CN105022034B - The Optimization Design of the transmitting OFDM waveforms of centralized MIMO radar - Google Patents
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Abstract
The invention discloses a kind of Optimization Design of the transmitting OFDM waveforms of centralized MIMO radar, comprise the following steps:(1) randomly generating M length is, obey the vectorial φ of [0 1] distribution1,...,φm,...,φM;(2) initial value for defining m-th of sub- CF signal isAnd solve m-th of sub- CF signal(3) according to m-th of sub- CF signalThe subcarrier weight vector of m-th transmitting antenna of the design with pilotaxitic textureAnd sub- carrier frequency interpolation is carried out successively to M sub- CF signals, obtain sub- carrier frequency sequence U0,...,Um,...,UM‑1, matrix form is written as, sub- carrier frequency matrix U is obtained;(4) discrete Fourier transform is carried out by row to sub- carrier frequency matrix U, obtains time domain discrete baseband signal matrix u, and expanded to the OFDM transmitted waveform matrix v=[v with cyclic prefix1,…,vm,…,vM];(5) to the OFDM transmitted waveform sequences v of m-th of transmitting antennamSteering D/A conversion is carried out, and upconverts to radar carrier frequency fc, obtain the transmission signal of the centralized MIMO radar of m-th of antenna.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an optimal design method for transmitting OFDM waveforms of a centralized MIMO radar.
Background
With the development of radar technology, the performance of the traditional single-station radar cannot meet the requirements of people on the radar, so that a Multiple Input Multiple Output (MIMO) radar has attracted great interest of researchers, and becomes one of the important directions for the development of modern radars. Different from the traditional single-station radar, the MIMO radar transmits a plurality of orthogonal or nearly orthogonal waveforms by using a plurality of transmitting antennas, so that the degree of freedom of a system can be increased, the resolution of the radar is improved, the flexibility of the design of a transmitting beam mode can be increased, and the capability of the radar for tracking a plurality of moving targets at the same time is improved.
In a centralized MIMO radar, the waveform design of multiple transmit antennas is an important and challenging problem. Generally, the transmission waveform of the centralized MIMO radar needs to satisfy not only orthogonality, but also time-domain constant modulus property in order to improve transmission efficiency; in order to improve the signal-to-noise ratio, the designed emission waveform needs to meet the frequency domain constant modulus characteristic; to guarantee high range resolution, the transmit signal bandwidth needs to occupy the entire system bandwidth. Time domain orthogonal waveforms adopted by the traditional centralized MIMO radar cannot completely meet the requirements, and further the performance of subsequent radar signal processing is lost.
Orthogonal Frequency Division Multiplexing (OFDM) waveforms have been successfully applied in communication systems for broadband high-speed data transmission, and in recent years, OFDM waveforms have also been studied in radar applications. The radar for transmitting the OFDM waveform realizes multi-carrier transmission by simultaneously transmitting a plurality of carriers, and has the excellent characteristics of high distance resolution, low autocorrelation function side lobe, high frequency spectrum utilization rate and the like. However, the existing centralized MIMO-OFDM waveform has large time domain envelope fluctuation, does not meet the time domain constant modulus characteristic, and influences the application of a transmitting signal in practical engineering.
