Abstract
Radar signal detection and parameter estimation is central in passive surveillance systems, providing inputs for many information processing modules in order to detect, localize, indentify and intercept hostile targets. The proposed method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments consists of several stages: magnitude-squared envelopes calculation, adaptive noise floor estimation, detection statistics calculation, rising edge detection, time of arrival estimation, falling edge detection, time of departure estimation, pulse width estimation, amplitude estimation and center frequency and bandwidth estimation. Estimated intra-pulse parameters are wrapped into pulse descriptor words (PDWs) for information processing tasks, where each PDW consists of time of arrival, time of departure, pulse width, pulse amplitude, center frequency, signal bandwidth, noise floor level and additional useful information. The method is sequential, implemented in hardware platforms for real-time surveillance applications. The proposed method yielded much better performance than classical threshold-based edge (TED) detection methods.
Claims
1. A method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments, the said method comprising the steps of: performing pre-processing tasks on input wideband IQ samples; estimating a noise floor level from magnitude-squared envelopes; calculating detection statistics for rising and falling edge decision; detecting a rising edge of radar pulses (i.e., a presence of radar pulses); estimating a time of arrival (TOA) of radar pulses; detecting a falling edge of radar pulses (i.e., a termination of radar pulses); estimating a time of departure (TOD) of radar pulses; calculating a pulse width (PW) of radar pulses; estimating an amplitude (AMP) of radar pulses; estimating a center frequency (FC) and bandwidth (BW) of radar pulses; wrapping intra-pulse parameters into pulse descriptor words (PDWs).
2. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of performing pre-processing tasks on input wideband IQ samples comprises the following sub-steps: performing digital down conversion (DDC) on the input wideband IQ samples in order to obtain baseband IQ samples, where the DDC operation consists of frequency mixer, digital down-sampling and low-pass filtering; the baseband IQ samples are denoted as x.sub.n=I.sub.n+jQ.sub.n, where j is a complex operator, I.sub.n is a real (in-phase) component and Q.sub.n is a complex (quadrature) component of the baseband IQ samples x.sub.n; calculating magnitude-squared envelopes X.sub.n of the said baseband IQ samples by a sum of squares of the in-phase component (I.sub.n) and a quadrature component (Q.sub.n) of the complex baseband IQ samples, i.e., X.sub.n=I.sub.n.sup.2+Q.sub.n.sup.2.
3. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of estimating the noise floor level from the magnitude-squared envelopes comprises the following sub-steps: estimating a local average value X.sub.n of the magnitude-squared envelopes X.sub.n using a FMA filter of length L; estimating the noise floor level h.sub.X.sub.n as the minimum between a current local average value X.sub.n and a previous noise floor level h.sub.X.sub.n?1; updating the noise floor level h.sub.X.sub.n periodically by multiplying itself with an offset coefficient K.sub.?>1 for each time period T.sub.?.
4. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of calculating detection statistics for rising and falling edge decision comprises the following sub-steps: estimating an expectation ?.sub.n of a distribution of random noises; estimating a standard deviation ?.sub.n of the distribution of random noises; estimating a tentative pulse amplitude ?.sub.X for the magnitude-squared envelopes; calculating a log-likelihood ratio (LLR) s.sub.n between a distribution of tentative intra-pulse samples and a distribution of random noises; calculating a detection statistic g.sub.n for rising edge decision from the said LLR s.sub.n; calculating a detection statistic d.sub.n for falling edge decision from the said LLR s.sub.n.
5. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of estimating the expectation ?.sub.n of the distribution of random noises comprises estimating the expectation ?.sub.n of the distribution of random noises by multiplying the estimated noise floor level h.sub.X.sub.n with an offset coefficient K.sub.?, where K.sub.?>0 is a calibration coefficient for expectation which is chosen for compensating for an approximation of the distribution of random noises as a Chi-squared distribution.
6. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of estimating the standard deviation ?.sub.n of the distribution of random noises comprises estimating the standard deviation ?.sub.n of the distribution of random noises by multiplying the estimated noise floor level h.sub.X.sub.n with an offset coefficient K.sub.?, where K.sub.?>0 is the calibration coefficient for standard deviation which is chosen for compensating for an approximation of the distribution of random noises as a Chi-squared distribution.
7. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of estimating the tentative pulse amplitude ?.sub.X for the magnitude-squared envelopes consists of estimating the tentative pulse amplitude ?.sub.X by multiplying the estimated noise floor level h.sub.X.sub.n by an offset coefficient K.sub.?, where K.sub.?>1 is the tentative coefficient which should be chosen for balancing between false alarm and detection rates in both low and high SNR levels.
8. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of calculating the log-likelihood ratio (LLR) s.sub.n between the distribution of tentative intra-pulse samples and the distribution of random noises comprises calculating the LLR s.sub.n from the magnitude-squared envelopes X.sub.n, the estimated expectation un of the distribution of random noises, the estimated standard deviation ?.sub.n of the distribution of random noises, the estimated tentative pulse amplitude ?.sub.X of the magnitude-squared envelopes, the distribution of tentative intra-pulse samples and the distribution of random noises, wherein the said distributions must be chosen in such a way that the LLR s.sub.n satisfies following special properties: the LLR s.sub.n must be negative in a pre-change and post-change regions where there is only random noises; the LLR s.sub.n must be positive in and intra-pulse region where there are intra-pulse samples buried in random noises.
9. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of calculating detection statistic for rising edge decision g.sub.n comprises recursively calculating the detection statistic g.sub.n from its previous value g.sub.n?1 and the LLR s.sub.n, wherein the recursive relationship between the detection statistic g.sub.n and the LLR s.sub.n must be chosen in such a way that the detection statistic g.sub.n satisfies following special properties: the detection statistic g.sub.n fluctuates around zero in a pre-change region where there is only random noises; the detection statistic g.sub.n starts increasing in an intra-pulse region and its value reflects the accumulated pulse energy from the presence of radar pulses; the detection statistic g.sub.n starts decreasing to zero from its peak in the post-change region and then fluctuates round zero until the presence of next radar pulses.
10. The method for calculating detection statistics for rising and falling edge decision in claim 4, wherein the said sub-step of calculating detection statistic for falling edge decision d.sub.n consists of recursively calculating the detection statistic d.sub.n from its previous value d.sub.n?1 and the LLR s.sub.n , wherein the recursive relationship between the detection statistic d.sub.n and the LLR s.sub.n must be chosen in such a way that the detection statistic d.sub.n satisfies following special properties: the detection statistic d.sub.n is set to zero in a pre-change region before the detection of radar pulses; the detection statistic d.sub.n fluctuates around zero in an intra-pulse region after the detection of radar pulses; the detection statistic d.sub.n starts increasing in a post-change region from the termination of radar pulses.
11. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of detecting the rising edge of radar pulses (the presence of radar pulses) comprises comparing the detection statistic for rising edge decision g.sub.n with a pre-defined threshold h.sub.TOA which is chosen for balancing between false alarm and detection rates; the radar pulses are said to be detected if the detection statistic g.sub.n is greater than or equal to the said threshold h.sub.TOA.
12. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of estimating the time of arrival (TOA) of radar pulses comprises the following sub-steps: finding a maximum value X.sub.max of the magnitude-squared envelopes X.sub.n around a search region, from the gating TOA value to a maximum possible length of the rising edge; calculating an amplitude threshold value X.sub.TOA=0.25*X.sub.max in order to search for a middle point of the rising edge; finding a time instant n.sub.0 in the search region that satisfies conditions X.sub.n.sub.0?X.sub.TOA and X.sub.n.sub.0.sup.+1?X.sub.TOA; calibrating the TOA value by an interpolation method corresponding to the amplitude threshold value X.sub.TOA from a pulse envelopes X.sub.n.sub.0 and X.sub.n.sub.0.sup.+1 at time instants n.sub.0 and n.sub.0+1.
13. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of detecting the falling edge of radar pulses (the appearance of radar pulses) comprises comparing the detection statistic for falling edge decision d.sub.n with a pre-defined threshold h.sub.TOD; the radar pulses are said to be terminated if the detection statistic d.sub.n is greater than or equal to the threshold h.sub.TOD.
14. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of estimating the time of departure (TOD) of radar pulses comprises the following sub-steps: estimating a running average value X.sub.n of the magnitude-squared envelopes X.sub.n from a time instant n.sub.0 to a current time instant n; calculating the amplitude threshold value X.sub.TOD=0.25*X.sub.n in order to search for a middle point of the falling edge; finding a time instant n.sub.1 in a search region that satisfies conditions X.sub.n.sub.1?X.sub.TOD and X.sub.n.sub.1.sup.+1?X.sub.TOD; calibrating the TOD value by an interpolation method corresponding to the amplitude threshold value X.sub.TOD from the pulse envelopes X.sub.n.sub.1 and X.sub.n.sup.+1 at time instants n.sub.1 and n.sub.1+1.
15. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of calculating the pulse width (PW) of radar pulses comprises computing pulse width (PW) of radar pulses from the TOA value and the TOD value more precisely, the pulse width is calculated as PW=TOD?TOA, wherein the said step of estimating the time of arrival (TOA) of radar pulses comprises the following sub-steps: finding a maximum value X.sub.max of the magnitude-squared envelopes X.sub.n around a search region, from the gating TOA value to a maximum possible length of the rising edge; calculating an amplitude threshold value X.sub.TOA=0.25*X.sub.max in order to search for a middle point of the rising edge; finding a time instant n.sub.0 in the search region that satisfies conditions X.sub.n.sub.0?X.sub.TOA and X.sub.n.sub.0.sup.+1?X.sub.TOA; and wherein the said step of estimating the time of departure (TOD) of radar pulses comprises the following sub-steps: estimating a running average value X.sub.n of the magnitude-squared envelopes X.sub.n from a time instant n.sub.0 to a current time instant n; calculating the amplitude threshold value X.sub.TOD=0.25*X.sub.n in order to search for a middle point of the falling edge; finding a time instant n.sub.1 in the search region that satisfies conditions X.sub.n.sub.1?X.sub.TOD and X.sub.n.sub.1.sup.+1?X.sub.TOD; calibrating the TOD value by an interpolation method corresponding to the amplitude threshold value X.sub.TOD from the pulse envelopes X.sub.n.sub.1 and X.sub.n.sub.1.sup.+1 at time instants n.sub.1 and n.sub.1+1; calibrating the TOA value by an interpolation method corresponding to the amplitude threshold value X.sub.TOA from a pulse envelopes X.sub.n.sub.0 and X.sub.n.sub.0.sup.+1 at time instants n.sub.0 and n.sub.0+1.
16. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of estimating the amplitude (AMP) of radar pulses comprises computing the squared-root of the running average value X.sub.n.sub.1 at time instant n.sub.1 in a search region that satisfies conditions X.sub.n.sub.1?X.sub.TOD and X.sub.n.sub.1.sup.+1?X.sub.TOD.
17. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of estimating the center frequency (FC) and bandwidth (BW) of radar pulses comprises the following sub-steps: calculating a power spectral density (PSD) of intra-pulse samples by performing the Fast Fourier Transform (FFT) on intra-pulse IQ samples from the estimated TOA to the estimated TOD; finding a peak value P.sub.max in PSD bins; calculating threshold h.sub.p which is of k-dB from the peak value P.sub.max; searching for crossing points F.sub.1 and F.sub.2 in rising and falling edges of PSD bins; estimating center frequency FC as an average value of F.sub.1 and F.sub.2; estimating signal bandwidth BW as a difference between F.sub.2 and F.sub.1.
18. The method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments of claim 1, wherein the said step of wrapping the intra-pulse parameters into pulse descriptor words (PDWs) comprises wrapping the estimated time of arrival (TOA), the estimated time of departure (TOD), the estimated pulse amplitude (AMP), the estimated center frequency (FC), the estimated bandwidth (BW), the estimated noise floor level (NO) and additional useful information into pulse descriptor words (PDWs), wherein these PDWs are then transmitted to other modules for information processing tasks.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0032] FIG. 1 is a diagram depicting the intra-pulse parameters of a radar pulse in time domain.
[0033] FIG. 2 is a diagram depicting the intra-pulse parameters of a radar pulse in frequency domain.
[0034] FIG. 3 is a diagram depicting the flow chart and signal processing modules for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments.
[0035] FIG. 4 is a diagram depicting the flow chart of pre-processing module.
[0036] FIG. 5 is a diagram depicting the flow chart of adaptive noise floor estimation module.
[0037] FIG. 6 is a diagram depicting the estimated noise floor level in non-stationary noises.
[0038] FIG. 7 is a diagram depicting the flow chart of detection statistics calculation module.
[0039] FIG. 8 is a diagram demonstrating the detection of rising edges (presence of radar pulses).
