CN113075623A - Orthogonal waveform design method of MIMO radar based on quantum particle swarm optimization - Google Patents

Orthogonal waveform design method of MIMO radar based on quantum particle swarm optimization Download PDF

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CN113075623A
CN113075623A CN202110353058.4A CN202110353058A CN113075623A CN 113075623 A CN113075623 A CN 113075623A CN 202110353058 A CN202110353058 A CN 202110353058A CN 113075623 A CN113075623 A CN 113075623A
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姜宏
颜廷玉
刘运昌
朱昭华
杨锐
刘一鹏
董宁
张琪
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Jilin University
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Abstract

The invention relates to a MIMO radar orthogonal waveform design method based on a quantum particle swarm algorithm, and belongs to the field of radar signal processing. Optimizing the phase encoding sequence by adopting a quantum particle swarm algorithm to finally obtain a waveform set with good orthogonality, encoding the phase of a sub-pulse of the waveform set into 0 and 1 by taking an autocorrelation side lobe peak value and a cross-correlation peak value of the sequence as fitness functions, updating the position of the particle by adopting a quantum revolving gate, and passing through HεThe gate corrects the algorithm, so that the algorithm has better global convergence and searching capability, and quantum not gate updating operation is carried out on the positions of the particles according to a certain variation probability, so that the performance of the algorithm is further improved; simulation experiments show that the effectiveness of the algorithm is improved, and compared with a particle swarm algorithm and a chaotic particle swarm algorithm, the experimental result is better.

Description

Orthogonal waveform design method of MIMO radar based on quantum particle swarm optimization
Technical Field
The invention relates to the field of radar signal processing, in particular to a method for designing orthogonal waveforms of an MIMO radar based on a quantum particle swarm algorithm.
Background
The MIMO radar has been widely paid attention by scholars in related fields since the proposal, and mechanisms such as lincoln laboratories, bell laboratories, washington university and the like in the united states contribute to the advancement of the MIMO radar technology. As a new system radar, the MIMO radar inherits and develops the phased array radar, also has the cross application of the MIMO communication technology in the radar field, and plays an irreplaceable role in the military field; the radar has incomparable advantages in low interception performance, anti-interference capability and weak target detection capability compared with the traditional radar, and the excellent performances are all based on effective waveform generation. Therefore, the orthogonal waveform is designed as one of the hot contents of the MIMO radar research.
The MIMO radar has a plurality of transmitting array elements, and the waveforms transmitted by each array element are orthogonal to each other, so that the receiving end matched filter is facilitated to extract the echoes of the corresponding array elements from the echo signal set, the independent information detected by each signal is accurately acquired, and the low interception performance, the system resolution, the measurement precision of the system, the anti-interference capability and the like of the radar are ensured. The frequency modulation and phase modulation signals are two most commonly used transmitting signals of the radar, compared with a linear frequency modulation signal, a phase coding signal has better orthogonality, and the aim of mutual orthogonality among waveforms can be achieved by constructing different coding sequences.
Many relevant documents at home and abroad take waveforms with orthogonal performance as design targets. For example, Deng Hai proposes to design orthogonal frequency coding and orthogonal polyphase codes based on a simulated annealing algorithm and a domain search method, and further, provides definition of a signal non-periodic correlation function and a cost function for designing a waveform; liu et al used a genetic algorithm for orthogonal waveform design, comparing it with the method of Deng Hai from the point of view of frequency and phase encoding, whose method is shorter in waveform generation period; at present, the method of orthogonal waveform design is mostly based on a group intelligent optimization algorithm and an improved algorithm thereof, an optimal solution is obtained by constructing an objective function, including a genetic algorithm, a simulated annealing algorithm, an ant colony algorithm, a particle swarm algorithm and the like, a mixed optimization algorithm of the algorithms is increasingly applied, but an intelligent optimization algorithm combined with a quantum theory is hardly adopted, the application of the quantum theory in intelligent calculation is a new mode, and the combination of the quantum calculation and the intelligent optimization algorithm is also a new research direction.
The traditional particle swarm optimization algorithm has the defects of too low convergence speed and easy falling into local extreme points, and a better or ideal optimal solution cannot be obtained even if a large amount of time is consumed. As a classical quantum group intelligent algorithm, the quantum particle swarm algorithm effectively utilizes the characteristics of a quantum theory principle and traditional intelligent calculation, and obtains ideal results in the prior research and application. In quantum space, for a particle in a quantum bound state, it can appear at any point in space in the form of a certain probability density, and the property of its aggregation state is satisfied by the probability density, and when the particle is searched, the condition that any place in space where a solution is likely to exist is searched by a hundred percent can be satisfied, and when the particle is moved to infinity, the probability density is moved to 0. Therefore, the global search capability of the quantum particle swarm is greatly improved, the method is superior to a classical particle swarm algorithm, the updating process of the algorithm is improved during application, and the performance of the algorithm can be further improved.
