Abstract:
A radar system and method for detecting targets using pulse-compressed signals is disclosed. In one application, the systems and methods can be used to detect one or more relatively small targets whose pulse-compressed signals are masked by the time-sidelobes of a larger target&#39;s return signal. The method includes an iterative, detect-and-subtract signal algorithm that processes the post-compressed signal to detect multiple targets. Specifically the processing algorithm operates on the post-compressed signal to identify a point spread function (PSF) that corresponds to the relatively large target. Once identified, the PSF corresponding to the largest target in the post-compressed signal is subtracted from the post-compressed signal to generate a residual signal. This residual signal, in turn, includes the PSFs for the other targets. This process of identifying and subtracting the PSF of the largest target in the residual signal is then repeated until all targets are detected.

Description:
The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided for by the terms of Contract No. F30602-03-C-0240 awarded by the Missile Defense Agency, Rome AFRL/SNR. 

   FIELD OF THE INVENTION 
   The present invention pertains generally to radar systems and methods for detecting a plurality of closely spaced targets. More particularly, the present invention pertains to systems and methods that use pulse-compressed radar signals for target detection. The present invention is particularly, but not exclusively, useful for detecting a relatively small target that is located in close proximity to a relatively large target. 
   BACKGROUND OF THE INVENTION 
   Pulse radar systems are capable of detecting remote targets and measuring the position (e.g. range), the radar cross section (i.e. size) and the velocity of the detected targets. When pulsed signals are used, the time period corresponding to the round trip travel of the pulse can be used to calculate target range. When pulses having relatively long pulse durations are employed, it is often difficult to detect and accurately calculate the range of two or more closely spaced targets. Specifically, with long pulses, the scattered returns from closely spaced targets overlap, preventing the return signals from being properly distinguished. 
   Short pulses, on the other hand, can be used to resolve closely spaced targets. However, with the use of short pulses, pulse energy becomes a consideration. Indeed, all other things being equal, a short pulse has less energy than a long pulse. When pulses having insufficient energy are used, the return signals produced have a correspondingly low energy, and cannot be detected. Since radar systems are limited in terms of peak power, it is difficult to produce a short pulse having sufficient energy to detect relatively small targets. 
   Pulse compression is a technique that can be used to reduce the duration of a pulse while maintaining a relatively large pulse energy. Typically, modern pulse compression techniques introduce a wideband, coded modulation into the pulse. Examples of this wideband modulation include linear frequency modulation and pseudo-random phase modulation. 
   When a coded pulse encounters a target, a scattered signal containing the code (or a variation thereof) is created. This scattered signal is then received and processed to “find” the code within the scattered return signal data. For this purpose, the correlation property of the code can be used. More specifically, a correlation function defined by 
             r   ⁡     (   k   )       =       ∑     l   =   1     N     ⁢       c   ⁡     (     k   -   l     )       ⁢     c   ⁡     (   l   )                 
can be used to find a so-called “zero offset” between the code and the correlation function. The location of this “zero offset” results in a peak when pulse power (usually measured in db) is plotted against range. This peak is indicative of the target range. Unfortunately, during this process, so-called “time-sidelobes” are created and show up, together with a peak, in the pulse-compressed signal. Oftentimes, the time-sidelobes of a relatively large target&#39;s return signal mask the peak of a relatively small target&#39;s signal return. In the absence of a suitable technique to overcome this problem, small targets that are in close proximity of a large target may be undetectable.
 