[0040] FIG. 9 is a diagram demonstrating the estimation of the time of arrival TOA.
[0041] FIG. 10 is a diagram demonstrating the detection of falling edges (termination of pulses).
[0042] FIG. 11 is a diagram demonstrating the estimation of the time of departure TOD.
[0043] FIG. 12 is a diagram depicting the flow chart of FC and BW estimation module.
[0044] FIG. 13 is a diagram depicting the experimental results with real IQ samples.
DETAILED DESCRIPTION OF THE INVENTION
[0045] The present invention is now described in details with reference to FIGS. 1-13.
[0046] Referring to FIG. 1 and FIG. 2, each radar pulse is specified by multiple intra-pulse parameters in both time domain and frequency domain. The time-domain parameters consist of rising edge, falling edge, time of arrival (TOA), time of departure (TOD), pulse width (PW), pulse amplitude (AMP), noise floor level (in time domain). The time of arrival (TOA) is defined as the middle point of the rising edge and the time of departure (TOD) is defined as the middle point of the falling edge. On the other hand, the frequency-domain parameters include center frequency (FC), bandwidth (BW), modulation on pulse (MOP), and noise floor level (in frequency domain).
[0047] The problem consists of detecting the presence of radar pulses buried in random noises and estimating their intra-pulse parameters from a sequence of input IQ samples. It is the purpose of the present invention to propose an efficient method for real-time detection and parameter estimation of radar signals in time-varying noisy environments.
[0048] Referring to FIG. 3, the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention consists of following steps: [0049] Step 1: performing pre-processing tasks on the input wideband IQ samples; [0050] Step 2: estimating the noise floor level from the magnitude-squared envelopes; [0051] Step 3: calculating detection statistics for rising and falling edge decision; [0052] Step 4: detecting the rising edge of radar pulses (i.e., the presence of radar pulses); [0053] Step 5: estimating the time of arrival (TOA) of radar pulses; [0054] Step 6: detecting the falling edge of radar pulses (i.e., the termination of radar pulses); [0055] Step 7: estimating the time of departure (TOD) of radar pulses; [0056] Step 8: calculating the pulse width (PW) of radar pulses; [0057] Step 9: estimating the amplitude (AMP) of radar pulses; [0058] Step 10: estimating the center frequency (FC) and bandwidth (BW) of radar pulses; [0059] Step 11: wrapping intra-pulse parameters into pulse descriptor words (PDWs);
[0060] Referring to FIG. 3, the first step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 301. Referring to FIG. 4, the first step of the said method consists of performing multiple pre-processing tasks on the sequence of input wideband IQ samples 400 in order to obtain the sequence of magnitude-squared envelopes 404. The pre-processing tasks are comprised of performing digital down conversion 401, calculating magnitude-squared envelopes 402 and filtering the magnitude-squared envelopes by a fixed-length Finite Moving Average (FMA) filter 403. It is noted that the FMA filter 403 is optional as demonstrated as a dashed rectangle in FIG. 4.
[0061] Let x.sub.n=I.sub.n+jQ.sub.n be the baseband IQ samples after the Digital Down Converter (DDC) module at time instant n, where I.sub.n is the in-phase (real) component and Q.sub.n is the quadrature (complex) component. Let also X.sub.n be the magnitude-squared envelopes of the input IQ samples. Then, the magnitude-squared envelopes of the baseband IQ samples are calculated as the sum of squares of the in-phase and quadrature components, .i.e., X.sub.n=I.sub.n.sup.2+Q.sub.n.sup.2.
[0062] Referring to FIG. 3, the second step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 302. Referring to FIG. 5, the second step of the said method consists of estimating the noise floor level 504 from the input magnitude-squared envelopes 500. The said method for estimating the noise floor level proposed in the present invention is comprised of three following sub-steps: [0063] The sub-step 1, which is performed in block 501, consists of estimating the local average value X.sub.n of the magnitude-squared envelopes X.sub.n using the FMA filter of length L. In other words, the local average value X.sub.n is calculated as the average value of the last L samples of the magnitude-squared envelopes X.sub.n. [0064] The sub-step 2, which is performed in block 502, consists of estimating the noise floor level h.sub.X.sub.n as the minimum between the current local average value X.sub.n and the previous noise floor level h.sub.X.sub.n?1. [0065] The sub-step 3, which is performed in block 503, consists of periodically updating the noise floor level h.sub.X.sub.n by multiplying itself with an offset coefficient K.sub.?>1 for each time period T.sub.?.
