The invention relates generally to multiple input multiple output (MIMO) radar detection of targets. In particular, the invention relates to improving the detection of multiple input multiple output radar signal processing of targets in clutter.
Conventional multiple input multiple output radar detection techniques yield disadvantages addressed by various exemplary embodiments of the present invention. In particular, various exemplary embodiments provide a computer-implemented method for detecting a target amidst clutter by a radar system able to transmit individual electromagnetic signals, wherein a sequence of the transmitted signals are sent from first to last on separate transmit antennae, receive the signals reflected off the target and the clutter, and process the received signals.
The method includes determining a baseband signal for each of the transmitted signals; calculating a convolution matrix for each of the transmitted signals; estimating a clutter amplitude for each range cell using modeling estimations; calculating a clutter covariance matrix for the clutter; determining a noise variance for the transmitted signals; calculating an interference correlation matrix for the transmitted signals; and forming a target detector for the radar system. The target detector for the radar system further includes simultaneously processing all the received signals, rejecting received clutter cross talk between the transmitted signals, and maximizing the signal-to-interference ratio, thereby optimizing the detectability of the target.
These and various other features and aspects of various exemplary embodiments will be readily understood with reference to the following detailed description taken in conjunction with the accompanying drawings, in which like or similar numbers are used throughout, and in which:
In the following exemplary embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific exemplary embodiments in which the inventions may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and logical, mechanical, and other changes may be made without departing from the spirit or scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.
In accordance of a presently preferred embodiment of the present invention, the components, process steps, and/or data structures may be implemented using various types of operating systems, computing platforms, computer programs, and/or general purpose machines. In addition, artisans of ordinary skill will readily recognize that devices of less ordinary purpose nature, such as hardwired devices, may also be used without departing from the scope and spirit of the inventive concepts disclosed herewith. General purpose machines include devices that execute instruction code. A hardwired device may constitute an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), digital signal processor (DSP) or other related component. The disclosure generally employs quantity units with the following abbreviations: signal strength in decibels (dB) and frequencies in hertz (Hz).
Conventional methods for MIMO signal processing implement the use of a matched filter to separate the transmitted signal. The matched filter, however, is not the optimum detector for targets that are competing with noise and clutter. Due to the improbability of perfectly orthogonal MIMO signals, there is the possibility of clutter cross talk between channels, thus increasing clutter in the received signal. The optimum detector offers an improvement on MIMO radar signal processing in clutter as visualized in the following illustrations.
Section I—MIMO Radar Signal Processing and Improvements: Multiple Input Multiple Output (MIMO) radar detection is done by dividing the transmit antenna into multiple antennas enabling additional degrees of freedom to achieve a number of design goals. Each of these antennas transmits a distinct orthogonal signal. Additionally, there are multiple receive antennas each receiving the orthogonally transmitted signals. Conventional practice requires the transmitted signals are received and separated by matched filtering for each transmitted signal.
The conventional matched filtering approach, however, is not the optimum detector for MIMO radar signal processing when clutter is involved. The reason for this is that matched filters are optimal when the interference process is only additive white Gaussian noise (AWGN). Once targets are competing with noise and clutter the matched filter has a notable drop in accuracy. Further, it is virtually impossible to generate signals that are perfectly orthogonal, thus providing the opportunity of clutter cross talk between channels of matched filters. It should be noted that the optimum detector and matched filter perform similarly in the presence of AWGN only. Therefore, the optimum detector seeks to improve target detectability in clutter for MIMO radar signal processing. This process can be visualized with some illustrations:
Section II—Long Pulse/Short Pulse Problem: Before addressing the full MIMO problem, a related problem of clutter cross talk in long pulse/short pulse radar processing must be considered. In this problem, it is shown that crosstalk is present even though the transmit signals are thought to be orthogonal. This is a practical problem for existing radars and should be viewed as a simplified version of MIMO radar signal processing.
s(t)=s1(t)exp(−j2πf0t)+s2(t−td)exp(−j2πf0t) , (1)
where s1(t) and s2(t) are the two baseband signals, f0 is the frequency offset that gives orthogonality to s1(t) and s2(t), and td is the time delay 330 between the pulses. The received data due to a point target 210 is
y
t(t)=α[s1(t−tr)exp(−j2πf0t)+s2(t−td−tr)exp(−j2πf0t)], (2)
where α is the complex amplitude of the target 210 and tr is time delay of the target 210 based on range.