   In light of the above, it is an object of the present invention to provide radar systems and methods suitable for the purposes of detecting a plurality of closely spaced targets of differing radar cross section. It is another object of the present invention to provide radar systems and methods for detecting a relatively small target having a return signal that is masked by the time-sidelobe of a relatively large target&#39;s return signal. Yet another object of the present invention is to provide radar systems and methods for detecting targets which are easy to use, relatively simple to implement, and comparatively cost effective. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to radar systems and methods for detecting targets using pulse-compressed signals. In one application, the systems and methods can be used to detect one or more relatively small targets whose radar return signals are masked by the radar return signal created by a relatively large target. More specifically, the present invention can be used to detect a target whose return signal is masked by the time-sidelobes of another target&#39;s return signal. 
   For the present invention, the system includes a radar transmitter for generating and transmitting one or more coded pulse signal(s). Each pulse signal is typically modulated with a pre-selected waveform. For example, the signal can be modulated with a pseudo-random coded waveform, or alternatively, a linear frequency modulated (e.g. chirped) waveform can be used. For the system, the transmitter is oriented to direct at least one pulse toward a targeted area. At the targeted area, the transmitted signal is scattered by each target located in the target area. This scattered signal is then received by a receiver and pulse-compressed. The pulse-compressed signal is then processed to detect the targets. 
   In greater detail, for the present invention, an iterative, detect-and-subtract signal algorithm is used to process the pulse-compressed signal and detect the targets. Recall, that the present invention is applicable to operational environments where the pulse-compressed signal of a relatively small target may be masked by the time-sidelobes of another, typically larger, target&#39;s return signal. With this in mind, the processing algorithm operates on the pulse-compressed signal to identify a point spread function (PSF) corresponding to a relatively large (i.e. masking) target. For these methods, the PSF can be characterized as having a central peak and accompanying time-sidelobes. 
   In one implementation of the invention, the peak of the PSF of the largest target is identified using a constant false alarm rate (CFAR) technique. Once identified, the PSF (including the peak and the time sidelobes) which corresponds to the largest target is then subtracted from the pulse-compressed signal to generate a first residual signal. This first residual signal, in turn, includes the PSFs for the other targets in the targeted area. 
   After the PSF for the largest target has been detected and subtracted from the pulse-compressed signal, the next step in the present method is to use the first residual signal to identify other targets. For this purpose, the processing algorithm outlined above is repeated. Specifically, the PSF of the largest target in the first residual signal is identified, for example, using the constant false alarm rate (CFAR) technique. Once identified, the PSF corresponding to the largest target in the first residual signal is then subtracted from the residual signal. This process is repeated until all targets having signal returns with energies above a pre-selected threshold are detected. 
   Many currently operational radar systems use Doppler filtering to process return signals and determine a detected target&#39;s velocity. As described above, the present invention can be used to process pulse-compressed return signals irregardless of whether they have been manipulated by Doppler filtering. When used with Doppler filtered return signals, the present invention uses PSFs corresponding to targets in two-dimensional (range×Doppler) space (i.e. signal power is a function of both range and frequency). 
   In a first implementation, Doppler filtering can be performed on a single pulse. An example of this type of Doppler filtering is used on the AEGIS SPY-1 radar. For this type of Doppler filtering, the pulse-compressed signal can be characterized as having a frequency, f c , a pseudo-random coded waveform, c(r) and a chip interval, T c . When a pulse is scattered by a target having a radial speed, v, the pseudo-code of the pulse-compressed signal will be modulated by scattering targets as
 