Disclosure of Invention
In view of the above deficiencies of the prior art, the present invention provides an optimal design method for transmitting OFDM waveforms of a centralized MIMO radar, which uses a communication waveform design theory and a communication signal processing technology for reference, and can ensure that the transmitted waveforms of the centralized MIMO radar not only satisfy orthogonality and high distance resolution, but also satisfy a time domain constant modulus characteristic and a maximum signal-to-noise ratio characteristic.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
An optimal design method for transmitting OFDM waveforms of a centralized MIMO radar is characterized by comprising the following steps:
step 1, randomly generating M lengths ofAnd obey [01]Uniformly distributed vector phi1,...,φm,...,φMWherein M is 1,2, …, M is the number of transmitting antennas, and N is the subcarrier frequency number of the transmitted signal;
step 2, defining the initial value of the mth sub-carrier frequency signalDefining i as iteration times, and enabling an initial value of the iteration times i to be 1; designing iterative algorithm to solve mth sub-carrier frequency signalWherein, I is the total number of iterations, M is 1,2, …, M;
step 3, firstly, according to the m sub-carrier frequency signalDesigning subcarrier weight vector [ U ] of mth transmitting antenna with interleaving structurem]k,Wherein,to make the m sub-carrier frequency signalThe signal obtained by performing M-fold interpolation, M being 1,2, …, M, k being 0,1, …, N-1,then, a subcarrier weight vector [ U ] according to the mth transmitting antenna having an interleaving structurem]kFor the mth sub-carrier frequency signalPerforming sub-carrier frequency interpolation to obtain the mth sub-carrier frequency sequence U with the length of Nm(ii) a Finally, sub-carrier frequency interpolation is carried out on the M sub-carrier frequency signals in sequence to obtain M sub-carrier frequency sequences U with the length of N0,...,Um,...,UM-1;
Step 4, mixingM sub-carrier frequency sequences U with length of N0,...,Um,...,UM-1Writing into a matrix form to obtain a sub-carrier frequency matrix U ═ U0,...,Um,...,UM-1]TThe dimension of the sub-carrier matrix U is N × M [ ·]TRepresenting a matrix transposition; then, the sub-carrier frequency matrix U is subjected to discrete Fourier transform according to columns to obtain a time domain discrete baseband signal matrix U ═ U0,...,um,...,uM-1]T(ii) a Wherein u ismIs the mth time domain discrete baseband signal sequence;
step 5, passing the time domain discrete baseband signal matrix u through a formulaOFDM transmitting waveform matrix v extended with cyclic prefix1,…,vm,…,vM]With dimension of (N + L) × M, where L is the length of the cyclic prefix, vmV (1: L) represents the 1 st to L th rows of an OFDM transmission waveform matrix v with a cyclic prefix, v (L +1: N + L) represents the L +1 th to N + L th rows of the OFDM transmission waveform matrix v with the cyclic prefix, and u (N-L +1: N) represents the N-L +1 th to N th rows of a time-domain discrete baseband signal matrix u; OFDM transmitting wave form sequence v for m transmitting antennamPerforming D/A conversion and up-converting to radar carrier frequency fcAnd obtaining the transmission signal of the centralized MIMO radar of the mth antenna.
Compared with the prior art, the invention has the following advantages:
firstly, the invention adopts the weight vector of the subcarrier of the transmitting antenna with the interweaving structure to carry out the optimal design on the OFDM wave form transmitted by the centralized MIMO radar, thereby not only enabling the OFDM wave forms transmitted by the centralized MIMO radar to be mutually orthogonal, but also enabling a plurality of OFDM wave forms transmitted to occupy the whole system bandwidth, and further ensuring the high-distance resolution.
Secondly, the OFDM waveform transmitted by the centralized MIMO radar optimally designed by the invention can meet the constant modulus characteristics of a time domain and a frequency domain, so that the maximum working efficiency and the maximum signal-to-noise ratio of a transmitter can be obtained.
Drawings
The invention is described in further detail below with reference to the following description of the drawings and the detailed description.
