A MIMO radar orthogonal waveform design method and system

Abstract

The present invention proposes a MIMO radar orthogonal waveform design method and system. The method designs the orthogonal waveform of the MIMO radar by constraining the spectrum shape. The MIMO radar is a multi-input multi-output radar. The method includes: obtaining the transmission waveform of the transmission signal of the MIMO radar transmission platform, constructing a non-periodic correlation signal model of the transmission signal based on the transmission waveform, and the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function; establishing a spectrum model of the transmission waveform to construct a spectrum matching model of the transmission waveform, and further determining an optimization model of the transmission waveform based on spectrum shape constraints based on the spectrum matching model and an optimization model of the transmission waveform based on expected correlation performance matching; using the optimization model of the transmission waveform based on spectrum shape constraints, the optimal transmission waveform is obtained through cyclic iterative calculation, and the cutoff condition of the iterative calculation is that the change of the adjacent step objective function is less than a threshold.

Description

Technical Field

[0001] The invention belongs to the field of radar system and radar signal processing, and in particular relates to a MIMO radar orthogonal waveform design method and system. Background Art

[0002] As a new type of radar, MIMO radar has attracted widespread attention from many scholars since it was proposed. Compared with traditional phased array radar, MIMO radar can transmit arbitrary waveforms, has higher degrees of freedom, and has very superior performance in target detection, parameter estimation, etc. According to the different antenna configuration methods, it can be divided into statistical MIMO radar and coherent MIMO radar. The configuration spacing of the statistical MIMO radar transceiver array elements is large, and the target can be observed from different directions. Therefore, it has good spatial gain, structural gain and polarization gain, and can effectively overcome the target RCS flicker effect. The target echo of the coherent MIMO radar can be coherently processed after matched filtering, and a good waveform diversity gain is obtained, which is more conducive to the detection of weak targets under strong interference background.

[0003] Waveform design is an important basis for the superior performance of MIMO radar. Under different working conditions, the performance of the waveform required by MIMO radar is different, and the corresponding waveform design criteria are also different. Generally speaking, MIMO radar waveform design can be divided into the following situations: 1. Transmitting waveform design under the expected pattern matching, the purpose is to achieve the focusing of the transmitting power in the specified airspace by controlling the correlation of the waveform, and increase the signal-to-noise ratio of the data at the receiving array; 2. The waveform design that maximizes the output signal-to-interference-noise ratio, the purpose is to improve the detection ability of the receiving array for spatial target signals; 3. Orthogonal waveform design, the purpose is to achieve matched filtering of spatial signals by optimizing the correlation between waveforms, extract the phase information of different transmit and receive path pairs, and lay the foundation for subsequent efficient parameter estimation; In addition, there are waveform designs based on information theory, as well as waveform designs based on similarity constraints or low peak-to-average ratio constraints or constant modulus constraints that are more in line with actual engineering applications. The patent of this invention mainly takes orthogonal waveform design as the research object.

[0004] When designing orthogonal waveforms, most existing methods use the waveform's auto-correlation / cross-correlation performance as the optimization target to establish a cost function. Although this can improve the orthogonality between waveforms, it will still cause mutual interference between different systems in a complex electromagnetic environment. In actual work, the presence of interference signals often deteriorates the performance of the radar system. Summary of the invention

[0005] In view of the shortcomings of the existing technology, this application further considers the mutual interference problem between different electronic devices on the basis of traditional orthogonal waveform design, and proposes a MIMO radar orthogonal waveform design scheme. The orthogonal waveform that meets the system performance requirements is designed by utilizing the idle spectrum gaps in space, which can not only complete the predetermined radar function but also coexist with other radars and communication equipment of the same party.

[0006] The first aspect of the present invention discloses a method for designing orthogonal waveforms of MIMO radars. The method designs the orthogonal waveforms of the MIMO radar by constraining the spectrum shape, and the MIMO radar is a multiple-input multiple-output radar, and the method comprises:

[0007] Step S1, obtaining a transmission waveform of a transmission signal of a MIMO radar transmission platform, and constructing a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;

[0008] Step S2, establishing a spectrum model of the transmission waveform to construct a spectrum matching model of the transmission waveform, and further determining an optimization model of the transmission waveform based on spectrum shape constraints based on the spectrum matching model and an optimization model of the transmission waveform based on expected related performance matching;

[0009] Step S3, using the optimization model of the transmission waveform based on the spectrum shape constraint, the optimal transmission waveform is obtained through cyclic iterative calculation, and the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold value.

[0010] According to the method of the first aspect of the present invention, in step S1, the non-periodic autocorrelation function A of the non-periodic correlation signal model l,k and the aperiodic cross-correlation function C p,q,k They are:

[0011]

[0012]

[0013] Among them, A l,k represents the autocorrelation of the lth transmitted waveform at the kth time delay, C p,q,k represents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q, k=0,1,...,N-1,s l (n) represents the value of the lth transmission waveform at the nth moment, let is the k-time delay shift matrix:

[0014]

[0015] in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows:

[0016]

[0017] Among them, Z p,q represents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0, represents the Kronecker product, based on the matrix J p,q,k The definition of , then the compact expressions of the non-periodic autocorrelation function and the non-periodic cross-correlation function of the transmit waveform are respectively:

[0018] A l,k =s H J l,l,k s

[0019] C p,q,k =s H J p,q,k s

[0020] Where s = [s 1 ,s 2 ,...,s L ] H is the vector expression of the transmit waveform.