Disclosure of Invention
The invention provides a quantum-behaved particle swarm optimization-based MIMO radar orthogonal waveform design method, which aims to solve the problems that the convergence speed of the traditional particle swarm optimization algorithm is too low and the traditional particle swarm optimization algorithm is easy to fall into local extreme points.
The technical scheme adopted by the invention is that the method comprises the following steps:
step 1, generating phase coding signals, wherein the number of transmitted waveforms is L, and the length of a coding sequence is N;
initializing parameters of a quantum particle swarm algorithm, including population number, maximum iteration times, particle dimension and the like, and initializing a population;
step 3, calculating the fitness of the particles in the population to obtain an initial individual extreme value, wherein the minimum value is an initial global extreme value, and the corresponding particle position is a global optimal position;
step 4, determining the rotation angle of the quantum revolving door, updating the positions of the particles by adopting the quantum revolving door, calculating the fitness of the updated particles, replacing the optimal positions of the particles with the current positions if the fitness is smaller than that of the particles before updating, and otherwise, keeping the original positions; if the global extreme value after updating is smaller than the global extreme value before updating, replacing by adopting the current global optimal position, otherwise, keeping the original position;
step 5, updating the positions of the particles by a quantum not gate according to the self-adaptive variation probability, and calculating the fitness of the updated particles, wherein the updating of the self optimal positions and the global optimal positions of the particles is the same as that in the step 4;
step 6, entering next iteration, circularly updating operation until the maximum iteration times is reached, terminating iteration and outputting an optimal solution;
and 7, generating an orthogonal phase coding signal by using the optimized phase coding sequence to complete orthogonal waveform design of the MIMO radar.
In step 1 of the present invention, the phase encoded signal is a pulse pressure signal with good orthogonality, which is obtained by dividing the time width of the signal into a plurality of sub-pulses, modulating the phases of the sub-pulses, transmitting a number of waveforms of L and a number of sub-pulses of N, i.e. when the length of the code sequence is N, collecting a set s of phase encoded signalslThe expression of (n) is:
Figure BDA0003002146600000021
wherein phi isl(n) is the phase of the nth sub-pulse of the ith transmit waveform, and is also the variable to be optimized, e is the base of the exponential function, j is the imaginary unit, when M-phase encoding is used,
Figure BDA0003002146600000031
using two-phase coding, i.e. M is 2, when philThe value of (n) is 0 or pi, the autocorrelation function of the orthogonal phase coded signal in an ideal situation is similar to an impulse function, and the cross-correlation function is zero, but in practice, the signal does not exist, and only the autocorrelation side lobe peak value and the cross-correlation peak value of the signal can be made as small as possible.
In the step 2 of the invention, the particle dimension of the quantum particle swarm algorithm is L multiplied by N, phi is optimizedlThe value of (n) can be encoded as 0 and 1, the variable of each dimension of the particle is expressed by a quantum bit, and the particle collapses to a definite state with a certain probability, the population is initialized, namely at [0,2 pi ]]The middle random value is taken as the phase theta of the quantum bitiWherein cos θiAnd sin θiI.e. the probability amplitude of the qubit, can be used [ alpha ]i,βi]TTo represent; to generate [0,1]Inner random number rand, when rand>|cosθi|2The qubit collapses to 1, otherwise to 0.
In step 3 of the present invention, the fitness of the particles is calculated, the fitness function of the particles follows the criterion that the autocorrelation sidelobe peak value and the cross-correlation peak value are minimum, and the autocorrelation function a (phi) of the phase encoded signallK) and the cross-correlation function C (phi)p,φqThe expressions for k) are respectively:
Figure BDA0003002146600000032
Figure BDA0003002146600000033
the fitness function E of a particle is expressed as:
Figure BDA0003002146600000034
wherein, ω is1,ω2Is a weighting coefficient of phip(n) is the phase of the nth sub-pulse of the pth transmit waveform, φq(n) is the phase of the nth sub-pulse of the qth transmit waveform, and k represents the time delay in order to distinguish the code phase at different times.