 c   R ( rT   c )= c ( rT   c )exp( i 2 πθ d   rT   c ),
 
where
 
               f   d     =       -       2   ⁢   v     c       ⁢     f   c         ,         
and r denotes the range bin index. For this case, the PSF corresponding to the scattering target p f  can be computed as a convolution of c R (r) with c(r), namely,
   p   f ( r ) =c   R ( r )             c ( r ).
   For another type of Doppler filtering (so-called conventional Doppler filtering), a pulse-compressed signal includes a plurality of pulses in a coherent pulse interval. For this type of Doppler filtering, a two-dimensional PSF can be generated by: 1) weighting the return signal corresponding to a point source, and 2) applying a fast Fourier transform to the weighted return signal. Using the PSF generated in this manner, a detect-and-subtract process as described above can be employed to detect each target. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which: 
       FIG. 1  is a schematic of a radar system for detecting a plurality of targets; 
       FIG. 2A  illustrates a delta function representing a point source of unit strength placed at the 0 th  range bin; 
       FIG. 2B  illustrates a compressed pulse shape generated from the delta function shown in  FIG. 2A  using a bi-phase code consisting of 32 chips; 
       FIG. 3A  illustrates a return signal for a group of targets wherein the largest target has a PSF peak of approximately 42 db; 
       FIG. 3B  illustrates a residual signal for the group of targets generated by subtracting the PSF of the largest target from the return signal shown in  FIG. 3A ; 
       FIG. 3C  illustrates the residual signal after another detect-and-subtract iteration wherein the PSF of the largest target in the residual signal shown in  FIG. 3B  has been subtracted; 
       FIG. 3D  illustrates the residual signal after a detect-and-subtract iteration has been performed on the residual signal shown in  FIG. 3C , and shows that after this final detect-and-subtract iteration, there are no other target return signals that exceed the base noise level; 
       FIG. 4  shows a flowchart architecture for employing the detect-and-subtract technique with the AEGIS crude Doppler filtering; 
       FIG. 5A  shows a cross-section through a two dimensional range×Doppler PSF, showing a section parallel to the Doppler frequency axis; and 
       FIG. 5B  shows a cross-section through a two dimensional range×Doppler frequency PSF, showing a section parallel to the range axis. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Referring to  FIG. 1 , a radar system  20  is shown for detecting a plurality of targets, such as exemplary targets  22   a - c  shown. Although three targets  22   a - c  are shown in  FIG. 1 , it is to be appreciated that more than three and as few as one target  22  can be detected with the system  20 . As further shown in  FIG. 1 , the radar system  20  can include a radar transmitter  24  configured to generate and transmit a pulse signal  26 . The transmitted signal  26  typically consists of a pulse train having one or more pulses. For the system  20 , the transmitted signal  26  can be modulated with a pre-selected waveform. Suitable waveforms can include, but are not necessarily limited to: 1) a pseudo-random coded waveform, and 2) a linear frequency modulated (e.g. chirped) waveform. 
   Continuing with  FIG. 1 , it can be seen that the transmitted signal  26  is scattered by each target  22   a - c  generating a respective target scatter signal  28   a - c.  These scatter signals  28   a - c  combine to create a return signal  30 . For the system  20 , the return signal  30  is then received by a receiver  32  for subsequent processing (e.g. by processor  34 ). Although the system  20  is shown having a receiver  32  that is collocated with the transmitter  24 , it is to be appreciated that this arrangement is merely exemplary. As an alternate to this collocated arrangement, the skilled artisan will quickly gather that an operational system  20  can be prepared wherein portions of the receiver  32  and transmitter  24  are common (i.e. a transceiver) or that the system  20  can be configured as a bistatic radar (i.e. having a receiver  32  that is distanced from the transmitter  24 ). 
   For the system  20 , each target  22   a - c  is considered to consist of point sources/scatterers.  FIG. 2A  shows a delta function  36  representing a point source of unit strength placed at the 0 th  range bin. A corresponding compressed pulse shape generated using a bi-phase code consisting of  32  chips is shown in  FIG. 2B . As seen there, the operation of pulse compression spreads out a point source represented by the delta function  36  ( FIG. 2A ) to a PSF  38  that can be characterized as having a single peak  40  at the target location and accompanying time-sidelobes  42   a,b.    
