A Signal Level Simulator for Multistatic and Netted Radar Systems

A Signal Level Simulator for Multistatic and Netted Radar Systems
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   A Signal Level Simulator forMultistatic and Netted RadarSystems MARC BROOKER,  Member, IEEE MICHAEL INGGS,  Member, IEEEUniversity of Cape Town Efficient analysis of modern multistatic and netted radarsystems requires a new generation of dedicated radar simulationsoftware. Key requirements for such software are simulationaccuracy and flexibility in choosing system parameters. Inthis paper, algorithms for the simulation of raw radar returnsignals are presented based on interpolation and modificationof the transmitted signal and modelling of the radar hardwareand environment. This method supports simulation of pulsedand CW systems; monostatic, multistatic, and netted systems;phased-array radars; and most physically realizable radar systemconfigurations. Manuscript received February 15, 2008; revised November 30,2008; released for publication August 1, 2009.IEEE Log No. T-AES/47/1/940023.Refereeing of this contribution was handled by Y. Abramovich.This work was supported by the South African National DefenceForce.Authors’ address: Dept. of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch, 7701, South Africa, E-mail:($26.00 c °  2011 IEEE I. INTRODUCTION The ability to simulate the performance of a radarsystem early in the design life cycle is becomingincreasingly important due to increases in systemcomplexity and demand for radar systems that offerexcellent performance at a low cost. Analysis of simple monostatic radar systems is well understoodand can be performed without the assistance of specialised software [1]. In contrast, the analysis of complex radar systems is often intractable withoutthe application of a dedicated radar simulationsystem.Recent research into radar simulation has focusedprimarily on simulators for specific types of radarsystems such as synthetic aperture radar (SAR) andmoving target indication (MTI) systems. While specialpurpose simulators ([2] and [3], for example) areextremely useful in particular fields, the developmentof a general purpose simulator applicable to manytypes of radar systems (including future systems)is interesting. Many past flexible simulators (suchas [4]), while suited to the simulation of traditionalradar applications, have severe limitations suchas the inability to simulate multistatic and CWradars.This paper presents the design of general purposesoftware for the digital simulation of raw radar returnsignals based on the modelling of radar hardwareand the environment and the modification of thetransmitted signal using digital signal processing(DSP) techniques. The simulator has been designedfor the accurate simulation of raw returns in complex,multistatic, and netted radars and is applicable topulsed and continuous wave (CW) systems as wellas both active and passive radar systems. In addition,active and passive electronically scanned arraydesigns are supported. The algorithm is expected tobe especially valuable for the simulation of emergingradar technologies, such as passive coherent location[5, 6] (PCL), netted radar [7, 8] and phased-arrayradar.This paper describes the algorithms and modelsused for simulation, discusses their implementation,and compares simulation results with measuredreturns from the NetRad experimental netted radarsystem [7, 8], and theoretical predictions of MTI radarperformance. II. RADAR SIMULATION MODEL It is a convenient simplification to model the radarreturn signal as the sum of multiple independent targetreturns. In a simulated scene with  T  transmitters and S  scatterers, the discrete-time return signal to thereceiver  r ,  y r [ k  ] can be modelled as the sum of   N  responses (1) where  N   = T ( S +1). This simplificationallows each scatterer to be considered independently, 178 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011  Fig. 1. Functional model of receiver hardware. greatly reducing the complexity of the calculationsrequired to simulate the return signal.  y r [ k  ] =  N  X i =0 s i [ k  ] :  (1)The scatterer returns  s i [ k  ] are modelled as copies of the transmitted signal  x [ k  ] which have been modifiedby the effects of transmission, propagation, interactionwith the scatterer, and reception. The signal  s i [ k  ]can therefore be expressed as the product of threeprocesses which modify the transmitted signal  x ( n ):transmission (  H  t (  x )), environmental interaction (  E  (  x )),and reception (  H  r (  x )).  