In step 4 of the present invention, the rotation angle Δ θ of the quantum rotary gateiDetermined by the following update formula:
Figure BDA0003002146600000041
wherein t is the iteration number of the algorithm, and rand is [0,1]]Inner random number, θiD represents the dimension of the particle, and for the sake of easy discrimination, the phases of the self-optimum position and the global optimum position of the particle are respectively represented by thetaid,θgdAnd w is the inertial weight of the algorithm, a linear decreasing updating mode is adopted, and the formula is as follows:
Figure BDA0003002146600000042
c1 and c2 are learning factors of the algorithm and are adjusted along with the change of the inertia weight, wherein c1 is 2.4-1.4 × cos (w · pi), and c2 is 0.9+1.6 × cos (w · pi);
in particular when
Figure BDA0003002146600000043
When the difference is less than 2 pi, the difference is determined
Figure BDA0003002146600000044
Then, the difference should be added by 2 pi; in the same way, the method for preparing the composite material,
Figure BDA0003002146600000045
the same is true for the same;
after the rotation angle of the quantum revolving door is determined, the positions of the particles are updated by adopting the quantum revolving door, and the probability amplitude after updating is as follows:
Figure BDA0003002146600000046
h is selected to avoid the phenomenon that the algorithm falls into the local optimal solution to generate premature convergenceεThe gate corrects the quantum revolving gate, and takes epsilon (0, 1)]If |. alpha'i|2Is less than or equal to epsilon and beta'i|2Greater than or equal to 1-epsilon, the corrected probability amplitude
Figure BDA0003002146600000047
If α'i|2Is not less than 1-epsilon and beta'i|2If the probability is less than or equal to epsilon, the corrected probability amplitude
Figure BDA0003002146600000048
Otherwise the probability amplitude remains unchanged. To generate [0,1]Inner random number rand, when rand>|α″i|2The qubit collapses to 1, otherwise to 0.
In step 5 of the present invention, whether the particle is to be subjected to the quantum not gate update is determined according to a preset adaptive mutation probability, where the adaptive mutation probability P is:
Figure BDA0003002146600000049
therein, fitiAs the current fitness of the particle, fitgIs a global extremum; when P is less than or equal to PminWhen P is equal to PminOtherwise, P is not changed;
after the adaptive variation probability is determined, a random number rand in [0,1] is taken, and only when rand < P, the particle carries out quantum not gate updating operation, and the quantum not gate operation actually changes the tendency of the original collapse to a certain state, so that the particle collapses to another state with the tendency of the degree. The probability after mutation is:
Figure BDA0003002146600000051
to generate [0,1]Inner random number rand, when rand>|α″′i|2The qubit collapses to 1, otherwise to 0.
In step 7 of the present invention, an optimized phase-encoding sequence is obtained
Figure BDA0003002146600000052
The optimized phase is
Figure BDA0003002146600000053
By using
Figure BDA0003002146600000054
And modulating the phase of the signal to complete the orthogonal waveform design of the MIMO radar.
The invention enables the particles to be searched in the whole feasible solution space, increases the randomness of the particles, overcomes the defects of over-slow convergence speed and easy falling into local extreme points of the traditional particle swarm optimization algorithm, obtains the optimal solution and completes the design of the orthogonal waveform.
The invention has the beneficial effects that: the invention applies the quantum particle swarm algorithm to the orthogonal waveform design of the MIMO radar, so that the particles can be searched in the whole feasible solution space, the randomness of the particles is increased, and the overall convergence and the searching capability are better than those of the traditional particle swarm algorithm; updating the position of the particle by adopting a quantum revolving gate and a quantum NOT gate, and passing through HεThe gate further modifies the algorithm to improve the convergence of the whole algorithm.