   For the system  20 , it can be assumed that targets  22   a - c  consist of a collection of point scatterers. As a consequence, the pulse-compressed signal  43  (see  FIG. 3A ) can be considered to represent a summation of shifted and scaled PSFs, with one PSF for each target  22   a - c.  Functionally, for the system  20 , the pulse compression operation is performed to recover the corresponding delta function for each target  22   a - c  from the summation of scaled and shifted PSFs in the pulse-compressed signal  43 . 
     FIGS. 3A-3D  illustrate, step by step, a detect-and-subtract processing routine to detect the three targets  22   a - c  (shown in  FIG. 1 ). Beginning with  FIG. 3A , the signal power is plotted against range bin number for the pulse-compressed signal  43 . For the illustration shown in  FIGS. 3A-3D , targets are detected using a constant false alarm rate (CFAR) technique. Specifically, for this example, a peak is identified as a target if the peak exceeds twelve decibels above the CFAR average. Thus, peak  44  is identified as the largest target (i.e. target  22   a ) because peak  44  is more than twelve decibels above the CFAR average  46   a  for the pulse-compressed signal  43 .  FIG. 3A  also illustrates that although the largest target (i.e. target  22   a ) can be detected from the pulse-compressed signal  43 , peaks corresponding to the other targets (i.e. targets  22   b  and  22   c ) are masked by the PSF of the largest target. 
   Once the largest target has been identified, the PSF corresponding to the largest target in the pulse-compressed signal  43  is then subtracted from the pulse-compressed signal  43 . This PSF includes the peak  44  and accompanying time-sidelobes (see also  FIG. 2B ). For this example, the detect-and-subtract step described immediately above generates the residual signal  48  shown in  FIG. 3B . This residual signal  48 , which is a compressed signal, includes the PSF for the other targets (i.e. targets  22   b  and  22   c ). With the residual signal  48  generated, a CFAR average  46   b  for the residual signal  48  is calculated. Again, for this example, a peak is identified as a target if the peak exceeds twelve decibels above the CFAR average. Thus, peak  50  is identified as the largest target (i.e. target  22   b ) in the residual signal  48  because peak  50  is more than twelve decibels above the CFAR average  46   b  for the residual signal  48 . 
   Next, the PSF corresponding to the largest target (i.e. target  22   b ) in the residual signal  48  is then subtracted from the residual signal  48 . For this example, this second detect-and-subtract iteration results in the residual signal  52  shown in  FIG. 3C . From  FIG. 3C , it can be seen that after subtracting the PSFs corresponding to the two largest targets (i.e. targets  22   a  and  22   b ), a peak  54  corresponding to the smallest target (i.e. target  22   c ) is revealed. 
     FIGS. 3C and 3D  illustrate another iteration of the detect-and-subtract process. Specifically, for the residual signal  52  generated as described above, a CFAR average  46   c  is calculated. Again, for this example, a peak is identified as a target if the peak exceeds twelve decibels above the CFAR average. Thus, peak  54  is identified as a target (i.e. target  22   c ) in the residual signal  52  because peak  54  is more than twelve decibels above the CFAR average  46   c  for the residual signal  52 .  FIG. 3D  shows the residual signal  56  that results after subtraction of the target  22   c  PSF from the residual signal  52  shown in  FIG. 3C . For this new residual signal  56 , a new CFAR average  46   d  is calculated. From  FIG. 3D , it can be seen that no other peaks are present in the residual signal that exceed the CFAR average  46   d  by more that twelve decibels. Thus, there are no other targets to detect. 
   The system  20  can also be configured to incorporate the effects of Doppler frequency shifts that are caused by the movement of the targets  22   a - c.  For this configuration of the system  20 , moving targets are characterized not only by amplitude and phase but also by Doppler frequency. In general, to accommodate these characteristics (i.e. amplitude, phase and Doppler frequency) the above-described detect-and-subtract methods can be used by generating PSFs in two-dimensional range×Doppler space. 
   Mathematically, the Doppler shift can be computed as: 
             f   d     =       -       2   ⁢   v     c       ⁢     f   c             
where v is the target radial speed and f, is the radar frequency. In addition, the pseudo-code received by a radar is modulated by the target as:
   c   R ( rT   c )= c ( rT   c )exp( i 2πƒ d   rT   c ) 
where T c  is the chip interval and r denotes the range bin index. For simplicity of notation, T c  can be dropped as long as it does not cause confusion. The corresponding PSF can then be computed as a convolution of c R (r) with c(r):
   p   f ( r )= c   R ( r )             c ( r ) 
where the suffix f of the PSF indicates the dependence on Doppler frequency.