The output of the AID converter 280 is represented as:
y1=α{tilde over (S)}δk, (3)
where
such that Si1=s1[(i−1)Ts]exp(−j2πf0(i−1)Ts)
and s12=s2[(i−1)Ts]exp(+j2πf0(i−1)Ts),
while i is the time index, Ts is the sample time, and δk is a vector of all zeros except the kth element which is one indicating the location of the target 210. The matrix {tilde over (S)} has the size (P+N−1)×(P+2(N−1)), where
Note eqn. (3) indicates that the target response is the convolution of the target 210 and incident signal that produces {tilde over (S)} as the convolution matrix.
The signal model for the long pulse 340 channel is represented as:
yr1=α{tilde over (S)}1δk, (5)
where {tilde over (S)}1 is the signal convolution matrix for the long pulse 340 calculated as:
The signal model for the short pulse 350 channel is represented as:
yt2=α{tilde over (S)}2δk, (7)
where {tilde over (S)}2 is the signal convolution matrix for the short pulse 350 calculated as:
The received data due to interference is represented as:
y
1
={tilde over (S)}c+n, (9)
where c is a vector of length P+2(N−1) reverse range ordered complex clutter voltage and n is a vector of length P+N−1 of AWGN.
The interference correlation matrix is determined by:
R
I
=E{y
I
y
I
H
}=E{{tilde over (S)}cc
H
{tilde over (S)}
H
}+E{nn
H}, (10)
where E{ } denotes and expectancy function and superscript H indicates conjugate transpose. This matrix RI assumes that the noise and clutter are zero mean and uncorrelated. Factoring in the assumption that the clutter is spatially white produces:
R
I
={tilde over (S)}{tilde over (R)}
C
{tilde over (S)}+σ
2
I, (11)
where I represents the identity matrix and σn2 is the noise variance,
and σi2 is the variance of the clutter at the ith cell.
Subsection (a)—Optimum Detector and Matched Filter for Long Pulse/Short Pulse: Under the assumption that clutter is a compound Gaussian process whitening matched filters operate as an optimum detector as described herein. Detectors are formed operating on data 290 using estimates of the clutter parameters to produces near optimum performance. Referencing the signal and interference models developed above, the detector processing short and long pulse data is formed as:
where η is the detection threshold selected to achieve the desired probability of false alarm. This method utilizes all of the data to make a detection decision. The optimum detector for the long pulse 340 channel is:
Note that the long pulse 340 optimum detector can detect partially eclipsed targets, but not fully eclipsed targets. The optimum detector for the short pulse 350 channel is:
Note that the short pulse 350 optimum detector can detect fully eclipsed targets missed by the long pulse 340 detector.
Use of matched filters is the current state of the art for radar processing detection statistics. When only AWGN is involved the matched filter operates similarly to an optimum detector. A combined short pulse 350 and long pulse 340 matched filter is formed as:
Standard operation utilizes separate channels for each pulse. The long pulse 340 matched filter is formed as:
The short pulse 350 matched filter is formed as:
The matched filter is designed to maximize signal power in the presence of white noise power when making a detection decision. The matched filter will also attenuate the other interfering signal (long pulse signal in the short pulse channel or the short pulse signal in the long pulse channel). However, this attenuation is incidental to the filter's function. Thus, making the optimum detector an improvement on the current state of the art for radar signal processing in clutter, due to the detectors ability to reject clutter cross talk.
