CN116451461A - Waveform optimization method of frequency modulation continuous wave multi-transmitting multi-receiving radar - Google Patents
Waveform optimization method of frequency modulation continuous wave multi-transmitting multi-receiving radar Download PDFInfo
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Abstract
The invention provides a waveform optimization method of a frequency modulation continuous wave multi-transmitting multi-receiving radar, which comprises the following steps: initializing a transmitting waveform and a phase coding matrix of the frequency modulation continuous wave multi-transmitting multi-receiving radar; acquiring sidelobes of a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the joint matrix of the echo signals and the reference vector; obtaining a cost function under a normalized constraint condition based on side lobes of the fuzzy function; obtaining a final cost function with regularization parameters based on the cost function and an iterative convex relaxation optimization algorithm; and iterating the final cost function, and obtaining the transmitting signal of the frequency modulation continuous wave multi-transmitting multi-receiving radar under the condition that the final cost function meets the set condition based on the initialized transmitting signal. The method optimizes the coding matrix of the CDMA method, avoids the problem that the TDMA method can not realize detection when multiple targets overlap, and the problem of high cost and complex hardware of the FDMA method, and improves the target detection probability.
Description
Technical Field
The invention relates to the technical field of waveform optimization of radars, in particular to a waveform optimization method of a frequency modulation continuous wave multi-transmission multi-reception radar.
Background
Frequency Modulated Continuous Wave (FMCW) refers to a continuous wave whose transmitted frequency is modulated by a particular signal. The frequency modulation continuous wave radar obtains the distance information of the target by comparing the difference method between the echo signal frequency at any moment and the frequency of the transmitting signal at the moment. The radial velocity and distance of the target can be obtained by processing the measured frequency difference between the two. Compared with other range-finding speed-measuring radars, the frequency-modulation continuous wave radar has simpler structure, lower required transmitting power peak value, easy modulation, low cost and simple signal processing, and is widely applied to radars. An advantage of using a MIMO (Multiple-Input Multiple-Output) radar method is that it allows combining Multiple Transmit (TX) and Receive (RX) antennas with more synthetic virtual array elements than conventional radar array elements to improve the performance of detecting the angle of arrival of Multiple targets, thereby improving the angular resolution, enabling three-dimensional imaging. The frequency modulation continuous wave MIMO radar three-dimensional imaging is a novel radar imaging technology, and the three-dimensional imaging is realized by utilizing the multiplexing characteristic of frequency modulation continuous wave signals. The frequency modulation continuous wave is one of main waveforms of human body security inspection and automobile radar because of high efficiency and low cost of distance, speed and angle estimation. While the key to improving the performance of such radars is the orthogonality of the waveforms. In recent years, frequency modulation continuous wave MIMO radars are widely studied in the fields of automobile radars, human body security inspection, intelligent home furnishings and the like.
In a MIMO radar system, the number of virtual receivers corresponds to the product of the number of TX antennas and RX antennas. These virtual array elements will help to achieve better angular resolution without increasing the number of physical antennas. To achieve MIMO operation, FMCW MIMO radar needs to apply orthogonal waveforms. Different methods currently used mainly to achieve orthogonal FMCW waveforms are Time Division Multiple Access (TDMA), frequency Division Multiple Access (FDMA) and Code Division Multiple Access (CDMA). CDMAFMCW radar is modulated by a carrier signal within each pulse, and the computational load of the FMCW phase-encoded waveform is quite low (similar to a conventional pulsed doppler radar waveform). CDMA achieves a higher SNR (Signal to Noise Ratio, signal-to-noise ratio) than TDMA at all angles because all transmitters transmit power simultaneously, rather than one by one, while CDMA methods can achieve a higher range resolution than FDMA because it utilizes more bandwidth than FDMA, or can achieve a higher clear range than FDMA for the same resolution. In order to realize space equidistant energy emission by using CDMA, code sequences of different emission array elements need to be orthogonal, phase coding matrixes need to be optimized, a blurring function (the blurring function of signals is a powerful tool for waveform design and analysis when the distance and the speed of two targets are different), in three-dimensional imaging, the accuracy and the resolution of radar waveforms in the distance, the radial speed and the angle are reflected, the coding matrixes are optimized by using the characteristics of the blurring function, and the optimized waveforms have the advantages of low cost, high orthogonality and high detection rate and are widely adopted in future frequency modulation continuous wave MIMO radar three-dimensional imaging. The method for optimizing the related waveforms comprises the following steps: TDMA optimization, traditional FDMA optimization, DDMA optimization (Doppler Division MultipleAccess, doppler frequency division multiple access). TDMA cannot utilize the full frequency band resources, resulting in time inefficiency. The traditional FDMA optimization method has higher distance side lobe and speed side lobe, and a weak target and an overlapped target with a relatively close distance are easy to lose during target detection. The DDMA optimization method has the problem of small range of the non-fuzzy speed interval, so that the DDMA optimization method cannot quickly respond to a target with high doppler frequency.