[0021] According to the method of the first aspect of the present invention, in step S2:

[0022] (1) The spectrum model of the transmission waveform is:

[0023] y z =s H F z

[0024] in, I L represents the L-dimensional unit matrix.

[0025] (2) The optimization model of the transmission waveform based on the expected correlation performance matching is:

[0026]

[0027] st|s(m)|=1,m=1,2,...,LN

[0028] Among them, w k≥0 indicates the weighted coefficients at different delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay;

[0029] (3) The spectrum matching model of the transmission waveform constructed is:

[0030]

[0031] st|s(m)|=1,m=1,2,...,LN

[0032] in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum;

[0033] (4) The optimization model of the transmission waveform based on the spectrum shape constraint is:

[0034]

[0035] st|s(m)|=1,m=1,2,...,LN

[0036] Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmission waveform.

[0037] According to the method of the first aspect of the present invention, in step S3, an equivalent optimization model of the optimization model of the transmit waveform based on spectrum shape constraints is obtained:

[0038]

[0039] st|s(m)|=1,m=1,2,...,LN

[0040] in, θ z =[θ z1 ,θ z2 ,...,θ zL ], Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

[0041] According to the method of the first aspect of the present invention, in step S3, using the equivalent optimization model to perform the cyclic iterative calculation process specifically includes:

[0042] (1) Input variable w = [w 1-N ,...,w N-1 ]、 and the initial value of β.

[0043] (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) .

[0044] (3) Let t = t + 1, and calculate the following formula:

[0045]

[0046]

[0047]

[0048] (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , the following formula is used to update s:

[0049]

[0050] st|s(m)|=1,m=1,2,...,LN

[0051] Simplify the above equation into a linear programming problem with equality constraints:

[0052]

[0053] st|s(m)|=1,m=1,2,...,LN

[0054] Where Re(·) represents the real part operation, and the closed-form solution of s is: s=e (jarg(βu+(1-β)v)) , the specific update process is as follows:

[0055] (4.1) Update u (t,b) :

[0056]

[0057]

[0058]

[0059] in, Further obtain:

[0060]

[0061] in, diag(·) means to matrix the vector elements with them as diagonal elements. LN Represents a vector whose elements are all 1.

[0062] (4.2) Update v (t,b) :

[0063]

[0064]

[0065] Further obtain:

[0066] v (t,b) =λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)

[0067] in,

[0068] (4.3) Let b = b + 1, update s (t,b) :

[0069]

[0070] Determine whether the internal convergence condition is met, wherein the internal convergence condition is whether the change of the objective function value between two adjacent iteration steps is less than a first preset threshold. If so, proceed to step (5); otherwise, proceed to step (4.1);

[0071] (5) Let s (t) =s (t,b) , determine whether the external convergence condition is met, the external convergence condition being whether the change of the objective function value of two adjacent iteration steps is less than a second preset threshold, if so, proceed to step (6), otherwise, proceed to step (3);

[0072] (6) The optimal transmission waveform is obtained as s * =s (t) .

[0073] The second aspect of the present invention discloses a MIMO radar orthogonal waveform design system. The system designs the orthogonal waveform of the MIMO radar by constraining the spectrum shape, and the MIMO radar is a multiple-input multiple-output radar, and the system includes:

[0074] A first processing unit is configured to obtain a transmission waveform of a transmission signal of a MIMO radar transmission platform, and construct a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;

[0075] A second processing unit is configured to establish a spectrum model of the transmit waveform to construct a spectrum matching model of the transmit waveform, and further determine an optimization model of the transmit waveform based on a spectrum shape constraint based on the spectrum matching model and an optimization model of the transmit waveform based on expected related performance matching;

[0076] The third processing unit is configured to use the optimization model of the transmission waveform based on the spectrum shape constraint to obtain the optimal transmission waveform through cyclic iterative calculation, and the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold.

[0077] According to the system of the second aspect of the present invention, the first processing unit 401 is specifically configured to: l,k and the aperiodic cross-correlation function C p,q,k They are:

[0078]

[0079]

[0080] Among them, A l,k represents the autocorrelation of the lth transmitted waveform at the kth time delay, C p,q,k represents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q, k=0,1,...,N-1,s l (n) represents the value of the lth transmission waveform at the nth moment, let is the k-time delay shift matrix:

[0081]

[0082] in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows:

[0083]

[0084] Among them, Z p,qrepresents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0, represents the Kronecker product, based on the matrix J p,q,k The definition of , then the compact expressions of the non-periodic autocorrelation function and the non-periodic cross-correlation function of the transmit waveform are respectively:

[0085] A l,k =s H J l,l,k s

[0086] C p,q,k =s H J p,q,k s

[0087] Where s = [s 1 ,s 2 ,...,s L ] H is the vector expression of the transmit waveform.

