CN113093116A - MIMO-OFDM radar communication integration-based waveform design method - Google Patents

MIMO-OFDM radar communication integration-based waveform design method Download PDF

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CN113093116A
CN113093116A CN202110389242.4A CN202110389242A CN113093116A CN 113093116 A CN113093116 A CN 113093116A CN 202110389242 A CN202110389242 A CN 202110389242A CN 113093116 A CN113093116 A CN 113093116A
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radar
antenna
communication
signals
signal
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CN113093116B (en
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吴亮
刘天辰
张在琛
党建
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2626—Arrangements specific to the transmitter only
    • H04L27/2627—Modulators
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a radar communication integrated waveform design method based on MIMO-OFDM, which is used for obtaining an optimal auto-covariance matrix of radar transmitting signals by using a convex optimization method to enable the optimal auto-covariance matrix to be close to an ideal radiation characteristic spectrum as far as possible by combining the radiation characteristic of a radar and aiming at the problem that the radiation characteristic of the existing radar waveform design can not be considered to limit communication energy. Meanwhile, the invention improves the existing OFDM waveform, bears the same frequency domain signals at the corresponding subcarrier positions of different antennas and gives different weights to the signals, so that the statistical correlation of the detection signals transmitted by different antennas meets the covariance matrix. The invention is suitable for multi-target detection and multi-communication target service, can flexibly adjust parameters according to different scenes, and has good universality.

Description

MIMO-OFDM radar communication integration-based waveform design method
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a waveform design method based on MIMO-OFDM radar communication integration.
Background
The integration of radar communication is a technology combining radar and communication as the name implies, and aims to integrate the radar and a communication system on a platform in a certain scientific mode. Radar and communication have been developed and studied as two independent systems throughout the development history of radio. One for the detection of long-distance targets and the other for the transmission of information data. However, due to the faster and faster data rate of wireless communication, the frequency band of communication is forced to be continuously improved, and together with the pursuit of miniaturization, integration and multi-functional products in the current society and even military fields, the demand of integration of radar and communication is greatly promoted.
At present, the research direction of radar communication integration is mainly divided into 3 modes. The first is a time-sharing scheme, i.e. the radar and the communication are separated in time, i.e. they have respective working times belonging to their own system. This approach is the simplest to implement, but has the great disadvantage that the radar and communication systems do not work continuously. The radar may lose the tracked target and the communication may be interrupted, which is intolerable in severe application scenarios. The second is a beam division system, that is, radar signals and communication signals are directed to different directions in space, so that the radar and communication can be isolated in space domain. However, this approach has the disadvantage that the two cannot be completely isolated in space, which may cause interference with each other; also, the system energy used for radar detection is reduced and detection performance is lost. The third is a simultaneous system, which means that radar and communication use the same signal waveform or orthogonal signal waveform to synthesize a signal waveform, and radar detection can be performed while communication is performed. The advantage of the simultaneous system is that all system energy can be used for radar and communication, and the disadvantage is that communication is limited by the direction of radar beams, which affects flexibility.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems that communication is limited by the direction of radar wave beams and flexibility is influenced in the simultaneous system radar communication integration technology mentioned in the background technology, the invention provides a radar communication integration waveform design method, which is based on a 5G MIMO-OFDM scene, so that the radiation power spectrum of a radar can meet the power limitation requirement of communication, can be suitable for multi-target detection and serve multi-communication targets, can flexibly adjust parameters according to different scenes and has good universality.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a radar communication integrated waveform design method based on MIMO-OFDM comprises the following steps:
step 1, determining the scale of an antenna and a digital modulation method, calculating a guide vector of a radar according to the scale and the digital modulation method, and calculating a uniform radar radiation characteristic spectrum when all antennas transmit uncorrelated signals according to the guide vector;
