High range resolution radar through non-uniform sampling

A frequency modulated continuous wave (FMCW) radar system having a voltage controlled oscillator (VCO) for transmitting a RF signal and a linearizer for linearizing the VCO. The FMCW receives the transmitted RF signal as an input and outputs a signal to a modulator, which successively sweeps the VCO frequency over a defined range. The receiver mixes a return signal with a sample of the transmitted RF signal to derive an IF signal. An adaptive frequency sample clock drives an analog to digital converter to sample and digitize the IF signal, with the clock being derived from the transmitted RF signal.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates to the field of electronic radar, and more
 particularly to apparatus for reducing the operating requirements on a
 linearizer by accounting for non-linearities in the transmitted waveform
 via processing in the radar receiver.
 2. Description of the Related Art
 A frequency modulated continuous wave (FMCW) radar system often uses linear
 frequency modulation to provide accurate range information. The resolution
 of the ranging information is directly dependent on the linearity of the
 transmit signal. A great deal of prior art exists related to linearizers.
 For example, applicant owns U.S. Pat. Nos. 5,642,081 and 5,379,001, both
 directed to closed loop linearizers. The entire contents of U.S. Pat. Nos.
 5,642,081 and 5,379,001 are hereby incorporated by reference. Applicant
 also owns U.S. Pat. Nos. 5,172,123 and 4,692,766, which are directed to
 linearizers for FMCW radar transmitters, and the entire contents of U.S.
 Pat. Nos. 5,172,123 and 4,692,766 are hereby incorporated by reference.
 Other prior art related to linearizers are found in U.S. Pat. Nos.
 4,539,565, 4,593,287 and 4,754,277, all assigned to The Boeing Company.
 U.S. Pat. No. 5,189,427 assigned to U.S. Philips Corporation also relates
 to FMCW radar linearizers.
 The prior art corrects for non-linearities in the transmitted waveform via
 further processing in the transmitter, which makes the transmitter
 circuitry unduly complicated. What is needed is a circuit which can
 correct for non-linearities in the transmitted waveform without unduly
 increasing the operating requirements on the transmitter circuitry.
 SUMMARY OF THE INVENTION
 Applicant has overcome the problems of the prior art by inventing a FMCW
 radar system which reduces the operating requirements on the linearizer
 portion of the transmitter circuitry by taking account of the
 non-linearities in the transmitted waveform via processing in the radar
 receiver.
 This is accomplished by replacing the fixed frequency sample clock used to
 digitize the IF signal in the prior art FMCW radar system with a sample
 clock which is derived from the transmitted waveform itself. Rather than
 sample uniformly spaced in time using the fixed frequency sample clock,
 the inventive FMCW radar system shows small deviations from linearity as
 nonuniform time sampling, but uniform phase sampling in the receiver
 analog/digital (A/D) converter.
 The output of the linearizer delay and mixing circuitry portion of the
 transmitter circuitry is multiplied in frequency, if necessary, by a fixed
 factor N, to achieve at least the Nyquist sampling rate, to directly
 become the A/D sample clock. As is well known in the art, the Nyquist
 sampling rate is the sample rate above which no aliasing or spectral
 overlap occurs.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
 While this invention may be embodied in many different forms, there are
 shown in the drawings and described in detail herein specific preferred
 embodiments of the invention. The present disclosure is an exemplification
 of the principles of the invention and is not intended to limit the
 invention to the particular embodiments illustrated.
 FIG. 1 is a block diagram showing a simplified prior art FMCW radar system.
 As is well known in the art, a typical prior art transmitter includes a
 voltage controlled oscillator (VCO) 10 for transmitting a RF signal, a
 linearizer 12 for linearizing the VCO, which receives the transmitted RF
 signal as an input and outputs a signal to a modulator 14, which
 successively sweeps the VCO frequency over a defined range. For linear
 sweep modulation the transmitted frequency linearly changes from the
 starting to the stopping frequency over the modulation period. If the
 instantaneous frequency deviates from the linear frequency ramp during the
 modulation period, the linearizer 12 senses the deviation and feeds that
 error to the modulator to correct the deviation.
 The prior art receiver typically mixes a return signal 16 with a sample of
 the transmitted RF signal 18 with receiver mixer 20 to derive an IF
 signal. The return signal 16 is a time-delayed version of the transmitted
 signal, aside from amplitude weighting due to path loss and target
 effects. While the signal returned from the target is in transit, the
 transmitter frequency continues to sweep. The frequencies of the two
 signals 16 and 18 then differ at the receiver by an amount equal to the
 product of the slope of the transmitted frequency vs. time and the time
 delay to the target and back. The receiver mixer 20 mixes the two signals
 16 and 18 with the output, amplified and filtered at 21 resulting in an IF
 difference frequency proportional to range to the target. Simultaneous
 signals from several targets at different ranges are separated by a filter
 bank, each filter 22 corresponding to a different target range. The filter
 outputs are then detected at detectors 24, and integrated, if desired,
 with integrators 26, to form the radar range gate outputs.