[0088] According to the system of the second aspect of the present invention, the second processing unit 402 is specifically configured as follows:

[0089] (1) The spectrum model of the transmission waveform is:

[0090] y z =s H F z

[0091] in, I L represents the L-dimensional unit matrix.

[0092] (2) The optimization model of the transmission waveform based on the expected correlation performance matching is:

[0093]

[0094] st|s(m)|=1,m=1,2,...,LN

[0095] Among them, w k ≥0 indicates the weighted coefficients at different delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay;

[0096] (3) The spectrum matching model of the transmission waveform constructed is:

[0097]

[0098] st|s(m)|=1,m=1,2,...,LN

[0099] in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum;

[0100] (4) The optimization model of the transmission waveform based on the spectrum shape constraint is:

[0101]

[0102] st|s(m)|=1,m=1,2,...,LN

[0103] Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmission waveform.

[0104] According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to obtain an equivalent optimization model of the optimization model of the transmit waveform based on spectrum shape constraints:

[0105]

[0106] st|s(m)|=1,m=1,2,...,LN

[0107] in, θ z =[θ z1 ,θ z2 ,...,θ zL ], Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

[0108] According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to use the equivalent optimization model to perform the loop iterative calculation process, which specifically includes:

[0109] (1) Input variable w = [w 1-N ,...,w N-1 ]、 and the initial value of β.

[0110] (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) .

[0111] (3) Let t = t + 1, and calculate the following formula:

[0112]

[0113]

[0114]

[0115] (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , the following formula is used to update s:

[0116]

[0117] st|s(m)|=1,m=1,2,...,LN

[0118] Simplify the above equation into a linear programming problem with equality constraints:

[0119]

[0120] st|s(m)|=1,m=1,2,...,LN

[0121] Where Re(·) represents the real part operation, and the closed-form solution of s is: s=e (jarg(βu+(1-β)v)) , the specific update process is as follows:

[0122] (4.1) Update u (t,b) :

[0123]

[0124]

[0125]

[0126] in, Further obtain:

[0127]

[0128] in, diag(·) means to matrix the vector elements with them as diagonal elements. LN Represents a vector whose elements are all 1.

[0129] (4.2) Update v (t,b) :

[0130]

[0131]

[0132] Further obtain:

[0133] v (t,b) =λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)

[0134] in,

[0135] (4.3) Let b = b = 1, update s (t,b) :

[0136]

[0137] Determine whether the internal convergence condition is met, wherein the internal convergence condition is whether the change of the objective function value between two adjacent iteration steps is less than a first preset threshold. If so, proceed to step (5); otherwise, proceed to step (4.1);

[0138] (5) Let s (t) =s (t,b) , determine whether the external convergence condition is met, the external convergence condition being whether the change of the objective function value of two adjacent iteration steps is less than a second preset threshold, if so, proceed to step (6), otherwise, proceed to step (3);

[0139] (6) The optimal transmission waveform is obtained as s * =s (t) .

[0140] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps in the MIMO radar orthogonal waveform design method described in any one of the first aspects of the present disclosure are implemented.

[0141] The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps in any one of the MIMO radar orthogonal waveform design methods described in the first aspect of the present disclosure are implemented.

[0142] In summary, the beneficial effects of the present invention are as follows: (1) The present invention constructs a generalized MIMO radar waveform design criterion, which can well compromise the integral sidelobe frequency and peak sidelobe level of the waveform correlation function by adjusting the expected correlation performance. The existing MIMO radar orthogonal waveform design can be regarded as a special case of the present invention; (2) The present invention considers the MIMO radar orthogonal waveform design under spectrum constraints. While optimizing the correlation performance of the transmission waveform, the spectrum shape of the transmission waveform can be effectively controlled, so that it can achieve electromagnetic compatibility with other radars and communication equipment in a complex electromagnetic environment; (3) The present invention proposes a joint optimization method of twice Minorization-maximization (MM) technology and acceleration strategy, which transforms the original non-convex problem into a series of linear programming problems. Compared with the existing SDR or gradient algorithm, it has lower computational complexity and better optimization effect, laying a favorable foundation for the online design of MIMO radar transmission waveform. BRIEF DESCRIPTION OF THE DRAWINGS

[0143] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0144] Figure 1 A flowchart of a MIMO radar orthogonal waveform design method according to an embodiment of the present invention;

[0145] Figure 2 A correlation function of a waveform obtained by simulating the second embodiment according to the optimization of the first embodiment of the present invention is given;

[0146] Figure 3 The spectrum of the waveform obtained by simulating the second embodiment according to the optimization of the first embodiment of the present invention is given;

[0147] Figure 4 4 is a structural diagram of a MIMO radar orthogonal waveform design system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0148] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0149] The first aspect of the present invention discloses a method for designing orthogonal waveforms of a MIMO radar. The method designs the orthogonal waveforms of the MIMO radar by constraining the spectrum shape, and the MIMO radar is a multiple-input multiple-output radar. Figure 1 Flow chart of a MIMO radar orthogonal waveform design method according to an embodiment of the present invention; Figure 1 As shown, the method includes:

[0150] Step S1, obtaining a transmission waveform of a transmission signal of a MIMO radar transmission platform, and constructing a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;

[0151] Step S2, establishing a spectrum model of the transmission waveform to construct a spectrum matching model of the transmission waveform, and further determining an optimization model of the transmission waveform based on spectrum shape constraints based on the spectrum matching model and an optimization model of the transmission waveform based on expected related performance matching;

[0152] Step S3, using the optimization model of the transmission waveform based on the spectrum shape constraint, the optimal transmission waveform is obtained through cyclic iterative calculation, and the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold value.

[0153] In some embodiments, in step S1, the non-periodic autocorrelation function A of the non-periodic correlation signal model l,k and the aperiodic cross-correlation function C p,q,k They are:

[0154]

[0155]

[0156] Among them, A l,k represents the autocorrelation of the lth transmitted waveform at the kth time delay, C p,q,krepresents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q, k=0,1,...,N-1,s l (n) represents the value of the lth transmission waveform at the nth moment, let is the k-time delay shift matrix:

[0157]

[0158] in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows:

[0159]

[0160] Among them, Z p,q represents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0, represents the Kronecker product, based on the matrix J p,q,k The definition of , then the compact expressions of the non-periodic autocorrelation function and the non-periodic cross-correlation function of the transmit waveform are respectively:

[0161] A l,k =s H J l,l,k s

[0162] C p,q,k =s H J p,q,k s

[0163] Where s = [s 1 ,s 2 ,...,s L ] H is the vector expression of the transmit waveform.

[0164] In some embodiments, in step S2:

[0165] (1) The spectrum model of the transmission waveform is:

[0166] y z =s H F z

[0167] in, I L represents the L-dimensional unit matrix.

[0168] (2) The optimization model of the transmission waveform based on the expected correlation performance matching is:

[0169]

[0170] st|s(m)|=1,m=1,2,...,LN

[0171] Among them, w k ≥0 indicates the weighted coefficients at different delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay;

[0172] (3) The spectrum matching model of the transmission waveform constructed is:

[0173]

[0174] st|s(m)|=1,m=1,2,...,LN

[0175] in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum;

[0176] (4) The optimization model of the transmission waveform based on the spectrum shape constraint is:

[0177]

[0178] st|s(m)|=1,m=1,2,...,LN

[0179] Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmission waveform.

[0180] In some embodiments, in step S3, an equivalent optimization model of the optimization model of the transmit waveform based on spectrum shape constraints is obtained:

[0181]

[0182] st|s(m)|=1,m=1,2,...,LN

[0183] in, θ z =[θ z1 ,θ z2,...,θ zL ], Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

[0184] In some embodiments, in step S3, the equivalent optimization model is used to perform the loop iterative calculation process, which specifically includes:

[0185] (1) Input variable w = [w 1-N ,...,w N-1 ]、 and the initial value of β.

[0186] (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) .

[0187] (3) Let t = t + 1, and calculate the following formula:

[0188]

[0189]

[0190]

[0191] (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , the following formula is used to update s:

[0192]

[0193] st|s(m)|=1,m=1,2,...,LN

[0194] Simplify the above equation into a linear programming problem with equality constraints:

[0195]

[0196] st|s(m)|=1,m=1,2,...,LN

[0197] Where Re(·) represents the real part operation, and the closed-form solution of s is: s=e (jarg(βu+(1-β)v)) , the specific update process is as follows:

[0198] (4.1) Update u (t,b) :

[0199]

[0200]

[0201]

[0202] Among them, Furthermore, it is obtained that:

[0203]

[0204] Among them, diag(·) represents matrixing it with the vector elements as the diagonal elements, and E LN represents a vector with all elements being 1.

[0205] (4.2) Update v (t,b) :

[0206]

[0207]

[0208] Furthermore, it is obtained that:

[0209] v (t,b) = λ max (P)s (t,b) + α (t) q (t,b) - Ps (t,b)

[0210] Among them,

[0211] (4.3) Let b = b + 1 and update s (t,b) :

[0212]

[0213] Judge whether the internal convergence condition is satisfied. The internal convergence condition is whether the change in the objective function value between two adjacent iteration steps is less than the first preset threshold. If so, go to step (5); otherwise, go to step (4.1);

[0214] (5) Let s (t) = s (t,b) , and judge whether the external convergence condition is satisfied. The external convergence condition is whether the change in the objective function value between two adjacent iteration steps is less than the second preset threshold. If so, go to step (6); otherwise, go to step (3);

[0215] (6) Obtain the optimal transmission waveform as s * = s (t) .

[0216] The first embodiment

[0217] 1. Construct the non-periodic correlation signal model of the MIMO radar transmission waveform. The specific non-periodic autocorrelation function A l,k and the cross-correlation function C p,q,k The expression is as follows:

[0218]

[0219]

[0220] Among them, l, p, q = 1, 2, ..., L, p ≠ q, k = 0, 1, ..., N-1.