Drawings
FIG. 1 is a flow chart of the present invention for implementing orthogonal waveform design of MIMO radar by using quantum particle group algorithm;
FIG. 2(a) is an image of the autocorrelation function of each signal at waveform 1, the number of transmitted waveforms being 4, and the length of the code sequence being 128, with the ordinate being the normalized amplitude level value;
fig. 2(b) is an image of the autocorrelation function of each signal when the waveform 2, the number of transmitted waveforms is 4, and the length of the code sequence is 128, and the ordinate is a normalized amplitude level value;
FIG. 2(c) is an image of the autocorrelation function of each signal for waveform 3, the number of transmit waveforms being 4, and the length of the code sequence being 128, with the ordinate being the normalized amplitude level value;
FIG. 2(d) is an image of the autocorrelation function of each signal with waveform 4, the number of transmit waveforms being 4, and the length of the code sequence being 128, the ordinate being the normalized amplitude level value;
FIG. 3(a) is a cross-correlation function image of waveforms 1 and 2, with the number of transmit waveforms being 4, and the length of the code sequence being 128, and with the ordinate being the normalized amplitude level value;
FIG. 3(b) is a cross-correlation function image of each waveform with waveform 1 and waveform 3, transmit waveform number 4, code sequence length 128, and ordinate is a normalized amplitude level value;
FIG. 3(c) is a cross-correlation function image of waveforms 1 and 4, with a transmit waveform number of 4, and a code sequence length of 128, with the ordinate being the normalized amplitude level value;
FIG. 3(d) is a cross-correlation function image of waveforms 2 and 3, with the number of transmit waveforms being 4, and the length of the code sequence being 128, the ordinate being the normalized amplitude level value;
FIG. 3(e) is a cross-correlation function image of waveforms 2 and 4, with a transmitted waveform number of 4, and a code sequence length of 128, and with the ordinate being the normalized amplitude level value;
FIG. 3(f) is a cross-correlation function image of waveforms 3 and 4, with a transmit waveform number of 4, and a code sequence length of 128, and with the ordinate being the normalized amplitude level value;
FIG. 4 is a graph of performance comparison of discrete binary particle swarm algorithm, chaotic binary particle swarm algorithm and quantum particle swarm algorithm in the invention, comparing the average autocorrelation function sidelobe peak values of waveforms under different coding sequence lengths;
fig. 5 is a performance comparison graph of the discrete binary particle swarm algorithm, the chaotic binary particle swarm algorithm and the quantum particle swarm algorithm in the invention, but compares the average cross-correlation function peak values of waveforms under different coding sequence lengths.
Detailed Description
The technical scheme of the invention is explained in detail below with reference to specific embodiments, and as shown in fig. 1, the invention provides a MIMO radar orthogonal waveform design method based on quantum particle swarm optimization, which comprises the following specific steps:
step 1, generating phase coding signals, wherein the number of transmitted waveforms is L, and the length of a coding sequence is N; specifically, the phase coded signal is a pulse pressure signal with good orthogonality, has a large time-width bandwidth product, has good ranging precision and ranging distance, is widely applied to radar, and is characterized in that the time width of the signal is uniformly divided into a plurality of sub-pulses, the phases of the sub-pulses are modulated, the purpose of mutual orthogonality of waveforms can be achieved by constructing different coding sequences, the number of transmitted waveforms is L, the number of the sub-pulses is N, namely when the length of the coding sequence is N, a phase coded signal set s is formedlThe expression of (n) is:
Figure BDA0003002146600000061
wherein phi isl(n) is the phase of the nth sub-pulse of the ith transmit waveform and is also the variable we want to optimize, e is the base of the exponential function, which is equal to about 2.728 …, j is the imaginary unit. When the M-phase encoding is adopted,
Figure BDA0003002146600000062
the invention uses bi-phase coding, i.e. M is 2, when phil(n) takes the value 0 or pi, which can also be represented by a matrix:
Figure BDA0003002146600000063
in order to effectively detect weak targets and avoid mutual interference among different waveforms, the autocorrelation function of the orthogonal phase coding signal under ideal conditions should be similar to an impulse function, the signal cross-correlation function of different transmitting array elements is zero, but in practice, such a signal does not exist, and only the autocorrelation side lobe peak value and the cross-correlation peak value of the signal can be made as small as possible,
initializing parameters of a quantum particle swarm algorithm, including population number, maximum iteration times, particle dimension and the like, and initializing a population; specifically, the population number is set to 50, the maximum number of iterations is 100, the particle dimension is L N, and φ is optimizedlThe value of (n) can be encoded as 0 and 1, the variables of each dimension of the particle are represented by a qubit and collapse to a definite state with a certain probability, the qubit can be represented as a vector of a two-dimensional complex space, which differs from the classical information bit by the largest: a qubit can be at |0>And |1>On both basic states, can also be in |0>And |1, i.e. at an intermediate state of a linear combination of |0>And |1>In the superimposed state. Is formulated as:
Figure BDA0003002146600000071
where α, β is a pair of complex numbers, called qubits
Figure BDA0003002146600000072
Satisfies | alpha ∞ within the spectrum of probability2+|β|21, a qubit can collapse into a deterministic state determined by the magnitude of the probability that the last state of a quantum is a probabilistic problem, measured by quantum, as | α |2Is collapsed to state |0>Is not more than | beta2Is collapsed to state |1>When the qubit is in real space, there is another representation:
Figure BDA0003002146600000073
wherein, the phase θ of the qubit is arctan (sin θ/cos θ), θ belongs to [0,2 π ], and the vector form of the qubit is:
Figure BDA0003002146600000074
the population is initialized to be [0,2 pi ]]The middle random value is taken as the phase theta of the quantum bitiWherein cos θiAnd sin θiThe probability amplitude of the quantum bit is obtained; to generate [0,1]Inner random number rand, when rand>|cosθi|2The qubit collapses to 1, otherwise to 0,
step 3, calculating the fitness of the particles in the population to obtain an initial individual extreme value, wherein the minimum value is an initial global extreme value, and the corresponding particle position is a global optimal position; in particular, the fitness function of the particles follows the criterion that the autocorrelation sidelobe peak and the cross-correlation peak are minimal, the autocorrelation function A (φ) of the phase encoded signallK) and the cross-correlation function C (phi)p,φqThe expressions for k) are respectively:
Figure BDA0003002146600000081
Figure BDA0003002146600000082
the fitness function of the particle is expressed as:
Figure BDA0003002146600000083
wherein, ω is1,ω2The values of the weighting coefficients are all 0.5 phip(n) is the phase of the nth sub-pulse of the pth transmit waveform, φq(n) is the phase of the nth sub-pulse of the qth transmit waveform, k represents the time delay, and further, the phase of each particle in the initial population is calculated separately in order to distinguish the code phases at different timesThe fitness is taken as an initial individual extreme value, the minimum value is taken as an initial global extreme value, the position of the particle is the initial global optimal position, and the subsequent iteration is updated on the basis of the initial global optimal position;
step 4, determining the rotation angle of the quantum revolving door, updating the positions of the particles by adopting the quantum revolving door, calculating the fitness of the updated particles, replacing the optimal positions of the particles with the current positions if the fitness is smaller than that of the particles before updating, and otherwise, keeping the original positions; if the global extreme value after updating is smaller than the global extreme value before updating, replacing by adopting the current global optimal position, otherwise, keeping the original position; specifically, the computation of classical information bits is performed by nand gates and the like, and similarly, the computation of qubits is performed by various quantum gates, the transformations of which are unitary transformations, the main role of the quantum gates is to cause the probability amplitudes of the qubits to converge to 0 or 1 so as to extract the final result, and the quantum revolving gate is one of the following equations:
Figure BDA0003002146600000084
wherein, the delta theta is a quantum rotation angle, and different quantum rotation doors can be obtained by setting different rotation angles. In the algorithm of the present invention, the magnitude of the rotation angle is determined by the following update formula:
Figure BDA0003002146600000085
wherein t is the iteration number of the algorithm, and rand is [0,1]]Inner random number, θiD represents the dimension of the particle, and for the sake of easy discrimination, the phases of the self-optimum position and the global optimum position of the particle are respectively represented by thetaid,θgdAnd w is the inertial weight of the algorithm, a linear decreasing updating mode is adopted, and the formula is as follows:
Figure BDA0003002146600000091
wherein, wmaxIs the maximum value of the inertial weight, and is set to 0.9, wminIs the minimum value of the inertia weight and is set to 0.4, tmaxIs the maximum iteration number; c1 and c2 are learning factors of the algorithm and are adjusted along with the change of the inertia weight, wherein c1 is 2.4-1.4 × cos (w · pi), and c2 is 0.9+1.6 × cos (w · pi);
in particular when
Figure BDA0003002146600000092
When the difference is less than 2 pi, the difference is determined
Figure BDA0003002146600000093
Then, the difference should be added by 2 pi; in the same way, when
Figure BDA0003002146600000094
When the difference is less than 2 pi, the difference is determined
Figure BDA0003002146600000095
Then, the difference should be added by 2 pi;
after the rotation angle of the quantum revolving door is determined, the positions of the particles are updated by adopting the quantum revolving door, and the probability amplitude after updating is as follows:
Figure BDA0003002146600000096
h is selected to avoid the phenomenon that the algorithm falls into the local optimal solution to generate premature convergenceεThe gate corrects the quantum revolving gate, and takes epsilon (0, 1)]If |. alpha'i|2Is less than or equal to epsilon and beta'i|2Greater than or equal to 1-epsilon, the corrected probability amplitude
Figure BDA0003002146600000097