y [ k  ] =  N  X i =0  H  r (  E  (  H  t (  x [ n ]))) :  (2)The radar simulation problem is equivalentto finding the functions  H  t (  x ),  E  (  x ), and  H  r (  x ),understanding how these functions affect thetransmitted signal, and applying these effects to copiesof the transmitted signal. In the simulator describedhere, the hardware simulation functions  H  t (  x ) and  H  r (  x ) are derived from a parametric hardware model,and the environment interaction function  E  (  x ) isderived from an environment model. The effects of these functions are applied to the transmitted functionusing DSP techniques.  A. Radar Hardware Models The radar hardware model is based on twoparametrized functional hardware models. Thereceiver model, as illustrated in Fig. 1, consists of a receive antenna, amplifier, quadrature downmixer,and signal capture hardware. The transmitter modelis similar to the receiver model and consists of asignal source, quadrature upmixer, amplifier, andtransmission antenna. Both models include a timingsource which provides time and frequency informationto the other blocks, and both consider the effects of imperfections in the timing information received fromthis source.The parameters of each functional block inthe hardware model are changed to reflect theperformance of the hardware of the system undersimulation. Each functional block includes multipletunable parameters, for example, gain, noisetemperature, and bandwidth in the amplifier blocksand the shape and amplitude of the phase noise curvefor timing blocks. This functional model is sufficientlyflexible to describe the performance of a large numberof modern radar system designs. B. Modelling the Effects of System Hardware The effects of transmission (  H  t (  x )) and reception(  H  r (  x )) on the radar signal are calculated using thehardware model.The intended effects of the transmission chainare to produce an analog signal, upmix it to therequired transmission frequency, amplify it to therequired transmission power, and transmit it using therequired antenna gain pattern. The intended effects of transmission are therefore gain (from the amplifierand antenna) and the upmixing of the inphase andquadrature parts of the transmitted signal to a higherfrequency. The unintended effects of transmissionare linear effects (nonflat frequency response, etc.),nonlinear effects (amplifier distortion, digital-to-analogconversion (DAC) distortion, and timing source phasenoise effects), and the addition of noncorrelated noise.The intended effects of reception are to addgain to the signal (from the antenna and front-endamplifier), downmix the signal to IF or baseband,and possibly convert the signal into a stream of digital samples. Unintended effects of reception aresimilar to those of transmission, but also includethe addition of distortion and quantization noise inthe analog-to-digital converter (ADC). Where theradar hardware of interest performs more complexoperations, such as beam forming and filtering, theseoperations can be included in the hardware modellingfunctions  H  t (  x ) and  H  r (  x ). C. Radar Environment Model 1)  The Object Model : The environment modelof the simulator recognises three kinds of objects:transmitters, receivers, and scatterers and accepts anynumber of each type of object in arbitrary geometricconfigurations. In addition, the model can includea single surface which reflects radar energy forthe simulation of specular multipath propagation.Each object in the environment is assigned a spatialposition, path of motion through space, and rotation.Positions, velocities, and paths can be assigned exactvalues or statistical distributions of values.Each transmitter in the model is independentlyassigned a waveform to transmit, an associatedhardware model, and a transmission schedule. Thetransmission schedule models the pulse repetitionfrequency (PRF) of the transmitter. The transmitterobject is intended to be used to model radartransmitters, the transmission part of monostaticradars, transmitters of opportunity (such as FMtowers), noise sources, and active electronic warfare(EW) systems. BROOKER & INGGS: A SIGNAL LEVEL SIMULATOR FOR MULTISTATIC AND NETTED RADAR SYSTEMS 179  Fig. 2. Monostatic return paths in bistatic radar system.Fig. 3. Multistatic and direct return paths in bistatic radarsystem. Receivers in the model are independently assigneda hardware model and receive schedule. The receiveschedule is used to model range gating and can beslaved to the schedule of an associated transmitter.The receiver object models radar receivers and thereception part of monostatic radars.Scatterers in the model are independently assignedmonostatic or bistatic radar cross sections (RCS) andare used to model both intended targets, unintendedtargets (clutter) and mechanical