Ultra-wideband radar using Fourier synthesized waveforms

Ultra-Wideband Radar Using Fourier Synthesized WaveformsGurnam Singh GillAbstract—Traditional methods of ultra-wideband(UWB)radar signal generation suffer from several disadvantages such as low antenna radiation efficiency and lack of accurate control of signal parameters like pulse shape,pulse repetition interval(PRI),and its spectrum.UWB signals can be generated by expanding the desired radar waveform in Fourier series and then synthesizing the waveform by generating the individual terms in the expansion from harmonically related oscillators.Signals thus produced overcome the disadvantages of traditional methods of UWB signal generation.In this paper,Fourier series based method for generation of complex amplitude coded waveforms is developed which can be used to generate time domain equivalent of Barker and other codes for application in radar and communication areas.In radar applications,these coded waveforms,with accurate and stable waveform parameters,shall allow pulse compression and coherent integration.The additional processing gain provided by these operations reduces the need for high peak power in radar transmitters which is one of the bottlenecks in the implementation of operational UWB radars.This paper also describes a UWB radar concept which in-corporates Fourier synthesized waveforms.Related digital signal processing issues are also discussed.I.I NTRODUCTIONO VER THE last several years there has been wide interest in large relative bandwidth signals[1]–[3].Relative bandwidth is defined as the ratio of absolute bandwidth of the signal to its center frequency.Various terms such as impulse, monocycle,baseband,nonsinusoidal,and carrier free have been used for these large relative bandwidth signals.The name “impulse”is derived from the Dirac delta function.Many sources do produce high voltage impulse,but the radiated signal looks less like an impulse because of the suppression of dc and low frequency components of the impulse by the antenna.The name monocycle implies transmission of a single cycle of sinusoid which has large relative bandwidth [4].The terms baseband and carrier-free refer to the fact that these signals do not have a carrier frequency associated with tely,all these terms have been put under the umbrella of ultra-wideband(UWB)signals.Signals are said to be UWB if their relative bandwidth is0.25or larger [3].Although all signals with wide relative bandwidths are classified as UWB,there are subtle but important differences among them depending upon their method of generation. Waveforms described in this paper are closer to baseband Manuscript received August5,1996;revised December6,1996.This work was funded by the Office of Naval Research.The author is with the Department of Electrical and Computer Engineering, Naval Postgraduate School,Monterey,CA93943-5121USA.Publisher Item Identifier S0018-9375(97)03699-5.and nonsinusoidal than to monocycle and are generated by summing the harmonics of the signal to be synthesized. Most of the significant advantages of UWB radar signals reported in the literature stem from their two characteristics, i.e.,low frequency components in the signal and their narrow pulse width.The low frequency components penetrate ground and foliage more easily and thus can be used for detection of targets hidden in foliage or underground.Low frequency components may also excite target resonances which may lead to detection of stealthy targets.Very narrow pulse widths givefine range resolution and intercept less clutter.The latter is a big advantage as in most situations the target detec-tion is limited by clutter.Fine range resolution will produce detailed target range profiles which can be used for target identification.It should be noted that conventional narrow band signals can achieve the same large absolute bandwidths at higher frequencies,for example,in the millimeter wave region,but they do not have the same propagation and target scattering characteristics as do the UWB signals of comparable bandwidth.Most of the UWB sources reported in the literature are impulse types which are implemented by Marx bank or similar techniques.The concept behind impulse generation is the storage of energy over a long period of time followed by its sudden release.If the release time is of the order of a nanosecond or less,the resulting signal will be UWB impulse. At the present time,the typical method of storing energy is capacitive,such as the Marx bank,and the release of energy is accomplished by switches such as spark gap,diode, laser actuated semiconductor,etc.The problem with these techniques are that a significant amount of energy of the waveform lies around zero frequency which cannot be radiated by antenna.Pulse shape and pulse repetition interval(PRI) cannot be precisely controlled.There is nofine control of spectrum to avoid interference with friendly receivers.The Fourier method of waveform generation overcomes these disadvantages of conventional impulse generation.This method can synthesize any periodic waveform(such as train of baseband pulses of approximately rectangular shape)by expanding the desired waveform by Fourier series,then gen-erating and transmitting the sinusoidal components obtained from Fourier series expansion.Thus,the signal is generated in the frequency domain by summing the relatively low power harmonics of the desired signal instead of generating it by a single high power source in the time domain[5], [6].The resulting signal,unlike traditional UWB signals, is truly baseband and free of carrier and it overcomes the0018–9375/97$10.00©1997IEEEdisadvantages of the former.Since the signal is produced by summation of sinusoids,its spectrum is well defined and controlled.Any frequency which may interfere with the friendly users of the spectrum may not be transmitted with a minimal effect on the transmitted waveform.Stability and accuracy of time domain waveform parameters,i.e., pulse shape,PRI depends upon the stability of frequency components which constitute the signal.The stability of these