   Below, two implementations of the system  20  are described, each of which account for Doppler effects. In these two implementations, PSFs corresponding to targets are generated in two-dimensional range×Doppler space. It is to be appreciated and understood that these two implementations are merely exemplary, and those skilled in the pertinent art can routinely extend the teachings provided herein to other Doppler filtering schemes using PSFs that are generated in two-dimensional range×Doppler space. 
   In one implementation, the system  20  can be configured for processing a return signal that has been Doppler filtered using a common Doppler signal processing technique that is currently employed in AEGIS SPY-1 radars. These AEGIS SPY-1 radars typically use a pseudo-random coded waveform, and accordingly, a pseudo-random coded waveform is considered here. It is to be appreciated that the algorithm described herein can also be extended to LFM radar waveforms without difficulty. One advantage of the AEGIS crude Doppler filtering is that it requires only one pulse. 
   In order to make the derivation applicable to general pulse compression techniques, a complex notation is used to represent a code: exp(jφ(r)), where φ(r) denotes the phase at the r th  chip. For a bi-phase coding system, φ(r) may be set to either 0 or π. 
   For a target with Doppler frequency shift ƒ D , the returned pulse may be represented as
 
 s ( r )=exp( j 2πƒ D   r )exp( j φ( r ))  (1)
 
where a signal of unit power is assumed for simplicity. In equation (1), the effects of the carrier frequency can be ignored assuming an appropriate downconversion followed by filtering. Also, the sampling interval has been suppressed in equation (1). In equation (1), the term, exp(j2πƒ D r), represents the effect of target Doppler in a pulse. The AEGIS Doppler filtering technique is a crude technique which capitalizes on this Doppler shift term. If the signal is pulse-compressed using the code exp(j2πƒ D r)exp(jφ(r)), no performance degradation results. Since the target Doppler frequency ƒ D  is unknown, a finite number of candidate (fixed) Doppler frequencies are assumed and are used for pulse compression. Specifically, L candidate frequencies can be assumed, for which a pulse can be compressed using L “modified” pseudo-codes:
 
exp( j 2π{circumflex over (ƒ)} 1   r )exp( j φ( r )), l =1,2, . . . ,  L.   (2)
 
These “modified” codes generate a crude Doppler filter bank.
 
     FIG. 4  shows a flowchart architecture for employing the detect-and-subtract technique with the AEGIS crude Doppler filtering. Specifically, as shown, single pulse radar data (box  58 ) is used to generate L×N R  two-dimensional data (box  60 ), where N R  denotes the number of range bins. Specifically, in box  60 , a single pulse of radar is compressed using the modified code generated according to equation (2), above. Next, basic PSFs (i.e. PSFs generated under the assumption of zero Doppler frequency) are generated and cleaned (box  62 ) using the detect-and-subtract method. The cleaned data is then used to find the maximum sample from each range bin (box  64 ). For each detection range bin, the filter with the largest output power is identified and the corresponding frequency is chosen to be the estimate of the target Doppler (box  66 ). 
   In another implementation, the system  20  can be configured for processing a return signal that has been Doppler filtered using what is commonly called conventional Doppler filtering. This conventional Doppler filtering technique typically requires multiple pulses in a coherent pulse interval (CPI), unlike the above-described AEGIS crude filtering which requires only one pulse. To describe the implementation of the system  20  for use with conventional Doppler filtering, the post-compressed radar signal of the n th  pulse at the r th  range bin, y(r, n), is weighted and a fast Fourier transform (FFT) is applied: 
                       y   ^     ⁡     (     r   ,   m     )       =       ∑     n   =   0       M   -   1       ⁢       w   ⁡     (   n   )       ⁢     y   ⁡     (     r   ,   n     )       ⁢     exp   ⁡     (       -   ⅈ     ⁢       2   ⁢   π     M     ⁢   n   ⁢           ⁢   m     )             ,           (   3   )               
where {w(n)} denote weights that are used to reduce high sidelobes associated with a FFT and M is the number of pulses.
 