jamming (chaff, etc.).Currently only point scatterers with arbitrary RCSsare supported. Note that this model does not make adistinction between intended targets and unintendedtargets (clutter)–the effects on the radar signal of both of these types of scatterers are the same.2)  Responses : Using the number of transmitters,receivers and targets in the environment, the modelcalculates the total number of responses for eachtransmitted pulse. In multistatic systems, monostatic(Fig. 2), multistatic (Fig. 3), and direct return pathsare included in the total number of pulses. Thepresence of a multipath surface increases the numberof responses as reflection paths are added to eachbistatic pair.In a multistatic radar system, the total number of returns per pulse seen by each receiver in a systemwith  T  transmitters,  P  targets, and  S  multipathsimulation surfaces is  RT ( P  +1)( S +1). Each of thesereturns can be considered independently and summedfor each receiver, as in (1). This number is an upperbound on the number of responses–in some systemsresponses may be lost due to range gating, the effectsof antenna gain patterns, and propagation effects.Multiscatter (return paths which contain morethan one scatterer) are not included in the calculationof   N   in Section II. Low-order mulitscatter pathscan be included directly in the calculation of (2) byextending  E  (  x ) to consider the effects of interactionwith all targets on the path. The extension of (1) toa complete global illumination model (see [9], forexample) would be required to consider higher ordermultiscatter paths, as direct calculation of these pathswith (2) would not be computationally efficient. D. Propagation Effects Propagation through the atmosphere has twomajor effects on signals transmitted at common radarfrequencies: delay and attenuation.The effects on the received radar signal due tothe delay caused by propagation can be decomposedinto two effects: a phase shift on the carrier (phasedelay) and a time shift of the envelope of thetransmitted signal (group delay), assuming that thetransmitted signal consists of a complex bandlimitedsignal that is mixed with a carrier at a constantfrequency. Considering these two effects separatelysimplifies the computational task of signal processingas the computationally complex group delaysimulation only needs to be applied to the basebandsignal.Most simulators described in the literatureassume that the phase and group delay are constantthroughout each pulse ([4], for example) and thatmotion occurs during the inter-pulse interval. Thisstop-go assumption is only valid for radar systemswith short pulses and those where the target range ischanging slowly. The maximum allowable simulationerror depends on the type of processing used onsimulation results. Doppler velocitometry techniques,for example, do not consider the change of phase andgroup delay over the pulse interval, making the errorsintroduced by assuming stop-go behaviour irrelevant.The second major effect of signal propagationthrough the atmosphere is attenuation. The powerof the return signal, for the case where the signalbandwidth is much less than the carrier frequency, canbe computed using the radar (3) for target reflectionsand (4) for direct return paths [1]. P r  =  P t G t G r ½ b ¸ 2 (4 ¼ ) 3 R 2 t  R 2 r (3)and P r  =  P t G t G r ¸ 2 (4 ¼ ) 3 R 2  (4)where  P t  is the transmitted power,  G t  and  G r  arethe gain of the transmit and receive antennas in thedirection of the target,  ¸  is the carrier wavelength,and  R ,  R t , and  R r  are the lengths of the direct path,transmitter-target path, and target-receiver path,respectively.  ½ b  is the bistatic RCS of the targetcorresponding to the arrival and departure angles.For monostatic paths, (3) is used, with  R t  = R r  and ½ b  equal to the monostatic RCS. 180 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011  For wideband signals, the return strength isfrequency dependent. In this case, a linear phasedigital filter matching  P r / ¸ 2 is designed using thefast Fourier transform (FFT) and applied to the signal.The radar equation provides a simple calculationfor the power of the return signal, but does notinclude attenuation due to atmospheric factors.Attenuation due to propagation through theatmosphere is frequency dependent and varies widelyacross commonly used radar bands. The attenuationcoefficient can be found in many standard references(such as [1]) and multiplied by the propagationdistance ( R  or  R t  + R r ) to find the attenuation due toatmospheric propagation.This model is not limited to the linear phenomenaof attenuation and delay. In order for the calculationin (2) to be valid, the propagation medium must belinear. It is not assumed, however, that the permittivity( ² ) and permeability ( ¹ ) of the medium are constantand scalar. The environment model can include effectssuch as dispersion (where  ²  and  ¹  are functionsof frequency) and anisotropy (where  ²  and  ¹  aresecond-rank tensors). III. SIGNAL PROCESSING Following the identification of the simulationtransfer functions  H  t ,  H  r , and  E  , DSP approaches areused to modify the transmitted signal to match theexpected parameters of the received signal.  