Abstract:
A time-reversal imaging radar system for acquiring an image of a remote target includes an antenna array having a plurality of spaced-apart antennas, and a transceiver coupled to the antenna array for alternately transmitting a radar signal via the antenna array toward the target and for receiving target-reflected radar signals. The transceiver includes means for multiple-pass time-reversing the transmitted and received radar signals whereby coherent beam focusing is realized at both the target and at the receiver to thereby enhance the resolution of the acquired target image.

Description:
FIELD OF THE INVENTION 
   This invention relates generally to high resolution imaging radar. In particular, the invention relates to a time-reversed scanning imaging radar with an enhanced-resolution acquired target image. 
   BACKGROUND OF THE INVENTION 
   Time-reversal (sometimes referred to as phase-conjugation) has characteristics that make it highly attractive for radar applications. These include automatic tracking of moving targets and self-focusing, regardless of atmospheric turbulence without a need for any prior knowledge or iterative adaptive processing. However, the time-reversal proposed to date is limited to one-way distortion compensation. The operation of the conventional single-pass time-reversal radar is shown in  FIG. 1  and is as follows: 
   
     
       
             
           
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Operational principle of conventional single-pass time-reversal. 
             
           
        
         
             
               BEAM 
               BEAM CHARACTERISTICS 
             
             
                 
             
             
               a′ 
               A pilot beam illuminates the area that includes an intended 
             
             
                 
               target. 
             
             
               b′ 
               Part of the beam is reflected from the target. Its wavefront is 
             
             
                 
               distorted by the shape of the target. 
             
             
               b 
               Beam propagates through the atmosphere. Wavefront is 
             
             
                 
               further distorted. 
             
             
               c 
               Part of beam b arriving at transmitter/receiver (Tx/Rx) is time- 
             
             
                 
               reversed by Time-Reversal Mirror (TRM), and is reflected 
             
             
                 
               back toward the target. The wavefront c partially resembles b. 
             
             
               c′ 
               After transmission through the atmosphere, the beam c′ 
             
             
                 
               resembles b′ and so is focused on the target. Coherent beam 
             
             
                 
               focusing on a target 
             
             
                 
             
           
        
       
     
   
