CA2309109A1 - Phase error cancellation method for fm-cw radar - Google Patents
Phase error cancellation method for fm-cw radar Download PDFInfo
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- CA2309109A1 CA2309109A1 CA 2309109 CA2309109A CA2309109A1 CA 2309109 A1 CA2309109 A1 CA 2309109A1 CA 2309109 CA2309109 CA 2309109 CA 2309109 A CA2309109 A CA 2309109A CA 2309109 A1 CA2309109 A1 CA 2309109A1
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- tramp
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- mixer output
- frequency sweep
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/08—Systems for measuring distance only
- G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
- G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
A signal processing method is presented for FM-CW radar where coherency in time of the mixer output signal is restored between the frequency sweep intervals, by the cancellation of the phase error (shift) between consecutive intervals. The restoration of coherency allows much higher resolution of the frequency spectra to be achieved, thus -improving the spatial resolution of the radar and reducing the dead zone. At the same time, the signal processing method allows for automatic correction of the frequency sweep function.
Description
Phase Error Cancellation Method for FM-CW radar DESCRIPTION OF THE INVENTION
1. Introduction.
Principle of operation of conventional FM-CW radar, basic theory.
We shall asssume that the radar is transmitting continuously an FM
triangularily modulated carrier signal. That is, the frequency is increasing linearly from Fmin to Fmax, over the time Tramp, then decreasing linearly from Fmax down to Fmin, over the time Tramp2 (Tramp2=Tramp or Tramp2«Tramp). The cycle is repeated continuously. On a frequency versus time, this could be represented as a triangular "saw-tooth" curve with symmetrical or asymmetrical "teeth". The signal reflected from ~ 5 a target situated at front of the radar, and received back, has a different frequency than the transmitter (most of the time). The mixed product of the received and the transmitted signal will exhibit a dominant frequency equal to DF = 2*DFmax*DtlTramp = DFmax*4*L/(c*Tramp) [eq.l]
where 2o DFmax = Fmax - Fmin , Dt =2*L/c - time delay c is the light speed (3e8m/s), L = the distance between the reflecting target and the radar. The target position resolution dL is inversely dependent on the spectral width W=d(DF) of the frequency peak DF at the output of the mixer. W in turn is determined by the duration of the ramp Tramp, by virtue of the sampling theorem:
25 W = 1/(2*Tramp) = d(DF) [eq.2]
from eq.l and 2 we obtain::
dL = k*c/(8*DFmax) [eq.3]
where k is a dimensionless constant dependent on how accurately does the signal processing circuit lock onto the top of the frequency peak (at DF); it depends also on the 3o amount of averaging, transmitter and mixer noises etc. Typically: k=0.02 -0.2.
Since 1/(2*Tramp) is the lowest non-zero frequency bin on an FFT spectrum, it also determines the extent of the dead zone: Ldead = k'*c/(8*DFmax) (where k' is about 1) 35 In FM-CW radars, the distance L is determined by measuring the frequency difference DF
either through analog filtering and averaging, or through digitizing and FFT
processing, followed by averaging. In either method, we have a guaranteed coherence of the mixer output, only over the duration Tramp of the slope of the transmit frequency ramp. This lack of data coherence prevents the proportional increase in the frequency peak 4o resolution and the reduction of the dead zone through the simple increase of the FFT
span beyond the Tramp. Note: there is an increase in the accuracy of the peak position measurement with the increased FFT sample span; however this is due to the averaging effect and is much weaker than would have been possible had the data been coherent. In an ideal FM-CW system, the spectral peak width is determined by coherency length.
According to the theory, the spectral resolution W=d(DF) and the dead zone would improve if we could make the mixer output signal coherent for more than the duration of the single sweep (Tramp).
5o 2. Embodiment of the invention.
a) Basic theory.
