Abstract:
A double side band diplex linear frequency modulated superimposed radar system determines the range of targets as a function of the amplitude variation of reflected target Doppler signals. The present invention includes a real radar system that accurately determines the range of fading targets and the magnitude of the velocity of the targets. The present invention also includes a complex radar system that determines the relative velocity of targets in addition to the range of targets. The present invention also includes a real radar system having BPSK modulation. The selection of BPSK modulation enables or facilitates. the implementation of a portion of the system in digital form.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    This invention relates to radar systems (and sonar and ladar) and methods for determining the range of objects, and more particularly to radar systems and methods for determining the range of objects having little or zero relative velocity.  
           [0003]    2. Description of Related Art  
           [0004]    Radio Detection and Ranging (“Radar”) is commonly employed to detect and determine the range of objects or targets relative to the radar system. FIG. 1 is a diagram of a general radar system  1  and a channel or medium  2  that includes a target  30 . As shown in FIG. 1, the radar system includes a transmitter  10  having a transmit antenna  12  and a receiver  20  having a receive antenna  22 . In simple terms, the transmitter  10  generates a signal s(t) that is converted to an electromagnetic wave  14  by the transmit antenna  12 . The signal travels at the speed of light, c away from the transmit antenna  12  in the medium of the channel  2 . The signal may reflect off targets or objects Such as the target  30  in the channel  2 . The receive antenna  22  receives the reflected electromagnetic waves and generates a signal s r (t), which is processed by the receiver  20 . It is noted that the transmit antenna  12  and the receive antenna  22  may be in close proximity (monostatic radar systems). Alternatively, the transmitter  10  and the receiver  20  may be separated by a large distance (e.g., in bistatic radar systems).  
           [0005]    In radar systems the received signal s r (t) is nominally equal to αs(t−t r ). In such systems, t r  is the round trip delay or the time required for the electromagnetic wave to travel from the radar transmit antenna to the target and back to the receive antenna and α is an amplitude scaling coefficient. In such systems the target range is nominally equal to c×t r /2 where c is the speed of light (approximately equal to 3(10 8 )m/s in a vacuum). If the target is moving away from or toward the radar system (i.e., has a non-zero relative velocity), the relative velocity of the target may be determined from the frequency or Doppler shift of s(t). In particular, it is well known that the velocity of the target, v, is nominally equal to −ƒ d ×c/(2×ƒ 0 ) where ƒ d  is the Doppler frequency and ƒ 0  is the frequency of the transmitted wave  14  of s(t). These principles also apply to sonar and ladar (laser-based) target detection and ranging systems. In ladar the velocity of propagation is also the speed of light (the same as for radar). In sonar the velocity of propagation is the speed of sound (which varies with the nature of the medium in the channel).  
           [0006]    Various radar systems and methods have been developed to exploit these well-known attributes to measure the range or velocity of targets in different environments. For example, a prior art system  100  that is used to measure the range and velocity of objects is shown in FIG. 2. As is described below in more detail, the radar system  100  is a homodyned frequency shift keyed (“FSK”) diplex radar system. As shown in FIG. 2, the system  100  includes a signal generator or oscillator  101 , a transmit antenna  102 , a transmit coupler  103 , a receive antenna  106 , a mixer  104 , a switch  108 , a dual anti-alias filter  105 , and a signal processor  107 . The signal generator  101  alternately generates two transmit signals: s 1 (t)=Cos((ω 0 +ω 1 )t−θ 0 ) and s 2 (t)=Cos((ω 0 −ω 1 )t−θ 0 ). The signal generator  101  is thus a diplexed signal generator that alternates between the generation of the s 1 (t) and s 2 (t) signals. The transmit signals s 1 (t) and s 2 (t) are transmitted by the transmit antenna  102  via the transmit coupler  103 . The receive antenna  106  receives the reflected signals s r (t) from target objects where the signals are in the form of s(t−τ) (switching between s 1 (t−τ) and s 2 (t−τ)). Accordingly, s r (t) is equal to either:  
           Cos((ω 0 +ω 1 )( t −τ)−θ 0 ) or Cos((ω 0 −ω 1 )( t −τ)−θ 0 ).  
           [0007]    The received signal s r (t) and the transmit signals s 1 (t) and s 2 (t) are downconverted (mixed and low-pass-filtered) by the mixer  104  with the “local oscillator” (“LO”) signal Cos((ω 0 +ω 1 )t) and Cos((ω 0 −ω 1 )t). The variable θ 0  represents the phase delay of the signal generator&#39;s signal between the transmit antenna  102  and the mixer  104  LO signal. The resultant signal is the low pass filter (“LPF”) of s r (t)×s 1 (t) or s 2 (t) , which is either:  
           LPF {Cos((ω 0 +ω 1 ) t )Cos((ω 0 +ω 1 )( t −τ)−θ 0 )}=Cos((ω 0 +ω 1 )τ+θ 0 )  Eq. 1  
           LPF {Cos((ω 0 −ω 1 ) t )Cos((ω 0 −ω 1 )( t −τ)−θ 0 )}=Cos((ω 0 −ω 1 )τ+θ 0 )  Eq. 2  
           [0008]    The switch  108  is synchronized to the changes in frequency at the diplexed transmit signal generator  101  and thus generates two different outputs at ports  110  and  112  having signals, F1 and F2 nominally equal to Eq. 1 and Eq. 2 after anti-alias filtering by the dual anti-alias filter  105 .  
           [0009]    In the above equations, “τ” is the round trip propagation delay to the target. By substituting τ=(2/c)(R+Vt) and by letting ω d =ω 0 (2V/c) (note that the Doppler frequency is ƒ d =2Vƒ 0 /c), θ 0 ′−ω 0 (2R/c)+θ 0 , ω 1 ′=ω 1 (1−(2V/c))≈ω 1 , then ω 0 τ+θ 0 =ω 0 (2V/c)t+ω 0 (2R/c)+θ 0 =ω d t+θ 0 ′ and ω 1 τ+θ 1 =ω 1 (2V/c)t+ω 1 (2R/c)+θ 1 =ω 1 (2V/c)t+θ 1 +2ω 1 R/c=θ 1 +2ω 1 R/c. Therefore the equations that were written in terms of τ can also be written as:  
             F 2=Cos(ω d   t+θ   0 ′+2ω 1   R/c )) and  
             F 1=Cos(ω d   t+θ   0 ′−2ω 1   R/c )).  