Subsection (b)—Determining Output Interference Ratio (SIR) for Detectors: Using the previously outlined equations SIR for these detectors is determined. SIR information enables further proof of the optimum detector's exemplary relative performance over the matched filter. The output SIR for the combined short/long pulse optimum detector is determined by substituting the signal model for y in eqn. (13) giving:
z
t=δkH{tilde over (S)}HRI−1{tilde over (S)}αδk. (19)
The power output of the combined detector due to the target 210 is:
|zt|2=|α|2(δkH{tilde over (S)}HR1−1{tilde over (S)}αδk)2. (20)
The output of the combined detector due to the interference is:
z
i
=δ
k
H
{tilde over (S)}
H
R
I
−1
y
I. (21)
The power output of the detector due to the interference applying eqns. (9) and (10) is determined as:
E{z
iI
z
i
*}=E{δ
k
H
{tilde over (S)}y
I
y
I
H
{tilde over (S)}δ
k
}=δ
k
H
{tilde over (S)}
H
R
I
{tilde over (S)}δ
k. (22)
Taking the ratio of the output signal and interference powers gives the output SIR as:
SIRcomb=|α|2δkH{tilde over (S)}HRI−1yIyIHRI−1{tilde over (S)}δk. (23)
Taking a similar approach on developing eqn. (23) the SIR for the long pulse 340 is found as:
Taking a similar approach on developing eqn. (23) the SIR for the short pulse 350 is found as:
Using matched filter processing the signal amplitude for the detector is found using output due to the target 210 as:
zt=δkH{tilde over (S)}H{tilde over (S)}αδk (26)
This gives the power output from the detector due to the target 210 as:
|zt|2=|α|2(δkH{tilde over (S)}H{tilde over (S)}αδk)2. (27)
The output of the matched filter with interference is:
zt=δkH{tilde over (S)}H{tilde over (S)}yI. (28)
The interference power output of the matched filter that processes both pulses is:
E{z
i
z
i
*}=E{δ
k
H
{tilde over (S)}
H
y
I
y
I
H
{tilde over (S)}δ
k}=δkH{tilde over (S)}HRI{tilde over (S)}δk. (29)
Utilizing eqns. (26) and (27) the SIR for the matched filter is found as:
Using eqn. (30) as a reference the SIR for the long pulse 340 matched filter is found as:
Using eqn. (30) as a reference the SIR for the short pulse 350 matched filter is found as:
A situation may occur in which the optimum detector is mismatched to the clutter scene and receives errors in the clutter parameters. For the mismatched optimum detector, the SIR for the detector is found using power output due to the target 210 as:
|zt|2=|α|2(δkH{tilde over (S)}HRID−1{tilde over (S)}αδk)2,
where RID is the design interference correlation matrix or misestimated matrix.
The output of the combined detector due to interference is:
z
t=δkH{tilde over (S)}HRID−1yI, (34)
from eqn. (34), the power output due to interference for the combined detector is:
E{z
i
z
i
*}=E{δ
k
H
{tilde over (S)}
H
y
I
y
I
H
{tilde over (S)}δ
k}=δkH{tilde over (S)}HRI{tilde over (S)}δk. (35)
where RIA is the actual interference correlation matrix. Taking the ratio of eqns. (33) and (35) the SIR for the mismatched optimum detector is:
Using the approach in deriving eqn. (36), the SIR for the long pulse 340 mismatched optimum detector is found as:
Using the approach in deriving eqn. (36), the SIR for the short pulse 350 mismatched optimum detector is found as:
Section III—Performance Examples for Comparing Short/Long Pulse Radar Detectors: To illustrate the improvements in long/short pulse radar signal processing in clutter, made possible by the optimum detector, the following example is provided.
Skipping ahead,
Improvements in the presence of real world effects, further demonstrates the optimum detectors effectiveness, even though it requires knowledge of the CNR. This information is not known, but it is estimated as described in T. L. Foreman, “Derivation of Optimum Detector for Range Migrating Targets In The Presence Of Clutter,” NSWCDD/TR-20/167, April 2020. This estimation introduces errors that reduce the performance of detectors. To assess these errors, a Monte Carlo simulation is run using a clutter scene with fifty decibels minimum range CNR and Log-Normal fluctuations. Random changes are made to the clutter scene and errors from trial to trial. The error is Log-Normal with a standard deviation of ten decibels. This level of error was selected based on the accuracy of the Littoral Clutter Model to predict clutter.
One can reasonably assume a scenario in which the two signals are frequency separated.
Section IV—MIMO Detectors: Previously it was determined that two signals with maximum frequency separation (presumed to be orthogonal) retained some degree of clutter cross talk between channels. Further, a method for improving the radar signal processing within the clutter was developed. Applying the approach implemented above, a similar detector is developed to improve MIMO radar signal processing in clutter.
where sq(t) is the baseband signal transmitted by the qth antenna 1510, tr is the range induced time delay of the target 210, 1540, α is the complex amplitude of the target 210, 1540, aq is the phase shift corresponding to the target angle relative to transmit antenna q 235, 1510, and br is the phase shift corresponding to the target angle relative to receive antenna r 255, 1520.