This technique of phase error cancelation is best applied in case of asymmetrical triangular waveform, with the slower, i.e. the rising frequency slope of the FM
modulation having a duration of Tramp (time-ramp), and the fast (falling frequency) slope Tramp2 being much shorter than Tramp. For the purpose of this analysis, we assume that Tramp2=0. For a non zero Tramp2 there is a small additional phase shift which can be easily compensated by a small constant time-shifting of the consecutive ramps;
(this will 6o be discussed later).
In a situation of the linear frequency sweep, the target being stationary, the waveform of the mixer output A(t) versus time can be approximated by the following formulae:
A(t) = AO * cos( OMEGA*t - n*4*PI*DFmax*L/c + CO) _ = AO * cos( P*( 2*(t/Tramp) - n) + CO) [eq.4]
and the phase angle is:
PHI(t) = P*( 2*(t/Tramp) - n) + CO [eq.5]
where OMEGA - 8*PI*DFmax*L/(c*Tramp) P = 4*PI*DFmax*L/c n = INT(t/Tramp) (INT(x) is the integer portion of x, i.e INT(5.25)=5) The idea of this invention is based on the observation (see eq.4,5) that the phase angle PHI of the waveform at the end of the ramp (t=n*Tramp), as described by eq.5 , is equal to the phase angle in the middle of the ramp of the next or of the preceeding interval, that is:
PHI(t=n*Tramp-eps) = PHI(t=(n+1/2)*Tramp) [eq.6]
and PHI(t=n*Tramp+eps) = PHI(t=(n-1/2)*Tramp) [eq.7]
8o where eps-->0 and eps>0 Using this property, it is possible to concatenate an arbitrary number of consecutive intervals of duration Tramp, such that the continuity of the phase angle is preserved. A
method of concatenation is described below.
b) Phase-preserving method of concatenation.
Note that the signal processing method described here can be implemented in many ways, analog or digital, but to keep it simple, we shall choose the digital technique as an so example. Suppose that the mixer output is digitized by an analog to digital converter, with the period of Ts (samples per second). Thus we have Ns=Tramp/Ts samples in every ramp interval. We shall assume, for the sake of simplicity, that Ns is an even number (the argumentation looks similiar if it is odd). Let us use the subscript k to index the samples within each ramp interval, k=O..Ns-1, and let us use n to index the 95 individual intervals, n=0,1,2... (same as in eq.4 and 5).
The samples can be represented by eq.4 and 5 written in a discrete form, such as:
A(k,n) = AO * cos( P*( 2*((k*Ts)/Tramp) - n) + CO) [eq.8]
and the phase angle (which is not directly sampled, but may be derived from the data) 10o PHI(k,n) = P*( 2*((k*Ts)/Tramp) - n) + CO [eq.9]
Let us denote the samples belonging to the first half portion of each frequency ramp as A1(n,k), PHI1(n,k), k=0,2,...Ns/2-1, and the samples of the second half of the ramp as A2(n,j), PHI2(nj) j=k-Ns/2=0,1,..Ns/2-1.
105 Equations 6 and 7 are telling us that for all n, PHI1(n,0) = PHI1(n-l,Ns/2-1) PHI2(n,0) = PHI2(n-l,Ns/2-1 ) therefore the data stream such as:
al = {... A1(n-1,0),A1(n-1,1),...,A1(n-l,Ns/2-1),A1(n,0),A1(n,l), 11o A1(n,Ns/2-1),A1(n+l,o),...}
should represent a coherent waveform, as well as the following series:
a2 = {... A2(n-1,0),A2(n-1,1),...,A2(n-l,Ns/2-1),A2(n,0),A2(n,2),..., A2(n,Ns/2-1 ),A2(n+1,0),... }
In order to make it easier to read, we shall renumerate the above series using a single index m=0,1,2... such that: m(n,j) = n*Ns/2 + j , n=0,1,2,... and j=0,1,2,...,Ns/2-1.