   As a result, the returned beam is coherently summed and focused at the target (c′). However, one should note that the coherent beam focusing is limited to the target side only, not at the transmitter/receiver (Tx/Rx) side, as can be appreciated by the distorted wavefront (b, c). This feature of target side-only focusing of the conventional time-reversal has limited its use for imaging or radar applications, which require compensation of distortion occurred by round trip and beam focusing at both target and Tx/Rx. 
   In order to obtain an image using time-reversal, the DORT (Decomposition of the time reversal operator) method has been proposed by Prada et al. (Prada C, Manneville S, Spoliansky D and Fink M, “Decomposition of the time reversal operator: detection and selective focusing on two scatterers,”  J. Acoust. Soc. Am.  99 2067-76, 1996.). 
   The method reconstructs targets by back propagation of the first temporal eigenvectors obtained by singular value decomposition. However, it has limited application to narrowband signal with a small number of discrete target points. Also, it requires information on detailed background boundary condition in order to back propagate the wave and to reconstruct an image. Further, these operations require a significant amount of computation time. 
   BRIEF SUMMARY OF THE INVENTION 
   According to the invention, a time-reversal imaging radar system for acquiring an image of a remote target includes an antenna array having a plurality of spaced-apart antennas, and a transceiver coupled to the antenna array for alternately transmitting a radar signal via the antenna array toward the target and for receiving target-reflected radar signals. The transceiver includes means for multiple-pass time-reversing the transmitted and received radar signals whereby coherent beam focusing is realized at both the target and at the receiver to thereby enhance the resolution of the acquired target image. 
   Also according to the invention, a method for radar imaging includes i) transmitting a first radar signal toward the target to reflect off the target as a first reflected radar signal; ii) receiving the first reflected radar signal; iii) processing the first reflected radar signal to generate a time-reversed radar signal; iv) transmitting the time-reversed radar signal toward the target whereby coherent beam focusing with the first radar signal is realized at the target, with the time-reversed radar signal reflecting from the target as a second reflected radar signal time-reversed with the first radar signal; v) receiving the second reflected radar signal whereby coherent beam focusing with the first radar signal is realized at the receiver; and vi) repeating steps i)-v) for a desired number of steering angles to thereby acquire a high resolution radar image. 
   The invention overcomes limitations of conventional time-reversal using double-pass time-reversal imaging and photonic beam scanning. The radar beam is coherently focused not only on the target (as is the case with conventional phase conjugation) but also at the transmitter/receiver (Tx/Rx), satisfying the conjugate imaging requirements. The beam is then scanned along both azimuth and elevation directions using a photonic beam forming network to obtain an entire image. The time-reversal imaging is a combination of conventional radar scanning and time-reversal. It can generate a high resolution image without requiring background information or any computation other than time-reversal. To improve resolution even further, the invention further includes extended virtual aperture (EVA) that is provided by ionospheric turbulence and sea clutter in case of HF-OTHR (high frequency-over-the-horizon radar). The multipath interference is coherently summed using phase conjugation and thus increases effective aperture size. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram of time-reversal imaging radar; 
       FIG. 2  is a schematic diagram of a time-reversal imaging radar process according to the invention; 
       FIG. 3  is a schematic diagram of an embodiment of a time-reversal imaging radar system according to the invention; 
       FIG. 4  is a schematic diagram of an embodiment of a time-reversal imaging radar system according to the invention; 
       FIG. 5  is a schematic diagram of an embodiment of a variable optical attenuator and delay generator array according to the invention; 
       FIG. 6  is a schematic diagram of an embodiment of a variable optical attenuator and delay generator array according to the invention; 
       FIG. 7  is a schematic diagram of an embodiment of a time-reversal imaging radar system according to the invention; 
       FIG. 8A  is a schematic diagram of a multiple digital beam former receiver according to the invention; 
       FIG. 8B  is a schematic diagram of a multiple digital beam former transmitter according to the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Consider a monochromatic beam propagating through a linear lossless distorting medium in  k  direction
 
 E   1 (   r ,t )= Re [ψ(    r   )· e   i(ωt−  k ·  r )   ]=Re[A   1 (   r   )· e   iωt ].
 
A 1 (  r ) reflects spatial modulation of information such as distortion and diffraction. Phase conjugation of E 2 (  r ,t) is defined as
 
 E   2 (   r ,t )= Re[ψ   • (    r   )· e   i(ωt+  k ·  r )]   =Re[A   2 (   r   )· e   iωt ],
 
where A 2 (  r )=A 1 (  r ).
 
To get E 2  from E 1 , we take the complex conjugate of the spatial part only, leaving the factor e iωt  intact. This is equivalent to leaving the spatial part alone but reversing the sign of t. That&#39;s why phase conjugation is often called time-reversal.
 
However, traditional phase conjugation works for only monochromatic waves and has limited applications, while time-reversal works for arbitrary waveforms.
 
   Referring now to  FIG. 2  and Table 2, the operational principle of the time-reversed double-passed extended virtual aperture (DPEVA) radar is described below in Table 2, noting that the “BEAM” is as shown in  FIG. 2  with the corresponding number. To illustrate the concept described in Table 2, a basic radar system is illustrated in  FIG. 2  that includes a TRM, a switch array, an antenna array, and a beam former. 
   
     
       
             
             
           
             
           
             
             
           
             
           
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
               BEAM 
               BEAM CHARACTERISTICS 
             
             
                 
             
           
           
             
               a 
               Beam Former (Scanner) sends collimated beam at an angle θ 
             
             
               a′ 
               Beam propagates through the atmosphere and its wavefront is 
             
             
                 
               distorted due to atmospheric turbulence, clutter and 
             
             
                 
               diffraction. 
             