Disclosure of Invention
The embodiment of the invention aims to provide a waveform optimization method of a frequency modulation continuous wave multi-transmission multi-reception radar, which is used for solving the problems of low target detection probability, high target distance side lobe and low detection speed in a related waveform optimization method.
The embodiment of the invention adopts the following technical scheme: a waveform optimization method of a frequency modulation continuous wave multi-transmitting multi-receiving radar comprises the following steps:
initializing a transmitting waveform of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain an initialized transmitting signal, and initializing a phase encoding matrix of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain a joint matrix of echo signals;
obtaining side lobes of a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the joint matrix of the echo signals and the reference vector;
obtaining a cost function under a normalized constraint condition based on the side lobe of the fuzzy function;
obtaining a final cost function with regularization parameters based on the cost function and an iterative convex relaxation optimization algorithm;
and iterating the final cost function, and obtaining the transmitting signal of the frequency modulation continuous wave multi-transmitting multi-receiving radar under the condition that the final cost function meets the set condition based on the initialized transmitting signal.
In some embodiments, initializing a transmit waveform of the frequency-modulated continuous wave multiple-input multiple-output radar, and obtaining an initialized transmit signal includes:
initializing N transmitting antenna array elements of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain a transmitting signal of an nth transmitting antenna.
In some embodiments, the initializing the phase encoding matrix of the frequency-modulated continuous wave multiple-input multiple-output radar to obtain a joint matrix of echo signals includes:
initializing a phase coding matrix based on the number of array elements of a transmitting antenna and the number of phase codes of a single transmitting antenna to obtain an initialized phase coding matrix;
multiplying a single linear sweep frequency signal in a target echo at a determined distance with the frequency modulation continuous wave multi-transmitting multi-receiving radar by a reference signal to obtain a distance vector containing the determined distance;
multiplying the initialized phase coding matrix with a Doppler frequency shift matrix, the angular reflection response of a transmitting array to echo signals and the response of a receiving antenna to the angular response of the echo signals to obtain a target Doppler matrix about Doppler frequencies and about the angular response of the echo signals;
and obtaining the joint matrix of the echo signals based on the distance vector, the angle and the target Doppler matrix.
In some embodiments, the initializing of the phase encoding matrix includes: the phase encoding matrix with amplitude of 1 is initialized based on the independent and equi-distributed encoding phases (0, 2 pi).
In some embodiments, the obtaining the sidelobe of the ambiguity function of the fm continuous wave multiple-transmit multiple-receive radar based on the joint matrix of echo signals and the reference vector includes:
obtaining a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the matched filter response of the joint matrix of the echo signals and the reference vector;
and obtaining a side lobe of the fuzzy function under the condition of determining the average distance difference between the target and the reference distance based on the fuzzy function.
In some embodiments, the average distance difference between the determined target and the reference distance is: an average distance of the target from the reference distance is determined in a case where the plurality of targets overlap within the detection interval range.
In some embodiments, the obtaining the cost function under the normalized constraint based on the side lobe of the blur function includes:
setting a phase encoding matrix optimization standard model;
obtaining side lobes of an optimized ambiguity function based on a matrix comprising a phase encoding matrix, a transmit array response, a Doppler frequency, and a matrix representing the attenuation of the ambiguity function due to the receive array beam;
optimizing and limiting the phase coding matrix to an orthogonal coding set to obtain a constraint condition;
and optimizing a standard model and side lobes of an optimized fuzzy function based on the phase encoding matrix to obtain a cost function under a normalized constraint condition.