[0221] make is the shift matrix,

[0222]

[0223] Among them, δ is the impact function, and the definition matrix J p,q,k as follows:

[0224]

[0225] Among them, Z p,q represents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0. represents the Kronecker product.

[0226] Based on the above definition, a compact expression for the non-periodic correlation function of the MIMO radar transmit waveform can be given as:

[0227] A l,k =s H J l,l,k s

[0228] C p,q,k =s H J p,q,k s

[0229] Where s = [s 1 ,s 2 ,...,s L ] H .

[0230] 2. Construct a spectrum model of the MIMO radar transmission waveform:

[0231] Defining the Matrix

[0232]

[0233]

[0234] Where z = 0, 1, ..., N-1, I L represents the L-dimensional unit matrix.

[0235] Then the spectrum of the transmitted waveform s can be expressed as:

[0236] y z =s H F z

[0237] 3. Construct a MIMO radar transmit waveform optimization model based on spectrum shape constraints:

[0238] (1) Establish a MIMO radar transmit waveform optimization model based on expected correlation performance matching:

[0239]

[0240] st|s(m)|=1,m=1,2,...,LN

[0241] Among them, w k ≥0 indicates the weighted coefficients at different delays, Indicates the expected correlation level.

[0242] (2) Establish a spectrum matching model for the transmitted waveform:

[0243]

[0244] st|s(m)|=1,m=1,2,...,LN

[0245] in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, and α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum.

[0246] (3) Based on the above two expressions, the MIMO radar transmit waveform optimization model based on spectrum shape constraint can be given:

[0247]

[0248] st|s(m)|=1,m=1,2,...,LN

[0249] Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmission waveform.

[0250] 4. Iteratively solve the optimization problem based on the MM method:

[0251] The MIMO radar transmission waveform optimization model based on spectrum shape constraints is a quartic optimization problem under constant modulus constraints. This problem is highly non-convex and difficult to solve by existing algorithms. Therefore, this invention provides an equivalent optimization model as follows:

[0252]

[0253] st|s(m)|=1,m=1,2,...,LN

[0254] in, θ z =[θ z1 ,θ z2 ,...,θ zL ] and Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] is the defined auxiliary variable. For the above problem, a loop iteration algorithm can be used to solve it, as follows:

[0255] (1) Input variable w = [w 1-N ,...,w N-1 ], and the initial value of β.

[0256] (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) .

[0257] (3) Let t = t + 1, and calculate the following formula:

[0258]

[0259]

[0260]

[0261] (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , s needs to be updated below, and the corresponding optimization model is:

[0262]

[0263] st|s(m)|=1,m=1,2,...,LN

[0264] The above formula can be simplified into a linear programming problem with equality constraints by using the Minorization-maximization (MM) algorithm twice, as follows:

[0265]

[0266] st|s(m)|=1,m=1,2,...,LN

[0267] Where Re(·) represents the real part operation. According to the above formula, it is easy to obtain the closed-form solution of s: s=e (jarg (βu+(1-β)v)) , the specific update process is as follows:

[0268] (4.1) Update u (t,b) , as follows:

[0269]

[0270]

[0271]

[0272] in, According to the above formula, we can get

[0273]

[0274] in, diag(·) means to matrix the vector elements with them as diagonal elements. LN Represents a vector whose elements are all 1.

[0275] (4.2) Update v (t,b) , as follows:

[0276]

[0277]

[0278] According to the above formula, we can get:

[0279] v (t,b) =λ max (P)s (t,b) +α (t) q (t,b) -Ps (t,b)

[0280] in,

[0281] (4.3) Let b = b + 1, update s (t,b) :

[0282]

[0283] Determine whether the internal convergence condition is met. The convergence condition is whether the change in the objective function value of two adjacent iteration steps is less than the preset threshold. If it is met, go to step (5), otherwise go to step (4.1). For the solution of s, the Minorization-maximization (MM) algorithm can be used in conjunction with the acceleration algorithm to further improve the convergence rate of the internal loop.

[0284] (5) Let s (t) =s (t,b) , determine whether the external convergence condition is met. The convergence condition is whether the change of the objective function value in two adjacent iteration steps is less than the preset threshold. If it is met, go to step (6), otherwise go to step (3).

[0285] (6) The optimal transmission waveform of the MIMO radar is obtained as s * =s (t) .

[0286] Second embodiment (simulation of the first embodiment)

[0287] Simulation conditions: The number of array elements of the MIMO radar is L = 3, and the encoding length of the waveform transmitted by each array element is N = 256. When the change of the objective function value in adjacent iteration steps is less than 0.1, the iteration is stopped.

[0288] Figure 2 The correlation function of the waveform obtained by simulating the second embodiment according to the optimization of the first embodiment of the present invention is given; Figure 2 As shown in Figure 3, the correlation sidelobe level of the optimized MIMO radar waveform is very low, which provides a good basis for matched filtering between different waveforms.