             
               b′ 
               Part of the beam is reflected from the target. Its wavefront is 
             
             
                 
               further distorted by the shape of the target. 
             
             
               b 
               Beam propagates through the atmosphere. Wavefront is even 
             
             
                 
               further distorted. 
             
             
               c 
               Part of beam b arriving at antenna array is time-reversed by 
             
             
                 
               TRM and is reflected back toward the target, with its 
             
             
                 
               wavefront partially resembling b. 
             
             
               c′ 
               After transmission through the atmosphere, the beam 
             
             
                 
               resembles b′ and so is focused on the target. 
             
           
        
         
             
               Coherent beam focusing on a target 
             
           
        
         
             
               d′ 
               c′ (part of b′), after reflection from target, resembles part of b′ 
             
             
                 
               (reversability of wave) 
             
             
               d 
               d′ (part of a′) converges to original a, resulting in beam 
             
             
                 
               focusing due to coherent summation at Tx/Rx 
             
           
        
         
             
               Coherent beam focusing at Rx 
             
           
        
         
             
                 
               Vary the beam angle sequentially along the azimuth and 
             
             
                 
               elevation directions (as with conventional radar) and repeat 
             
             
                 
               the above procedures (a-d) to cover the entire field of regard 
             
             
                 
               (FOR) and to obtain high resolution imaging radar 
             
             
                 
                 
             
           
        
       
     