FIG. 1 is a flow chart of the present invention;
fig. 2a, 2b and 2c are time domain envelope diagrams of transmission waveforms of the transmitting antenna 1, the transmitting antenna 2 and the transmitting antenna 3, respectively, with the abscissa being a sampling point and the ordinate being a signal amplitude;
fig. 3a, fig. 3b and fig. 3c are sub-carrier frequency envelope diagrams of transmission waveforms of the transmitting antenna 1, the transmitting antenna 2 and the transmitting antenna 3, respectively, with frequency points on the abscissa and spectral magnitudes on the ordinate;
fig. 4a, 4b and 4c are graphs of autocorrelation functions of transmission waveforms of the transmission antenna 1, the transmission antenna 2 and the transmission antenna 3, respectively, with the abscissa being the sampling shift and the ordinate being the autocorrelation amplitude;
fig. 5a is a graph of the cross-correlation function of the transmit waveform of transmit antenna 1 and the transmit waveform of transmit antenna 2, with sample shift on the abscissa and cross-correlation amplitude on the ordinate;
fig. 5b is a graph of the cross-correlation function of the transmit waveform of transmit antenna 1 and the transmit waveform of transmit antenna 3, with sample shift on the abscissa and cross-correlation amplitude on the ordinate;
fig. 5c is a graph of the cross-correlation function of the transmit waveform of transmit antenna 2 and the transmit waveform of transmit antenna 3 with sample shift on the abscissa and cross-correlation amplitude on the ordinate.
Detailed Description
Referring to fig. 1, the method for optimally designing the transmitted OFDM waveform of the centralized MIMO radar of the present invention includes the following specific steps:
step 1, randomly generating M lengths ofAnd obey [01]Uniformly distributed vector phi1,...,φm,...,φMWherein M is 1,2, …, M is the number of transmitting antennas, and N is the subcarrier frequency of the transmitted signal.
Step 2, defining the initial value of the mth sub-carrier frequency signalDefining i as iteration times, and enabling an initial value of the iteration times i to be 1; designing iterative algorithm to solve mth sub-carrier frequency signalWherein, I is the total number of iterations, and M is 1,2, …, M.
The iterative algorithm comprises the following specific steps:
2.1 for the mth sub-carrier signal when the iteration number is iTo carry outPoint discrete Fourier inverse transformation (IDFT) is carried out to obtain a time domain signal corresponding to the mth sub-carrier frequency signal when the iteration number is i
2.2 extracting the time domain signal corresponding to the mth sub-carrier frequency signal when the iteration number is iPhase of Wherein ∠ denotes the phase of the complex signal, atan denotes the inverse tangent function, real and imag denote the real and imaginary parts of the complex number, respectively;
2.3 defining the mth constant modulus time domain signalAnd for the mth constant modulus time domain signalTo carry outPoint Discrete Fourier Transform (DFT) to obtain mth frequency domain signal
2.4 extracting the mth frequency domain signalPhase ofAnd calculating to obtain the mth constant modulus frequency domain signal
2.5 judging whether the iteration frequency I meets the condition that I is less than I, if so, increasing the iteration frequency I by 1, and returning to the step 2.1; if not, the mth sub-carrier frequency signal is obtained
Step 3, firstly, according to the m sub-carrier frequency signalDesigning subcarrier weight vector [ U ] of mth transmitting antenna with interleaving structurem]k,Wherein,to make the m sub-carrier frequency signalThe signal obtained by performing M-fold interpolation, M being 1,2, …, M, k being 0,1, …, N-1,then, a subcarrier weight vector [ U ] according to the mth transmitting antenna having an interleaving structurem]kFor the mth sub-carrier frequency signalPerforming sub-carrier frequency interpolation to obtain the mth sub-carrier frequency sequence U with the length of Nm(ii) a Finally, sub-carrier frequency interpolation is carried out on the M sub-carrier frequency signals in sequence to obtain M sub-carrier frequency sequences U with the length of N0,...,Um,...,UM-1。
Step 4, M sub-carrier frequency sequences U with the length of N0,...,Um,...,UM-1Writing into a matrix form to obtain a sub-carrier frequency matrix U ═ U0,...,Um,...,UM-1]TThe dimension of the sub-carrier matrix U is N × M [ ·]TRepresenting a matrix transposition; then, the sub-carrier frequency matrix U is subjected to discrete Fourier transform according to columns to obtain a time domain discrete baseband signal matrix U ═ U0,...,um,...,uM-1]T(ii) a Wherein u ismAt the m-th timeA sequence of domain discrete baseband signals.