step 2: determining angular distance position information of a communication target, limiting the total power transmitted by a radar to be a fixed value, limiting the Frobenius norm of the difference between the radiation characteristic spectrum of a transmission signal in the detection direction (except the communication direction) and the radiation characteristic spectrum of the uniform radar in the step 1 to be less than a certain threshold value, and minimizing the radiation power of an antenna in the communication direction by a convex optimization method to obtain a corresponding transmission signal autocovariance matrix;
and step 3: calculating the number of OFDM subcarriers used by a transmitting terminal for bearing information, determining the number of discrete Fourier transform points, sequentially filling signals to be transmitted into subcarriers of different antennas according to the transmitted signal auto-covariance matrix obtained in the step 2, and giving corresponding weights to the signals, so as to ensure that the signals borne by only one subcarrier among the different antennas are the same, and setting the weight of the signal borne by the subcarrier, which is not correlated with other antennas, of each antenna to be 0 and marking the weight;
and 4, step 4: calculating the radiation power spectrum of the antenna by using the autocovariance matrix obtained in the step 2, finding the radiation power value of the radiation power spectrum at the position of 3dB of the inflection point of the communication direction, calculating the difference value between the radiation power value and the communication power limit, and uniformly distributing the energy difference value to the subcarrier position marked in the step 3;
and 5: performing discrete inverse Fourier transform on the arranged and weighted symbols to obtain OFDM symbols, and adding a CP window to the OFDM symbols of each period;
step 6: calculating appropriate pulse width and pulse period of a transmitted signal according to the detection range of the radar, and sequentially arranging a plurality of OFDM symbols of adjacent periods together to form a pulse for the same antenna, wherein the duration time is equal to the pulse width; after waiting for a pulse period, sending a next pulse signal consisting of OFDM symbols, and repeating the operation until all the OFDM signals are sent;
and 7: assuming that the communication channel is known, synchronizing the received signals at the communication receiving end; after the synchronization is finished, removing the CP end, and connecting signals in adjacent pulses; equalizing the signal in a frequency domain, and dividing the equalized signal by the guide vector calculated in the step 1;
and 8: at a communication receiving end, performing discrete Fourier transform on the signal in the step 7, and performing maximum likelihood estimation on the restored modulation signal according to the filling sequence of the modulation signal in the step 3 and the weight of different antenna carrier positions in the step 4;
and step 9: at a radar receiving end, synchronizing the received signals, and calculating the time from the emission to the reception of the detection signals so as to calculate the distance between a detection target and the radar; and obtaining a complex amplitude spectrum by using Amplitude Phase Estimation (APES) on the synchronized signals, wherein the maximum position of the spectrum is an angle formed by the detection target and the antenna array.
Further, in step 2, the convex optimization method is completed by a Matlab convex optimization tool box CVX, where the convex optimization variable is an autocovariance matrix R of the transmission signal x (n), and the optimization target specifically is:
Figure BDA0003015828620000021
wherein min (. cndot.) is the minimum value, P (. theta.)c)＝aH(θc)Ra(θc) P is the radiation characteristic spectrum of the radar, thetacAngle at which communication is targeted, a (theta)c) Is a mineThe superscript H of the reached guide vector is conjugate transpose transformation;
the limiting conditions are specifically as follows:
the conditions are as follows: r is a semi-positive definite Hermite matrix (R is the definition of covariance matrix R, and the semi-positive definite Hermite matrix is the property of R, and the two are not contradictory);
Figure BDA0003015828620000031
where p is the number of the detection target, θpAn angle of a probe signal transmitted for the radar; l is the threshold value in the step 2 and can be set artificially; phi (theta)p) The uniform radar radiation characteristic spectrum in the step 1 is obtained;
∑diag(R)＝Ptcondition (c)
Wherein: diag (-) denotes the diagonal element of the extraction matrix, PtA total power limit for the transmitted signal;
Figure BDA0003015828620000032
wherein: ruvThe element of the u th row and the v th column in the R is represented, and the condition (R) is derived from a basic inequality.
In step 3, the total number of subcarriers carrying information by OFDM is
Figure BDA0003015828620000033
Wherein: n is a radical oftThe number of antennas at the transmitting end; the specific method for filling the digital modulation symbol is as follows: for the s sub-carrier carrying information of the ith antenna, if
Figure BDA0003015828620000034
This location is called the parent node, which carries the QPSK symbol and the second node
Figure BDA0003015828620000035
QPSK symbols carried by the s-th information-bearing subcarrier of each antenna are the same, and the position is called as a subcarrierA node; if a certain position is a father node, sequentially taking out a modulation symbol and filling the modulation symbol in the position; if a certain position is a child node, tracing back the modulation symbol filling of the parent node, and if the non-parent node and the non-child node at the certain position are not the child node, sequentially taking out one modulation symbol to fill in the position.