In some embodiments, after the final cost function with regularization parameters is obtained based on the cost function and the iterative convex relaxation optimization algorithm, the waveform optimization method further includes:
and calculating a closed solution of the final cost function after each iteration by using the intermediate vector matrix to obtain the optimized phase code.
In some embodiments, the iterating the final cost function, and obtaining a transmission signal of the fm continuous wave multiple-transmit multiple-receive radar with a final cost function satisfying a set condition based on the initialized transmission signal includes:
initializing iteration indexes and optimizing regularization parameters to calculate and obtain a determined intermediate vector matrix;
calculating to obtain a determined phase code based on the determined intermediate vector matrix;
after the iteration of the determined times, the final cost function reducing speed meets the set condition, and the optimized phase encoding matrix is obtained.
In some embodiments, after obtaining the optimized phase encoding matrix, obtaining a final cost function based on the initialized transmission signal to obtain a transmission signal of the fm continuous wave multiple-transmit multiple-receive radar under a set condition, and further including:
substituting the phase code corresponding to the optimized phase code matrix into the initialized transmitting signal to obtain the transmitting signal of the FM continuous wave multi-transmitting multi-receiving radar.
The embodiment of the invention has the beneficial effects that: the frequency modulation continuous wave CDMA waveform optimization system based on the fuzzy function is designed and applied to the MIMO radar waveform orthogonality improvement, and the sidelobes of the fuzzy function are reduced when the main lobe detection energy is kept at a certain time. The problem that detection cannot be realized when multiple targets are overlapped due to low detection efficiency of the traditional TDMA is avoided, and meanwhile, the problems of high cost and complex hardware of the FDMA method are also avoided. The novel algorithm based on the minimized fuzzy function sidelobe average energy is designed, and the traditional non-convex function optimization algorithm is improved, so that a phase coding matrix with high orthogonality is searched through fewer target iteration times, the target detection probability is improved, and the method has an obvious improvement effect on the condition of multi-target overlapping.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the related art, the drawings that are required to be used in the embodiments or the related technical descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained according to the drawings without inventive effort for those skilled in the art.
FIG. 1 is a flow chart of a waveform optimization method of the frequency modulation continuous wave multi-transmitting multi-receiving radar.
FIG. 2 is a graph of the blur function of the invention without starting the optimization.
FIG. 3 is a graph of the blur function after optimization of the present invention.
Detailed Description
Various aspects and features of the present invention are described herein with reference to the accompanying drawings.
It should be understood that various modifications may be made to the embodiments of the application herein. Therefore, the above description should not be taken as limiting, but merely as exemplification of the embodiments. Other modifications within the scope and spirit of the invention will occur to persons of ordinary skill in the art.
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with a general description of the invention given above, and the detailed description of the embodiments given below, serve to explain the principles of the invention.
These and other characteristics of the invention will become apparent from the following description of a preferred form of embodiment, given as a non-limiting example, with reference to the accompanying drawings.
It is also to be understood that, although the invention has been described with reference to some specific examples, a person skilled in the art will certainly be able to achieve many other equivalent forms of the invention, having the characteristics as set forth in the foregoing summary of the invention and hence all coming within the field of protection defined thereby.
The above and other aspects, features and advantages of the present invention will become more apparent in light of the following detailed description when taken in conjunction with the accompanying drawings.
Specific embodiments of the present invention will be described hereinafter with reference to the accompanying drawings; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention, which can be embodied in various forms. Well-known and/or repeated functions and constructions are not described in detail to avoid obscuring the invention in unnecessary or unnecessary detail. Therefore, specific structural and functional details disclosed herein are not intended to be limiting, but merely as a basis for the "summary of the invention" and as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed structure.
The specification may use the word "in one embodiment," "in another embodiment," "in yet another embodiment," or "in other embodiments," which may each refer to one or more of the same or different embodiments in accordance with the invention.
In order to solve the problems in the background technology, the invention discloses a waveform optimization method of a frequency modulation continuous wave multi-transmission multi-reception radar.