Step 5, passing the time domain discrete baseband signal matrix u through a formulaOFDM transmitting waveform matrix v extended with cyclic prefix1,…,vm,…,vM]With dimension of (N + L) × M, where L is the length of the cyclic prefix, vmV (1: L) represents the 1 st to L th rows of an OFDM transmission waveform matrix v with a cyclic prefix, v (L +1: N + L) represents the L +1 th to N + L th rows of the OFDM transmission waveform matrix v with the cyclic prefix, and u (N-L +1: N) represents the N-L +1 th to N th rows of a time-domain discrete baseband signal matrix u; OFDM transmitting wave form sequence v for m transmitting antennamPerforming D/A conversion and up-converting to radar carrier frequency fcAnd obtaining the transmission signal of the centralized MIMO radar of the mth antenna.
The effect of the present invention can be further illustrated by the following simulation experiments:
1) simulation conditions are as follows:
setting the number of transmitting antennas of the centralized MIMO radar system as M to be 3, and setting the vector phimIs 200, m is 1,2,3, the frequency of the transmitted signal subcarrier is 600, and the total number of iterations is 30.
2) Simulation content:
simulation 1: the time domain envelope of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the invention is simulated, and the result is shown in FIG. 2, wherein FIG. 2a, FIG. 2b and FIG. 2c are respectively the time domain envelope diagrams of the transmitted waveforms of the transmitting antenna 1, the transmitting antenna 2 and the transmitting antenna 3;
simulation 2: the sub-carrier frequency envelopes of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the invention are simulated, and the result is shown in figure 3, only the envelopes of the first 20 sub-carrier frequencies are drawn for clear display, wherein figures 3a, 3b and 3c are the sub-carrier frequency envelopes of the transmitted waveforms of a transmitting antenna 1, a transmitting antenna 2 and a transmitting antenna 3 respectively;
simulation 3: the result of simulating the autocorrelation function of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention is shown in fig. 4, where fig. 4a, 4b, and 4c are the autocorrelation functions of the transmitted waveforms of the transmitting antenna 1, the transmitting antenna 2, and the transmitting antenna 3, respectively;
and (4) simulation: the simulation result of the cross-correlation function of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention is shown in fig. 5, where fig. 5a is the cross-correlation function of the transmitted waveform of the transmitting antenna 1 and the transmitted waveform of the transmitting antenna 2, fig. 5b is the cross-correlation function of the transmitted waveform of the transmitting antenna 1 and the transmitted waveform of the transmitting antenna 3, and fig. 5c is the cross-correlation function of the transmitted waveform of the transmitting antenna 2 and the transmitted waveform of the transmitting antenna 3.
3) And (3) simulation result analysis:
simulation 1: as can be seen from fig. 2a, fig. 2b and fig. 2c, the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention has a constant modulus value in the time domain, that is, the envelope is constant, which enables the transmitter to have maximum working efficiency;
simulation 2: as can be seen from fig. 3a, 3b and 3c, the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention has a constant modulus value in the frequency domain, and satisfies the frequency domain interleaving structure, so as to ensure high distance resolution and obtain the maximum snr;
simulation 3: as can be seen from fig. 4a, 4b and 4c, the sidelobe of the autocorrelation function of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention is very low, which indicates that the transmitted waveform has very low range sidelobe performance;
and (4) simulation: as can be seen from fig. 5a, 5b, and 5c, the sidelobe of the cross-correlation function of the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention is very low, which indicates that the transmitted OFDM waveform of the centralized MIMO radar optimally designed by the present invention has good orthogonality.