           [0010]    Thus, the F1 and F2 signals of the radar system  100  have the same amplitude and frequency but have a different phase. The phase difference between the F1 and F2 signals is Δφ=2ω 1 τ=2(2ω 1 R/c)=(4π(2ƒ 1 )R/c). Accordingly for this system  100 , the range R is computed by the signal processor  107  as follows: R=(Δφ)c/(4π(Δƒ)) where Δƒ=2ƒ 1  is commonly called the “deviation frequency”. Targets of the prior art system (real FSK diplex Doppler radar) appear as signals of the form Cos(ω d t+θ 0 ′−2ω 1 R/c))−Cos(ω 0 (2V/c)t+θ 0 ′−2ω 1 R/c)).  
           [0011]    For outbound targets, i.e., targets with increasing range with time, the Doppler shift ƒ d  is negative. For inbound targets, i.e., targets with decreasing range with time, the Doppler shift ƒ d  is positive. The FFT spectrum for real receivers, however, is always symmetrical about its origin. Specifically, the negative frequency portion of the spectrum is equal to the complex conjugate of the positive frequency portion of the spectrum. It is because of this symmetry that target Doppler signals appearing in any Doppler bin may either be inbound targets or outbound targets, thus there exists a velocity direction ambiguity.  
           [0012]    Since the two halves of the spectrum in real receivers contain essentially the same information it is customary in real receivers to only process target information in only one half of the spectrum, e.g., in the positive frequency portion of the spectrum. In the prior art system  101  the direction ambiguity is resolved by observing the polarity of the measured delta phase. Since it is known that target ranges must always be positive it can be inferred whether the target information corresponds to an inbound or outbound target. It must be pointed out that resolving this ambiguity does not resolve inbound and outbound targets in the sense of having independent measurements. It is a weakness of the prior art system that the information for two targets with the same Doppler frequency, e.g., one inbound at +ƒ d  and one outbound at −ƒ d , will have their information appearing in the same FFT Doppler bin, resulting in a single corrupted measurement. The resulting measurement cannot be independent for each target since there is only one measurement. If it were possible for the Doppler information for each target to appear in separate FFT Doppler bins then the two targets would actually be resolved in the sense of having independent measurements for each target.  
           [0013]    As described above, in homodyned FSK radars, the transmit signal is alternated between a first frequency ƒ 0 +ƒ 1  and a second frequency ƒ 0 −ƒ 1  signal by the signal generator  101 . The signal generator  101  is commonly implemented using a Gunn oscillator. In operation a Gunn oscillator voltage bias or a varactor diode is used to tune the Gunn&#39;s frequency. The voltage is varied between two values to generate the s 1 (t) and s 2 (t) transmit signals. Any changes to the deviation frequency creates errors in the range calculations for the system  100 . Changes to the deviation frequency may occur, for example, due to temperature variations or aging of the oscillator  101 .  
           [0014]    Radars may be utilized in many different applications. In some applications, it may desirable to be able to determine the range of a target that has zero relative velocity. Such a system may be desirable when used in conjunction with a cruise control system in a vehicle or a side-facing radar to detect vehicles in adjacent lanes. Given the equations provided above, it is apparent that the prior radar system  100  is unable to determine the range of a target having zero relative velocity since the phase of the DC Doppler return voltage cannot be measured by a real receiver. In some applications for the radar system  100  this limitation may be undesirable or unacceptable.  
           [0015]    Another common problem with the performance from the prior art is that the diode mixers that are commonly employed as mixers in radar systems (such as the mixer  104 ) generate excessive low frequency noise. The range information present in the F1 and F2 signals of the prior art system  100  also occurs at low frequencies for these applications. Consequently these signals may become corrupted or distorted.  
           [0016]    In addition to being unable to determine the range of a target having zero relative velocity, the prior art system  100  also has difficulty determining the range of “fading targets”. A target appears as a fading target to a radar system when the radar signal reflected by the target has multiple reflections off the target such as from different points along the surface of a target. The numerous reflections of the signal that are reflected by the target generate constructive and destructive interference. In particular, the reception of multiple signals reflected from a single target can distort the phase of the received signal. In the prior art system  100  shown in FIG. 2, such a distortion of the phase also distorts or limits the accuracy of range determinations.  
           [0017]    Finally, the prior art system  100  of FIG. 2 may not be able to resolve range ambiguities. Target range is calculated by a phase measurement. All phase measurements are ambiguous in multiples of 360°. Therefore, it is possible for the prior art system  100  to detect a target and calculate its range with a large range ambiguity. Consequently, a need exists for a radar system that can accurately determine the range of targets with little ambiguity.  
         SUMMARY OF THE INVENTION  
         [0018]    The present invention includes a linear frequency modulation (“FM”) superimposed on diplex Doppler radar system that calculates target range using target Doppler amplitude information instead of target Doppler phase information. The system generates and transmits a double side band (“DSB”) modulated signal that is superimposed on a linear FM modulated radio frequency (“RF”) signal. The system is ideally a heterodyned system that has a low noise floor relative to typically high mixer noise levels at low target Doppler frequencies.  
           [0019]    The present invention includes a radar system for determining the range of targets. The system preferably includes a linear FM superimposed RF signal generator, an IF frequency generator, an IF modulator, an RF downconverter, an in-phase IF demodulator, and an out-of-phase IF demodulator. The linear FM superimposed RF signal generator generates a linear FM superimposed RF signal. The IF frequency generator generates an IF modulation signal, an in-phase IF modulation signal, and an out-of-phase IF modulation signal. The IF modulator is coupled to the linear FM superimposed RF signal generator and IF frequency generator and mixes the linear FM superimposed RF signal and the IF modulation signal to generate a transmit signal. The RF downconverter is coupled to the linear FM superimposed RF signal generator and mixes a received signal and the linear FM superimposed RF signal to generate an intermediate IF signal.  