[0289] Figure 3 The spectrum of the waveform obtained by simulating the second embodiment according to the optimization of the first embodiment of the present invention is given; Figure 3 As shown in the figure, the spectrum of the optimized MIMO radar waveform is highly accurate and approximates the expected spectrum, which provides technical support for MIMO radar to synthesize the required signal by utilizing the available spectrum gaps in space, and lays a favorable condition for MIMO radar to achieve electromagnetic compatibility with other electronic equipment.

[0290] The second aspect of the present invention discloses a MIMO radar orthogonal waveform design system. The system designs the orthogonal waveform of the MIMO radar by constraining the spectrum shape, and the MIMO radar is a multiple-input multiple-output radar. Figure 4 1 is a structural diagram of a MIMO radar orthogonal waveform design system according to an embodiment of the present invention; Figure 4 As shown, the system 400 includes:

[0291] The first processing unit 401 is configured to obtain a transmission waveform of a transmission signal of a MIMO radar transmission platform, and construct a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function;

[0292] The second processing unit 402 is configured to establish a spectrum model of the transmission waveform to construct a spectrum matching model of the transmission waveform, and further determine an optimization model of the transmission waveform based on a spectrum shape constraint based on the spectrum matching model and an optimization model of the transmission waveform based on expected related performance matching;

[0293] The third processing unit 403 is configured to obtain the optimal transmission waveform through cyclic iterative calculation using the optimization model of the transmission waveform based on spectrum shape constraints, wherein the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold.

[0294] According to the system of the second aspect of the present invention, the first processing unit 401 is specifically configured to: l,k and the aperiodic cross-correlation function C p,q,k They are:

[0295]

[0296]

[0297] Among them, A l,k represents the autocorrelation of the lth transmitted waveform at the kth time delay, C p,q,k represents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q, k=0,1,...,N-1,s l (n) represents the value of the lth transmission waveform at the nth moment, let is the k-time delay shift matrix:

[0298]

[0299] in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows:

[0300]

[0301] Among them, Z p,q represents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0, represents the Kronecker product, based on the matrix J p,q,k The definition of , then the compact expressions of the non-periodic autocorrelation function and the non-periodic cross-correlation function of the transmit waveform are respectively:

[0302] A l,k =s H J l,l,k s

[0303] C p,q,k =s H J p,q,k s

[0304] Where s = [s 1 ,s 2 ,...,s L ] H is the vector expression of the transmit waveform.

[0305] According to the system of the second aspect of the present invention, the second processing unit 402 is specifically configured as follows:

[0306] (1) The spectrum model of the transmission waveform is:

[0307] y z =s H F z

[0308] in, I L represents the L-dimensional unit matrix.

[0309] (2) The optimization model of the transmission waveform based on the expected correlation performance matching is:

[0310]

[0311] st|s(m)|=1,m=1,2,...,LN

[0312] Among them, w k ≥0 indicates the weighted coefficients at different delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay;

[0313] (3) The spectrum matching model of the transmission waveform constructed is:

[0314]

[0315] st|s(m)|=1,m=1,2,...,LN

[0316] in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum;

[0317] (4) The optimization model of the transmission waveform based on the spectrum shape constraint is:

[0318]

[0319] st|s(m)|=1,m=1,2,...,LN

[0320] Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmission waveform.

[0321] According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to obtain an equivalent optimization model of the optimization model of the transmit waveform based on spectrum shape constraints:

[0322]

[0323] st|s(m)|=1,m=1,2,...,LN

[0324] in, θ z =[θ z1 ,θ z2 ,...,θ zL ], Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

[0325] According to the system of the second aspect of the present invention, the third processing unit 403 is specifically configured to use the equivalent optimization model to perform the loop iterative calculation process, which specifically includes:

[0326] (1) Input variable w = [w 1-N ,...,w N-1 ]、 and the initial value of β.

[0327] (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) .

[0328] (3) Let t = t + 1, and calculate the following formula:

[0329]

[0330]

[0331]

[0332] (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , the following formula is used to update s:

[0333]

[0334] st|s(m)|=1,m=1,2,...,LN

[0335] Simplify the above equation into a linear programming problem with equality constraints:

[0336]

[0337] st|s(m)|=1,m=1,2,...,LN

[0338] Where Re(·) represents the real part operation, and the closed-form solution of s is: s=e (jarg(βu+(1-β)v)) , the specific update process is as follows:

[0339] (4.1) Update u (t,b) :

[0340]

[0341]

[0342]

[0343] in, Further obtain:

[0344]

[0345] in, diag(·) means to matrix the vector elements with them as diagonal elements. LN Represents a vector whose elements are all 1.