Further, in step 3, a specific method for assigning weights is as follows: in the first step, if the s-th information-bearing subcarrier of the ith antenna is a parent node, the weight is given
Figure BDA0003015828620000036
βms＝conj(βis) Wherein:
Figure BDA0003015828620000037
Figure BDA0003015828620000038
i.e. the antenna position, N, at which the child node is locatedcTotal number of information-carrying sub-carriers, P, for each antennaxFor the mean symbol power of the modulated signal, conj (-) means the conjugation, βisFor the weight at the s-th information-carrying subcarrier of the ith antenna, βmsIs the weight at the s-th information-bearing subcarrier of the m-th antenna, RimIs the value of R at row i, column m; if a position is not a father node or a child node, marking the position and temporarily setting the weight to be zero; second, calculating the total power P of the emission symbols corresponding to the current weight matrix betanWhether or not to equal the total power limit PtIf not, multiplying all values of the beta matrix by the scale factor mu,
Figure BDA0003015828620000041
further, in step 4, a specific method for uniformly distributing the weights is as follows: all the weights at all the marked positions obtained in the step 3 are changed into
Figure BDA0003015828620000042
Wherein: pΔIs the difference in step 4.
Compared with the prior art, the invention has the following beneficial effects:
the invention improves the prior OFDM waveform, bears the same frequency domain signals at the corresponding subcarrier positions of different antennas and gives different weights to the signals, so that the statistical correlation of the detection signals transmitted by different antennas meets a specific covariance matrix. The method has the advantages that the reliable radar detection performance is obtained, meanwhile, the problem of limitation on communication energy is solved, and the radiation characteristic spectrum of the radar is close to the ideal radiation characteristic spectrum as far as possible. The invention is suitable for multi-target detection and multi-communication target service, can flexibly adjust parameters according to different scenes, and has good universality.
Drawings
Fig. 1 is a schematic diagram of modulation symbol position allocation in an OFDM modulation process in an embodiment;
FIG. 2 is a diagram illustrating simulation results of the power spectrum of the radar radiation in step 4 according to the embodiment;
FIG. 3 is a diagram illustrating simulation effects of detecting a complex amplitude spectrum of an object in step 9 according to an embodiment;
FIG. 4 is a schematic flow chart of the present invention;
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
A waveform design method based on MIMO-OFDM radar communication integration aims at the problem that the radiation characteristics of the existing radar waveform design can not be considered to limit communication energy, a convex optimization method is used for obtaining an optimal auto-covariance matrix of radar emission signals, the optimal auto-covariance matrix is made to be close to an ideal radiation characteristic spectrum as far as possible, the same frequency domain signals are borne at the corresponding subcarrier positions of different antennas, different weights are given to the frequency domain signals, and the statistical correlation of detection signals emitted by different antennas meets the covariance matrix. As shown in fig. 4, the method comprises the following steps:
step 1:
number of transmitting-end antennas N in this embodimenttThe array of the radar antenna is a uniform linear array 64, the distance between adjacent antennas is 2.5 wavelengths, the carrier frequency of the radar is 10MHz, the direction of a detected target is 30 degrees, and the distance is 20 km. There are three communication targets, respectively in 40 deg., 50 deg. and 60 deg. directions, the distance is 1km, the number of receiving antennas is Nr64. In which the transmitting power of the radar is limited to P r1, the maximum power limit allowed for reception by the communications receiver is PlIf the channel gain is 1 at 0.3, the maximum power limit for the communication direction allowed by the transmitter to transmit is Pl。
Calculating a steering vector a (theta) of the radar by formula (1)
Figure BDA0003015828620000051
In the formula [ ·]TFor transposition, f0The carrier frequency of the radar signal is represented by e, a natural base number, j, a complex symbol and pi, namely a circumferential rate. Tau is1(theta) is the time from the emission of the signal from the 1 st antenna to the arrival at the detection target, tau2(theta) is the time from the transmission of the signal from the 1 st antenna to the arrival at the detection target, and so on,
Figure BDA0003015828620000052
for signals from NthtThe root antenna transmits the time to reach the detection target.