           [0020]    The in-phase IF demodulator is coupled to the RF downconverter and the IF frequency generator and mixes the intermediate IF signal and the in-phase IF modulation signal to generate an in-phase baseband signal. The out-of-phase IF demodulator is coupled to the RF downconverter and the IF frequency generator and mixes the intermediate IF signal and the out-of-phase IF modulation signal to generate an out-of-phase baseband signal. The system may also include an RF coupler, a dual anti-alias filter, and a signal processor. The dual anti-alias filter suppresses undesirable non-baseband signal residuals from the demodulation process. The ratio of the amplitudes of the in-phase baseband signal and the out-of-phase baseband signal calculated in the signal processor includes information about the range of targets.  
           [0021]    The radar system may also include a transmit antenna. The transmit antenna is coupled to the IF modulator and converts the transmit signal to an electromagnetic wave. In addition, the radar system may include a receive antenna. The receive antenna is coupled to the RF downconverter. The RF downconverter receives electromagnetic waves and converts them to a receive signal. In a preferred embodiment, the IF frequency generator uses BPSK signals In the form of a pseudo random sequence for the IF modulation signal, the in-phase IF modulation signal and the out-of-phase modulation signal. In this embodiment, the three signals are related to each other by time delays. The in-phase IF modulation signal and the out-of-phase IF modulation signal always have a non-zero time delay relationship between them whereas the IF modulation signal usually has a nearly zero delay relationship with the in-phase IF modulation signal.  
           [0022]    Another possible embodiment would only restrict the in-phase and out-of-phase signals to be real valued signals with a non-constant cross-correlation amplitude function, preferably strongly correlated with the transmit modulation signal.  
           [0023]    In another embodiment, the IF frequency generator may include an oscillator and a plurality of counters. The oscillator generates a predetermined clock rate. The plurality of counters is coupled to the oscillator and generates at least two different signals. In this embodiment the clock rate of one of the at least two different signals corresponds to the IF modulation signal. The time delay between two of the at least two different signals corresponds to the phase delay between the in-phase IF modulation signal and the out-of-phase IF modulation signal. The IF modulation signal may have a clock rate of 1.25 MHz. The in-phase IF modulation signal and the out-of-phase IF modulation signal may have a clock rate of 83.33 KHz. One other signal may have a clock rate of 1.333 MHz for downconverting 1.25 MHz received signals to 83.33 KHz. In this embodiment the output of the first IF demodulator may nominally have a frequency of 83.33 KHz which is commonly called the “second IF” frequency. The signals at second IF frequency may be coupled to a second downconverter mixer. This receiver architecture is called a “dual downconversion receiver” when the signals output by the second downconversion mixer are at baseband. One skilled in the art may extend the idea of a dual downconversion receiver to a triple downconversion or a quadruple downconversion receiver, and so on.  
           [0024]    Any downconversion mixer could be implemented as an analog to digital (“A/D”) converter or sample and hold circuit. By making the A/D converter or sample and hold circuit sample the input signal at a rate equal to any harmonic of the IF frequency, the output samples will have essentially the same values as if the input signals were at baseband. This technique is called an “aliased downconversion receiver”. Such receiver implementations are also covered by the scope of this invention.  
           [0025]    The preferred embodiment of this invention includes the use of BPSK IF signals for modulation and/or demodulation. BPSK signals differ from sinusoidal signals in that they are comprised of principally two discrete states, such as from digital logic. The mathematical formulas presented in this document only describe the signals for the case of the use of sinusoidal IF signals, however this not a limitation of the scope of this invention. The use of squarewave BPSK IF signals results in very analogous behavior as when sinusoidal IF signals are used. A 90° phase delay of a squarewave BPSK IF signal, for example, can be produced by a time delay of ¼ period of the squarewave waveform.  
           [0026]    In another embodiment of the invention, the radar system includes an linear FM superimposed RF signal generator, an IF frequency generator, an IF modulator, a first RF downconverter, a first in-phase IF demodulator, a first out-of-phase IF demodulator, a phase shifter, a second in-phase IF demodulator, and a second out-of-phase IF demodulator. The first RF downconverter is coupled to the linear FM superimposed RF signal generator and mixes a received signal and the linear FM superimposed RF signal to generate a first intermediate IF signal. The first in-phase IF demodulator is coupled to the first RF downconverter and the IF frequency generator and mixes the first intermediate IF signal and the in-phase IF modulation signal to generate a real in-phase baseband signal. The first out-of-phase IF demodulator is coupled to the first RF downconverter and the IF frequency generator and mixes the first intermediate IF signal and the out-of-phase IF modulation signal to generate a real out-of-phase baseband signal. The phase shifter is coupled to the linear FM superimposed RF signal generator and shifts the phase of the linear FM superimposed RF signal by 90 degrees.  
           [0027]    The second RF downconverter is coupled to the phase shifter and mixes the received signal and the phase-shifted linear FM superimposed RF signal to generate a second intermediate IF signal. The second in-phase IF demodulator is coupled to the second RF downconverter and the IF frequency generator and mixes the second intermediate IF signal and the in-phase IF modulation signal to generate an imaginary in-phase baseband signal (“imaginary” in the mathematical sense of complex numbers). The second out-of-phase IF demodulator is coupled to the second RF downconverter and the IF frequency generator and mixes the second intermediate IF signal and the out-of-phase IF modulation signal to generate an imaginary out-of-phase baseband signal. Whenever an embodiment includes both a real and an imaginary component of a baseband time-domain target signal, such as with the in-phase baseband and out-of-phase baseband signals, it is usually called a “complex receiver”. The ratio of the amplitudes of the real in-phase baseband signal and the real out-of-phase baseband signal includes information about the range of targets.  