[0066] The principle of the proposed method for estimating the noise floor level h.sub.X.sub.n can be briefly explained as follows. In the pure noise (pre-change) region, the local average value X.sub.n is an unbiased estimate of true noise floor level. However, the local average value X.sub.n starts increasing in the transient-change region (or intra-pulse region), causing the estimated noise floor level to be biased (due to the presence of radar pulses). In order to circumvent this problem, it is proposed in the present invention to estimate the noise floor level h.sub.X.sub.n as the minimum value between the current local average value X.sub.n at time instant n and the previous noise floor level h.sub.X.sub.n?1 at time instant n-1. However, the said minimum operation causes the estimated noise floor level h.sub.X.sub.n to converge to a value smaller than true noise floor level. In order to overcome this problem, it is proposed in the present invention to periodically update the noise floor level h.sub.X.sub.n by multiplying itself with an offset coefficient K.sub.?>1 for each time period T.sub.?. It is illustrated in FIG. 6 that the estimated noise floor value h.sub.X.sub.n proposed in the present invention is able to keep track of the true noise floor level in both stationary and time-varying noisy environments for both pre-change, intra-pulse and post-change regions.
[0067] Referring to FIG. 3, the third step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 303. Referring to FIG. 7, the third step of the said method consists of calculating the detection statistics for rising and falling edge decision 708 from the magnitude-squared envelopes 700 and the estimated noise floor level 701. The said method for calculating the detection statistics for rising edge and falling edge decision proposed in the present invention is comprised of following six sub-steps: [0068] Sub-step 1, which is performed in block 702, consists of estimating the expectation ?.sub.n of the distribution of random noises. [0069] Sub-step 2, which is performed in block 703, consists of estimating the standard deviation ?.sub.n of the distribution of random noises. [0070] Sub-step 3, which is performed in block 704, consists of estimating the tentative pulse amplitude ?.sub.X for magnitude-squared envelopes. [0071] Sub-step 4, which is performed in block 705, consists of calculating the log-likelihood ratio (LLR) s.sub.n between the distribution of tentative intra-pulse samples and the distribution of random noises. [0072] Sub-step 5, which is performed in block 706, consists of calculating the detection statistic g.sub.n for rising edge decision from the said s.sub.n. [0073] Sub-step 6, which is performed in block 707, consists of calculating the detection statistic d.sub.n for falling edge decision from the said LLR s.sub.n.
[0074] The principle of the proposed method for calculating the detection statistics for rising edge and falling edge decision is briefly explained as follows.
[0075] It is proposed in the present invention to approximate the distribution of random noises as the Chi-squared distribution with two degrees of freedom. Under this assumption, the expectation ?.sub.n of the distribution of random noises, which is performed in block 702, is estimated by multiplying the estimated noise floor level h.sub.X.sub.n by an offset coefficient K.sub.?, where K.sub.?>0 is the calibration coefficient for expectation which is chosen for compensating for the approximation of the distribution of random noises as the Chi-squared distribution. If the distribution of the random noises is exactly the Chi-squared distribution, the calibration coefficient for expectation is K.sub.?=1.
[0076] Similar to the expectation, the standard deviation ?.sub.n of the distribution of random noises, which is performed in block 703, is estimated by multiplying the estimated noise floor level h.sub.X.sub.n by an offset coefficient K.sub.?, where K.sub.?>0 is chosen in order to compensate for the approximation of the distribution of random noises as the Chi-squared distribution. If the distribution of the random noises is exactly the Chi-squared distribution, the calibration coefficient for standard deviation is K.sub.?=1.
[0077] Since the true pulse amplitude is unknown and time-varying, it is proposed in the present invention to employ the tentative pulse amplitude instead of its true value. The tentative pulse amplitude ?.sub.X, which is performed in block 704, is estimating by multiplying the estimated noise floor level h.sub.X.sub.n by an offset coefficient K.sub.?, where K.sub.?>1 is the tentative coefficient which should be chosen carefully for balancing between false alarm and detection rates in both low and high SNR levels.