The radiation characteristic spectrum P (theta) of the radar is a function of the power of a radar detection signal and theta, and the formula is as follows:
P(θ)＝aH(θ)Ra(θ) (2)
in the formula, the superscript H is the conjugate transpose transform, R is the autocovariance matrix of the transmitted signal x (n): r ═ E { x (n) x*(n), E (-) is the function expectation. x (n) ═ x1(n),x2(n)，x3(n)…xNt(n)]T，x1(n) represents the signal emitted by the 1 st antenna at time n, x2(n) represents the 2 nd radicalThe signal sent by the antenna at the time n, and so on. x (n) is the OFDM symbol transmitted by the antenna. Wherein: the ith antenna sends out a signal x at time niThe calculation formula of (n) is:
Figure BDA0003015828620000053
wherein N is the length of the discrete inverse Fourier transform, the length including the virtual sub-carrier, Xi(k) For the k-th QPSK symbol at the ith antenna for OFDM modulation, betaikIs the weight at the kth subcarrier of the ith antenna.
The autocovariance matrix R of x (n) is specified as follows:
Figure BDA0003015828620000054
x (n) autocovariance matrix R, u row, v matrix element RuvThe calculation method of (2) is as follows:
Figure BDA0003015828620000055
Figure BDA0003015828620000061
wherein x isu(n) the u-th antenna sends out signal at n time, xv(n) for the v-th antenna sending out signal at time n, Xu(k) For the kth QPSK symbol at the u antenna for OFDM modulation, Xs(l) For the l-th QPSK symbol at the s-th antenna for OFDM modulation, betaukFor the weight at the k information-bearing subcarrier of the u antenna, βvlFor the weight at the l information-carrying subcarrier of the v antenna, βslFor the weight at the l information-carrying subcarrier of the s-th antenna, a conjugate is represented.
If the QPSK symbols are arranged in a non-repeated sequenceAt different subcarriers of the same antenna, where no virtual subcarrier is contained, the signals transmitted by different antennas are uncorrelated, i.e. R is a diagonal matrix. Let P at this timet＝Pr-PlWhen the weight average of ownership is the same, then
The radiation characteristic spectrum of the radar can be obtained from equation (2), where phi (theta) is Pt＝Pr-Pl。
Step 2:
using a convex optimization method, changing an autocovariance matrix R, wherein the optimization target is to minimize the sum of radiation power of the radar in each communication direction, namely:
Figure BDA0003015828620000062
wherein min (. cndot.) is the minimum value, P (. theta.)c)＝aH(θc)Ra(θc) P is the radiation characteristic spectrum of the radar, thetacAngle at which communication is targeted, a (theta)c) The upper mark H is conjugate transpose transformation for the guiding vector of the radar;
the limiting conditions are specifically as follows:
the conditions are as follows: r is a semi-positive definite Hermite matrix (R is the definition of covariance matrix R, and the semi-positive definite Hermite matrix is the property of R, and the two are not contradictory);
Figure BDA0003015828620000063
where p is the number of the detection target, θpAn angle of a probe signal transmitted for the radar; l is a threshold (the threshold in step 2) of similarity between the ideal radiation characteristic and the real radiation characteristic in the non-communication direction, and may be set manually; phi (theta)p) Is the uniform radar radiation characteristic spectrum in step 1.
∑diag(R)＝PtCondition (c)
Wherein: diag (-) denotes the diagonal element of the extraction matrix, PtIs the total power limit of the transmitted signal.
If the QPSK symbols corresponding to a same subcarrier of each two different antennas are guaranteed to be the same, and there is only one such same symbol in each two different antennas, the correlation between each two antennas is determined only by the same symbol, then equation (4) can be simplified as follows:
Figure BDA0003015828620000071
u, v diagonal elements Ruu、RvvThe calculation formula of (2) is as follows:
Figure BDA0003015828620000072
Figure BDA0003015828620000073
in the formula: n is a radical ofcIs the number of sub-carriers actually carrying the information. Beta is aukFor the weight at the k information-bearing subcarrier of the u antenna, βvkFor the weight at the kth information-bearing subcarrier of the vth antenna, denotes the conjugate.