The waveform optimization method comprises the following steps: initializing a transmitting signal, improving a fuzzy function model, solving a non-convex function model, and optimizing four parts of a coding matrix cyclic-bad iteration. Firstly, according to the characteristics of the frequency modulation continuous wave MIMO radar, the radar parameters, the transmitting signals and the phase coding matrix are initialized. The Chirp signal is a spread spectrum signal, which exhibits a characteristic of linear frequency modulation, and the frequency of the signal varies linearly with time, also called a linear sweep signal. The large bandwidth fast chirp FMCW sequence is a common waveform for radar because it has high range resolution, good discrimination between different range objects (due to low side lobes in the ambiguity function along the range domain), decoupling between range and doppler, and relatively low hardware and processing complexity (low cost and power consumption). Non-chirped waveforms can achieve lower sidelobes in the blur function than chirped waveforms, but the complexity and cost of hardware and computation increases. Since overlapping targets may cause aliasing due to the masking of weak targets at different Chirp times during beam exposure, improvements in radar blurring functions are needed. In the case of multiple targets, the detection performance of the radar increases as the ratio between the main lobe peak and the side lobes of its blurring function increases. The current problem is therefore to find a phase encoding matrix that minimizes the average sidelobe level of the ambiguity function at a given distance difference, rewrite the optimization problem to the minimum sidelobe level of the ambiguity function, by rewriting the matrix, and apply the vectorized identities, the optimization problem is converted into a non-convex function optimization problem, a novel convex relaxation algorithm is designed, two regularization terms are added in the model, forward evolution of the iterative result of the phase encoding matrix is ensured, and a final iterative model is obtained. In an iteration, each minimization function is a convex function and has a closed-loop solution. And when the speed of reducing the cost function is obviously reduced, obtaining the optimized phase encoding matrix.
The waveform optimization method specifically comprises the following steps:
step S100: initializing a transmitting waveform of a Frequency Modulation Continuous Wave (FMCW) multiple-input multiple-output (MIMO) radar to obtain an initialized transmitting signal, and initializing a phase coding matrix of the frequency modulation continuous wave multiple-input multiple-output radar to obtain a joint matrix of echo signals. The initialization of the FMCW MIMO radar is mainly divided into the initialization of a transmitting waveform and the initialization of a phase coding matrix C.
Step S200: and obtaining side lobes of a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the joint matrix of the echo signals and the reference vector. The radar fuzzy function is solved by utilizing the joint matrix, and the cost function model is solved by the fuzzy function.
Step S300: and obtaining the cost function under the normalized constraint condition based on the sidelobes of the fuzzy function.
Step S400: based on the cost function and the iterative convex relaxation optimization algorithm, a final cost function with regularization parameters is obtained.
Step S500: and iterating the final cost function, and obtaining the transmitting signal of the frequency modulation continuous wave multi-transmitting multi-receiving radar under the condition that the final cost function meets the set condition based on the initialized transmitting signal.
The invention designs a frequency modulation continuous wave CDMA waveform optimization system based on a fuzzy function, and applies the frequency modulation continuous wave CDMA waveform optimization system to the improvement of the orthogonality of the MIMO radar waveform, and reduces the sidelobes of the fuzzy function when the detection energy of the main lobe is kept at a certain time. The invention not only avoids the problems that the traditional TDMA detection efficiency is low and the detection can not be realized when multiple targets are overlapped, but also avoids the problems of high cost and complex hardware of the FDMA method. The novel algorithm based on the minimized fuzzy function sidelobe average energy is designed to improve the traditional non-convex function optimization algorithm, so that a phase coding matrix with high orthogonality is searched through fewer target iteration times, the target detection probability is improved, the obvious improvement effect on the condition of multi-target overlapping is achieved, and the algorithm has the characteristics of flexibility and high efficiency.
