.6.4. Compression sampling points 5 3 35 4 45 5 (a).8.6.4. Range profile synthetic result X: 49. Y:.3 X: 47.8 Y:.366 5 3 35 4 45 5 55 (b) Fig.5. Ghost images when f = MHz, B = 4 MHz
Applied Mechanics and Materials Vols. 347-35 5 Set simulation parameters as f = MHz, B = 4 MHz, based on B, make fs=4 MHz. The compression sampling points and range image are shown in Figure 5. There are three points sampled to synthetic the range profile, there are also ghost images in Figure 5(b), although it decreases lower compared with Figure 4(b). The stepped frequency bandwidth needs to be improved if the refined range profile resolution is wanted to be improved, also the sampling frequency needs to be improved to make the range bin smaller. According to section Ⅱ, the simulation parameters are set as f = 3 MHz, B =4.5 MHz, fs=9 MHz. Figure 6 shows the compression sampling points and final range profile result. There are eleven sampling points, and after the range profile synthetic algorithm, the ghost images are vanished. Conclusion.8.6.4. Compression sampling points 5 3 35 4 45 5 (a).8.6.4. Range profile synthetic result 5 3 35 4 45 5 55 (b) Fig.6. Ghost images when f = 3 MHz, B = 4.5 MHz Stepped-frequency chirp train waveform is a new kind waveform, it can be used in many place. In this paper, a range profile synthetic algorithm is proposed based on the signal model, the parameters setting issues are discussed with the help of autocorrelation function, and the non-uniform weighting effect is analyzed, the ghost images problem is solved using the range profile synthetic algorithm with suitable parameters. Reference [] N. Levanon and E. Mozesona, Eds., Radar Signals. New Jersey: John Wiley & Sons, Inc., 4, pp. 6-58. [] I. Gladkova, "Analysis of Stepped-Frequency Pulse Train Design," in IEEE Transactions on Aerospace and Electronic Systems City College of New York, 9, pp. 5-6. [3] I. G. D. Chebanov, "Grating lobes suppression in stepped-frequency pulse train " IEEE Transactions on Aerospace and Electronic Systems vol. 44, pp. 65-75, 8. [4] Z. Huan-ying, Z. Shou-hong and L. Qiang, "A Method of ISAR Imaging via Stepped Frequency Modulated Radar," Acta Electronica Sinica, vol. 35, pp. 39-334, 7. [5] R. T. Lord and M. R. Inggs, "High resolution SAR processing using stepped-frequencies," in 997 IEEE International Geoscience and Remote Sensing Symposium, 997, pp. 49-49. [6] P. Gonzalez-Blanco, E. d. Diego, E. Millan, et al., "Stepped-Frequency Waveform radar demonstrator and its jamming " in 9 International Waveform Diversity and Design Conference 9, pp. 9-93. [7] Z. Yunhua, L. Haibin and W. Jie, "Subaperture processing method for stepped-frequency Chirp signal," Systems Engineering and Electronics, vol. 8, pp. -6,48, 6. [8] R. T. Lord and M. R. Inggs, "High resolution VHF SAR processing using synthetic range profiling," in International Geoscience and Remote Sensing Symposium, 996, pp. 454-456.
Instruments, Measurement, Electronics and Information Engineering.48/www.scientific.net/AMM.347-35 Study on Imaging Algorithm for Stepped-Frequency Chirp Train Waveform.48/www.scientific.net/AMM.347-35.