As is apparent from the formula (6),
Figure BDA0003015828620000074
as can be seen from the basic inequality,
Figure BDA0003015828620000075
then
Figure BDA0003015828620000076
Wherein: o, g are the serial numbers of the two antennas that produce correlation at the k-th subcarrier position, (o)<g) And the value of o, g can be determined by k; beta is aokFor the weight at the kth information-bearing subcarrier of the mth antenna,βgkthe weight at the kth information-bearing subcarrier for the g-th antenna.
Since R is a semi-positive definite Hermite matrix (R is the definition of covariance matrix R, and the semi-positive definite Hermite matrix is the property of R, the two are not contradictory):
Figure BDA0003015828620000077
therefore, it is
Figure BDA0003015828620000081
And step 3:
after obtaining the optimal autocovariance matrix R, considering that a filling position and a corresponding weight are allocated to each QPSK symbol, the number N of antennas at the transmitting end in this embodimenttThe specific method is as follows:
(1) determining the number of subcarriers actually carrying information
Figure BDA0003015828620000082
Taking the number N of discrete Fourier transform (i.e. the total number of OFDM sub-carriers, including virtual sub-carriers) as the nearest NcPower of 2 2048.
(2) Determining the positions of the father node and the child nodes, and for the s-th information-bearing subcarrier of the ith antenna, if
Figure BDA0003015828620000083
This position is the parent node carrying the QPSK symbol and the second node
Figure BDA0003015828620000084
The QPSK symbols carried by the s-th information-bearing subcarrier of each antenna are the same, and the position is a sub-node. Fig. 1 is a schematic diagram of the positions of a parent node and a child node, and arrows mean that the parent node points to the child node.
(3) Traversing all information-bearing subcarrier positions of all antennas, and if a certain position is a father node, sequentially taking out a QPSK symbol to be sent and filling the QPSK symbol into the position; if a certain position is a child node, tracing back the QPSK symbol filling of the parent node, and if a non-parent node and a non-child node at the certain position are not the child node, sequentially taking out a QPSK symbol to be sent and filling the QPSK symbol into the position.
(4) The weight is preliminarily calculated, and if the s sub-carrier of the ith antenna for bearing the information is a father node, the weight is calculated
Figure BDA0003015828620000085
Weight beta of the position of the corresponding child nodems＝conj(βis) Wherein
Figure BDA0003015828620000086
Figure BDA0003015828620000087
If a location is not a parent or child node, the location is marked and the weight is temporarily set to zero.
(5) Calculating the total power P of the emission symbols corresponding to the current weight matrix betanWhether or not to equal PtIf not, multiplying all values of the beta matrix by the scale factor mu,
Figure BDA0003015828620000088
and 4, step 4:
and after the weight distribution is finished, calculating an autocovariance matrix R 'under the actual condition according to the formulas (6) to (7), and substituting the autocovariance matrix R' into the formula (2) to obtain the radiation power spectrum of the current radar. The simulation results are shown in fig. 2.
Respectively finding three radiation power values of the radiation power spectrum at the minimum inflection point 3dB of the three communication directions, and taking the maximum value of the three radiation power values as PmThen P isΔ＝Pl-Pm；
The total number of nodes marked in step 3 should be Nt(Nc-Nt+1), since the mark position is not the father node or the son node, changing the weight of the mark position will not change the relativity between different antennas, only the total transmitting power will be changed, i.e. the self-coordination is changedThe size of the diagonal elements of the variance matrix R. Let the total power added equal P according to equation (8)ΔThe modulo-squared sum of the weights of all the mark positions is equal to
Figure BDA0003015828620000091
Is equally distributed to each mark position betamarkObtaining:
Figure BDA0003015828620000092
the total transmission power is Pt+PΔThe power value is necessarily less than the transmitting power limit of the radar, and is limited to PrAnd the limitation requirement is met.