           [0028]    The present invention also includes a radar system having an linear FM superimposed RF signal generator, an IF frequency generator, a BPSK modulator, an RF downconverter and a BPSK demodulator. The linear FM superimposed RF signal generator generates an RF signal. The IF frequency generator generates a BPSK modulation signal, an in-phase BPSK demodulation signal, and an out-of-phase BPSK demodulation signal. The BPSK modulator is coupled to the linear FM superimposed RF signal generator and the IF frequency generator and modulates the linear FM superimposed RF signal with the BPSK modulation signal to generate a transmit signal. The RF downconverter is coupled to the RF signal generator and mixes the received signal and the RF signal to generate an intermediate IF signal.  
           [0029]    The BPSK demodulator is coupled to the RF downconverter and the BPSK demodulator and demodulates the intermediate IF signal to generate an in-phase baseband signal and an out-of-phase baseband signal. The ratio of the amplitudes of the in-phase baseband signal and the out-of-phase baseband signal includes information about the range of targets.  
           [0030]    The radar system may also include a transmit antenna. The transmit antenna converts the transmit signal into an electromagnetic wave. The radar system may also include a receive antenna. The receive antenna converts the received electromagnetic wave into an electrical signal. The radar system may also include a circulator. The circular allows the radar to use a single antenna for both transmitting signals and receiving signals by passing the transmit signal to the antenna and also passing the receive signal to the RF downconverter. It is also understood that in a ladar system using this invention, the antenna corresponds to an optical lens, mirror, laser, diode, or other apparatus for interfacing the transmit and/or receive signals into the medium of the channel. It is also understood that in a sonar system using this invention, the antenna correspond to an acoustical transducer, Such as an electromagnetic, electrostatic or piezoelectric speaker or microphone, for interfacing the transmit and/or receive signals into the medium of the channel.  
           [0031]    The radar system may also include a low-pass filter (“LPF”). The LPF is coupled to the demodulator output and lowpass filters the in-phase baseband signal and the out-of-phase baseband signal to remove non-baseband frequencies. The radar system may also include a sampling circuit and a signal processor. The sampling circuit may be an A/D converter or a sample and hold circuit. The sampling circuit samples the in-phase baseband signal and the out-of-phase baseband signal for use by the signal processor. The signal processor may transform the in-phase baseband signal and out-of-phase baseband signal from the time domain to the frequency domain by a Fourier transform operation before the calculation of target range from the in-phase baseband signal and the out-of-phase baseband signal.  
           [0032]    In this embodiment, the IF frequency generator may include an oscillator and digital logic. The oscillator generates a predetermined clock rate signal. The digital logic is coupled to the oscillator and generates at least two different signals. At least one of the two signals is used as the BPSK modulation signal. At least one of the two signals is used as the in-phase BPSK demodulation signal and a separate signal is used as the out-of-phase BPSK demodulation signal. In this embodiment the three signals are related to each other by time delays. The BPSK modulation signal often has a zero delay relationship with the in-phase BPSK demodulation signal. The out-of-phase BPSK demodulation signal always has a non-zero delay relationship with the in-phase BPSK demodulation signal.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0033]    The objects, advantages, and features of this invention will become readily apparent in view of the following description, when read in conjunction with the accompanying Figures, in which:  
         [0034]    [0034]FIG. 1 is a diagram of an application of a basic radar system in a channel.  
         [0035]    [0035]FIG. 2 is a block diagram of a prior art homodyned frequency shift keyed diplexed radar system.  
         [0036]    [0036]FIG. 3 is a block diagram of a real heterodyned linear FM superimposed DSB diplexed radar system in accordance with the present invention.  
         [0037]    [0037]FIG. 4 is a block diagram of a preferred complex linear FM superimposed radar system in accordance with the present invention.  
         [0038]    [0038]FIG. 5A is a block diagram of another preferred real heterodyned linear FM superimposed DSB diplex radar system using BPSK IF signals in a dual downconversion receiver made in accordance with the present invention.  
         [0039]    [0039]FIG. 5B is a block diagram of an exemplary BPSK IF signal generator for a dual downconversion receiver in accordance with one embodiment of the present invention.  
         [0040]    [0040]FIGS. 6A and 6B show plots of desirable linear FM ramping functions for use in the present invention. 
     
    
       [0041]    Like reference numbers and designations in the various drawings refer to like elements.  
       DETAILED DESCRIPTION OF THE INVENTION  
       [0042]    Throughout this description, the preferred embodiment and examples shown should be considered as exemplars, rather than limitations on the present invention.  
         [0043]    [0043]FIG. 3 is a block diagram of an exemplary linear FM superimposed radar system  200  according to the present invention. The system  200  is a real heterodyned linear FM superimposed DSB diplex radar system. As shown in FIG. 3, the system  200  preferably includes a linear FM superimposed RF signal generator  201 , a transmit antenna  202 , a receive antenna  203 , an RF downconverter  204 , an intermediate frequency (“IF”) modulator  205 , an in-line amplifier  207 , an in-phase IF downconverter  208 , a quadrature IF downconverter  209 , an RF coupler  211 , an intermediate frequency generator  212 , a dial anti-alias filter  217 , and a signal processor  215 . The linear FM superimposed RF generator  201  includes a linear frequency modulator  218  coupled to a varactor  219 . In the embodiment shown in FIG. 3, the linear FM superimposed RF generator  201  nominally generates an RF signal, s(t) having the form of Cos(ω′ 0 t−θ 0 )=Cos((ω 0 +2πγt)t−θ 0 ); where θ 0  is the phase delay of the generator signal between the RF generator  201  and the RF downconverter  204  and ω′ 0 =ω 0 +2πγt. The parameter γ describes the linear FM ramp rate in units of Hertz per second. Ideally θ 0  is set to a value so that the phase of the linear FM superimposed RF signal is zero at the LO port of the RF downconverter  204 . In one embodiment of the present invention, the linear FM superimposed signal generator  201  operates at a nominal frequency of 24.125 GHz. The linear FM superimposed RF signal is amplified by the inline amplifier  207  prior to the IF modulation stage.  
