Abstract:
A method and system for SNR enhancement in pulse-Doppler coherent target detection for applications in the fields of radar and ultrasound. In accordance with the method of the invention, complex signals are obtained for each of two or more sub-intervals of the time-on-target interval, allowing simultaneous range and Doppler measurements. A coherent integration is the performed on the signals to generate complex-valued folded matrices. The folded matrices are unfolded and target detection is then performed in a process involving one or more of the unfolded matrices. A pulse-Doppler coherent system is also provided configured for target detection by the method of the invention.

Description:
FIELD OF THE INVENTION 
     The present invention relates to methods and systems for SNR enhancement in a pulse Doppler coherent system. 
     BACKGROUND OF THE INVENTION 
     The pulse Doppler technique is common to most modern surveillance and tracking radars, and ultrasound systems. This technique employs a sequence of transmitted pulses which impinge on a target, are reflected from the target and are collected back in the receiver. This technique is particularly convenient when the velocity of the target is significantly different from the velocity of the background scatterers such as the ground, trees, foliage and so on. Under this condition, the detection capability of the system is maximized in terms of the signal to noise ratio (SNR) so that the probability of detection is improved. 
     Most modern surveillance radars scan the surrounding space using a relatively narrow radiation beam. The total scan time is usually the user specified parameter of the system. The fraction of scan time, allocated to collect target return from each beam direction, is called time-on-target. During this fraction of time a sequence of pulses is transmitted by the radar. The interval between the rise of any two consecutive pulses is called the PRI (Pulse Repetition Interval) and the rate of the pulses is called PRF (Pulse Repetition Frequency). Detection and measurement processes can be realized by using constant or variable PRF during the time-on-target interval. The maximum SNR can be achieved by coherent integration of all target returns during the entire time-on-target interval. Prima facie, the most tempting scheme for realization of such concept would appear to be to use a single constant pulse repetition frequency (PRF) for transmitting pulse sequence and utilization of target returns. However this scheme does not support unambiguous measurement of range or velocity or both. 
     Another problem related to a single PRF scheme of detection is the problem of blind zones (blind ranges and Doppler frequencies) in the detection map. This problem reflects the periodic nature of transmitting and receiving in pulse radar detection scheme and is known as the visibility problem. 
     One solution, known in the prior art, to both the ambiguity and the visibility problems is to transmit two or more pulse sequences consecutively, each sequence having a different PRF. Each sub-interval with constant PRF provides a different “scale” of ambiguous but simultaneous measurement of the target range and Doppler frequency. The combination of all measurements (each with a different PRF) during time-on-target interval allows ambiguity resolution, but requires independent attempts of detection. In other words, the requirement to provide simultaneous detection and measurement of the target leads to partitioning of the time-on-target interval to several independent sub-intervals, each of which represents a relatively small part of the entire time-on-target interval. The detection process in each sub-interval, known also as “Coherent Processing Interval” and for short CPI, can be performed optimally by using coherent integration, but the maximum energy collected from the target return is only a fraction of the entire energy that could be collected during the entire time-on-target interval. Any logical or arithmetical combination of the results of sub-interval leads to losses and degradation in probability of detection in comparison with coherent integration of the signal during entire time-on-target interval. 
     The concept of ambiguity resolution in range is presented in  FIG. 1 , showing the signals received when three pulse sequences shown respectively as PRF 1 , PRF 2  and PRF 3  are transmitted, each having a different PRF. The returned signals consist of a first pulse sequence  10  having a first PRI  11 , a second pulse sequence  12  having a second PRI  13 , and a third pulse sequence  14  having a third PRI  15 . By using several frequencies, the unambiguous range can be solved. This is depicted in  FIG. 1 , where the unambiguous range  16  is detected at a position where pulses in the three pulse sequences coincide. Generally, the unambiguous range and Doppler of the target can be imagined as “coordinates” of the target detection hit of the unfolded range-Doppler map, which covers full range of the radar specified detection ranges and velocities (Doppler frequencies). This map is not explicitly represented in firmware or software of the radar, but one can think of it as sets of target hit coordinates, each for every detected target. 