And 5, 6:
and performing discrete inverse Fourier transform on the arranged and weighted symbols to obtain OFDM symbols, wherein the sampling point number of each symbol is 2048. In the embodiment, the distance of the radar detection target is 20km, and the time length of the radar signal propagation back and forth is that the back and forth distance/the light speed is equal to 133.3 mu s. And the OFDM subcarrier interval is taken as 60khz, the OFDM symbol length is 1/60000s, and the sampling period is 1/60000/2048 s. The 7 OFDM symbols constitute one slot, each of which is 125 μ s in length. Within each slot, the first CP (cyclic prefix) length is 160 sample periods, and the remaining 6 CPs have a length of 144 sample periods. Each radar pulse transmits an OFDM symbol of one slot length with a pulse period of 4 slot lengths, i.e. 500 mus.
And 7:
and at the communication receiving end, synchronizing the received signals. Consider two sliding windows W1 and W2, the length (number of samples) of which is the same as the length of the first CP in each slot, 160 points, denoted NG(ii) a The spacing distance is 2048 sampling points, the sliding window sliding distance is denoted as δ, and when the cyclic prefix CP of the first OFDM symbol in the slot coincides with W1, the similarity between W1 and W2 is maximum. The correlation of two sliding windows of W1 and W2 is used for synchronization, and the formula for calculating the delta is as follows:
Figure BDA0003015828620000093
in the formula: y [ n + i ]]For signals received at time (N + i), y [ N + N + i]Is the signal received at time (N + i). arg maxδ(. cndot.) means the value of the variable δ at which the latter equation reaches a maximum.
And after the synchronization is finished, cutting off the CP end, and connecting the adjacent pulse signals end to end. Frequency domain equalization is then performed.
For the signal y in a certain OFDM period received by the s-th antennas(n) there are:
Figure BDA0003015828620000094
Figure BDA0003015828620000095
in the formula:
Figure BDA0003015828620000096
for the convolution symbols, his(n) is a time domain representation of the channel, zis(n) is the channel noise and (n),
Figure BDA0003015828620000097
for transmitting signal x of ith antennai(n) multiplied by the value of the steering vector.
Figure BDA0003015828620000098
Is defined as equation 12, which has no meaning in itself,
Figure BDA0003015828620000099
is xi(n) deriving ys(n) an intermediate amount in the process.
The two sides of the equation are simultaneously used for the discrete Fourier transform of N2048
Figure BDA0003015828620000101
Wherein: y iss(k)、
Figure BDA0003015828620000102
His(k)、Zis(k) Are each the above-mentioned ys(n)、
Figure BDA0003015828620000103
his(n)、zis(n) fourier transform form.
Neglecting noise, writing into a matrix form, and obtaining:
Figure BDA0003015828620000104
noting that the channel matrix at the k point is H, the frequency domain at the k point is equalized by Xa(k) The formula of (1) is:
Xa(k)＝H-1(k)Y(k) (16)
wherein: h-1(k) The inverse of H (k), Y (k), is the vector representation to the left of the equation of equation (15).
Obtain all X in the symbol perioda(k) Then carrying out discrete Fourier transform to obtain xa(n) according to formula (12), mixing xaThe division by the steering vector yields x', which is an estimate of the transmitted signal. The discrete fourier transform X 'of X' is an estimate of the QPSK symbol array with weights.
And 8:
for the s-th information-bearing subcarrier of the ith transmitting antenna, the QPSK symbol with weight obtained after frequency domain equalization is X'i,sIf the position is not a parent node or a child node, the QPSK symbol estimation of the position
Figure BDA0003015828620000105
Comprises the following steps:
Figure BDA0003015828620000106
in the formula: sgn (. cndot.) denotes a sign function, real (. cndot.) denotes taking a real part of the parenthesis content, and image (. cndot.) denotes taking an imaginary part of the parenthesis content. Beta is ai,sThe weight at the s-th information-bearing subcarrier position for the ith transmit antenna.
If the position is a parent node or a child node, the QPSK symbol of the position is estimated as:
Figure BDA0003015828620000107
in the formula: x'w,qQPSK symbol with weight after equalization of parent node (or child node) position corresponding to s-th information-bearing subcarrier of ith transmitting antennaw,qJ is the complex symbol, which is the weight of the corresponding location.
And step 9:
and in the same step 7, synchronizing the signals received by the radar to obtain the round-trip time tau of the detection signals in the space, and multiplying the round-trip time tau by the light speed to divide by 2 to obtain the distance between the detection target and the radar.