A. Phase Delay and Doppler Shift  The phase of the carrier at the receiver isdetermined by the signal propagation time. Where thistime is not constant, the changing phase shift is seenas a frequency or Doppler shift on the received signal.In this simulation, the per-sample phase shift  ' ( t )is calculated from the carrier frequency and bistaticrange of the transmitter, target, and receiver usingstandard relativistic Doppler calculations. Consideringthe phase effects of propagation as a per-sample phaseshift  ' ( t ) rather than a fixed frequency shift, allowsthe model to offer per-sample Doppler accuracywithout making assumptions about the speed of targetmovement or the length of pulses.Using a relativistic model to consider the phaseshift introduces further accuracy by relaxing theassumption that targets are moving at a small fractionof the speed of propagation.The inphase  I   and quadrature  Q  parts of thedownmixed return pulse are calculated from  ' ( t ) andthe real and complex parts of the transmitted pulse.  I  [ k  ] =  12 R (  y [ k  ])cos( Á ) ¡ 12  I  (  y [ k  ])sin( Á ) (5) Q [ k  ] =  12 R (  y [ k  ])sin( Á )+  12  I  (  y [ k  ])cos( Á ) (6)where  R (  x ) and  I  (  x ) are the real and imaginary partof   x , respectively, and  Á = ' ( k=f  0 ). B. Group Delay The application of time-dependent group delay toa digital signal requires a tradeoff to be made betweencomputational speed and accuracy. For constant groupdelay of an integer number of samples, the samplestream can simply be shifted. For noninteger delays,simulation of group delay requires interpolation of thesamples.Finite impulse response (FIR) fractional delayfilters, based on windowed truncation of the idealbandlimited interpolation [10] filter, are used toapply time-dependent group delay to discrete-timesignals. The exact values of the samples of thedelayed signal  d i [ k  ] (properly sampled at  f  0  Hz) canbe calculated from the transmitted signal  x [ n ] andthe time-dependent delay function  T d ( t ) using thesummation in (7) [11] d i [ k  ] = 1 X n = ¡1  x [ n ] h s μ k  ¡ T d μ n f  0 ¶ ¡ n ¶  (7) h s ( t ) = sin( ¼t ) ¼t :  (8)If the delay function is not constant, the delayedsignal  d i [ k  ] undergoes an apparent shift in frequency.In cases where the frequency shift causes a netincrease in frequency, it is critical that the samplerate  f  0  is sufficiently high that the delayed signal  d i [ k  ]is properly sampled, or distortion will occur due toaliasing.The process described in (7) can be understoodas convolution of the transmitted signal with a digitalfilter with the required group delay. The filter function h s ( t ) cannot be precomputed as the group delay istime varying.1)  Implementation of Group Delay Algorithm :A direct implementation of the summation (7) isimpractical as it requires  O (  N  2 ) operations for  x [ n ] with length  N  . Evaluating (7) using a FIRapproximation of the ideal interpolation filter (8)reduces the runtime to  O (  N  ) at the cost of numericalaccuracy.Simple truncation of the filter function  h s ( t )will severely reduce the stopband attenuation of the interpolation function, increasing distortion andaliasing. This effect can be effectively reduced bythe application of a suitable window function to  h s ( t )prior to truncation. The Kaiser window [12, 13] isideal for this application [14], as the compromiseruntime, flatness of the passband, and bandwidthcan be adjusted with the window parameters  ¯   and  N   without changing the algorithm implementation.The desired value of   ¯   and window width  M  can be calculated using the method described byKaiser [12].Application of the Kaiser window functionto truncate  h s ( t ) to  M   samples produces (9) to BROOKER & INGGS: A SIGNAL LEVEL SIMULATOR FOR MULTISTATIC AND NETTED RADAR SYSTEMS 181  replace (8) h s ( t ) = 8<: w( j t j )sin( ¼t ) ¼t  ,  j t j·  M  ,0, otherwise(9)where w( t ) is the zero-centered Kaiser windowfunction with length  M   and shape  ¯  .The Kaiser window function is computationallyexpensive–evaluating it requires two calculations of the value of the zeroth-order modified Bessel functionand one