         [0044]    The intermediate frequency (“IF”) generator  212  produces three signals  215 ,  216 , and  217 , including an IF modulation signal, I mod    215 , an In-phase IF signal, I if    216 , and a Quadrature IF signal, Q if    217 . Nominally, the I mod , I if , and Q if  signals are equal to Cos(ω 1 t−θ 1 ), Cos(ω 2 t), and Sin(ω 2 t), respectively where θ 1  is the phase delay of the IF signal between the IF generator  212  and the IF modulator  205 . θ 1  is an offset phase to correct for any phase delay between the generation of the signal by the IF generator  212  and the IF modulator  205 . For the I if  and Q if  signals, ω 2  is an offset frequency when it is not equal to ω 1 . In some embodiments of the present invention, described below, ω 2  may equal ω 1  (no frequency offset). The IF modulator  205  modulates s(t) with I mod  to generate the transmit signal X mt (t) at the antenna  202 . The antenna  202  converts the transmit signal X mt (t) to an electromagnetic wave. Given the nominal values of s(t) and I mod , it can be shown that the transmit signal X mt (t) is equal to:  
         Cos(ω′ 0   t−θ   0 )Cos(ω 1   t−θ   1 )=Cos((ω′ 0 −ω 1 ) t −(θ 0 −θ 1 ))+Cos((ω′ 0 +ω 1 ) t −(θ 0 +θ 1 )).  
         [0045]    This last expression for X mt (t) shows that there are two sidebands present in the transmit waveform that are spaced ±ω 1  from the carrier frequency (ω 0 +2πγt), and hence the name Double Sideband Diplex Radar. In other embodiments of the invention the transmit signal X mt (t) could be a beam of light as in a ladar, or an acoustic wave as in sonar.  
         [0046]    The receive antenna  203  receives any reflected electromagnetic energy from targets and generates a receive signal R cv (t) where the signal is nominally equal to X mt (t−τ). Accordingly, R cv (t) is equal to:  
         =Cos(ω′ 0 ( t −τ)−θ 0 )Cos(ω 1 ( t −τ)−θ 1 ).  
         [0047]    The RF downconverter  204  mixes the linear FM superimposed RF signal s(t) with the receive signal R cv (t) and low pass filters the result to generate an intermediate IF signal DI if  which is nominally equal to:  
         =Cos(ω′ 0 τ+θ 0 )Cos(ω 1 )( t−τ)−θ   1 );  
         =Cos((ω 0 +2 πγt )τ+θ 0 )Cos(ω 1 ( t −τ)−θ 1 ).  
         [0048]    The In-phase IF downconverter  208  mixes the DI if  signal with the In-phase IF signal I if  and the dual anti-alias filter  217  anti-alias filters the result to generate a baseband In-phase DII signal  214  which is nominally equal to:  
         =Cos(ω′ 0 τ+θ 0 )Cos((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ); and  
         =Cos((ω 0 +2 πγt )τ+θ 0 )Cos((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ).  
         [0049]    The Quadrature IF downconverter  209  mixes the DI if  signal with the Quadrature IF signal Q if  and the dual anti-alias filter  217  anti-alias filters the result to generate a baseband Quadrature DIQ signal  213  which is nominally equal to:  
         =Cos(ω′ 0 τ+θ 0 )Sin((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ); and  
         Cos((ω 0 +2 πγt )τ+θ 0 )Sin((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ).  
         [0050]    As described above in the background of the invention section, “τ” is the round trip propagation delay to the target given by the expression τ=(2/c)(R+Vt). To simplify these equations lets define ω offset =(ω 2 −ω 1 ) and expand τ=(2/c)(R+Vt). With these substitutions the equations that nominally represent DII and DIQ can be written as follows:  
           DII =Cos{(2 /c )[(ω 0   V )+(2 πγR )+(2 πγVt )] t +[2ω 0   R/c −θ 0 ]}Cos{[ω offset +2ω 1   V/c]t+[ 2ω 1   R/c +θ 1 ]}; and  
           DIQ =Cos{(2 /c )[(ω 0   V )+(2 πγR )+(2 πγVt )] t +[2ω 0   R/c −θ 0 ]}Sin{[ω offset +2ω 1   V/c]t+[ 2ω 1   R/c +θ 1 ]} 
         [0051]    These equations can be simplified further by using some practical assumptions. For target velocities that are well below the speed of light we can assume that (2ω 1 V/c)t≈0. Likewise, for practical target ranges that are not astronomically large compared to the BPSK modulation rate we can assume that (2ω 1 R/c)≈0. To be rigorous, though, we will define ω′ offset [ω offset +2ω 1 V/c] and θ′ 1 =[2ω 1 R/c+θ 1 ]. The Doppler effect describes the frequency shift of the received signal due to relative motion between the target and the radar. Because of this we will define (2ω 0 V/c) =(ω d  as the Doppler (radian) frequency and (4πγR/c)=ω r  as the “range” (radian) frequency. (Note that the Doppler frequency is ƒ d =2Vƒ 0 /c.) We will also define θ′ 0 =[2ω 0 R/c−θ 0 ]. For most practical applications the extent of the LFM ramp is well below the RF center frequency (i.e. (γt)&lt;&lt;(ƒ 0 )) so the (2πγVt) tern will be ignored. Therefore the equations that nominally represent DII and DIQ can also be written as follows:  
           DII =Cos{[ω d +ω r   ]t+θ′   0 }Cos{ω offset   t+θ′   1 }; and  
           DIQ=Cos{[ω   d +ω r   ]t +θ′ 0 }Sin{ω offset   t+θ′   1 }.  
         [0052]    It is customary to refer to ω b =[ω d +ω r ]=[(2ω 0 V/c)+(4πγR/c)] as the “beat” (radian) frequency since the target appears at this frequency in the FFT processor. The beat frequency is sometimes (erroneously) called the Doppler frequency by practitioners in the art of LFM-CW radar but such usage is not consistent with the definition of the word “Doppler”.  