And giving a matrix form Y of the radar receiving end signal:
Y＝ψ(θ)bc(θ)a*(θ)X+Z (19)
in the formula, θ is the angle at which the radar detects the target, ψ (θ) is complex amplitude, and is proportional to the radar scattering cross section (RCSs) of the target, which is set to 1.5 in this embodiment; x is NtX N transmitting signal matrix, the radar receiving array and the transmitting array using the same antenna, so that Y is NtX N matrix of received signals, Z being NtAn interference noise signal matrix of x n; a is*(θ) referring to formula (1); b (θ) is a guide vector of the reflected signal, and in the embodiment, b (θ) is a (θ) (·)cIs complex conjugation.
The angle of the probe object is estimated using Amplitude Phase Estimation (APES), which can be expressed as
minw,ψ||w*Y-ψ(θ)a*(θ)X||2 s.t.w*bc(θ)＝1 (20)
In the formula: w is NtThe purpose of the x 1 weight vector, equation (20), is to find a beamformer that has an output that matches a as closely as possible*The waveform signals obtained by (θ) X are similar. Taking psi (theta) as a variable, the cost function of equation (20) can be minimized to obtain an estimate thereof
Figure BDA0003015828620000111
In the formula:
Figure BDA0003015828620000112
for the observation data sample covariance matrix:
Figure BDA0003015828620000113
the optimization problem in equation (20) can be simplified as follows:
Figure BDA0003015828620000114
wherein
Figure BDA0003015828620000115
The optimization problem in equation (23) is given by the APES beamformer giving a weight vector estimate of
Figure BDA0003015828620000116
APES with formula (25) taken into formula (21) with easy ψ (θ) was estimated as
Figure BDA0003015828620000117
And after the complex amplitude spectrum of the detection signal is obtained, the abscissa corresponding to the peak value is the angle of the detection target.
Assuming that the interference noise is gaussian noise of 15dB, the complex amplitude spectrum in this embodiment is shown in fig. 3.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. A radar communication integrated waveform design method based on MIMO-OFDM is characterized by comprising the following steps:
step 1, determining the scale of an antenna and a digital modulation method, calculating a guide vector of a radar, and calculating a uniform radar radiation characteristic spectrum when all antennas transmit uncorrelated signals;
step 2: determining angular distance position information of a communication target, limiting the total power transmitted by the radar to be a fixed value, limiting the Frobenius norm of the difference between the radiation characteristic spectrum of the transmission signal in the detection direction and the uniform radar radiation characteristic spectrum in the step 1 to be less than a certain threshold value, and minimizing the radiation power of an antenna in the communication direction by a convex optimization method to obtain a corresponding transmission signal auto-covariance matrix;
and step 3: calculating the number of OFDM subcarriers used by a transmitting terminal for bearing information, determining the number of discrete Fourier transform points, sequentially filling signals to be transmitted into subcarriers of different antennas according to the transmitted signal auto-covariance matrix obtained in the step 2, and giving corresponding weights to the signals, so as to ensure that the signals borne by only one subcarrier among the different antennas are the same, and setting the weight of the signal borne by the subcarrier, which is not correlated with other antennas, of each antenna to be 0 and marking the weight;
and 4, step 4: calculating the radiation power spectrum of the antenna by using the autocovariance matrix obtained in the step 2, finding the radiation power value of the radiation power spectrum at the position of 3dB of the inflection point of the communication direction, calculating the difference value between the radiation power value and the communication power limit, and uniformly distributing the energy difference value to the subcarrier position marked in the step 3;
and 5: performing discrete inverse Fourier transform on the arranged and weighted symbols to obtain OFDM symbols, and adding a CP window to the OFDM symbols of each period;
step 6: calculating appropriate pulse width and pulse period of a transmitted signal according to the detection range of the radar, and sequentially arranging a plurality of OFDM symbols of adjacent periods together to form a pulse for the same antenna, wherein the duration time is equal to the pulse width; after waiting for a pulse period, sending a next pulse signal consisting of OFDM symbols, and repeating the operation until all the OFDM signals are sent;
and 7: setting a communication channel to be known, and synchronizing the received signals at a communication receiving end; after the synchronization is finished, removing the CP end, and connecting signals in adjacent pulses; equalizing the signal in a frequency domain, and dividing the equalized signal by the guide vector calculated in the step 1;
and 8: at a communication receiving end, performing discrete Fourier transform on the signal in the step 7, and performing maximum likelihood estimation on the restored modulation signal according to the filling sequence of the modulation signal in the step 3 and the weight of different antenna carrier positions in the step 4;
and step 9: at a radar receiving end, synchronizing the received signals, and calculating the time from the emission to the reception of the detection signals so as to calculate the distance between a detection target and the radar; and obtaining a complex amplitude spectrum by using amplitude phase estimation on the synchronized signals, wherein the maximum value position of the spectrum is the angle formed by the detection target and the antenna array.