 The spectrum of the return signal 16 from an ideal target will be a single
 spectral line if the transmitted waveform is truly linear. Since the
 transmitted waveform is periodic, the return signal spectrum will consist
 of spectral lines spaced at intervals of 1/(modulation period T) Hz. The
 minimum width of the spectrum will be one spectral line. Nonlinearities in
 the transmitted waveform will broaden the return signal spectrum and
 reduce the peak power. The broadening limits the achievable range
 resolution and reduction in peak power reduces the signal-to-interference
 ratio and hence system probability of detection.
 FIG. 2 is a block diagram showing a simplified prior art
 linearizer/modulator system, with a sampled version of the transmitted
 signal 28 mixed with a time delayed version of the transmitted signal 30
 at mixer 32, to form the difference frequency. The transmitted signal 28
 is time delayed using delay device 29 as is well known in the art. The
 difference frequency will be constant if the transmitter waveform is
 linear and will change in proportion if the waveform is not linear. The
 difference frequency is filtered at 34 and the instantaneous difference
 frequency is measured by the frequency discriminator 36 and compared at 38
 to the set value frequency 40. The error output signal 42 is filtered at
 lowpass loop filter 44 and added to the basic modulation waveform,
 produced with modulation waveform generator 47, at 46 to produce a tuning
 signal which frequency modulates the VCO 10.
 FIG. 3 is a block diagram of a prior art digital receiver implementation of
 the FMCW radar system of FIG. 1, in which the receiver IF signal is
 sampled with an A/D converter 50 driven with a fixed frequency sample
 clock 52 and digitally downconverted to baseband with an I/Q mixer pair,
 shown generally at 54. The range gate filters are formed by Fourier
 transforming samples of the receiver IF signal, by inputting the I/Q
 signals to window weighting block 56, and performing the Fourier transform
 using FFT 58, and changing the coordinate system from rectangular to polar
 at block 60 to provide magnitude and phase outputs. This type of prior art
 digital receiver implementation is well known in the art.
 FIG. 4 is a block diagram of the inventive FMCW radar system, which is
 similar to a combination of FIGS. 1-3, but with the A/D converter 50 being
 driven by a clock derived from the transmitted waveform itself The output
 signal 70 of the linearizer delay, mixing and filtering circuitry is
 multiplied in frequency at 72 by a fixed factor N, to achieve at least the
 Nyquist sampling rate (which is well known in the art), to directly become
 the A/D converter 50 sample clock. Thus small deviations from linearity
 will be reflected as nonuniform time sampling, but uniform phase sampling
 in the receiver AID converter 50. Signal 70 is exactly analogous to a
 nearly ideal target located in the radar field of view at a known
 distance, referred to hereafter as a fixed delay target.
 The frequency multiplier 72 is a generic functional block used to generate
 a Nyquist frequency or higher sample clock for the A/D converter 50. The
 frequency of the signal 70 output from the bandpass filter 34 is dependent
 on the VCO 10 waveform slope and the duration of the delay 29. The Nyquist
 sample frequency for A/D converter 50 is determined by the pass band
 characteristics of IF amplifier/filter 21. The multiplication factor N in
 frequency multiplier 72 is the ratio of (A/D converter 50 Nyquist sample
 frequency) to (frequency of bandpass filter output signal 70) or greater.
 Depending on the particular combination of relevant parameters the generic
 frequency multiplier 72 maybe:
 N&gt;1 frequency multiplier;
 N=1 not required, signal 70 may be used as is, or
 N&lt;1 frequency divider.
 Uniform time sampling results in non-uniformly spaced samples of signal
 phase and broadening of the return signal spectrum when transmitter
 waveform nonlinearities are present. However, the instantaneous frequency
 of the fixed delay target (signal 70) exactly reflects the transmitter
 waveform nonlinearities (at least for that exact delay). Therefore, by
 using the fixed delay target instantaneous frequency as the A/D sample
 clock, transmitter nonlinearities can be removed or minimized because they
 are actually being measured in real time. The nonuniform sampling in time
 results in uniform sampling of return signal phase, which is just what is
 required to allow the FFT processing to produce the narrow signal spectrum
 expected. The sampled output of 50 may optionally be output to a FIFO
 buffer 74, which then outputs its signal to I/Q mixer pair 54. The FIFO
 buffer 74 accepts the A/D samples at irregular time intervals and outputs
 them at regular intervals to simplify operation of the I/Q mixer pair 54
 hardware, discussed above in connection with FIG. 3.