         [0053]    In one embodiment of the present invention, the offset is set to zero (ω 2 =ω 1 ) and θ 1  is also set to zero. The equations simplify to the following:  
           DII =Cos((ω d +ω r ) t+θ   0 ′) Cos(2ω 1   R/c ); and  
           DIQ =Cos((ω d +ω r ) t+θ   0 ′) Sin(2ω 1   R/c ).  
         [0054]    In a preferred embodiment of the invention, the DII and DIQ signals are FFT processed separately by the signal processor  215 . Although these signals have the same frequency and phase, they have different amplitudes depending on target range. The amplitude relationship between the two channels is DIQ/DII=Sin(2ω 1 R/c)/Cos(2ω 1 R/c)=Tan(2ω 1 R/c). Given this relationship, the diplex radar range equation for this architecture is Δφ=Arctan(DIQ/DII). Accordingly, the measured phase angle is converted to a measurement of target range by the signal processor according to the relationship R=(Δφ)c/(4πƒ 1 ). Notice that the linear FM component does not appear in this range calculation.  
         [0055]    By reviewing the equations derived above, one skilled in the art will appreciate that the range of a target is determined as a function of the amplitude of the signals rather than as a function of the phase of the signals as in prior art systems. This technique prevents against range determination distortion due to target fading. Note that the present invention uses a heterodyned receiver by using ω 1  as an intermediate frequency. This raises the signal to noise ratio by processing target signals at IF frequencies that have a lower noise floor than in the low frequency 1/ƒ noise region where diode mixers commonly employed as downconverters typically have very poor noise performance. As can be appreciated from the above equations, the radar system  200  can also resolve targets in relative velocity by means of the FFT processing. However, only the magnitude of the relative velocity can be determined, not the direction. That is the system can not distinguish between incoming or outgoing targets by the spectral components of the DIQ and DII signals alone based upon a single linear FM component γ.  
         [0056]    The value added by introducing the linear FM modulation to the BPSK modulation is the ability to distinguish inbound from outbound target velocities. Inbound targets result in positive values of ω d  Doppler frequencies whereas outbound targets result in negative values of ω d  Doppler frequencies. The Doppler frequency ω d  is added to the range frequency ω r  to form the beat frequency ω b . Whenever there is a nonzero LFM ramp rate γ the beat frequency will be different for targets at the same range that have opposite velocities. The signal processor  215  typically uses an FFT algorithm for target resolution. This means that separate targets are independently detectable (in the beat frequency dimension) and have independent measurements. It is well known to practitioners in the art of LFM-CW radar that there is a range-velocity ambiguity function. This is because the beat frequency is a function of both target range and target velocity. The beat frequency is given by the equation ƒ b =(2ƒ 0 V/c)+(2γR/c).  
         [0057]    It is a problem with the prior art of LFM-CW radar that each target measurement has a range-velocity ambiguity. Each measurement has an infinite number of target ranges and velocities that are possible. The range-velocity ambiguity is left to the target tracker algorithm to be resolved (to the extent possible). It is a strength of the current invention that each target measurement includes an unambiguous range measurement via R=(Δφ)c /(4πƒ 1 ). When the beat frequency is unambiguous, which is always true for the complex form of this invention and sometimes true for the real form of this invention, the velocity can be calculated without ambiguity from the equation  
         ω b =(2ω 0   V/c )+(4 πγR/c )  
         [0058]    by the equation  
           V= 0.5 ƒ   b ( c/ƒ   0 )− R (γ/ ƒ   0 )  
         [0059]    With the real form of this invention only the absolute value of the beat frequency is known initially (upon detection of the target&#39;s spectral peak at it&#39;s beat frequency) so there are at most two velocities and one range possible for each target measurement. The strength of this invention, therefore, is that the range-velocity ambiguity has been reduced from an infinite number of ranges and velocities to at most two velocities and one range for each measurement. This improves the radar system performance by greatly reducing the ambiguity of the measurements that are input to the target tracker algorithm.  
         [0060]    [0060]FIG. 4 is a diagram of another exemplary radar system  300  made in accordance with the present invention. The radar system  300  is a complex DSB heterodyned diplex radar system. The radar system  300  includes all of the components of the radar system  200  of FIG. 3 but further includes components to process the imaginary components of the received target signals. In particular, the radar system  300  further includes a first and a second power splitter  301  and  302 , a second RF downconverter  304 , a delay circuit  306 , a second In-phase downconverter  308 , and a second Quadrature downconverter  309 . The first power splitter  302  divides the power of the linear FM superimposed RF signal s(t) between a first and second output. The first output from the power splitter  302  is coupled to the RF downconverter  204 . The second output from the power splitter  302  is coupled to the delay circuit  306 . In the preferred embodiment the delay circuit  306  causes a 90° phase shift of the linear FM superimposed RF signal s(t), nominally to Sin(ω 0 t).  
         [0061]    The second power splitter  301  divides the power of the received linear FM superimposed signal R cv (t) between a first and a second output. The first output from the power splitter  301  is coupled to the RF downconverter  204 . The second output from the power splitter  302  is coupled to the second RF downconverter  304 . The second RF downconverter  304  mixes the phase shifted linear FM superimposed RF signal s(t+90°) with the receive signal R cv  and low pass filters the result to generate a second intermediate IF signal DQ if  which nominally is equal to:  
         =Sin(ω′ 0 τ+θ 0 )Cos(ω 1 )( t −τ)−θ 1 ) where ω′ 0 =ω 0 +2 πγt.    
         [0062]    The second In-phase IF downconverter  308  mixes the DQ if  signal with the In-phase IF signal I if  and the quad anti-alias filter  317  anti-alias filters the result to generate a baseband In-phase DQI  314  that nominally is equal to:  
         =Sin(ω′ 0 τ+θ 0 )COS((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ).  
         [0063]    The second Quadrature IF downconverter  309  mixes the DQ if  signal with the Quadrature IF signal Q if  and the quad anti-alias filter  317  anti-alias filters the result to generate a baseband Quadrature DQQ  313  which nominally is equal to:  
         =Sin(ω′ 0 τ+θ 0 )Sin((ω 2 −ω 1 ) t+ω   1 τ+θ 1 ).  