[0078] The calculation of the log-likelihood ratio (LLR) s.sub.n between the distribution of tentative intra-pulse samples and the distribution of random noises is performed in block 705, wherein the LLR s.sub.n is computed from the magnitude-squared envelopes X.sub.n, the estimated expectation ?.sub.n of the distribution of random noises, the estimated standard deviation ?.sub.n of the distribution of random noises, the estimated tentative pulse amplitude ?.sub.X for the magnitude-squared envelopes, the distribution of tentative intra-pulse samples and the distribution of random noises. These two said distributions must be chosen in such a way that the LLR s, satisfies following special properties: [0079] The LLR s.sub.n must be negative in the pre-change and post-change regions where there is only random noises; [0080] The LLR s.sub.n must be positive in the intra-pulse region where there are intra-pulse samples buried in random noises.
[0081] The calculation of detection statistic for rising edge decision g.sub.n, which is performed in block 706, consists of recursively calculating the detection statistic g.sub.n from its previous value g.sub.n?1 and the LLR s.sub.n . Referring to FIG. 8, the recursive relationship between the detection statistic g.sub.n and the LLR s.sub.n must be chosen in such a way that the detection statistic g.sub.n satisfies following special properties: [0082] The detection statistic g.sub.n fluctuates around zero in the pre-change region where there is only random noises; [0083] The detection statistic g.sub.n starts increasing in the intra-pulse region and its value reflects the accumulated pulse energy from the presence of radar pulses; [0084] The detection statistic g.sub.n starts decreasing to zero from its peak in the post-change region and then fluctuates round zero until the presence of next radar pulses;
[0085] Similarly, the calculation of detection statistic for falling edge decision d.sub.n, which is performed in block 707, consists of recursively calculating the detection statistic d.sub.n from its previous value d.sub.n?1 and the LLR s.sub.n. Referring to FIG. 10, the recursive relationship between the detection statistic d.sub.n and the LLR s.sub.n must be chosen in such a way that the detection statistic d.sub.n satisfies following special properties: [0086] The detection statistic d.sub.n is set to zero in the pre-change region before the detection of radar pulses; [0087] The detection statistic d.sub.n fluctuates around zero in the intra-pulse region after the detection of radar pulses; [0088] The detection statistic d.sub.n starts increasing in the post-change region from the termination of radar pulses;
[0089] Referring to FIG. 3, the fourth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 304. Referring to FIG. 8, the fourth step of the said method consists of detecting the rising edge of radar pulses (the presence of radar pulses) by comparing the detection statistic for rising edge decision g.sub.n with a pre-defined threshold h.sub.TOA which is an adjustable parameter for balancing between false alarm and detection rates. The rising edge of radar pulses is decided if the detection statistic g.sub.n is greater than or equal to the threshold h.sub.TOA. The time instant that the detection statistic g.sub.n crosses the threshold h.sub.TOA is denoted as the gating TOA value. In addition, the locking TOA value is defined as the time instant that the detection statistic g.sub.n starts increasing from zero.
[0090] Referring to FIG. 3, the fifth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 305. Referring to FIG. 9, the fifth step of the said method consists of estimating the time of arrival (TOA) of radar pulses by searching for the middle point of the rising edge of radar pulses, which can be summarized as follows: [0091] Finding the maximum value X.sub.max of the magnitude-squared envelopes X.sub.n around the search region, from the gating TOA value to the maximum possible length of the rising edge; [0092] Calculating the amplitude threshold value X.sub.TOA=0.25*X.sub.max in order to search for the middle point of the rising edge. The coefficient 0.25 is used instead of 0.5 since the magnitude-squared envelopes are used instead of squared-root envelopes; [0093] Finding the time instant n.sub.0 in the search region that satisfies conditions X.sub.n.sub.0?X.sub.TOA and X.sub.n.sub.o.sup.+1?X.sub.TOA; [0094] Calibrating the TOA value by an interpolation method corresponding to the amplitude threshold value X.sub.TOA from the pulse envelopes X.sub.n.sub.0 and X.sub.n.sub.0.sup.1 at time instants n.sub.0 and n.sub.0+1.
[0095] Referring to FIG. 3, the sixth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 306. Referring to FIG. 9, the sixth step of the said method consists of detecting the falling edge of radar pulses by comparing the detection statistic for falling edge decision d.sub.n with a pre-defined threshold h.sub.TOD which is also an adjustable parameter. The radar pulses are said to be terminated if the detection statistic d.sub.n is greater than or equal to the threshold h.sub.TOD. The time instant that the detection statistic d.sub.n crosses the threshold h.sub.TOD is denoted as the gating TOD value. In addition, the time instant that the detection statistic d.sub.n starts rising from zero is denoted as the locking TOD value.