al = { ...al(m-1),a1(m),al(m+1),... } [eq.l0]
a2 = { ...a2(m-1),a2(m),a2(m+1),... } [eq.l l]
In fact, since both series (al and a2) represent the same waveform, with the same and continuous phase angle, it is suggested that they be combined together by interleaving or by averaging or by both (i.e.: interleaving plus window averaging). For example:
a = { ... a(m-1),a(m),a(m+1),... } where a(m) _ (al(m) + a2(m))/2 [eq.l2]
125 or a= { ...al(m-1),a2(m-1),al(m),a2(m),al(m+1),a2(m+1),... } [eq.l3]
or a= { ...(al(m-1)+a2(m-2))/2, (a2(m-1)+al(m-1))/2, (al(m)+a2(m-1))/2, (a2(m)+al(m)/2, (al(m+1)+a2(m))/2, (a2(nl+1)+al(m+1)),... } [eq.l4]
c) Signal processing.
Since the series of the type described by eq.12,13 or 14 represent a coherent (continuous phase) waveform, it is postulated that very high frequency resolution can be achieved by 135 Fast Fourier Transform run over an arbitrarily long interval of samples, and is NO
LONGER restricted to the duration of the single ramp (Tramp).
Additionally, since the data series by eq.l0 and 11 represent, theoretically the same waveform, their difference should be equal to zero:
14o b(m) = al(m) - a2(m) [eq.l5]
Theoretically, we should have:
b(m) = 0 for all m=0,1,2,... [eq.l6]
Eq.l6 is based on our assumptions regarding the linearity of the frequency ramp, the constancy of the ramp duration Tramp etc.
145 It is postulated that the b(m) is actually evaluated in real time as described above in eq.l5 in order to verify the radar system performance. Any deviation from b(m)=0, in the form, for example of the error sum = SUM( b(m)~2, m=1,2..) (to be minimized), may be used as a feed-back signal to automatically calibrate or to linearize the system.
15o d) Example of a hardware implementation.
The hardware consists of:
- FW-CW radar oscillator module containing a Gunn diode oscillator, a varactor diode 155 for frequency tuning, and a Schottky diode for mixing the transmit and the received signals.
- D/A conversion module to generate a ramp signal of period Tramp, to drive the varactor tuning diode.
- temperature compensation circuit to compensate the thermal drift of the FM-CW radar 1 so oscillator module - a pre-amp and A/D converter to digitize the mixer output of the FM-CW radar oscillator module.
- microprocessor (a DSP) to process the digitized data stream according to the rules described above (c), to drive the D/A converter in order to generate appropriate 165 frequency signal, to perform FFT, averaging and frequency peak search, to filter &
discriminate the correct peak frequency, to convert the measured peak frequency into the distance to the target.
e) Implications of the practically non-zero duration of the return frequency sweep.
The finite (non-zero) time Tramp 2 (Tramp2«Tramp) of the frequency return from Fmax to Fmin can be included in the Tramp time, if we extend the frequency ramp beyond Fmax and below Fmin. In other words, the situation is as if we had indeed the total ~~5 ramp length of Tramp' = Tramp + Tramp2 with zero return time and the frequency span was from Fmin' = Fmin - DFmax*Tramp2/(2*Tramp) to Fmax' = Fmax + DFmax*Tramp2/(2*Tramp) ~ 8o The formulae in the previous sections should still hold true, except that we replace DFmax with the DFmax' = DFmax*(Tramp2/Tramp), and that we use Tramp' = Tramp + Tramp2 in place of Tramp. Of course, the mixer output signal will exhibit some irregularities (in form of spurious frequency peaks) at the peak and at the bottom of the frequency sweep ramp due to deviation from the linearity and due to the ~ 85 boundary effect. This effect is small as long as Tramp2«Tramp and is normally averaged out by the spectral processing.
1. Introduction.
Principle of operation of conventional FM-CW radar, basic theory.