         [0064]    By generating both an undelayed IF and a delayed IF signal from downconversion mixers  204  and  304 , the radar system  300  becomes a complex receiver and the signal processor  315  can determine whether a target has a positive relative velocity or a negative relative velocity. In particular, due to the phase reference in the IF signals, the upper sideband can be distinguished from the lower sideband upon down-converting the received signals.  
         [0065]    It is an advantage of the radar system  300  that it can resolve the velocity direction ambiguity of the prior art system. The information for two targets of opposite directions and the same magnitude of Doppler frequency, e.g., one inbound at +ƒ d  and one outbound at −ƒ d  will have their information appearing in separate FFT Doppler bins. This is possible because in a complex receiver the time domain signals have the form:  
         Exp( j (ω d +θ 0 ′−2ω 1   R/c ))=Exp( j (ω′ 0 (2 V/c ) t+θ   0 ′−2ω 1   R/c ))  
         [0066]    where j equals the square root of minus one. As is well known to one of ordinary skill in the art, the information of targets with −ƒ d  Doppler frequency appear in the −ƒ d  FFT Doppler bin independently of the information of targets with +ƒ d  Doppler frequency, which appear in the +ƒ d  FFT Doppler bin. All that is needed here is to show how target signals received by the complex DSB diplex Doppler radar system  300  can be expressed as a complex rotating phasor time domain signal as given by the above equation. By using Euler&#39;s identity the complex rotating phasor time domain signal can be expressed as Exp(jX)=Cos(X)+jSin(X) where  
           X=(ω′   0 ω 1 )τ+θ 0 =(ω d τ+θ 0 ′−2ω 1   R/c=ω′   0 (2 V/c ) t+θ   0′ −2ω 1   R/c .  
         [0067]    This condition is satisfied when we form the following lower sideband signals for Exp(j((ω′ 0 −ω 1 )τ+θ 0 )):Cos(X)=DII+DQQ and Sin(X)=DQI−DIQ.  
         [0068]    This can be shown by using trigonometric identities. Ignoring scale factors, expanding on the four signals we get:  
           DII =Cos(ω′ 0 τ+θ 0 )Cos(ω 1 τ)=Cos((ω′ 0 +ω 1 )τ+θ 0 )+Cos((ω′ 0 −ω 1 )τ+θ 0 )  
           DQQ =Sin(ω′ 0 τ+θ 0 )Sin(ω 1 τ)=Cos((ω′−ω 1 )τ+θ 0 )−Cos((ω′ 0 +ω 1 )τ+θ 0 )  
           DQI =Sin(ω′ 0 τ+θ 0 )Cos(ω 1 τ)=Sin((ω′ 0 −ω 1 )τ+θ 0 )+Sin((ω′ 0 +ω 1 )τ+θ 0 )  
           DIQ =Cos(ω′ 0 τ+θ 0 )Sin(ω 1 τ)=Sin((ω′ 0 +ω 1 )τ+θ 0 )−Sin((ω′ 0 −ω 1 )τ+θ 0 )  
         [0069]    Alternatively, we could form the following upper sideband signals for Exp(j(ω′ 0 +ω 1 )τ+θ 0 )):Cos(X)=DII−DQQ and Sin(X)=DQI+DIQ.  
         [0070]    Notice that all four of the necessary signals, DII, DQQ, DQI, and DIQ, are formed by the complex DSB diplex Doppler radar system  300 . Thus the complex form of the present invention can both determine the direction of targets and resolve inbound and outbound targets with the same Doppler frequency, unlike the prior art system. Another benefit of such complex signal processing is that there are twice as many FFT Doppler bins (target resolution cells) with independent target information, for a given FFT length, than with a real receiver. This helps resolve targets that would otherwise collapse into the same FFT bin, improving target resolution and target detectability in applications with low target velocities (such as in cruise control) or applications with lots of target fluctuations (such as in detecting walking people).  
         [0071]    Another preferred embodiment of a real heterodyned DSB radar is presented with reference to FIG. 5A. The radar system  400  includes a linear FM superimposed RF signal generator  401 , a power splitter  402 , a circulator  403 , a receive and transmit antenna  404 , a Binary Phase Shift Keying (“BPSK”) Modulator  405 , an RF receive mixer  406 , a BPSK demodulator  408 , a dual BPSK demodulator  409 , a Dual Low Pass Filter (“LPF”)  410 , a Dual Analog-to-Digital (“A/D”) converter  411 , a BPSK Intermediate Frequency Generator for a Dual Downconversion Receiver  412 , and a Signal Processor  422 . As before, the linear FM superimposed RF signal generator  401  is an RF oscillator  419  and linear frequency modulator  418  that generate a linear FM superimposed RF signal s(t). The power splitter  402  splits the linear FM superimposed RF signal s(t) between the BPSK modulator  405  and the linear FM superimposed RF mixer or downconverter  406 . The intermediate frequency generator  412  generates a BPSK intermediate frequency modulation signal, I mod    415 , a demodulation signal, D emIn    418  and an In-phase signal and Quadrature IF signal, I if  and Q if    416  and  417 , respectively. The preferred operation of the IF generator  412  is explained in more detail below.  
         [0072]    The BPSK modulator  405  mixes the linear FM superimposed RF signal s(t) with the I mod  signal  415  to generate a transmit signal X mt (t) in a manner known to one of skill in the art. The transmit signal X mt (t) is passed through the circulator  403  to the transmit/receive antenna  404 . Note that separate transmit and receive antennas may be employed as shown in FIGS. 3 and 4. The transmitted signal X mt (t) is reflected off targets and received by the antenna  404  and converted to a receive signal R cv (t). The circulator  403  passes the received signal R cv (t) to the RF mixer  406 . The RF mixer  406  mixes or downconverts the received signal R cv (t) with the linear FM superimposed RF signal s(t) to generate an IF signal IF(t) as described above.  