   
   One of the most interesting features of the double-pass phase conjugation for radar imaging application is that the radar beam is focused at both target and receiver, satisfying imaging requirements regardless of atmospheric turbulence, as shown in  FIG. 2  and Table 2. 
   In addition, the focused second-time conjugate wave illumination increases signal-to-noise ratio by two times in dB. For example, 10 dB SNR with a single-pass becomes 20 dB with double-pass due to squaring effect after double-pass. 
   By varying the beam angle sequentially along the azimuth and elevation directions using a photonic beam former as described below with reference to  FIGS. 3-4 , high resolution imaging can be achieved due to the tight beam focusing at both ends (see  FIG. 2 : target  5  and Tx/Rx after beam forming ( 6 )), exactly the same way as an optical lens forms an image. 
   In this case, a returning beam after double-pass conjugation is along the same direction as the original steered transmitted beam regardless of distortion. As a result, after passing through the same beam former, the beam is coherently focused, making constructive interference at the receiver end. 
   Extended Virtual Aperture for High-Frequency Over-the-Horizon Radar (HF-OTHR) 
   To improve the resolution even further beyond the diffraction limit, the invention includes an extended virtual aperture mechanism. Traditionally, multipath interference has been one of the major hurdles in various communications. However, the multipath interference can be exploited to obtain super-resolution beam focusing in both space and time, e.g. as described in B. E. Henty and D. D. Stancil, “Multipath-Enabled Super-Resolution for rf and Microwave Communication using Phase-Conjugate Arrays,” Phys. Rev. Lett. 93, 243904 (2004), and in M. Fink, “Time-Reversed Acoustics,” Sci. Am. 281(5), 91 (1999). Such beam focusing is due to the randomly positioned EVA effect that stretches a signal beam both in space and time. In these publications, both groups experimentally demonstrated that in a multipath-rich environment, a beam can be focused to a spot that is more than an order of magnitude (15 times and 80 times along azimuth and range directions, respectively) smaller than would be possible in a line-of-sight configuration without multipath interference. Advantageously, OTHR operates in an environment where various multipath and bifurcation effects due to ionosphere, sea surface, and ground reflections, etc. are significant. Utilizing this phenomena, resolution can be drastically improved beyond the diffraction limit. 
   Implementations of Time-Reversed Double-Pass Extended Virtual Aperture (DP-EVA) Radar 
   There are several methods for implementing phase conjugation, including a nonlinear-optical approach using χ (3)  or χ (2) -photorefractive effect, time-reversal, an electrical mixer to multiply signal with double-frequency local oscillation signal, and so on. The invention in different embodiments includes both time-reversal and frequency-domain mixer techniques, as follows. 
   Time-Reversal Embodiment: 
   Referring now to  FIG. 3 , in one embodiment the invention employs time-reversal. A radar system  10  includes a transmitter/receiver (transceiver)  11  having a plurality 1 to N (1:N) of input/output (I/O) channels  26  each coupled to an antenna  28  of an antenna array  30 . Transceiver  11  includes a signal generator  12 , for generating a RF carrier signal to an input  13  of an optical circulator  42  and then via circulator input/output  16  to a TTD (True time delay) fiber-optic beam former circuit  18 . Beam former circuit  18  splits the input signal by an 1:N splitter  21  and introduces a time delay into each respective split signal to produce a plurality of time-delayed signals at outputs  20 . Each I/O  20  is coupled to an input  22  of a time-reverser  24  time-reverser with each input/output (I/O) channel  26  coupled to a corresponding antenna  28 . 
   Transceiver  11  transmits by antenna array  30  a first radar signal formed by the fiber-optic beam-former  18  directly through the path  39  (dotted line) without passing through the time-reverser  24 . The returning signal reflected off a target is input to each I/O channel  26  of time-reverser  24 . The signal is down-converted to slower baseband I(t)  36  and Q(t)  38  and is subsequently digitized and time-reversed by a computer  80 . The time-reversed baseband signals I(−t), Q(−t) and the phase control signal π/2  40  generate a time-reversed version of the first-time reflected signal by the time-reverser  24 . 
   The time-reversed signal is re-transmitted. This third beam experiences beam focusing at the target, and reflects from the target as a fourth beam. The fourth beam returning to the antenna  28  passes through the path  39  that bypasses time-reversal  24 . The signal is then passed through the same beam former  18 , combined by the 1:N splitter/combiner  21 , and is converted to an electrical signal by an optical electrical (O-E) converter  50  to form a sharply focused RF output  52 . The double-pass, double beam-focused, beam-steered signal  52  is output to a monitor, e.g. an oscilloscope (not illustrated), for displaying the acquired radar image of the target. 