frequency components can be assured by deriving them from a stable master oscillator.Radar performance in the presence of noise depends upon the energy of the pulse(or the average power)which increases with the increasing pulse width.However,target detection in the presence of clutter requires narrow pulse width as clutter is proportional to pulse width.These two contradictory re-quirements are often satisfied by the use of pulse compression which allows long transmit pulses for larger amounts of pulse energy and narrow compressed pulses for low clutter and good range resolution.UWB radars can benefit significantly from the use of pulse compression as UWB waveforms have low average power.Therefore,in this paper the Fourier synthesis is extended to a generation of complex amplitude coded waveforms with which we can generate Barker-like codes. This capability will allow the use of pulse compression in UWB radars and the stability of waveform parameters will allow the coherent integration of UWB signals.Both these operations reduce the need for very large power sources which are required for conventional implementation of impulse type radars.In contrast to conventional waveform which are pulsed carrier,the UWB waveforms do not contain carrier.Therefore, it is not possible to define target motion induced Doppler frequency shift for UWB signals.Thus,DFT implemented Doppler processing used for detection of narrowband radar signals cannot be employed in the processing of UWB radar signals.However,the change in round trip time of target from pulse to pulse can be used directly in the time domain to integrate pulses,discriminate clutter,and determine target velocity.The success of time domain processing depends upon the stability of time domain parameters of the radar wave-form.Unlike most conventional methods,these parameters can be accurately controlled for Fourier synthesized waveforms. This paper describes the generation of coded and uncoded waveforms,gives a coherent UWB radar system concept for Fourier based waveforms,and also describes important signal processing concepts required for implementation.II.W A VEFORM G ENERATIONThis section describes the waveform generation for both uncoded and coded waveforms for UWB radar.A.Generation of Uncoded WaveformsThe Fourier series is normally used to decompose periodic signals into sinusoids.However,the Fourier series can also be used in reverse to synthesize a periodic signal by generating and transmitting sinusoidal components obtained from the Fourier series expansion of the desired radar waveform.The Fourier series expansion will contain infinite terms,however, the number of oscillators which can be realistically employed isfinite.Furthermore,the direct current(dc)component cannot be transmitted by antenna and thus should not be included in the waveform generation.With these constraints a desired periodic radar waveform can be writtenas(1)where is the fundamental angular frequency corresponding to the desired pulse repetitioninterval(3)where(4)250MHz,0.5ns,Fig.1.Schematic diagram of the transmitter.based on this expansion wouldrequire oscillators or active phase control.However if the expansion is performed for time symmetric case where time axis is in the center of pulse the expansion will contain only cosine terms.Thus the terms to generate the waveform will requireonlyterms as givenbyin the Fourier series method will depend upon the power requirements (which are important for signal to noise ratio considerations),the pulse shape,the pulse width,and the practical considerations of having a certain number of oscillators.A related technique to Fourier Series based waveform gen-eration is stepped frequency waveforms in which successive pulses are monotonically increased in frequency by frequency steps.Note that,however,each pulse is composed of a single carrier frequency.Thus the frequency stepped waveform uses multiple frequencies over a group of pulses as compared to the Fourier series method which uses multiple frequencies in each pulse.In the stepped frequency method the received pulses are combined in signal processing to achieve an effective wide bandwidth or,equivalently,narrow pulses.Both methods achieve a large bandwidth,one sequentially and the other si-multaneously.The purpose of the stepped frequency waveform is to increase the effective bandwidth without increasingtheFig.2.Fourier series based rectangular pulse train.instantaneous bandwidth which is not the case for the Fourier series method.A lower instantaneous bandwidth waveform has several advantages including a lower sampling rate and a lower number of samples to be processed.However detection of moving targets with the stepped frequency method causes some complications and the signal processing becomes more involved [6],[7].B.Generation of Coded WaveformsCoded (pulse compression)waveforms are used in conven-tional narrow band radars to increase the average power (for higher detection performance)and still retain the advantages of short pulse.Average power is particularly low in UWB waveforms due to very narrow pulse width.Thus,it is all the more important to employ coded waveforms to increase the average power in UWB radars.In conventional radars pulse compression waveforms are generated by phase coding the carrier (i.e.,0,”and 180”).Binary coded waveforms for UWB radar can begenerated instead by polarity coding of the pulse,i.e.,positive amplitude for“with sum of sinusoids from Fourier series expansionas(10)If consists of delta function sequences,then it can beeasily expressed in the form of(9).Coefficients,are then computedas.1)Generation of Continuous Coded Waveforms:A gen-eral periodic code sequence shown in Fig.3(a)can bemathematically representedas(12)wheredepending upon a specific code.The codehas.Differentiating both sidesof(a)(b)Fig.3.Continuous wave and pulsed code sequences.(12)onegets(14)wherecan be representedasRewriting the above equationas(20)(23)Fig.4.Barker code of length7.