We shall asssume that the radar is transmitting continuously an FM
triangularily modulated carrier signal. That is, the frequency is increasing linearly from Fmin to Fmax, over the time Tramp, then decreasing linearly from Fmax down to Fmin, over the time Tramp2 (Tramp2=Tramp or Tramp2«Tramp). The cycle is repeated continuously. On a frequency versus time, this could be represented as a triangular "saw-tooth" curve with symmetrical or asymmetrical "teeth". The signal reflected from ~ 5 a target situated at front of the radar, and received back, has a different frequency than the transmitter (most of the time). The mixed product of the received and the transmitted signal will exhibit a dominant frequency equal to DF = 2*DFmax*DtlTramp = DFmax*4*L/(c*Tramp) [eq.l]
where 2o DFmax = Fmax - Fmin , Dt =2*L/c - time delay c is the light speed (3e8m/s), L = the distance between the reflecting target and the radar. The target position resolution dL is inversely dependent on the spectral width W=d(DF) of the frequency peak DF at the output of the mixer. W in turn is determined by the duration of the ramp Tramp, by virtue of the sampling theorem:
25 W = 1/(2*Tramp) = d(DF) [eq.2]
from eq.l and 2 we obtain::
dL = k*c/(8*DFmax) [eq.3]
where k is a dimensionless constant dependent on how accurately does the signal processing circuit lock onto the top of the frequency peak (at DF); it depends also on the 3o amount of averaging, transmitter and mixer noises etc. Typically: k=0.02 -0.2.
Since 1/(2*Tramp) is the lowest non-zero frequency bin on an FFT spectrum, it also determines the extent of the dead zone: Ldead = k'*c/(8*DFmax) (where k' is about 1) 35 In FM-CW radars, the distance L is determined by measuring the frequency difference DF
either through analog filtering and averaging, or through digitizing and FFT
processing, followed by averaging. In either method, we have a guaranteed coherence of the mixer output, only over the duration Tramp of the slope of the transmit frequency ramp. This lack of data coherence prevents the proportional increase in the frequency peak 4o resolution and the reduction of the dead zone through the simple increase of the FFT
span beyond the Tramp. Note: there is an increase in the accuracy of the peak position measurement with the increased FFT sample span; however this is due to the averaging effect and is much weaker than would have been possible had the data been coherent. In an ideal FM-CW system, the spectral peak width is determined by coherency length.
According to the theory, the spectral resolution W=d(DF) and the dead zone would improve if we could make the mixer output signal coherent for more than the duration of the single sweep (Tramp).
5o 2. Embodiment of the invention.
a) Basic theory.
This technique of phase error cancelation is best applied in case of asymmetrical triangular waveform, with the slower, i.e. the rising frequency slope of the FM
modulation having a duration of Tramp (time-ramp), and the fast (falling frequency) slope Tramp2 being much shorter than Tramp. For the purpose of this analysis, we assume that Tramp2=0. For a non zero Tramp2 there is a small additional phase shift which can be easily compensated by a small constant time-shifting of the consecutive ramps;
(this will 6o be discussed later).
In a situation of the linear frequency sweep, the target being stationary, the waveform of the mixer output A(t) versus time can be approximated by the following formulae:
A(t) = AO * cos( OMEGA*t - n*4*PI*DFmax*L/c + CO) _ = AO * cos( P*( 2*(t/Tramp) - n) + CO) [eq.4]
and the phase angle is:
PHI(t) = P*( 2*(t/Tramp) - n) + CO [eq.5]
where OMEGA - 8*PI*DFmax*L/(c*Tramp) P = 4*PI*DFmax*L/c n = INT(t/Tramp) (INT(x) is the integer portion of x, i.e INT(5.25)=5) The idea of this invention is based on the observation (see eq.4,5) that the phase angle PHI of the waveform at the end of the ramp (t=n*Tramp), as described by eq.5 , is equal to the phase angle in the middle of the ramp of the next or of the preceeding interval, that is:
PHI(t=n*Tramp-eps) = PHI(t=(n+1/2)*Tramp) [eq.6]
and PHI(t=n*Tramp+eps) = PHI(t=(n-1/2)*Tramp) [eq.7]
8o where eps-->0 and eps>0 Using this property, it is possible to concatenate an arbitrary number of consecutive intervals of duration Tramp, such that the continuity of the phase angle is preserved. A
method of concatenation is described below.
b) Phase-preserving method of concatenation.