   The above procedures are repeated for all beam angles by varying the beam direction using the TTD Fiber-optic beam former. 
   In this embodiment in which phase conjugation is obtained using a time-reversal technique, signal generator  12  includes a laser source  32 , e.g. a distributed feedback (DFB) laser, coupled to a modulator  34 , e.g. an analog intensity modulator (lithium niobate or electro-absorptive), that encodes the baseband laser optical signal onto a carrier wave ω that is input into modulator  34 . Output  16  from the circulator  42  is coupled to splitter/combiner  21  with a plurality of channels  16  that are the beam steerer  18  inputs. A reversed signal in the time-domain is equivalent to phase conjugation in the space domain. Time-reversal is useful for broadband beam operation since all the frequency components in a signal are simply stored and reversed and retransmitted. In order to process high speed signals, I-Q modulation is used to down-convert the rf signal, as is described in G. Lerosey, J. de Rosny, A. Tourin, A. Derode, G. Montaido, and M. Fink, “Time Reversal of Electromagnetic Waves,” Phys. Rev. Lett. 92(19), 193904 (2004), incorporated herein by reference. In addition, a photonic beam former is used prior to the phase conjugator to achieve beam scanning needed for acquiring a radar image. A baseband signal includes a inphase (I) cosine component and a quadrature (Q) sine component. The desired time-reversal can be obtained by changing I(t), Q(t) and phase=π/2 to I(−t), Q(−t) and phase=−π/2, respectively, while maintaining precise timing relationship among elements, as is illustrated in the lower left box in  FIG. 3 . In the time-reversal implementation shown in  FIG. 3 , a hybrid approach was employed in the sense that signal is digitized and time-reversed at the baseband using I-Q modulation. Also, fiber-optics was used for both time-delay generation and precise high speed signal distribution. 
   Operational Procedure 
   Initially, equalize the pathlengths and attenuation between modulator  34  and the antennas  28  using the VOADGA beam former  18  as follows: Using a network analyzer, measure amplitude and phase (delay) between the modulator  34  and a probe located at each antenna  28 . Adjust the amplitude and phase by using the VOADGA beam former  18 , with either I or Q at a constant DC voltage level. This procedure is repeated for all the antenna elements  28  one by one, while maintaining the probe position precisely in the same plane. Also, the same procedure is repeated for all the beam steering angles to form a look-up-table (LUT) for future calibration. Furthermore, using the similar procedure, make sure that both I and Q signals are synchronized across all the elements. After the equalization is completed, the following procedure is repeated for all different steering angles to obtain an entire image: 
   1) Steer beam direction along (θ, φ) using the VOADGA based on the LUT. 
   2) Send a train of signal through the path  39  by bypassing the time-reverser  24 . 
   3) Receive returning signal bounced back from a target. Down-convert the signal using the time-reverser  21  to generate baseband signals I(t) and Q(t). Digitize and store the signal  40  inside a computer  80  on a computer readable medium, e.g. in RAM, on a hard drive, or other computer readable media. 
   4) Calculate time-reversal of the baseband signals I(t) and Q(t) by reversing the signal in time. Also, set the phase angles of all the vector modulators to −π/2 in order to reverse carrier signal. 
   5) Send the time-reversed signal. 
   6) Switch the phase of vector modulator to normal mode by switching the phase angle from −π/2 to π/2. 
   7) Receive the double-pass returning signal through the bypassing path  39 . 
   8) Pass the signal through the originally steered beam former to negate the original beam steering by canceling out the steering angle at each element. 
   9) The unsteered collimated beam is summed and is converted to an electrical signal by O-E converter  50  to form a focused RF beam  52  after coherent summation. 
   The acquired radar image may then be displayed on an oscilloscope or other type of monitor, and analyzed for target identification. 
   Frequency-Domain Phase-Conjugation Method 
     FIG. 4  depicts another method to implement time-reversed DPEVA radar using mixers for narrow-band applications. In this case, beam is initially steered along some certain direction using the fiber-optic beam steerer  18 . In this embodiment, phase conjugation is carried out in the frequency domain using electrical mixers  44 . The laser input signal is modulated and split into N channels. The signal in each channel is then time-delayed by the fiber-optic beam steerer  18 , converted to electrical signal by electrical-optical/optical-electrical (E-O/O-E) converter  46 , and is directly connected to the corresponding Tx/Rx&#39;s antenna (as illustrated by the dotted line). The beam reflected off the target is passed through the antenna and is mixed with double frequency signal by the electrical mixer  44 . The output from the mixer  44  is a phase-conjugate signal of the received signal after bandpass filtering by a band pass filter (BPF)  48 . 