If α'i|2Is not less than 1-epsilon and beta'i|2If the probability is less than or equal to epsilon, the corrected probability amplitude
Figure BDA0003002146600000098
Otherwise the probability amplitude remains unchanged. To generate [0,1]Inner random number rand, when rand>|α″i|2When the qubit collapses to 1, otherwise the qubit collapses to 0;
it can be seen that HεThe gate changes the situation that the quantum bit upper value can not be changed during the measurement, so that the probability amplitude value is converged
Figure BDA0003002146600000099
Or
Figure BDA00030021466000000910
The method is beneficial to the algorithm to jump out of local optimum, avoids the premature convergence phenomenon and realizes the global convergence of the algorithm. Meanwhile, the value of the algorithm is greatly influenced by the value of different values of epsilon, and when epsilon is 0, HεThe gate becomes a traditional quantum revolving gate, when epsilon is too large, the convergence trend of an individual disappears again, and the epsilon is taken as 0.01;
step 5, performing quantum not gate updating operation on the positions of the particles according to the preset self-adaptive variation probability, and calculating the fitness of the updated particles, wherein the updating of the self optimal positions and the global optimal positions of the particles is the same as that in the step 4; in particular, a quantum not gate is another very common quantum gate, and the formula is:
Figure BDA00030021466000000911
judging whether the particles need to carry out quantum not gate updating according to a preset self-adaptive mutation probability, wherein the self-adaptive mutation probability P is as follows:
Figure BDA0003002146600000101
wherein, PmaxThe value is 0.5, which is the maximum value of the variation probability, PminThe value is 0.05, which is the minimum value of the variation probability; fitiAs the current fitness of the particle, fitgIs a global extremum; when P is less than or equal to PminWhen P is equal to PminOtherwise, P is not changed;
after the self-adaptive variation probability is determined, a random number rand in [0,1] is taken, only when rand < P, the particle carries out quantum not gate updating operation, the quantum not gate operation actually changes the tendency of the original collapse to a certain state, so that the particle collapses to another state according to the tendency of the degree, and the probability amplitude after variation is as follows:
Figure BDA0003002146600000102
to generate [0,1]Inner random number rand, when rand>|α″″i|2When the qubit collapses to 1, otherwise the qubit collapses to 0;
updating the self optimal position and the global optimal position of the particle, calculating the fitness of the updated particle, if the fitness value is smaller than the fitness value of the particle before updating, replacing the self optimal position of the particle with the current position, and otherwise, keeping the original position; if the global extreme value after updating is smaller than the global extreme value before updating, replacing by adopting the current global optimal position, otherwise, keeping the original position;
step 6, entering next iteration, circularly updating operation until the maximum iteration times is reached, terminating iteration and outputting an optimal solution; specifically, after the next iteration is carried out, the step 4 and the step 5 are executed, the positions of the particles are updated by adopting a quantum revolving gate and a quantum NOT gate, the self optimal positions and the global optimal positions of the updated particles are obtained, and the global extreme value of each generation is recorded; after the maximum iteration times are reached, namely after 100 iterations are performed, outputting the global optimal position of the last iteration, namely the optimal solution;
step 7, generating an orthogonal signal by using the optimized phase coding sequence to complete orthogonal waveform design of the MIMO radar; specifically, the optimized phase encoding sequence is
Figure BDA0003002146600000103
The optimized phase is
Figure BDA0003002146600000104
By using
Figure BDA0003002146600000105
And modulating the phase of the signal to complete the orthogonal waveform design of the MIMO radar.
The beneficial effects of the invention are further explained by combining simulation experiments and results, and all simulation tools of the simulation experiments are Matlab.
Experiment one: the method of the invention is adopted to optimize the phase coding sequence, and the orthogonal waveform design of the MIMO radar is completed.
Setting simulation parameters: the population number is set to be 50, the maximum iteration number is 100, the number of the transmitted waveforms is 4, the length of the coding sequence is 128, and the particle dimension is 512; the maximum value of the inertia weight w is 0.9, the minimum value is 0.4, the maximum value of the variation probability P is 0.5, the minimum value is 0.05, and the value of epsilon is 0.01. The sub-pulse width of the phase coding signal is 1 mus, the carrier frequency is 1MHz, and the sampling frequency is 20 MHz. Table 1 shows the obtained phase encoding sequence, fig. 2 and fig. 3 show the autocorrelation function and cross-correlation function images of each waveform, the ordinate is the normalized amplitude level value, and the autocorrelation side lobe peak value (ASP) and cross-correlation peak value (CP) of each waveform are shown in table 2; it can be seen that the average ASP of the optimized phase-coded signal set is-15.57 dB, the average CP is-14.67 dB, and the phase-coded signal set has good orthogonality.