In some embodiments, in step S100, initializing a transmit waveform of the frequency-modulated continuous wave multiple-input multiple-output radar, and obtaining an initialized transmit signal includes:
step S110: initializing N transmitting antenna array elements of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain an nth transmitting antenna Tx n Is a transmission signal of (a):
w(t-nT r ) Transmitting a frequency modulated continuous wave Chirp signal for the radar:
w(t)＝exp(j(2πf e t+πkt 2 ))0≤t≤T r (2)
where j is an imaginary number, f e Is carrier frequency, B is signal bandwidth, T r For the Chirp signal duration, k=B/T r For frequency modulation slope, C is the phase of the transmitting antenna whose dimension is N MBit coding matrix, wherein N is the number of antenna transmitting array elements, M is the number of single transmitting antenna phase codes, c m,n Is the mth phase code of the nth transmitting antenna, and t is the signal time.
In some embodiments, in step S100, initializing a phase encoding matrix of the frequency-modulated continuous wave multiple-input multiple-output radar to obtain a joint matrix of echo signals includes:
step S120: initializing a phase coding matrix based on the number of array elements of the transmitting antenna and the number of phase codes of a single transmitting antenna to obtain an initialized phase coding matrix. Specifically, let the phase coding matrix C be a phase coding matrix with dimensions n×m, where N is the number of antenna transmitting array elements, M is the number of single transmitting antenna phase codes, and the phase coding matrix C with the code phases being independently and identically distributed on [0,2 pi ] and the amplitude being 1 is obtained by using the encoder, and the phase coding matrix C is initialized:
step S130: the distance between the pair and the MIMO radar is r 1 After multiplying the single chirp signal in the target echo with the reference signal, a vector eta (r) containing the distance is obtained 1 )：
Wherein c light Is the speed of light.
Step S140: the initialized phase coding matrix C and Doppler frequency shift matrix D, and the angular reflection response a of the transmitting array to echo signals T Tx (θ 1 ) Response a of the receiving antenna to the angular response of the echo signal Rx (θ 1 ) Multiplying to obtain the Doppler frequency f 1 And an angular response θ with respect to the echo signal 1 Target Doppler matrix Q (θ) 1 ,f 1 )：
Q(θ 1 ,f 1 )＝C·D·a Rx (θ 1 )a T Tx (θ 1 ) (5)
Step S150: and obtaining a joint matrix of the echo signals based on the distance vector, the angle and the target Doppler matrix. The radar transmits a signal and receives an echo, the echo signal J being a noise-free down-converted signal from a receiving antenna Rx, comprising a distance vector η (r 1 ) Angle and target doppler Q (θ 1 ,f 1 ) Combined joint matrix J (θ 1 ,f 1 ,r 1 ) The following is shown:
J(θ 1 ,f 1 ,r 1 )＝vec(Q(θ 1 ,f 1 )×η(r 1 )) (6)
in some embodiments, in step S200, obtaining side lobes of a ambiguity function of the fm continuous wave multiple-receive radar based on the joint matrix of echo signals and the reference vector includes:
step 210: and obtaining a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the matched filter response of the joint matrix of the echo signals and the reference vector. Joint matrix J (θ) 1 ,f 1 ,r 1 ) The matched filter response with the reference vector (theta, f, r) is (theta) for the target w 1 ,f 1 ,r 1 ) Is a set of fuzzy functions χ (θ 1 ,f 1 ,r 1 θ, f, r), the frequency modulated continuous wave MIMO radar ambiguity function χ (θ) 1 ,f 1 ,r 1 θ, f, r) is:
step 220: and obtaining a sidelobe of the fuzzy function under the condition of determining the average distance difference between the target and the reference distance based on the fuzzy function.
When a plurality of detection targets overlap within the detection interval range, then this case is worst case, and the worst case distance is R 0 ：
Utilizing the target w in the worst case r 0 Average distance difference R from reference distance R (determined) w To approximate radar performance in the entire interval by a blurring function χ (θ 1 ,f 1 ,r 1 Obtaining a sidelobe χ (theta) of the fuzzy function under the distance difference 1 ,f 1 θ, f) is:
where H represents the conjugate transpose operator.