   The phase conjugate signal is retransmitted by the corresponding antenna through an electronic circulator  43 , which routes signal along the counter-propagation direction. The second-time returning signal is converted to an optical signal by E-O/O-E converter  46  after bypassing the mixer (along the connection path indicated by the dotted line). The optical signal passes through the same fiber-optic beam former  18  and is summed after 1:N splitter and the circulator  42  and is converted to electrical signal by O-E converter  50 . In this bi-directional architecture, the related components including VOADGA, O-E/E-O converters must be bi-directional. Also, in order to avoid unwanted coherent optical noise fluctuation after summing the optical signals, the coherence of E-O converter  46  should be reduced to a desired level. 
   In both embodiments shown in  FIGS. 3 and 4 , beam steerer  18  preferably is a variable optical attenuator and delay generator (VOADGA)  100 , shown in more detail in  FIGS. 5 and 6 . The VOADGA beam former  100  is an array of a combination of a variable optical attenuator (VOA)  102  and a variable delay generator (VDG)  104 . The VOA  102  should be able to reduce light intensity with a large dynamic range (e.g., at about a 13 bit resolution) so that it can function as an on/off switch as well. The VDG  104  preferably generates time delays up to about Ins (depending on N), with a resolution of about 0.5 ps. Although VOAs using various technologies such as liquid crystals, MEMS, PLC, etc, are readily available, and VDGs are commercially available as COTS components, the invention provides an integration of the two functions in a compact package. As such, VOADGAs  100  function as an optical equivalent of the delay and amplitude adjusting units in an RF front-end, and are amenable to other applications requiring the functionality including various coherent analog signal processing such as phased array antennas, coherent communications, RF link emulation, THz signal generation and femto-second pulse shaping, phase noise measurement, and optical signal processing. 
   VOADGA beamformer  100  can be implemented using bulk optics by inserting a corner cube  106  mounted on a translation stage inside a VOA  102 , as shown in  FIG. 5 . Light from a fiber is collimated by a micro-collimating lens (e.g. GRIN lens) and is modulated by a VOA which is a spatial light modulator to vary the amplitude of output light. Various devices such as liquid crystals, MEMS (micro-electro-mechanical system), electro-optic crystals (PLZT, lithium niobate, etc.) or acoustic modulators can be used for this purpose. The modulated light is suitably delayed by translating a corner cube to generate desired time delay and is passed through the VOA again. Such double-pass though a VOA increases dynamic range significantly—twice in dB. The output light from the VOA is coupled to an output fiber through a micro-focusing lens. To permit compact packaging, micro-optic miniaturization of components and integration technique can be used. The entire package is hermetically sealed to provide environmental stability. 
   VOADGA beamformer  100  can be implemented using the PLC technology as shown in  FIG. 6 . VOADGA beamformer  100  for VOA  102  utilizes a Mach-Zehnder waveguide interferometer-type VOA  108  to provide variable attenuation of light (VOA) input from a laser input signal. The attenuated light is then delayed in DGA  104  utilizing digital waveguide crossbar switches  110  (illustrated for N=4 channels). VOA  102  and DGA  104  are integrated on a single substrate, as discussed above. PLC-based DGA&#39;s are commercially available from several vendors including Little Optics in MD. By incorporating the VOA part with the existing PLC-based DGA, VOADGA functionality can be achieved. 
   All-Digital Time-Reversal Method 
   Another embodiment of implementing time-reversal in an all-digital manner is shown in  FIG. 7 . In the radar system  200  that includes a transceiver  61 , the received signal is digitized at the element (carrier frequency) level and all the subsequent operations are achieved digitally, without requiring any hardware such as down-converting mixers or bandpass filters. In this case, sampling speed must be approximately ten times higher than carrier frequency (much faster than Nyquist sampling rate) to faithfully depict high speed signals in the time domain. 
   Transceiver  61  includes a digital beam former  62  that generates an array of N (number of antenna elements) digital RF carrier signals (shown as ‘a’ in  FIG. 7 ), suitably delayed among elements to steer the beam along the desired direction. In a transmitter circuit  63 , The digital signal is buffered in a fast memory  76 , converted to an analog signal by a digital-to-analog converter (DAC)  74  at each element 
   Triggered by a synchronization signal  78 , the signal is transmitted by an antenna  28  after amplification by a high-power amplifier (HPA)  72  through a switch  70 . 