Note that the signal processing method described here can be implemented in many ways, analog or digital, but to keep it simple, we shall choose the digital technique as an so example. Suppose that the mixer output is digitized by an analog to digital converter, with the period of Ts (samples per second). Thus we have Ns=Tramp/Ts samples in every ramp interval. We shall assume, for the sake of simplicity, that Ns is an even number (the argumentation looks similiar if it is odd). Let us use the subscript k to index the samples within each ramp interval, k=O..Ns-1, and let us use n to index the 95 individual intervals, n=0,1,2... (same as in eq.4 and 5).
The samples can be represented by eq.4 and 5 written in a discrete form, such as:
A(k,n) = AO * cos( P*( 2*((k*Ts)/Tramp) - n) + CO) [eq.8]
and the phase angle (which is not directly sampled, but may be derived from the data) 10o PHI(k,n) = P*( 2*((k*Ts)/Tramp) - n) + CO [eq.9]
Let us denote the samples belonging to the first half portion of each frequency ramp as A1(n,k), PHI1(n,k), k=0,2,...Ns/2-1, and the samples of the second half of the ramp as A2(n,j), PHI2(nj) j=k-Ns/2=0,1,..Ns/2-1.
105 Equations 6 and 7 are telling us that for all n, PHI1(n,0) = PHI1(n-l,Ns/2-1) PHI2(n,0) = PHI2(n-l,Ns/2-1 ) therefore the data stream such as:
al = {... A1(n-1,0),A1(n-1,1),...,A1(n-l,Ns/2-1),A1(n,0),A1(n,l), 11o A1(n,Ns/2-1),A1(n+l,o),...}
should represent a coherent waveform, as well as the following series:
a2 = {... A2(n-1,0),A2(n-1,1),...,A2(n-l,Ns/2-1),A2(n,0),A2(n,2),..., A2(n,Ns/2-1 ),A2(n+1,0),... }
In order to make it easier to read, we shall renumerate the above series using a single index m=0,1,2... such that: m(n,j) = n*Ns/2 + j , n=0,1,2,... and j=0,1,2,...,Ns/2-1.
al = { ...al(m-1),a1(m),al(m+1),... } [eq.l0]
a2 = { ...a2(m-1),a2(m),a2(m+1),... } [eq.l l]
In fact, since both series (al and a2) represent the same waveform, with the same and continuous phase angle, it is suggested that they be combined together by interleaving or by averaging or by both (i.e.: interleaving plus window averaging). For example:
a = { ... a(m-1),a(m),a(m+1),... } where a(m) _ (al(m) + a2(m))/2 [eq.l2]
125 or a= { ...al(m-1),a2(m-1),al(m),a2(m),al(m+1),a2(m+1),... } [eq.l3]
or a= { ...(al(m-1)+a2(m-2))/2, (a2(m-1)+al(m-1))/2, (al(m)+a2(m-1))/2, (a2(m)+al(m)/2, (al(m+1)+a2(m))/2, (a2(nl+1)+al(m+1)),... } [eq.l4]
c) Signal processing.
Since the series of the type described by eq.12,13 or 14 represent a coherent (continuous phase) waveform, it is postulated that very high frequency resolution can be achieved by 135 Fast Fourier Transform run over an arbitrarily long interval of samples, and is NO
LONGER restricted to the duration of the single ramp (Tramp).
Additionally, since the data series by eq.l0 and 11 represent, theoretically the same waveform, their difference should be equal to zero:
14o b(m) = al(m) - a2(m) [eq.l5]
Theoretically, we should have:
b(m) = 0 for all m=0,1,2,... [eq.l6]
Eq.l6 is based on our assumptions regarding the linearity of the frequency ramp, the constancy of the ramp duration Tramp etc.