In some embodiments, step S300: obtaining the cost function under the normalized constraint condition based on the sidelobes of the fuzzy function comprises:
step S310: setting a phase encoding matrix optimization standard model. The same main lobe value of the fuzzy function can be obtained by setting all angles and Doppler so as to ensure the same detection performance. Fig. 2 shows a fuzzy function diagram when the optimization is not started. Radar detection performance χ (θ) as a function of ambiguity 1 ,f 1 ,r 1 θ, f, r) the ratio between the main lobe peak and the side lobe increases to increase, it is necessary to find the ratio of the side lobe level χ (θ 1 ,f 1 θ, f) minimum phase encoding matrix C, therefore the ambiguity function sidelobe optimization model is set to:
step S320: the side lobes of the optimized ambiguity function are obtained based on a matrix comprising a phase encoding matrix, a transmit array response, a Doppler frequency, and a matrix representing the attenuation of the ambiguity function due to the receive array beam. Further to the ambiguity function sidelobe χ (θ 1 ,f 1 Optimizing the theta, f) model, wherein the mathematical model is as follows:
χ(θ 1 ,f 1 ,θ,f)＝w(θ 1 ,θ,Δf,C)Y(θ 1 ,θ,-Δf) (11)
w (θ) 1 θ, Δf, C) is a matrix comprising a phase encoding matrix C, a transmit array response and doppler frequency, and Y (θ) 1 θ, - Δf) is a matrix independent of the phase encoding matrix C, representing the attenuation of the ambiguity function due to the receive array beam; Δf is the difference between the doppler frequency of the blur function and the doppler frequency of the received signal from the target. Fig. 3 shows an optimized blur function diagram. Comparing fig. 2 and 3, it can be seen that the optimized fuzzy function model achieves low sidelobes of about 15dB at doppler frequencies and AOA (Angle-of-Arrival ranging) at which the range offset and receive array beamforming resolution are insufficient to separate between targets. Therefore, when there are multiple targets, optimizing the code's ability to attenuate the side lobes of the band reduces interference between the targets and increases the probability that the targets are detected, i.e., increases the detection accuracy.
Wherein Y (θ) 1 The model for θ, - Δf) is:
Y(θ 1 ,θ,-Δf)＝c H B(θ 1 ,θ,Δf)cc H B H (θ 1 ,θ,Δf)c (12)
where c=vec (C), also known as vectorization of matrix C, and superscript H denotes the conjugate transpose operator of the matrix.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
step S330: optimizing and limiting the phase coding matrix to be an orthogonal coding set to obtain a constraint condition I Nx ：
CC H ＝I Nx (14)
Step S340: and optimizing a standard model and side lobes of an optimized fuzzy function based on the phase encoding matrix to obtain a cost function under a normalized constraint condition.
Finding a phase encoding matrix C that reduces the side lobe level of the blur function, substituting the formula (11) and the formula (12) into the formula (10), and substituting the constraint into the formula (14), the cost function model that performs the normalization constraint of the formula (14) is obtained as follows:
in some embodiments, step S400: based on the cost function and the iterative convex relaxation optimization algorithm, after obtaining the final cost function with regularization parameters, the waveform optimization method further comprises the following steps:
step S410: and calculating a closed solution of the final cost function after each iteration by using the intermediate vector matrix to obtain the optimized phase code.