   The first-time returning signals from a target pass through the antenna array  30  and an array of switches  70  that is now switched to a receiver circuit  67  that includes a low-noise amplifier (LNA)  68 . The signal is then amplified and is digitized by an ADC  66  at the carrier (or element) level without down-conversion. The digital signal is stored in a fast memory  64  and is transferred to a computer  80  (shown as ‘b’). 
   The signal is then time-reversed by the computer  80  and is loaded in a fast memory  76  (along ‘c’). The time-reversed signal is then converted to an analog signal by a DAC  74 , is amplified by the HPA  72  and is retransmitted by an antenna  28 . 
   Second-time returning signal is passed by the switch  70 , which, this time, is set to LNA. The signal is amplified ( 68 ), digitized ( 66 ), and is captured ( 64 ). The signal is then passed through the digital beam former  62  (along ‘d’), which was originally set to a particular direction. After passing through the beam former, the original steered beam angle is compensated and the resulting beam points along the broadside direction, which sums up coherently to form a sharp beam focusing by a computer  80 . 
   All the timing control and synchronization can be achieved using time-stamping with a fast digital clock. Also, recent fast-growing DSPs (digital signal processors) and FPGAs (Field programmable gate arrays) would allow massively parallel interconnection and computing necessary in this architecture. Such FPGA and DSP-based beam forming can be achieved either in frequency domain using fast Fourier transform or in time-domain using tapped delay lines. 
   Such an all-digital approach has many advantages: Hardware becomes much simpler without requiring any mixers, band-pass filters, and fiber optics. Also, the system can be very flexible since all the configuration can be re-configured using software. Such a flexible reconfigurability allows for more advanced architectures such as ubiquitous radars, which will be described later. 
   Current ADC technologies are not sufficient to digitize high frequency microwave signals at the carrier level. However, this technology is developing very fast these days. 
   Ubiquitous Digital Time-Reversed Radar 
   A ubiquitous digital time-reversed radar can be implemented with the same system shown in  FIG. 7 . The only difference is that the digital beam former  62  must be multiplexed to handle multiple beams simultaneously. 
   Such a multiple beam former can be implemented by duplicating the single beam former to cover various angles concurrently. Each set of time-delays in the beam-former corresponds to a specific beam direction, as is the case with conventional phased array antenna. Therefore, for ubiquitous operation, multiple sets of time-delays are required, which often causes prohibitive hardware complexities when multiplicity is large. 
   Another way of implementing the multiple beam former is by Fourier transformation. In this case, each Fourier component corresponds to a specific beam angle. 
   One such embodiment shown in  FIG. 8  ( a ) is a multiple digital beam former for reception, that is, a receiver. The incoming signal ( 90 ) from antenna elements I-N  28  is Fourier transformed by a Fast Fourier Transform (FFT) processor  92 . The output ( 94 ) from the FFT processor is the Fourier transform where represents a beam steering angle. Each Fourier component represents a sum of all the incoming beams steered along direction. The field pattern is a scaled (demagnified) version of the far-field radiation pattern on the target plane. 
     FIG. 8(   b ) shows a transmitter part of the multiple digital beam former. A set of 1-N inputs ( 94 ) is inverse Fourier transformed by the multiple digital beam former Inverse Fast Fourier Transform processor (IFFT)  96  to generate a set of output signals. Each output signal is converted to an analog signal  74  and is amplified before transmission by an antenna  28 . 
   These FFT/IFFT can be implemented using modern DSP or FPGA as described previously. Also, both transmitter and receiver may be combined into a single system using bi-directional components. 
   In order to insert time-reversal functionality, the output from the ADC  66  can be tapped into a computer  80 , as shown in  FIG. 7 . The time-reversed signal is then launched to the transmitter through DAC, HPA and switches. 
   III-3. Operational Modes 
   Systems  10  and  200  mainly operate in a pulsed mode whose pulsewidth is shorter than round-trip time of signal, as is common with conventional radars including synthetic aperture radars and HF-OTHRs (high-frequency over the horizon radars). However, it can also be operated in an iterative mode by resending the double-pass signal after switching the phase of the vector modulators between −π/2 (time-reversal) and π/2 (normal). In this way, iterative time-reversed signal can be focused to a target that has the strongest reflection. This feature is currently used for medical or mine detection applications. 
   The invention has been described with reference to certain preferred embodiments thereof. It will be understood, however, that modification and variations are possible within the scope of the appended claims.