Claims (1)
1. An optimal design method for transmitting OFDM waveforms of a centralized MIMO radar is characterized by comprising the following steps:
step 1, randomly generating M lengths ofAnd obey [01]Uniformly distributed vector phi1,..,φm,...,φMWherein M is 1,2, …, M is the number of transmitting antennas, and N is the subcarrier frequency number of the transmitted signal;
step (ii) of2, defining the initial value of the mth sub-carrier frequency signalDefining i as iteration times, and enabling an initial value of the iteration times i to be 1; designing iterative algorithm to solve mth sub-carrier frequency signalWherein, I is the total number of iterations, M is 1,2, …, M;
the iterative algorithm in the step 2 comprises the following specific steps:
2.1 for the mth sub-carrier signal when the iteration number is iTo carry outPoint discrete Fourier inverse transformation is carried out to obtain a time domain signal corresponding to the mth sub-carrier frequency signal when the iteration number is i
2.2 extracting the time domain signal corresponding to the mth sub-carrier frequency signal when the iteration number is iPhase of Wherein ∠ denotes the phase of the complex signal, atan denotes the inverse tangent function, real and imag denote the real and imaginary parts of the complex number, respectively;
2.3 defining the mth constant modulus time domain signalAnd for the mth constant modulus time domain signalTo carry outPoint discrete Fourier transform to obtain the mth frequency domain signal
2.4 extracting the mth frequency domain signalPhase ofAnd calculating to obtain the mth constant modulus frequency domain signal
2.5 judging whether the iteration frequency I meets the condition that I is less than I, if so, increasing the iteration frequency I by 1, and returning to the step 2.1; if not, the mth sub-carrier frequency signal is obtained
Step 3, firstly, according to the m sub-carrier frequency signalDesigning subcarrier weight vector [ U ] of mth transmitting antenna with interleaving structurem]k,Wherein,to make the m sub-carrier frequency signalThe signal obtained by performing M-fold interpolation, M being 1,2, …, M, k being 0,1, …, N-1,then, a subcarrier weight vector [ U ] according to the mth transmitting antenna having an interleaving structurem]kFor the mth sub-carrier frequency signalPerforming sub-carrier frequency interpolation to obtain the mth sub-carrier frequency sequence U with the length of Nm(ii) a Finally, sub-carrier frequency interpolation is carried out on the M sub-carrier frequency signals in sequence to obtain M sub-carrier frequency sequences U with the length of N0,...,Um,...,UM-1;
Step 4, M sub-carrier frequency sequences U with the length of N0,...,Um,...,UM-1Writing into a matrix form to obtain a sub-carrier frequency matrix U ═ U0,...,Um,...,UM-1]TThe dimension of the sub-carrier matrix U is N × M [ ·]TRepresenting a matrix transposition; then, the sub-carrier frequency matrix U is subjected to discrete Fourier transform according to columns to obtain a time domain discrete baseband signal matrix U ═ U0,...,um,...,uM-1]T(ii) a Wherein u ismIs the mth time domain discrete baseband signal sequence;
step 5, passing the time domain discrete baseband signal matrix u through a formulaOFDM transmitting waveform matrix v extended with cyclic prefix1,…,vm,…,vM]With dimension of (N + L) × M, where L is the length of the cyclic prefix, vmFor the OFDM transmit waveform sequence for the mth transmit antenna, v (1: L) represents the th of the OFDM transmit waveform matrix v with cyclic prefix1 to L rows, v (L +1: N + L) represents the L +1 to N + L rows of the OFDM transmission waveform matrix v with cyclic prefix, and u (N-L +1: N) represents the N-L +1 to N rows of the time-domain discrete baseband signal matrix u; OFDM transmitting wave form sequence v for m transmitting antennamPerforming D/A conversion and up-converting to radar carrier frequency fcAnd obtaining the transmission signal of the centralized MIMO radar of the mth antenna.
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CN112068081B (en) * | 2020-09-10 | 2022-07-12 | 西安电子科技大学 | OFDM frequency agile transmitting signal design method based on cyclic prefix |
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