Putting this in vector notation produces:
where δk is a vector with all zeros except the kth element being one (indicating target location), and {tilde over (S)}q is the convolution matrix for the qth qth signal calculated as:
Note that sq is the vector of baseband samples of sq(t) and the superscript indicates transpose. The receive data at the rth receive antenna 255, 1520 from the interference is:
where cq is the vector of complex clutter backscatter illuminated by the qth transmit antenna 235, 1510 observed by the rth receive antenna 255, 1520 and n is the vector of receiver noise that is complex AWGN.
One can assume that the clutter and receiver noise are zero mean and independent. Thus the correlation matrix of the interference is determined as:
The cross terms (i.e., q≠λ) in eqn. (43) need some consideration. The signals transmitted are desired to be orthogonal. Thus, for q≠λ, {tilde over (S)}q({tilde over (S)}λ)H≈[0]. The clutter resolution cell will generally be large in the angle (cross range) dimension. As a result the clutter resolution cells consist of many individual scatters with different phases. The receive antenna 255, 1520 sees the summation of these scatters, with random phase between the same scatterer, as it is illuminated by different antennas. The net effect of this will produce:
E{c
q(cλ)H}≈[0]. (44)
Therefore the assumption that {tilde over (s)}qE{cq(cλ)H}({tilde over (s)}λ)≈[0] is well justified. Based on that eqn. (43) becomes:
where RC was defined in eqn. (12) above.
Utilizing methods that enable assumption of clutter parameters an optimum detector is developed. Following the approach of T. L. Foreman, “Optimal Processing of Multiple-Pulse Radar Signals in Clutter,” NSWCDD/TR-00/112, August 2000 and referencing the signal and interference models developed above, the detector for the qth return observed by the rth antenna 1520 is:
MIMO radar signal processing coherently integrates the returns for the given receive antenna 255, 1520 and transmit sign. However, the current matched filter approach will result in eliminating all other transmitted signals, which is not desired. Applying the optimum detector in eqn. (46) to replace the matched filter in MIMO radar signal processing produces:
z=δ
k
H({tilde over (S)}q)HRI−1yr (47)
where z replaces the output of the matched filter as the optimum detector output. Note in this development that target motion was ignored. Applying the target motion to the detector is straight forward and illustrated in T. L. Foreman, (2020). For reference using the signal and interference models defined above, the matched filter detector is formed as:
Note that for the situation of noise only (no clutter) the matched filter behaves as an optimum detector and eqn. (46) becomes eqn. (48).
Using the approach to SIR calculation performed previously for the short/long pulse examples the SIR for the optimum detector is found as:
SIRMIMO_Opt=|α|2δkH({tilde over (S)}q)HRI−1{tilde over (S)}qδk (49)
While the SIR for the matched filter is:
and the SIR for the optimum detector with clutter parameter errors (mismatched optimum detector) is:
where RID is the design (i.e., assumed or estimated) interference correlation matrix and RIA is the actual interference correlation matrix.
Section V—Summary and Results: This study set out to develop a detector that could improve MIMO radar signal processing in clutter. Consequently, eqn. (46) is the detector that was derived for this problem. This optimum detector produces an output with improved SIR by rejecting clutter cross talk between transmitted signals. The potential for improvement upon the current state of the art was demonstrated conceptually using long pulse and short pulse signals with supposed orthogonality. To illustrate the improvements in MIMO radar signal processing in clutter, made possible by the optimum detector, the following example is provided. An MIMO radar transmitting four signals from four different antennas. The signals have different linear chirps. There is an up chirped pulse, down chirped pulse, up/down chirped pulse, and a down/up chirped pulse. The bandwidth of the signals is two and a half megahertz, and the data are sampled in-phase and quadrature (I/Q) at forty megahertz at baseband.
In order to show the benefit of this processing, not only in rejecting cross channel clutter, but also in mitigating the impact of imperfect orthogonality of waveforms, two waveform sets will be studied.
While certain features of the embodiments of the invention have been illustrated as described herein, many modifications, substitutions, changes, and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the embodiments.
The invention is a Continuation-in-Part, claims priority to and incorporates by reference in its entirety U.S. patent application Ser. No. 16/916,525 filed Jun. 30, 2020 and assigned Navy Case 113045.
The invention described was made in the performance of official duties by one or more employees of the Department of the Navy, and thus, the invention herein may be manufactured, used or licensed by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
Number | Date | Country | |
---|---|---|---|
Parent | 16916525 | Jun 2020 | US |
Child | 18071774 | US |