     The narrow band signal that is collected in the receiver is usually modeled as s(t)=A(t)cos(2πf c t+Φ(t))+N(t), where t is time, A is the amplitude, f c  is the carrier frequency, Φ is the phase, and N is the noise. A basic assumption in this model is that the bandwidth of the amplitude A is orders of magnitude smaller than f c . The signal is processed along the receiving channel. It is frequency down-converted, filtered, split into two channels called the in-phase and quadrature, de-modulated (or pulse compressed) and digitized—not necessarily in that order. It is customary to represent the result obtained at this stage of the processing of a single PRF as a complex value entity: x k   l =x l (t k )=B l e j(Φ     l       0     +2πf     d     t     k     ) +n l (t k ), where l is the index of the PRF and is related to the time interval of the measurement, t k  is the time of the specific sample, known as the “range gate” number, B l  is the amplitude which is constant within the period of the measurement, Φ l   0  is some phase constant within the period of the measurement, f d  is the Doppler frequency, and n l  is the complex noise. 
       FIG. 2  shows a prior art method for target detection in a pulse-Doppler coherent system using L different PRFs. As denoted by  20 , a signal x nm   (l) =x (l) (t nm ) is received for each PRF used, where l=0 to L−1 is the PRF index, n is the pulse number in the signal, m is the range gate, and t n,m  is the sampling time of the signal of the range gate m of the pulse n, and is given by t n,m   (l) =nPRI (l) +mRG, where PRI is the pulse rate interval and RG is the duration of a single range gate. At  22 , the signals X nm   (l)  are subjected to coherent integration. This involves performing a discrete Fourier transform on the signals x nm   (l)  to generate a signal spectrum for each range gate m. The combination of all spectra for all range gates, obtained for each CPI, composes the folded range-Doppler map given by: 
                 X   km     (   ℓ   )       =       ∑     n   =   0         N     (   l   )       -   1       ⁢       x   nm     (   l   )       ⁢     w   n     ⁢     ⅇ     -       2   ⁢   π   ⁢           ⁢   j   ⁢           ⁢   kn     K               ,     
     ⁢     k   =   1     ,   …   ⁢           ,   K   ,     l   =   1     ,   …   ⁢           ,   L   ,     m   =   1     ,   …   ⁢           ,     M     (   l   )             
where N (l)  is the number of pulses in the signal, k is an index of the Doppler frequency, K is the number of Doppler frequencies, w n  is a weighting factor, and M (l)  is the number of range gates of the PRF  1 . At  24 , real-valued range-Doppler maps are generated for each PRF  1 , a real-valued K by M (l)  matrix P (l)  is defined by setting, P km   (l) =|X km   (l) | 2  for each pair of indices k and m, and at  26 , the target detection is performed, whereby it is determined whether the value P km   (l)  is greater than or equal to a predetermined threshold T. If so, then at  28 , H km   (l)  is set to 1. If not, then at  30 , H k,m   (l)  is set to 0. This defines a K×M (l)  binary matrix H (l)  for each value of l. This process is repeated for each CPI independently, producing the sets of target hits for each CPI, which are determined by their range—Doppler cell addresses—each PRF defines its own (generally folded) scale of cell addressing. Thereafter, the algorithm obviously need not record the matrices, but rather the sets of target hits and their cell coordinates. At  32 , the hit sets for each PRF are unfolded by periodically increasing the cell addresses in range direction by a step of ambiguous range up to the maximum instrumental range and in Doppler direction by step of PRF up to the maximum Doppler frequency (the unfolded target hits for each PRF can be interpreted as non-zero values of some sparse matrices composed from zeros and ones)—the matrices H l  are subjected to a process known as “unfolding”. In this process, the dimensions of each matrix H l  are increased by defining H k′,m′   (l)  for values of m′ for which Rmin&lt;m′·RG&lt;Rmax where [R min ,R max ] is a predetermined detection region of interest, and for values of k′ for which Dmin&lt;k′·PRF/K&lt;Dmax, Where [Dmin,Dmax] is a predetermined region of Doppler frequencies of interest, by setting H k′m′   (l) =H km   (l) , where k=k′ mod K, and m=m′ mod M. In step  34 , the matrices H l  are resampled by defining, for each pair of indices k, m, new indices p and q, as follows. The range of interest is divided into subintervals of a predetermined length Δr. A value of p is found from among all allowed values of p (i.e. integral values of p for which 0≦pΔr≦R max −R min ) such that R p =R min +p·Δr is closest to the range represented by the range gate m. The interval [D min ,D max ] is divided into subintervals of a predetermined length Δd. A value of q is found from among all allowed values of q (i.e. integral values of q for which 0≦qΔd≦D max −D min ) such that D q =D min +q·Δd is closest to k. This generates at  36  new binary matrices U l  where U p,q   l =H k,m   l , wherein the indices p,q correspond to the indices k,m. The sum A of the unfolded matrices is then calculated at  37 , where
 
               A     p   ,   q       =       ∑     l   =   0       L   -   1       ⁢       U     p   ,   q     l     .             
At  38 , it is determined, for each pair of indices, whether the sum A p,q  is greater than or equal to a predetermined threshold A. If so, then at  40  a target is detected at the location having the associated indices p,q, and the process terminates. If not, then at  42  it is determined that a target is not detected at the location having the associated indices p,q, and the process terminates.
 
     To summarize, the following observations are made: 
     1. Although target coherency is maintained for all of the pulses transmitted within the time-on-target interval, in known methods, only the signal received within a single CPI is integrated coherently. 
     2. The effectiveness of the integration depends on the coherence of the signal. The notion of coherence means that the relative phases are constant within the period of the measurement (up to some relatively small noisy contribution) or they vary in a predictable manner. Normally this requirement implies that the radar contributes a phase and amplitude that are essentially constant, at least within the time of measurement, and that the contribution of the target to phase variation is mainly due to its motion. The greater the signal-to-noise ratio of a target, the greater is its maximal detection range. Thus, increasing the coherent integration interval to the whole period when a target is illuminated by the antenna (time-on-target interval), the maximum possible signal-to-noise ratio is obtained, and, as a result, the maximum detection range. 
     Although theoretically two PRFs are sufficient to resolve ambiguity, the required number of PRFs is actually higher. This is due to the fact that some range gates are blind in each PRF. In the simplified representation of  FIG. 1 , these are the ranges, corresponding to the time during which the system is transmitting and cannot receive. This was referred to above as the problem of visibility. The number of PRFs used typically varies from 2 to 8 depending on the level of visibility that is required. However, the amount of time that can be allocated to the integration procedure of each PRF is reduced as the number of PRFs is increased. Since the signal-to-noise ratio is proportional to the coherent integration interval duration, as the number of PRFs is increased, the signal to noise ratio of each PRF decreases. This impairs the effectiveness of the conventional technique. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to maximize the results of integration procedure to the extent allowed solely by the coherence of the target. 
     In its first aspect, the present invention provides a method for target SNR enhancement in a pulse-Doppler coherent system, while allowing simultaneous measurements of the target kinematical parameters. The method may be used, for example, in surveillance and tracking radar or an ultrasound system. A sequence of transmitted pulses, reflected from targets and collected by the radar, is processed. In accordance with the invention, the processing includes a two-step coherent integration procedure. This is in contrast to the prior art methods in which a one-step coherent integration procedure is followed by a detection decision. The non-coherent combination, i.e. binary integration of the results of detection, for each CPI, as is done in the prior art methods, is avoided in the method of the present invention. 