2. The MIMO-OFDM based radar communication integrated waveform design method of claim 1, wherein: in the step 2, the convex optimization method is completed by a Matlab convex optimization tool box CVX, where the convex optimization variable is an autocovariance matrix R of a transmission signal x (n), and the optimization target specifically is:
Figure FDA0003015828610000021
wherein min (-) is the minimum value,
Figure FDA0003015828610000022
p is the radiation characteristic spectrum of the radar, thetacAngle at which communication is targeted, a (theta)c) The upper mark H is conjugate transpose transformation for the guiding vector of the radar;
the limiting conditions are specifically as follows:
the conditions are as follows: r is a half positive definite Hermite matrix;
Figure FDA0003015828610000023
where p is the number of the detection target, θpAn angle of a probe signal transmitted for the radar; l is the threshold value in the step 2 and can be set artificially; phi (theta)p) The uniform radar radiation characteristic spectrum in the step 1 is obtained;
∑diag(R)＝Ptcondition (c)
Wherein: diag (-) denotes the diagonal element of the extraction matrix, PtA total power limit for the transmitted signal;
Figure FDA0003015828610000024
wherein: ruvThe element of the u th row and the v th column in the R is represented, and the condition (R) is derived from a basic inequality.
3. The MIMO-OFDM based radar communication integrated waveform design method of claim 1, wherein: in step 3, the total number of subcarriers for carrying information by the OFDM is
Figure FDA0003015828610000025
Wherein: n is a radical oftThe number of antennas at the transmitting end; specific method for filling digital modulation symbolThe method comprises the following steps: for the s sub-carrier carrying information of the ith antenna, if
Figure FDA0003015828610000026
This location is called the parent node, which carries the QPSK symbol and the second node
Figure FDA0003015828610000027
QPSK symbols carried by the s-th information-bearing subcarrier of each antenna are the same, and the positions are called as subnodes; if a certain position is a father node, sequentially taking out a modulation symbol and filling the modulation symbol in the position; if a certain position is a child node, tracing back the modulation symbol filling of the parent node, and if the non-parent node and the non-child node at the certain position are not the child node, sequentially taking out one modulation symbol to fill in the position.
4. The MIMO-OFDM based radar communication integrated waveform design method of claim 3, wherein: in step 3, the specific method for assigning the weight is as follows: in the first step, if the s-th information-bearing subcarrier of the ith antenna is a parent node, the weight is given
Figure FDA0003015828610000031
βms＝conj(βis) Wherein:
Figure FDA0003015828610000032
i.e. the antenna position, N, at which the child node is locatedcTotal number of information-carrying sub-carriers, P, for each antennaxFor the mean symbol power of the modulated signal, conj (-) means the conjugation, βisFor the weight at the s-th information-carrying subcarrier of the ith antenna, βmsIs the weight at the s-th information-bearing subcarrier of the m-th antenna, RimIs the value of R at row i, column m; if a position is not a father node or a child node, marking the position and temporarily setting the weight to be zero; second, calculating the total power P of the emission symbols corresponding to the current weight matrix betanWhether or not to equal the total power limit PtIf not, multiplying all values of the beta matrix by the scale factor mu,
Figure FDA0003015828610000033
5. the MIMO-OFDM based radar communication integrated waveform design method of claim 4, wherein: in the step 4, the specific method for uniformly distributing the weights includes: all the weights at all the marked positions obtained in the step 3 are changed into
Figure FDA0003015828610000034
Wherein: pΔIs the difference in step 4.
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