And (3) rewriting the optimization problem into a minimum problem of a side lobe level of the fuzzy function, and converting the optimization problem into a non-convex function optimization problem by rewriting the matrix and applying a vectorization identity. Specifically, the phase coding optimization model of the formula (15) is regarded as a polynomial non-convex function optimization problem, the fuzzy function sidelobe model of the formula (15) is rewritten by using an iterative convex relaxation optimization algorithm, and the improved cost function model is as follows:
wherein mu a ,μ b Is a regularization weight factor, i.e., the regularization parameter described above. Two regularization terms are added in the model to ensure that the result of the phase encoding matrix iteration evolves forward and a final iteration model is obtained. Let the intermediate vector matrix F (c) n-1 ) The method comprises the following steps:
in an iteration, each minimization function is a convex function and has a closed-loop solution. To solve the closed-loop solution problem for each iteration in the improved cost function model of equation (16), an intermediate vector matrix F (c) n-1 ) Searching for a closed solution after each iteration of the improved cost function model of formula (16)c n ：
In some embodiments, step S500: iterating the final cost function, and obtaining the transmitting signal of the frequency modulation continuous wave multi-transmitting multi-receiving radar under the condition that the final cost function meets the set condition based on the initialized transmitting signal, wherein the method comprises the following steps:
step S510: initializing an iteration index and optimizing regularization parameters to calculate a determined intermediate vector matrix. Encoding phase c using an optimized mathematical model in equation (18) n Performing iterative solution, initializing an iterative index n=1, and then calculating F (c) using formula (17) n-1 )。
Step S520: based on the determined intermediate vector matrix, a determined phase code is calculated. Mu (mu) a ,μ b Setting a random number less than or equal to one, then adjusting according to the model optimization condition, substituting the calculation result into a formula (17), and finally calculating the phase code c by using a formula (18) n 。
Step S530: after the iteration of the determined times, the final cost function reducing speed meets the set condition, and the optimized phase encoding matrix is obtained. Substituting the result into formula (16) after n iterations, and obtaining the final vectorized phase code c when the decreasing speed of the cost function is obviously reduced, namely when the decreasing speed of the cost function of formula (16) is very slow (the decreasing speed is 10-15), completing the optimization of the phase code matrix n To obtain an optimized phase encoding matrix C final ＝reshape(c n ,N,M)。
For a moving target, when the target is not moving, that is, the Doppler frequency is 0, the reference code is slightly better than other codes (eg: kasami code, FPSK and other code signals), and when Doppler frequency shift occurs, the frequency shift breaks the orthogonality of the code matrix, and the optimized phase code matrix has smaller influence, so that the detection effect of the moving target for small displacement is obviously better than that of the ordinary phase code, BPSK code and the like. Further, when the probability of the radar detecting a signal where only noise and interference occur is higher than the probability of a target containing noise and interference signals, the radar performance is significantly reduced, in which case the radar resolution target capability is significantly reduced, and the resolution probability of the optimal coding is 17 times higher, which is significantly better than BPSK phase coding. In addition, when the target distance is close, the detection rate for the main target passes the ROC detection curve (Receiver Operating Characteristic Curve, subject characteristic curve) at a target interference energy of 15dB, which is also significantly better than other codes.
In some embodiments, after obtaining the optimized phase encoding matrix, obtaining a transmission signal of the fm continuous wave multiple-transmit multiple-receive radar with a final cost function satisfying a set condition based on the initialized transmission signal, and further including:
step S540: substituting the phase code corresponding to the optimized phase code matrix into the initialized transmitting signal to obtain the transmitting signal of the FM continuous wave multi-transmitting multi-receiving radar. Upcoming C final ＝reshape(c n N, M) is applied to the initialized transmitting signal to obtain the transmitting signal of the fm continuous wave multi-transmit multi-receive radar, so as to optimize the transmitting waveform of the fm continuous wave multi-transmit multi-receive radar.
While various embodiments of the present invention have been described in detail, the present invention is not limited to these specific embodiments, and various modifications and embodiments can be made by those skilled in the art on the basis of the inventive concept, and these modifications and modifications should be included in the scope of the claimed invention.
Claims (10)
1. The waveform optimization method of the frequency modulation continuous wave multi-transmitting multi-receiving radar is characterized by comprising the following steps of:
initializing a transmitting waveform of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain an initialized transmitting signal, and initializing a phase encoding matrix of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain a joint matrix of echo signals;
obtaining side lobes of a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the joint matrix of the echo signals and the reference vector;
obtaining a cost function under a normalized constraint condition based on the side lobe of the fuzzy function;
obtaining a final cost function with regularization parameters based on the cost function and an iterative convex relaxation optimization algorithm;
and iterating the final cost function, and obtaining the transmitting signal of the frequency modulation continuous wave multi-transmitting multi-receiving radar under the condition that the final cost function meets the set condition based on the initialized transmitting signal.
2. The method for optimizing the waveform of a fm continuous wave multiple-transmit multiple-receive radar according to claim 1, wherein initializing the transmit waveform of the fm continuous wave multiple-transmit radar to obtain an initialized transmit signal comprises:
initializing N transmitting antenna array elements of the frequency modulation continuous wave multi-transmitting multi-receiving radar to obtain a transmitting signal of an nth transmitting antenna.