145 It is postulated that the b(m) is actually evaluated in real time as described above in eq.l5 in order to verify the radar system performance. Any deviation from b(m)=0, in the form, for example of the error sum = SUM( b(m)~2, m=1,2..) (to be minimized), may be used as a feed-back signal to automatically calibrate or to linearize the system.
15o d) Example of a hardware implementation.
The hardware consists of:
- FW-CW radar oscillator module containing a Gunn diode oscillator, a varactor diode 155 for frequency tuning, and a Schottky diode for mixing the transmit and the received signals.
- D/A conversion module to generate a ramp signal of period Tramp, to drive the varactor tuning diode.
- temperature compensation circuit to compensate the thermal drift of the FM-CW radar 1 so oscillator module - a pre-amp and A/D converter to digitize the mixer output of the FM-CW radar oscillator module.
- microprocessor (a DSP) to process the digitized data stream according to the rules described above (c), to drive the D/A converter in order to generate appropriate 165 frequency signal, to perform FFT, averaging and frequency peak search, to filter &
discriminate the correct peak frequency, to convert the measured peak frequency into the distance to the target.
e) Implications of the practically non-zero duration of the return frequency sweep.
The finite (non-zero) time Tramp 2 (Tramp2«Tramp) of the frequency return from Fmax to Fmin can be included in the Tramp time, if we extend the frequency ramp beyond Fmax and below Fmin. In other words, the situation is as if we had indeed the total ~~5 ramp length of Tramp' = Tramp + Tramp2 with zero return time and the frequency span was from Fmin' = Fmin - DFmax*Tramp2/(2*Tramp) to Fmax' = Fmax + DFmax*Tramp2/(2*Tramp) ~ 8o The formulae in the previous sections should still hold true, except that we replace DFmax with the DFmax' = DFmax*(Tramp2/Tramp), and that we use Tramp' = Tramp + Tramp2 in place of Tramp. Of course, the mixer output signal will exhibit some irregularities (in form of spurious frequency peaks) at the peak and at the bottom of the frequency sweep ramp due to deviation from the linearity and due to the ~ 85 boundary effect. This effect is small as long as Tramp2«Tramp and is normally averaged out by the spectral processing.
Claims (3)
1. Specific to this invention is the restoration of the coherency of the mixer output signal by piece-wise concatenation of the digitized or analog mixer output whereby the end or the beginning of the interval (as defined by the duration of the frequency sweep ramp) is concatenated to the middle of the next or to the middle of the previous interval, as described in the section 2b, eq.10-14 of the "DESCRIPTION".
2. Specific to this invention is the extension of the spectral processing of the restored coherent mixer output signal over multiple intervals of the frequency sweep, for the purpose of increasing the spectral and spatial resolution of the radar, and for the reduction of the extent of the close-range dead zone.
3. Specific to this invention is the method of automatic correction of the frequency sweep by zeroing the differential signal b(m) obtained after the piece-wise concatenation of the digitized or analog mixer output (see claim 1, and section 2c, eq.15 of "DESCRIPTION").
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2309109 CA2309109A1 (en) | 2000-05-23 | 2000-05-23 | Phase error cancellation method for fm-cw radar |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2309109 CA2309109A1 (en) | 2000-05-23 | 2000-05-23 | Phase error cancellation method for fm-cw radar |
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| Publication Number | Publication Date |
|---|---|
| CA2309109A1 true CA2309109A1 (en) | 2001-11-23 |
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ID=4166217
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA 2309109 Abandoned CA2309109A1 (en) | 2000-05-23 | 2000-05-23 | Phase error cancellation method for fm-cw radar |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7982661B2 (en) | 2005-03-29 | 2011-07-19 | Qinetiq Limited | Coherent frequency modulated continuous wave radar |
-
2000
- 2000-05-23 CA CA 2309109 patent/CA2309109A1/en not_active Abandoned
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7982661B2 (en) | 2005-03-29 | 2011-07-19 | Qinetiq Limited | Coherent frequency modulated continuous wave radar |
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