[0346] (4.2) Update v (t,b) :

[0347]

[0348]

[0349] Furthermore, it is obtained that:

[0350] v (t,b) = λ max (P)s (t,b) + α (t) q (t,b) - Ps (t,b)

[0351] wherein,

[0352] (4.3) Let b = b + 1 and update s (t,b) :

[0353]

[0354] Judge whether the internal convergence condition is satisfied. The internal convergence condition is whether the change in the objective function values of two adjacent iteration steps is less than a first preset threshold. If so, go to step (5); otherwise, go to step (4.1);

[0355] (5) Let s (t) = s (t,b) , and judge whether the external convergence condition is satisfied. The external convergence condition is whether the change in the objective function values of two adjacent iteration steps is less than a second preset threshold. If so, go to step (6); otherwise, go to step (3);

[0356] (6) Obtain the optimal transmit waveform as s * = s (t) .

[0357] The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the steps in any one of the methods for designing orthogonal waveforms of a MIMO radar in the first aspect of the present disclosure are implemented.

[0358] The fourth aspect of the present invention discloses a computer-readable storage medium. A computer program is stored on the computer-readable storage medium. When the computer program is executed by a processor, the steps in any one of the methods for designing orthogonal waveforms of a MIMO radar in the first aspect of the present disclosure are implemented.

[0359] In summary, the beneficial effects of the present invention are as follows: (1) The present invention constructs a generalized MIMO radar waveform design criterion, which can well compromise the integral sidelobe frequency and peak sidelobe level of the waveform correlation function by adjusting the expected correlation performance. The existing MIMO radar orthogonal waveform design can be regarded as a special case of the present invention; (2) The present invention considers the MIMO radar orthogonal waveform design under spectrum constraints. While optimizing the correlation performance of the transmission waveform, the spectrum shape of the transmission waveform can be effectively controlled, so that it can achieve electromagnetic compatibility with other radars and communication equipment in a complex electromagnetic environment; (3) The present invention proposes a joint optimization method of twice Minorization-maximization (MM) technology and acceleration strategy, which transforms the original non-convex problem into a series of linear programming problems. Compared with the existing SDR or gradient algorithm, it has lower computational complexity and better optimization effect, laying a favorable foundation for the online design of MIMO radar transmission waveform.

[0360] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. The above-mentioned embodiments only express several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present application, several variations and improvements can be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims

1. A MIMO radar orthogonal waveform design method, It is characterized in that The method designs an orthogonal waveform of the MIMO radar by constraining the spectrum shape, the MIMO radar being a multiple-input multiple-output radar, and the method comprises: Step S1, obtaining a transmission waveform of a transmission signal of a MIMO radar transmission platform, and constructing a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function; Step S2, establishing a spectrum model of the transmission waveform to construct a spectrum matching model of the transmission waveform, and further determining an optimization model of the transmission waveform based on spectrum shape constraints based on the spectrum matching model and an optimization model of the transmission waveform based on expected related performance matching; Step S3, using the optimization model of the transmission waveform based on the spectrum shape constraint, obtaining the optimal transmission waveform through cyclic iterative calculation, wherein the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold value; In step S1, the non-periodic autocorrelation function A of the non-periodic correlation signal model l,k and the aperiodic cross-correlation function C p,q,k They are: Among them, A l,k represents the autocorrelation of the first transmitted waveform at the kth time delay, C p,q,k represents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q,k=0,1,...,N-1,s l (n) represents the value of the first transmission waveform at the nth moment, let is the k-time delay shift matrix: in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows: Among them, Z p,q represents an L×L dimensional matrix whose (p,q)th element is 1 and the rest are 0, represents the Kronecker product, based on the matrix J p,q,k The definition of , then the compact expressions of the non-periodic autocorrelation function and the non-periodic cross-correlation function of the transmit waveform are respectively: A l,k =s H J l,l,k s C p,q,k =s H J p,q,k s Where s = [s 1 ,s 2 ,...,s L ] H is a vector expression of the transmission waveform; In step S2: (1) The spectrum model of the transmission waveform is: y z =s H F z in, I L represents the L-dimensional unit matrix; (2) The optimization model of the transmission waveform based on the expected correlation performance matching is: st|s(m)|=1,m=1,2,...,LN Among them, w k ≥0 indicates the weighted coefficients at different delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay; (3) The spectrum matching model of the transmission waveform constructed is: st|s(m)|=1,m=1,2,...,LN in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum; (4) The optimization model of the transmission waveform based on the spectrum shape constraint is: st|s(m)|=1,m=1,2,...,LN Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmitted waveform; In the step S3, an equivalent optimization model of the optimization model of the transmission waveform based on spectrum shape constraints is obtained: st|s(m)|=1,m=1,2,...,LN in, θ z =[θ z1 ,θ z2 ,...,θ zL ], Φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