 Mathematical Model Of System Operation
 The transmit frequency can be modeled as:
EQU f.sub.T (t)=f.sub.o +Bt/T+A(t)
 where A(t) describes the waveform frequency nonlinearities. The transmit
 phase is then the integral over time.
 ##EQU1##
 The transmit signal is (using the real part):
EQU S.sub.T (t)=expj.phi..sub.T (t)
 For the fixed delay path, the delayed phase and signal are:
EQU .phi..sub.96 (t)=.phi..sub.T (t-.tau.)
EQU S.sub..tau. (t)=expj.phi..sub..tau. (t)=expj.phi..sub.T (t-.tau.)
 Mixing the transmit and fixed delay signals in the linearizer mixer
 generates the difference signal:
 ##EQU2##
 If .alpha.(t)=0, no waveform nonlinearities, the difference frequency will
 be:
 ##EQU3##
 as expected for a linear waveform.
 The sample clock is derived from S.sub..tau.D with the frequency (phase)
 multiplied by a factor N.
EQU S.sub.s (t)=sin[.phi..sub.S (t)]=sin[N.phi..sub..tau.D (t)]
 Sample times are the zero crossings of S.sub.S (t) or:
 ##EQU4##
 or, rearranging,
EQU 2.beta..tau.t.sub.k +.alpha.(t.sub.k)-.alpha.(t.sub.k
 -.tau.)=2.pi.k/N-.omega..sub.o.tau.+.beta..tau..sup.2
 where k=0,1,2, . . . (choosing the rising crossing). The preceding equation
 is an equation in t.sub.k whose roots are the sample times. A system that
 implements this nonuniform sampling approach does not need to explicitly
 solve the above equation for the t.sub.k. A zero crossing detector acting
 on Ss(t) provides the sample times directly. Notice that for arbitrary
 .alpha.(t):
 ##EQU5##
 so the phase at the sample time t.sub.k is identical for S.sub..tau.D
 (t.sub.k) whether or not the waveform is perfectly linear.
 For a single point target in the field of the radar at range R the path
 delay .gamma.=2R/c.
 Generalizing to multiple point scatters and evaluating at sample times
 t.sub.k, the received difference signal is:
 ##EQU6##
 This expression generates the received signal time series present at the
 output of the A/D converter.
 EXAMPLES
 Suppose the nonlinearities in the waveform can be modeled by:
 ##EQU7##
 For example purposes the sample times t.sub.k must be found numerically by
 solving:
 ##EQU8##
 k=0,1,2, . . .
 These t.sub.k values are then substituted into S.sub.RD (t.sub.k) to define
 the nonuniformly sampled time series of the IF target return signal.
 Fourier transforming the series results in a spectrum representative of
 the range gate outputs.
 A radar system was defined with these characteristics:

Parameter Value Units
 f.sub.0 0 Ghz
 B 500 MHZ
 T 0.01 sec
 .tau. 0.512 .mu.sec
 Five unit-amplitude point targets were placed at delays of 0.1, 0.2, 0.5,
 0.8, and 1.2 .mu.sec. The radar parameters result in a waveform slope of
 50 kHz/.mu.sec. The target delays then correspond to IF difference
 frequencies of 5.0, 10.0, 25.0, 40.0, and 60.0 kHz.
 With a linear waveform the fixed delay target difference frequency over the
 modulation period is shown in FIG. 5. The frequency is constant as it
 should be with a linear sweep. The spectrum of the five point targets is
 shown in FIG. 6. The five spectral lines clearly identify the targets and
 are of equal power consistent with each being a unit-amplitude scatterer.
 For the next case a.sub.1 =1.0 MHZ was chosen. This adds a half-sinusoid
 nonlinearity to the transmit waveform. Now the fixed delay target shows a
 small change in difference frequency as shown in FIG. 7. The signal
 spectrum in FIG. 8 was computed using uniform time sampling and is
 dramatically impacted. Although still clearly separated in range, peak
 power drops and spectral width broadens as target delay increases.
 Next the nonuniform sample times t.sub.k were calculated. These times are
 shown in FIG. 9 as the time difference between the nonuniform sample and
 the corresponding uniform sample. The half-sinusoid loop seen results from
 the frequency deviation added to the waveform. Computing the signal series
 at the nonuniform sample times t.sub.k and Fourier transforming gives the
 spectrum in FIG. 10. Spectral line broadening has been removed and peak
 power restored. This is exactly the benefit expected for the inventive
 FMCW radar system described in this application. Transmitter waveform
 nonlinearities have been moved by receiver processing.
 A final example uses these A(t) coefficients.