   Following equation (1), above, the target return for the n th  pulse at the r th  range bin can be represented as:
 
 p   ƒ     D   ( r,n )=exp( j 2 πnT   p ƒ D )exp( j 2πƒ D   r )exp( j φ( r ))  (4)
 
   A pulse is compressed in the Doppler filtering technique using the code sequence, exp(jφ(r)). Thus, a PSF can be computed as:
 
 p   f     D   ( r, n )=exp ( j 2πnT p   f   D )exp( j 2πf D   r )exp( j φ( r ))           exp( j φ( r )).  (5)

   The target frequency ƒ D  can be restricted to those of integer multiples of 1/(MT p ) as usually assumed in Doppler filtering, i.e., ƒ D =m D /(MT p ) for some integer m D , m D =0, 1, 2, . . . , M-1. Under this assumption, the number of PSFs to be used can be reduced to M. Substituting ƒ D =m D /(MTP) into (5), leads to: 
                     p     m   D       ⁡     (     r   ,   n     )       =       exp   ⁡     (     j   ⁢       2   ⁢   π     M     ⁢   n   ⁢           ⁢     m   D       )       ⁡     [       (       exp   ⁡     (         2   ⁢   π       MT   P       ⁢     m   D     ⁢   r     )       ⁢     exp   ⁡     (     jϕ   ⁡     (   r   )       )         )     ⊗     exp   ⁡     (     jϕ   ⁡     (   r   )       )         ]               (   6   )               
where the subscript m D  is used to indicate the dependence of the PSF on target Doppler frequency. The PSF of equation (6) is herein named “time-PSF” to avoid confusion.
 
   A two-dimensional PSF can be computed by replacing y(r, n) in equation (3) with p m     i,    (r, n): 
   
     
       
         
           
             
               
                 
                   
                     
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   In order to distinguish this PSF from the PSF of equation (6), {circumflex over (p)} m     D    (r,m D ) is named a “Doppler-PSF.” A Doppler-PSF may be pre-computed given a basic PSF (i.e. a PSF generated under the assumption of zero Doppler frequency), the number of pulses and FFT size. 
   For the special case where w(n)=1 , n=0, 1, 2, . . . , N. substituting equation (6) into equation (7) yields: 
                 p   ^       m   D       ⁡     (     r   ,   m     )       =     {           M   ⁡     [       (       exp   ⁡     (     j   ⁢       2   ⁢   π       MT   p       ⁢     m   D     ⁢   r     )       ⁢     exp   ⁡     (     jϕ   ⁡     (   r   )       )         )     ⊗     exp   ⁡     (     jϕ   ⁡     (   r   )       )         ]               if   ⁢           ⁢   m     =     m   D               0           if   ⁢           ⁢   m     ≠     m   D                     
Note: such an orthogonality condition does not generally hold if w(n)≠1.
 
   Referring now to  FIGS. 5A and 5B , it can be seen that the cross-cut of a Doppler-PSF along range typically looks exactly like a one-dimensional PSF (see e.g.  FIG. 2B ), while the cross-cut along frequency looks like a conventional Doppler filter, i.e. has a wide beamwidth in frequency. 
   To detect targets, the system  20  identifies the largest signal in the pulse-compressed signal in range×Doppler space. Specifically, if the signal power level is greater than the pre-determined threshold, a two-dimensional Doppler-PSF corresponding to the range bin and Doppler of the detected target/scatterer is generated (according to equations (6) and (7)) and subtracted. The process is repeated until there are no samples in the residue greater than the threshold. 
   In some cases, the detection and estimation of target Doppler by the above-described techniques is dependent on the level of sidelobes of Doppler filters. Thus, it is desirable to mitigate sidelobes of Doppler filters and also increase the frequency resolution of Doppler filters. Specifically, this should be done without increasing the number of transmitted pulses to thereby conserve radar resources. One way that target detection may be significantly degraded is if the target Doppler frequencies do not exactly fall on the frequencies of the Doppler filters. However, using a FFT size significantly larger than the number of pulses (thus zero padding is required for Doppler filtering) can be used to significantly improve detection. 
   While the particular systems and methods for sidelobe reduction using detect-and-subtract techniques as herein shown and disclosed in detail are fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that they are merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.