square root. In simulations of long periods orhigh bandwidths, an optimisation of this calculationcould be desirable.The simulated described in this paper uses atwelfth-order polynomial approximation of   I  0 (  x ) (from[15]) as the base of an approximation to the trueKaiser window function. The maximum error of thisapproximation is less than 1 : 2 £ 10 ¡ 8 . The simulatoruses this function to populate a variable sized table of subsample delay filters. The loss in accuracy due tothis approach depends on the table size: for a table of 10 5 filters of length 32, the maximum interpolationdelay is  ¡ 83 dB. In cases where this accuracy wouldlimit the dynamic range of the simulation (that is,systems with over 13 bits of dynamic range), the tablesize can be increased. C. Addition of Noise and Distortion The key limiting factor on the performance of radar systems is the signal-to-noise ratio (SNR) of the return signal. It is therefore important to correctlymodel the noise received along with the return pulse.1)  Additive Noise : For narrowband radar systems(where the bandwidth is much smaller than the carrierfrequency), the additive noise can be consideredGaussian noise with a constant spectral density.The total system noise consists of the sum of thenoise picked up from the environment and the noisecreated by the transmission and reception systems.For simulation of most practical radar systems, itis sufficient to specify the equivalent system noisetemperature, generate bandlimited white Gaussianpseudonoise, and sum it with the return signal.The system noise temperature depends on theenvironment, the elevation and gain pattern of antennas, and the noise figure of the amplifiers usedin the transmitter and receiver.2)  Quantisation Effects : Additional noise anddistortion is added by the D/A converter in thetransmitter and the A/D converter in the receiver. Inpractical cases, the effects of A/D conversion can beassumed to be purely additive and the additive noisesignal  e [ n ] assumed to be stationary and uncorrelatedwith the signal being quantised [13, 16]. Thesignal-to-quantisation noise ratio (SQNR) dependson the properties of the return signal and the samplingrate. For a typical radar signal with bandwidth  B , theSQNR can be expressed asSQNR= 20log 10 2  N  +20log 10 r  32 +10log 10  f  s 2 B (10)for an  N  -bit ADC with sampling rate  f  s  [17].The simulator directly simulates A/D quantisationeffects by truncating simulation results to therequired number of bits. This approach, while morecomputationally expensive than the addition of pseudonoise, offers a more accurate simulation of A/Deffects, including the nonlinear effects of quantisationto a small number of bits. D. Phase Noise and Jitter Effects Errors in the time and frequency sources in theradar system have several effects on the receivedsignal.The most obvious effect is the gross errors due totiming inaccuracy which cause incorrect referencingof the time of the received signal compared with thetransmission time. The simulator handles these errorsby adding random perturbations to the timestampsrecorded for received data, corresponding to the jitteron the timing source in the receiver hardware model.Phase noise on the timing source has an effect onthe upmixing and downmixing steps of the hardwaremodel. To simulate these effects, the instantaneousphase deviations in the transmitter ( ' t ) and receiver( ' r ) timing sources are added to the phase shiftfactor  '  in (5) and (6). The instantaneous phasedeviations  ' r  and  ' t  are generated from a statisticalmodel of the phase noise present on the timingsource. The simulator uses a novel multirate filterstructure (described in [18]) to accurately generatesamples of phase noise matching the characteristicsof the oscillator technology used in the system undersimulation.A third effect of phase noise on the timing sourcesis a degradation of the performance of the A/Dand D/A converters in the receiver and transmitter.Presence of jitter on the data conversion of the clock reduces the SNR of the data converters. An error termis added to the group delay simulation (7) to simulatethe effects of jitter on data conversion [19]. Jittersamples are computed from numerical integration of the phase noise model of the timing source [18]. IV. CALCULATING THE RAW RETURN SIGNAL Using the equations developed above, a completeequation (11) for the samples of the raw radar signalas received by receiver  r  can be obtained.  y r [ k  ] = T X t =0 0@  A tr μ k  f  0 ¶ d tr [ k  ]+ P X  p =0  A tpr μ k  f  0 ¶ d tpr [ k  ] 1A : (11) 182 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011

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