     In one preferred embodiment of the invention, the received signals are subjected to a first coherent integration step by carrying out, for example, a discrete Fourier transform on the signals. This generates complex valued folded matrices (one for each PRF used). The folded matrices are unfolded and resampled. New matrices are then generated by complex value interpolation of the original matrices. To account for target motion, a Doppler phase correction is necessary for each of the interpolated matrices. Consecutive CPI-s have specific delays relative to the first one. These delays entail that each cell of the unfolded consecutive CPI-s be shifted by the phase which is determined by Doppler frequency of the cell and time delay of the CPI containing this cell. These phase shifts can be calculated and their effect can be compensated for each cell. The Doppler phase corrected matrices are then summed in a second coherent integration step. The resulting matrix is composed of the cells containing coherent sums of unfolded range-Doppler matrices received from different CPIs. It covers all radar specified ranges and Doppler frequencies. The resulting matrix is then converted into a real-valued matrix A, taking magnitudes of each cell. Detection is then performed in each cell of the matrix. 
     The decision regarding target detection is taken only after integration of the entire signal, collected during time-on-target interval, without any intermediate logical decisions. 
     In a second aspect, the present invention provides a pulse-Doppler coherent system configured for target detection by the method of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order to understand the invention and to see how it may be carried out in practice, a preferred embodiment will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: 
         FIG. 1  shows a prior art method for resolution of ambiguity of target detection; 
         FIG. 2  shows a prior art method for target detection in a pulse-Doppler coherent system; 
         FIG. 3  shows a method for target detection in a pulse-Doppler coherent system in accordance with one embodiment of the invention; and 
         FIG. 4  is a block diagram showing functionality of a system that implements the method of the invention. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       FIG. 3  shows a method for target detection in a pulse-Doppler coherent system, in accordance with one embodiment of the invention. At  50 , a signal x nm   (l) =x (l) (t nm ) is received for each PRF used, where l=1 to L is the PRF index, L is the number of PRFs used, n is the pulse number in the signal, m is the range gate, and t nm  is the sampling time of the signal of the range gate m of the pulse n, given by t n,m   (l) =nPRI (l) +mRG+t l , where PRI is the pulse rate interval, RG is the duration of a single range gate and ti is the start time of the l-th CPI counted from some reference point—for example the beginning of the 1-st CPI. At  52 , the signals x nm   (l)  are subjected to coherent integration in which a discrete Fourier transform is performed on the signals x nm   (l)  to generate a signal 
                 X   km     (   ℓ   )       =       ∑     n   =   0         N     (   l   )       -   1       ⁢       x   nm     (   l   )       ⁢     w   n     ⁢     ⅇ     -       2   ⁢   π   ⁢           ⁢   j   ⁢           ⁢   kn     K               ,     
     ⁢     k   =   0     ,   …   ⁢           ,     K   -   1     ,     l   =   0     ,   …   ⁢           ,     L   -   1     ,     m   =   0     ,   …   ⁢           ,       M     (   l   )       -   1     ,         
where k is an index of the Doppler frequency, K is the number of Doppler frequencies, N is the number of pulses in the signal, w n  is a weighting factor and M (l)  is the number of range gates of the PRF l. At  54 , the complex matrices X l  are unfolded by defining X k′,m′   (l)  for values of m′ for which R min &lt;m′·R G &lt;R max , where [R min ,R max ] is a predetermined detection region of interest, and for values of k′ for which D min &lt;k′·PRF/K&lt;D max , where [D min ,D max ] is a predetermined region of Doppler frequencies of interest, by setting X k′m′   (l) =X km   (l) , where k=k′ mod K, and m=m′ mod M. At  56 , the matrices X l  are resampled by defining, for each pair of indices k′m′, new indices p and q, as follows. The range of interest is divided into subintervals of a predetermined length Δr. A value of p is found from among all allowed values of p (i.e. integral values of p for which 0≦pΔr≦R max −R min ) such that R p =R min +p·Δr is closest to the range represented by the range gate m. The interval [D min ,D max ] is divided into subintervals of a predetermined length Δd. A value of q is found from among all allowed values of q (i.e. integral values of q for which 0≦qΔd≦D max −D min ) such that D q =D min +q·Δd is closest to k. New matrices XI (l)  are generated at  58  where XI p,q   (l)  is obtained by complex value interpolation of one or more values of X k′,m′   (l) , for indices k′m′ in a neighborhood of the indices p q. Any method of interpolation may be used in accordance with the invention. The interpolation may be linear interpolation or higher order interpolation. At  60 , a Doppler phase correction is performed on each of the matrices XI (l)  to yield matrices Y (l)  defined by Y pq   (l) =XI pq   (l) ·e −2πj·D     q     ·t     l   .