(25)(26)and(27),shown at the bottom of the next page.In principle,either of the two methods can be used forcoded waveform generation.The key difference is that thefirst method requires fewer oscillators and requires the use ofswitches whereas the second method does not requireswitchesbut requires a higher number of oscillators.In general,the first method will be more efficient in most situations,as it requires fewer oscillators.The second method is suitable for very high PRF waveforms.III.R ADAR I MPLEMENTATIONIn conventional narrowband radars,receiver,and processor are designed as matched filters,which is usually done in three steps,i.e.,IF filter is matched to short pulse,pulse compression is matched to long coded pulse,and Doppler processing is matched to groupofexperiences Doppler shift,given approximatelyby is wavelength of the carrier of the narrowband signal.Signal from a moving target and clutter from ground undergo different Doppler shifts due to their different radial velocities.This allows the separation of target signal from clutter by frequency discrimination which is usually done by taking the FFT of the returned signal from several pulses,known as Doppler processing in the radar literature.For UWB signals,Doppler effect cannot be represented by frequency shift as there is no carrier in these signals thus denying the use of traditional Doppler processing.However target range changes by small amount from one pulse to next due to target motion.Thus the time of arrival of target signal will also change from pulse to pulse (whereas arrival time of clutter from stationary ground will not change from pulse to pulse).This change in arrival time,as explained below,can be utilized to coherently integrate the target return over several pulses as well as discriminate clutter from the target signal.Assume a target moving with radialvelocitysecondsis,the resulting sum will notbuild up as is shown in Fig.6.However,if the returns from successive pulses are added together with a delayof(27)Fig.5.Block diagram of UWB radarsystem.Fig.6.Illustration for explanation of velocity processor.Since received signal is in digital format after being sampled and quantized with analog to digital converter,the velocity processing has to be done digitally too.This paragraph ex-plains the digital version of the velocity processing.Before processing is started,samples fromall(as shown in Fig.7)wherepulsesandrange bins for each pulse.It is assumed that pulse compression is already performed before the organization of the data.Although practical case of interest is detection of moving targets,but detection of stationary target will be considered momentarily.For target detection the returned signal from all the pulses within a coherent processing interval (CPI)is addedtogether to improve its signal to noise ratio.For stationary targets this is done by adding the signal from the same range bin number due to all the pulses in the CPI as the stationary target stays in the same range bin during the transmission and reception of all the pulses within the CPI.This implies the addition of columns in Fig.7.In contrast,a moving target changes range bins with pulses in a CPI and this change in range bin from one pulse to next is givenbyis intheth pulse it would appear in the binnumber givenby stands for the integer expression within the parenthesis.To integrate signal duetothe outputs in range bins given by the above expression will be added together.Fig.7shows range bins for a case where the target moves by one bin during the time between the pulses.Since target velocity is not known in advance,expected range of target velocities will be considered.For each velocity a different set of range bins from pulse-range bin matrix will be added together.For practical implementation,only finite numbers of velocity values within the expected range of target velocity will be considered.This is equivalent to forming parallel filters,each tuned to a different velocity.However,velocity processing in baseband radars is performed in the time domain as compared to Doppler processing in conventional narrowband radars which is performed in the frequency domain.IV.C ONCLUSIONThis paper describes Fourier synthesis based method for generation of amplitude coded baseband waveforms and an UWB radar implementation which uses this waveform.Inradar application these amplitude coded waveforms can be used to implement pulse compression techniques which in-creases signal energy without any loss of range resolution.Furthermore stability of parameters of Fourier synthesized waveform allows effective integration of pulses which further increases signal to noise ratio and the processing gain.These increases in gain reduce the required transmitter peak power which is one of the bottlenecks in implementation of medium or long range operational UWB radars.R EFERENCES[1]H.F.Harmuth,Nonsinusoidal Waves for Radar and Radio Communica-tion.New York:Academic,1981.[2]J.D.Taylor,Introduction to Ultra-Wideband Radar Systems.BocaRaton,FL:CRC,1995.[3] B.Noel,Ultra-Wideband Radar:Proceedings of the First Los AlamosSymposium.Boca Raton,FL:CRC,1991.[4]M.I.Skolnik,“An introduction to impulse radar,”NRL Tech.Rep.6755,Nov.1990.[5]R.Tang and K.Lee,“An ultrawide band adaptive transmitter forultrawide band radar feasibility demonstration,”in Ultrawide Radar,Haie,Ed.Bellingham,WA:SPIE,1992,p.1631.[6]J. D.Taylor,Ultra-wideband Radar Technology and Applications.Boca Raton,FL:CRC,to be published.[7]G.S.Gill,“Step frequency waveform design and processing for detec-tion of moving targets,”in Int.Conf.Proc.IEEE ,June1995.Gurnam Singh Gill received the B.Sc.degree from Panjab University,India,the M.Tech.degree from the Indian Institute of Technology,New Delhi,In-dia,and the Ph.D.degree from Southern Methodist University,Dallas,TX,all in electrical engineering.During most of his career he performed R&D with defense contractors in the areas of radar,elec-tronic warfare,and communications.For the last seven years he has been teaching at Naval Postgrad-uate School,Monterey,CA,where he developed courses in airborne radars and high resolution radarsand is also involved in research in radar related topics.。