[0096] Referring to FIG. 3, the seventh step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 307. Referring to FIG. 11, the seventh step of the said method consists of estimating the time of departure (TOD) of radar pulses by searching for the middle point of the falling edge, which can be summarized as follows: [0097] Estimating the running average value X.sub.n of the magnitude-squared envelopes X, from the time instant no to the current time instant n; -Calculating the amplitude threshold value XT.sub.TOD=0.25*X.sub.n in order to search for the middle point of the falling edge. The utilization of the running average value X.sub.n instead of the local maximum value X.sub.max leads to more exact estimation of TOD. In addition, the coefficient 0.25 is used instead of 0.5 since the magnitude-squared envelopes are employed instead of the squared-root pulse envelopes; [0098] Finding the time instant n.sub.1 in the search region that satisfies conditions X.sub.n.sub.1?X.sub.TOD and X.sub.n.sub.1.sup.+1?X.sub.TOD; [0099] Calibrating the TOD value by an interpolation method corresponding to the amplitude threshold value X.sub.TOD from the pulse envelopes X.sub.n.sub.1 and X.sub.n.sub.1.sup.1 at time instants n.sub.1 and n.sub.1+1.
[0100] Referring to FIG. 3, the eighth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 308. The eighth step of the said method consists of calculating the pulse width PW from the TOA and TOD values estimated in the fifth step and the seventh step of the said method, respectively. More precisely, the PW value is calculated from the TOA and TOD values as PW=TOD?TOA.
[0101] Referring to FIG. 3, the ninth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 309. The ninth step of the said method consists of estimating the pulse amplitude AMP by the squared-root of the average value of the magnitude-squared envelopes from the estimated TOA value to the estimated TOD value. In practice, the pulse amplitude can be estimated by performing the squared-root operation on the running average value X.sub.n.sub.1 at time instant n.sub.1 as described in the seventh step of the said method.
[0102] Referring to FIG. 3, the tenth step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 310. The tenth step of the said method consists of estimating the center frequency FC and bandwidth BW of radar pulses using intra-pulse IQ samples. It is proposed in the present invention to estimate the center frequency FC and bandwidth BW of radar pulses by following stages: [0103] Calculating the power spectral density (PSD) of intra-pulse samples by performing the Fast Fourier Transform (FFT) on the intra-pulse IQ samples from the estimated TOA to the estimated TOD; [0104] Finding the peak value P.sub.max in the PSD bins; [0105] Calculating threshold h.sub.p which is of k-dB from the peak value P.sub.max; [0106] Searching for crossing points F.sub.1 and F.sub.2 in the rising and falling edges of PSD bins; [0107] Estimating center frequency FC as the average value of F.sub.1 and F.sub.2; [0108] Estimating signal bandwidth BW as the difference between F.sub.2 and F.sub.1;
[0109] Referring to FIG. 3, the last step of the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention is performed in block 311. The last step of the said method consists of wrapping estimated intra-pulse parameters into pulse descriptor words (PDWs), where each PWD is comprised of time of arrival (TOA), time of departure (TOD), pulse width (PW), pulse amplitude (AMP), center frequency (FC), bandwidth (BW), noise floor level (NF) and additional useful information. The set of PDWs are then transmitted to information processing modules for multiple surveillance applications.
[0110] Referring to FIG. 13, the said method for detecting radar signals and estimating their intra-pulse parameters in time-varying noisy environments proposed in the present invention outperforms classical Threshold-based Edge Detection techniques introduced in reference Real-time radar pulse parameter extractor by V. Iglesias et al, in Proc. IEEE Radar Conf., pp. 1-5, 2014. The said method proposed in the present invention is able to work well in low SNR levels, various modulation types and multipath environments whereas the classical threshold-based edge detection techniques fail to work in such practical environments.
[0111] While a preferred embodiment of the present invention has been shown and described, it will be apparent to those skilled in the art that many changes and modifications may be made without departing from the invention in its broader aspects. The appended claims are therefore intended to cover all such changes and modifications as fall within the true spirit and scope of the invention.