 
     A real-valued matrix A is then calculated at  62 , where 
               A     p   ,   q       =                ∑     l   =   0       L   -   1       ⁢     Y     p   ,   q       (   l   )              2     .           
Since the Y pq   (l)  are complex values, the calculation of A is a coherent integration step. At  64 , it is determined, for each pair of indices, whether the sum A p,q  is greater than or equal to a predetermined threshold T. If so, then at  66  a target is detected at the location having the associated indices p,q, and the process terminates. If not, then at  68  it is determined that a target is not detected at the location having the associated indices p,q, and the process terminates.
 
       FIG. 4  is a block diagram showing functionality of a system  80  for implementing coherent integration of multiple CPI-s according to the method of the invention as described above with reference to  FIG. 3 . The system  80  includes a transmitter  81  having a Tx antenna for tracking an object  82  and a digital receiver  83  having an Rx antenna for receiving an echo signal reflected by the object. An FFT unit  84  is coupled to an output of the receiver  83 , and a plurality of CPI memories  86 - 89  is coupled to an output of the FFT unit  84 . A like plurality of interpolation units  90 - 93  is coupled to the CPI memories, and a like plurality of unfolding units  94 - 97  is coupled to respective outputs of the interpolation units. A phase correction unit  98  is coupled to the unfolding units, a summation unit  99  is coupled to an output of the phase correction unit and a detection decision unit  100  is coupled to an output of the phase correction unit. 
     The transmitter  81  generates and transmits via the Tx antenna sequences of signals characterized by their PRF values. An electromagnetic wave reaches the object  82  and its echo returns to the digital receiver  83  via its Rx antenna. Without loss of generality the Tx and Rx antennae can be implemented by the same physical device. The receiver  83  is matched to the transmitted signals and digitized samples are fed to the FFT unit  84 , whose output is a sequence of CPI spectra for each PRF. The spectrum of each CPI is stored in a respective one of the memories  86 - 89  so that each memory stores the respective CPI spectra for a specific PRF. The received signals are shifted slightly from CPI to CPI with respect to the range-Doppler cells. It is to be noted that the terms ‘grid’, ‘map’ and ‘cells’ are equivalent and are used interchangeably through-out the specification. The interpolation units  90 - 93  serve to align the CPI signals with respect to the aforementioned cells. The results of the interpolation are unfolded by the unfolding units  94 - 97  by repeating the CPI-s range—Doppler maps up to the instrumented values of range and velocity. Each unfolded map is then phase-corrected by the phase correction unit  98  by multiplying the contents of each cell of the map by a respective complex exponent. The phase of each complex exponent is proportional to the product of the Doppler frequency and the time of the beginning of the appropriate CPI measured with respect to some reference time. Successful operation of the system  80  requires accurate estimation of these times. The phased corrected maps are fed to the summation unit  99  which generates a single map, which is fed to the detection unit  100 . The detection unit  100  calculates the absolute value of each cell of the resulting map and compares the resulting absolute values to respective thresholds to provide target detection decision. 
     It will also be understood that the system according to the invention may be a suitably programmed computer. Likewise, the invention contemplates a computer program being readable by a computer for executing the method of the invention. The invention further contemplates a machine-readable memory tangibly embodying a program of instructions executable by the machine for executing the method of the invention.