TABLE 1 code length 128 phase code sequence
Figure BDA0003002146600000111
TABLE 2 ASP and CP of the sequences
Sequence 1 Sequence 2 Sequence 3 Sequence 4
Sequence 1 -15.30dB -12.60dB -15.70dB -15.70dB
Sequence 2 -12.60dB -16.57dB -14.54dB -14.91dB
Sequence 3 -15.70dB -14.54dB -13.84dB -14.54dB
Sequence 4 -15.70dB -14.91dB -14.54dB -16.57dB
Experiment two: comparing the algorithm with a particle swarm algorithm and a chaotic particle swarm algorithm, and performing performance analysis according to a simulation result; in order to reduce the contingency of the experiment and ensure the objectivity and reality, each group of data is obtained by averaging through multiple simulation experiments.
Setting simulation parameters: the particle swarm optimization and the chaotic particle swarm optimization have the same parameter setting, the number of the swarm is set to be 50, the maximum iteration number is 100, the number of the emission waveforms is 4, the inertia weight w is 0.9 at the maximum and 0.4 at the minimum, c1 and c2 are set to be 2, and the particle speed is set to be in [ -10,10 ]. The sub-pulse width of the phase coding signal is 1 mus, the carrier frequency is 1MHz, and the sampling frequency is 20 MHz. Carrying out multiple simulation experiments, and comparing the orthogonal performance of the waveform sets of the three algorithms under different coding sequence lengths; fig. 4 is a graph of an average Autocorrelation Sidelobe Peak (ASP) of a phase encoding signal set of three algorithms varying with a sequence length, and fig. 5 is a graph of an average cross Correlation Peak (CP) of a phase encoding signal set of three algorithms varying with a sequence length, it can be seen that, as the sequence length increases, the average ASP and the average CP of the phase encoding signal set decrease, and the orthogonality becomes better, and the algorithm performance of the present invention is superior to the particle swarm algorithm and the chaotic particle swarm algorithm, and the orthogonality of the obtained phase encoding signal set is the best; because quantum-behaved particle swarm optimization has better global convergence and search capability compared with the traditional algorithm.
The invention applies the quantum particle swarm algorithm to the orthogonal waveform design of the MIMO radar, updates and corrects the algorithm by adopting the quantum gate, improves the global convergence of the algorithm, proves the effectiveness of the method through simulation experiments, and proves that the experimental result is better compared with the traditional method.

Claims (7)

1. A MIMO radar orthogonal waveform design method based on quantum particle swarm optimization is characterized by comprising the following steps:
step 1, generating phase coding signals, wherein the number of transmitted waveforms is L, and the length of a coding sequence is N;
step 2, initializing parameters of a quantum particle swarm algorithm, including the population number, the maximum iteration number and the particle dimension, and initializing the population;
step 3, calculating the fitness of the particles in the population to obtain an initial individual extreme value, wherein the minimum value is an initial global extreme value, and the corresponding particle position is a global optimal position;
step 4, determining the rotation angle of the quantum revolving door, updating the positions of the particles by adopting the quantum revolving door, calculating the fitness of the updated particles, replacing the optimal positions of the particles with the current positions if the fitness is smaller than that of the particles before updating, and otherwise, keeping the original positions; if the global extreme value after updating is smaller than the global extreme value before updating, replacing by adopting the current global optimal position, otherwise, keeping the original position;
step 5, updating the positions of the particles by a quantum not gate according to the self-adaptive variation probability, and calculating the fitness of the updated particles, wherein the updating of the self optimal positions and the global optimal positions of the particles is the same as that in the step 4;
step 6, entering next iteration, circularly updating operation until the maximum iteration times is reached, terminating iteration and outputting an optimal solution;
and 7, generating an orthogonal phase coding signal by using the optimized phase coding sequence to complete orthogonal waveform design of the MIMO radar.
2. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 1, the phase-coded signal is a pulse pressure signal with good orthogonality, which is obtained by dividing the time width of the signal into a plurality of sub-pulses, modulating the phases of the sub-pulses, transmitting a set of phase-coded signals s with the number of waveforms L and the number of sub-pulses N, i.e. when the length of the code sequence is NlThe expression of (n) is:
Figure FDA0003002146590000011
wherein phi isl(n) is the phase of the nth sub-pulse of the ith transmit waveform, and is also the variable to be optimized, e is the base of the exponential function, j is the imaginary unit, when M-phase encoding is used,
Figure FDA0003002146590000012
using two-phase coding, i.e. M is 2, when philThe value of (n) is 0 or pi, the autocorrelation function of the orthogonal phase coded signal in an ideal situation is similar to an impulse function, and the cross-correlation function is zero, but in practice, the signal does not exist, and only the autocorrelation side lobe peak value and the cross-correlation peak value of the signal can be made as small as possible.
3. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 2, the particle dimension of the quantum particle swarm algorithm is L multiplied by N, phi is obtained during optimizationlThe value of (n) can be encoded as 0 and 1, the variable of each dimension of the particle is expressed by a quantum bit, and the particle collapses to a definite state with a certain probability, the population is initialized, namely at [0,2 pi ]]The middle random value is taken as the phase theta of the quantum bitiWherein cos θiAnd sin θiI.e. the probability amplitude of the qubit, can be used [ alpha ]i,βi]TTo represent; to generate [0,1]Inner random number rand, when rand>|cosθi|2The qubit collapses to 1, otherwise to 0.
4. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 3, the fitness of the particles is calculated, the fitness function of the particles follows the criterion that the autocorrelation sidelobe peak value and the cross-correlation peak value are minimum, and the autocorrelation function A (phi) of the phase coding signallK) and the cross-correlation function C (phi)p,φqThe expressions for k) are respectively:
Figure FDA0003002146590000021
Figure FDA0003002146590000022
the fitness function E of a particle is expressed as:
Figure FDA0003002146590000023
wherein, ω is1,ω2Is a weighting coefficient of phip(n) is the phase of the nth sub-pulse of the pth transmit waveform, φq(n) is the phase of the nth sub-pulse of the qth transmit waveform, and k represents the time delay in order to distinguish the code phase at different times.
5. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 4, the rotation angle size Delta theta of the quantum revolving dooriDetermined by the following update formula:
Figure FDA0003002146590000024
wherein t is the iteration number of the algorithm, and rand is [0,1]]Inner random number, θiD represents the dimension of the particle, and for the sake of easy discrimination, the phases of the self-optimum position and the global optimum position of the particle are respectively represented by thetaid,θgdAnd w is the inertial weight of the algorithm, a linear decreasing updating mode is adopted, and the formula is as follows:
Figure FDA0003002146590000031
c1 and c2 are learning factors of the algorithm and are adjusted along with the change of the inertia weight, wherein c1 is 2.4-1.4 × cos (w · pi), and c2 is 0.9+1.6 × cos (w · pi);
in particular when
Figure FDA0003002146590000032
When the difference between them should beMinus 2 π when
Figure FDA0003002146590000033
Then, the difference should be added by 2 pi; in the same way, the method for preparing the composite material,
Figure FDA0003002146590000034
the same is true for the same;
after the rotation angle of the quantum revolving door is determined, the positions of the particles are updated by adopting the quantum revolving door, and the probability amplitude after updating is as follows:
Figure FDA0003002146590000035
h is selected to avoid the phenomenon that the algorithm falls into the local optimal solution to generate premature convergenceεThe gate corrects the quantum revolving gate, and takes epsilon (0, 1)]If |. alpha'i|2Is less than or equal to epsilon and beta'i|2Greater than or equal to 1-epsilon, the corrected probability amplitude
Figure FDA0003002146590000036
If α'i|2Is not less than 1-epsilon and beta'i|2If the probability is less than or equal to epsilon, the corrected probability amplitude
Figure FDA0003002146590000037
Otherwise, the probability amplitude is kept unchanged; to generate [0,1]Inner random number rand, when rand>|α″i|2The qubit collapses to 1, otherwise to 0.
6. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 5, judging whether the particles need to be subjected to quantum not gate updating according to a preset self-adaptive mutation probability, wherein the self-adaptive mutation probability P is as follows:
Figure FDA0003002146590000038
therein, fitiAs the current fitness of the particle, fitgIs a global extremum; when P is less than or equal to PminWhen P is equal to PminOtherwise, P is not changed;
after the self-adaptive variation probability is determined, a random number rand in [0,1] is taken, and only when rand < P, the particle carries out quantum not gate updating operation, and the quantum not gate operation actually changes the original tendency of collapsing to a certain state and collapses to another state with the tendency of the degree; the probability after mutation is:
Figure FDA0003002146590000039
to generate [0,1]Inner random number rand, when rand>|α″′i|2The qubit collapses to 1, otherwise to 0.
7. The orthogonal waveform design method for MIMO radar based on quantum particle swarm optimization according to claim 1, characterized in that: in step 7, the optimized phase code sequence is obtained
Figure FDA0003002146590000041
Figure FDA0003002146590000042
The optimized phase is
Figure FDA0003002146590000043
By using
Figure FDA0003002146590000044
And modulating the phase of the signal to complete the orthogonal waveform design of the MIMO radar.
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