         [0073]    The BPSK demodulator  408  downconverts or demodulates the IF signal to a secondary IF frequency IF 2  by mixing the signal with the D emIn  signal  418 . An exemplary BPSK demodulator  408  is described below. The result of this demodulation is a secondary intermediate IF signal. The dual BPSK demodulator  409  downconverts the secondary intermediate IF signal by mixing it with the I if  and the Q if  signals generated by the IF generator  412 . A preferred embodiment of a IF demodulator  409  is also described below. The downconverted intermediate IF signals are then low pass filtered by the Dual LPF circuit  410 . The demodulation performed by the dual BPSK demodulator  409  and the low-pass-filtering performed by the LPF circuit  410  produce the DII and DIQ signals in a similar manner to those described above. In the embodiment shown, these signals are further processed by the signal processor  422  to determine operation or control data that may be used by a system employing the radar system  400 . The dual A/D converter  411  converts the DII and DIQ signals to digital signals DII[n] and DIQ[n]. The DSP circuit  422  may perform numerous signal processing algorithms to interpret information present in these signals, such as the range to targets. Some possible algorithms the DSP  422  may perform are described below in more detail.  
         [0074]    As noted above, the intermediate frequency generator  412  generates the BPSK intermediate frequency modulation signal, I mod    415 , a demodulation signal, D emIn    418 , and an In-phase signal and Quadrature IF signal, if and Q if    416  and  417 , respectively. A preferred embodiment of an IF generator  412  is shown in FIG. 5B. As shown in FIG. 5B, the IF generator  412  includes a square-wave oscillator  501 , counters  502 , and an IF and IQ generator  405 . In a preferred embodiment, the square-wave generator or oscillator  501  generates square-wave at a 40 MHz rate. The counters  502  generate other square-waves at sub-harmonic frequencies of oscillator  501 .  
         [0075]    The IF and IQ generator  504  uses the output of the counters  502  to generate I and Q reference signals, I if  and Q if  at a rate of 83 kHz in a preferred embodiment. A counter  502  is used to generate the I mod  signal  415  at a rate of 1.25 MHz. Two counters  502  are also used to generate the D emIn  signal  418  at a rate of 1.333 MHz. Thus, the BPSK IF generator  412  generates the I mod , D emIn , I if , and the Q if , signals  415 ,  418 ,  416 , and  417 , respectively. These signals are used in the preferred BPSK radar system  400  described above with reference to FIG. 5A.  
         [0076]    In one embodiment of the present invention, the IF generator  412  may be implemented in a Programmable Logic Device (“PLD”) such as PLD number CY7C373-PLCC available from Cypress® Semiconductor, Inc. The PLD should be programmed to include the counters  502  and I &amp; Q generator  504  necessary to generate the I mod , D emIn , I if , and the Q if  signals  415 ,  418 ,  416 , and  417 , respectively.  
         [0077]    As described above with reference to FIG. 5A, the BPSK demodulator  408  downconverts or demodulates the IF signal by mixing the signal with the D emIn  signal  418 . The result of this demodulation is a second intermediate IF signal having a frequency of 83.33 KHz where the D emIn  signal  418  has a frequency of 1.3333 MHz. The dual BPSK IF demodulator  409  (FIG. 5A) downconverts the differential IF signal generated by the BPSK demodulator  408  by mixing the signals with the I if  and the Q if  signals generated by the IF generator  412 . The downconverted IF signals are low pass filtered by the LPF circuit  410 . The result of the demodulation by the IF demodulator  409  and the low pass filtering by the LPF circuit  410  are the DII and DIQ signals described above. The I if  and Q if  signals are synchronized with the I mod  and D emIn  signals as each of these signals are derived from the same 40 MHz clock  501 . The switches of the IF demodulator  409  effectively demodulate the differential BPSK IF signals. This results in the quadrature, baseband DII and DIQ signals at the Doppler frequency. The LPF circuit  410  includes a pair of conventional low pass Butterworth filters that are used to anti-alias filter the DII and the DIQ signals generated by the IF demodulator  409 .  
         [0078]    As described above with reference to FIG. 5A, the radar system  400  preferably also includes circuitry to determine the target range information present in the resultant DII and DIQ signals. The circuitry includes a dual or stereo Analog-to-Digital (“A/D”) converter  411  and a Digital Signal Processing (“DSP”) circuit  422  to determine the target range information contained in the DII and DIQ signals. The A/D converter  411  converts the analog DII and DIQ signals to digital DII[n] and DIQ[n] signals for processing by the DSP circuit  422 . The DSP  422  first performs a Fast Fourier Transform (“FFT”) (i.e., translates the DII and DIQ signals from time domain signals to frequency domain signals) on the DII and DIQ signals. The frequency domain DII[f] and DIQ[f ] signals are processed to determine target range and other information about the targets. In complex radar systems such as the radar system  300  of FIG. 4, the frequency domain information would include FFT bins representing negative and positive target Doppler frequency data. In real radar systems such as tile radar systems  200  (FIG. 3) described above, the frequency domain information would only include FFT bins representing the magnitude of target Doppler frequency data.  
         [0079]    The target information present in the FFT frequency bins may be used for many different applications. For example, the information may be used to determine the range of targets and then used to control the operation of a vehicle to avoid collision with targets or to modify the velocity of the vehicle (cruise control) accordingly. U.S. Pat. No. 5,302,956 issued on Apr. 4, 1994 to Jimmie Asbury, et al., and assigned to the owner of the present application provides an example of such an exemplary application. This patent is incorporated by reference herein for its teachings on the use of the target information present in the FFT frequency bins.  
         [0080]    Several embodiments of the present invention have been described herein. One of skill in the art will appreciate that modifications may be made to these embodiments without departing from the spirit and scope of the invention. For example, FIGS. 6A and 6B depict exemplary functions to be generated by the linear frequency modulators  218  and  418  of the present invention. The function  600  of FIG. 6A consists primarily of a down chirp  601  while the function  610  of FIG. 6B consists of an up chirp  612  and down chirp  611 . The function  610  when generated by the linear frequency modulator  218  and  418  may improve ranging and prevent possible blinding for ranges having the same magnitude (forward and backward, positive and negative).