2. A MIMO radar orthogonal waveform design method according to claim 1, It is characterized in that In step S3, the equivalent optimization model is used to perform the loop iterative calculation process, which specifically includes: (1) Input variable w = [w 1-N ,...,w N-1 ]、 and the initial values ​​of β; (2) Let t represent the number of current external iterations, and initialize t = 0 and s (t) ; (3) Let t = t + 1, and calculate the following formula: (4) Let b represent the number of internal iterations, and initialize b = 0 and s (t,b) =s (t-1) , the following formula is used to update s: st|s(m)|=1,m=1,2,...,LN Simplify the above equation into a linear programming problem with equality constraints: st|s(m)|=1,m=1,2,...,LN Where Re(·) represents the real part operation, and the closed-form solution of s is: s=e (jarg(βu+(1-β)v)) , the specific update process is as follows: (4.1) Update u (t,b) : Among them, Further obtain: in, diag(·) means to matrix the vector elements with them as diagonal elements. LN Represents a vector whose elements are all 1; (4.2) Update v (t,b) : Further obtain: v (t,b) =λ max (P)s (t,b) +α (t) what (t,b) -Ps (t,b) in, (4.3) Let b = b + 1, update s (t,b) : Determine whether the internal convergence condition is met, wherein the internal convergence condition is whether the change of the objective function value between two adjacent iteration steps is less than a first preset threshold. If so, proceed to step (5); otherwise, proceed to step (4.1); (5) Let s (t) =s (t,b) , determine whether the external convergence condition is met, the external convergence condition being whether the change of the objective function value of two adjacent iteration steps is less than a second preset threshold, if so, proceed to step (6), otherwise, proceed to step (3); (6) The optimal transmission waveform is obtained as s * =s (t) .

3. A MIMO radar orthogonal waveform design system, It is characterized in that The system designs an orthogonal waveform of the MIMO radar by constraining the spectrum shape, the MIMO radar is a multiple-input multiple-output radar, and the system includes: A first processing unit is configured to obtain a transmission waveform of a transmission signal of a MIMO radar transmission platform, and construct a non-periodic correlation signal model of the transmission signal based on the transmission waveform, wherein the non-periodic correlation signal model is characterized by a non-periodic autocorrelation function and a non-periodic cross-correlation function; Among them, the non-periodic autocorrelation function A of the non-periodic correlation signal model l,k and the aperiodic cross-correlation function C p,q,k They are: Among them, A l,k represents the autocorrelation of the first transmitted waveform at the kth time delay, C p,q,k represents the cross-correlation between the p-th transmission waveform and the q-th transmission waveform at the k-th time delay, L represents the number of the transmission waveforms, N represents the coding length of the transmission waveform, l,p,q=1,2,...,L,p≠q,k=0,1,...,N-1,s l (n) represents the value of the first transmission waveform at the nth moment, let is the k-time delay shift matrix: in, represents the (l,m)th element of the k-time delay shift matrix, δ is the impulse function, and the matrix J is defined p,q,k as follows: Among them, Z p,q represents an \(L\times L\) dimensional matrix with the \((p,q)\)-th element being 1 and the remaining elements being 0, represents the Kronecker product. Based on the definition of the matrix J p,q,k the compact expressions of the aperiodic autocorrelation function and the aperiodic cross-correlation function of the transmitted waveform are respectively: A l,k =s H J l,l,k s C p,q,k =s H J p,q,k s Where s = [s 1 ,s 2 ,...,s L ] H is a vector expression of the transmission waveform; A second processing unit is configured to establish a spectrum model of the transmit waveform to construct a spectrum matching model of the transmit waveform, and further determine an optimization model of the transmit waveform based on a spectrum shape constraint based on the spectrum matching model and an optimization model of the transmit waveform based on expected related performance matching; The spectrum model of the emission waveform is: y z =s H F z in, I L represents the L-dimensional unit matrix; The optimization model of the transmission waveform based on the expected correlation performance matching is: st|s(m)|=1,m=1,2,...,LN where, w k ≥ 0 represents a weighting coefficient at different time delays, represents the expected correlation level between the p-th transmitted waveform and the q-th transmitted waveform at the k-th time delay; The spectrum matching model of the transmission waveform constructed is: st|s(m)|=1,m=1,2,...,LN in, represents the weighting coefficient at the zth frequency point, d z =[d z1 ,d z2 ,...,d zL ] is the expected power spectral density vector, represents the Hadamard product, α>0 is a scaling factor used to compromise the mismatch between the expected spectrum and the actual spectrum; The optimization model of the transmission waveform based on spectrum shape constraints is: st|s(m)|=1,m=1,2,...,LN Among them, 0≤β≤1 is a weighting coefficient, which is used to compromise the correlation performance and spectrum matching performance of the transmitted waveform; The third processing unit is configured to obtain the optimal transmission waveform by iterative calculation using the optimization model of the transmission waveform based on the spectrum shape constraint, wherein the cutoff condition of the iterative calculation is that the change of the objective function of adjacent iterations is less than a threshold value; Obtain an equivalent optimization model of the optimization model of the transmit waveform based on spectrum shape constraints: st|s(m)|=1,m=1,2,...,LN in, θ z =[θ z1 ,θ z2 ,...,θ zL ],φ=[φ 1,1,-N+1 ,...,φ 1,1,N-1 ,...,φ L,L,N-1 ] are predefined auxiliary variables.

4. An electronic device, It is characterized in that The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps in the MIMO radar orthogonal waveform design method described in any one of claims 1 to 2 are implemented.

5. A computer-readable storage medium, It is characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in the MIMO radar orthogonal waveform design method described in any one of claims 1 to 2 are implemented.

Images