3. The method for optimizing waveform of fm continuous wave multiple transmission multiple reception radar according to claim 1, wherein initializing a phase encoding matrix of the fm continuous wave multiple transmission multiple reception radar to obtain a joint matrix of echo signals comprises:
initializing a phase coding matrix based on the number of array elements of a transmitting antenna and the number of phase codes of a single transmitting antenna to obtain an initialized phase coding matrix;
multiplying a single linear sweep frequency signal in a target echo at a determined distance with the frequency modulation continuous wave multi-transmitting multi-receiving radar by a reference signal to obtain a distance vector containing the determined distance;
multiplying the initialized phase coding matrix with a Doppler frequency shift matrix, the angular reflection response of a transmitting array to echo signals and the response of a receiving antenna to the angular response of the echo signals to obtain a target Doppler matrix about Doppler frequencies and about the angular response of the echo signals;
and obtaining the joint matrix of the echo signals based on the distance vector, the angle and the target Doppler matrix.
4. A method of optimizing waveforms for a fm continuous wave multiple-transmit multiple-receive radar as claimed in claim 3, wherein said initializing of said phase encoding matrix comprises: the phase encoding matrix with amplitude of 1 is initialized based on the independent and equi-distributed encoding phases (0, 2 pi).
5. The method for optimizing waveform of fm continuous wave multiple-transmit multiple-receive radar according to claim 1, wherein obtaining sidelobes of a fuzzy function of fm continuous wave multiple-transmit multiple-receive radar based on the joint matrix of echo signals and a reference vector comprises:
obtaining a fuzzy function of the frequency modulation continuous wave multi-transmitting multi-receiving radar based on the matched filter response of the joint matrix of the echo signals and the reference vector;
and obtaining a side lobe of the fuzzy function under the condition of determining the average distance difference between the target and the reference distance based on the fuzzy function.
6. The method for optimizing the waveform of a fm continuous wave multiple-transmit multiple-receive radar according to claim 5, wherein the average distance difference between the determined target and the reference distance is: an average distance of the target from the reference distance is determined in a case where the plurality of targets overlap within the detection interval range.
7. The method for optimizing the waveform of a fm continuous wave multiple-transmit multiple-receive radar according to claim 1, wherein the obtaining a cost function under a normalization constraint based on the side lobes of the ambiguity function comprises:
setting a phase encoding matrix optimization standard model;
obtaining side lobes of an optimized ambiguity function based on a matrix comprising a phase encoding matrix, a transmit array response, a Doppler frequency, and a matrix representing the attenuation of the ambiguity function due to the receive array beam;
optimizing and limiting the phase coding matrix to an orthogonal coding set to obtain a constraint condition;
and optimizing a standard model and side lobes of an optimized fuzzy function based on the phase encoding matrix to obtain a cost function under a normalized constraint condition.
8. The method for optimizing a waveform of a fm continuous wave multiple-transmit multiple-receive radar according to claim 1, wherein after the final cost function with regularization parameters is obtained based on a cost function and an iterative convex relaxation optimization algorithm, the method for optimizing a waveform further comprises:
and calculating a closed solution of the final cost function after each iteration by using the intermediate vector matrix to obtain the optimized phase code.
9. The method for optimizing the waveform of a fm continuous wave multiple-transmit multiple-receive radar according to claim 8, wherein the iterating the final cost function, based on the initialized transmit signal, obtains a transmit signal of the fm continuous wave multiple-transmit multiple-receive radar with the final cost function satisfying a set condition, includes:
initializing iteration indexes and optimizing regularization parameters to calculate and obtain a determined intermediate vector matrix;
calculating to obtain a determined phase code based on the determined intermediate vector matrix;
after the iteration of the determined times, the final cost function reducing speed meets the set condition, and the optimized phase encoding matrix is obtained.
10. The method for optimizing waveform of fm continuous wave multiple transmission and multiple reception radar according to claim 9, wherein after obtaining the optimized phase encoding matrix, obtaining a fm continuous wave multiple transmission and multiple reception radar transmission signal with a final cost function satisfying a set condition based on the initialized transmission signal, further comprises:
substituting the phase code corresponding to the optimized phase code matrix into the initialized transmitting signal to obtain the transmitting signal of the FM continuous wave multi-transmitting multi-receiving radar.
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