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

Abstract

Translated fromChinese

本发明公开了一种基于MIMO‑OFDM的雷达通讯一体化波形设计方法，结合雷达的辐射特性，针对现有的雷达波形设计的辐射特性无法兼顾对通讯能量进行限制的问题，本方法使用凸优化方法获取最佳的雷达发射信号的自协方差矩阵，使其尽可能接近理想化的辐射特性谱。同时，本发明改进了现有的OFDM波形，在不同天线相应的子载波位置承载相同的的频域信号，并赋予它们不同的权重，使得不同天线发射的探测信号的统计相关性满足上述协方差矩阵。本发明可适用于多目标探测和多通讯目标服务，可根据不同场景灵活调整参数，具有良好的泛用性。

The invention discloses a radar communication integrated waveform design method based on MIMO-OFDM. Combined with the radiation characteristics of the radar, the radiation characteristics of the existing radar waveform design cannot take into account the problem of limiting the communication energy. The method uses convex optimization. The method obtains the best auto-covariance matrix of the radar transmit signal, making it as close as possible to the idealized radiation characteristic spectrum. At the same time, the present invention improves the existing OFDM waveform, carries the same frequency domain signals at the corresponding subcarrier positions of different antennas, and assigns them different weights, so that the statistical correlation of the probe signals transmitted by different antennas satisfies the above-mentioned covariance matrix. The invention can be applied to multi-target detection and multi-communication target service, can flexibly adjust parameters according to different scenarios, 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 thestep 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 thestep 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:

wherein min (. cndot.) is the minimum value, P (. theta.)_c)＝a^H(θ_c)Ra(θ_c) P is the radiation characteristic spectrum of the radar, theta_cAngle 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);

where p is the number of the detection target, θ_pAn 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 thestep 1 is obtained;

∑diag(R)＝P_tcondition (c)

Wherein: diag (-) denotes the diagonal element of the extraction matrix, P_tA total power limit for the transmitted signal;

wherein: r_uvThe 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

Wherein: n is a radical of_tThe 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

This location is called the parent node, which carries the QPSK symbol and the second node

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

β_ms＝conj(β_is) Wherein:

i.e. the antenna position, N, at which the child node is located_cTotal number of information-carrying sub-carriers, P, for each antenna_xFor the mean symbol power of the modulated signal, conj (-) means the conjugation, β_isFor the weight at the s-th information-carrying subcarrier of the ith antenna, β_msIs the weight at the s-th information-bearing subcarrier of the m-th antenna, R_imIs 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 beta_nWhether or not to equal the total power limit P_tIf not, multiplying all values of the beta matrix by the scale factor mu,

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

Wherein: p_ΔIs 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 embodiment_tThe 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 N_r64. In which the transmitting power of the radar is limited toP_r1, the maximum power limit allowed for reception by the communications receiver is P_lIf the channel gain is 1 at 0.3, the maximum power limit for the communication direction allowed by the transmitter to transmit is P_l。

Calculating a steering vector a (theta) of the radar by formula (1)

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,

for signals from Nth_tThe 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)＝a^H(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)…x_Nt(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 n_iThe calculation formula of (n) is:

wherein N is the length of the discrete inverse Fourier transform, the length including the virtual sub-carrier, X_i(k) For the k-th QPSK symbol at the ith antenna for OFDM modulation, beta_ikIs the weight at the kth subcarrier of the ith antenna.

The autocovariance matrix R of x (n) is specified as follows:

x (n) autocovariance matrix R, u row, v matrix element R_uvThe calculation method of (2) is as follows:

wherein x is_u(n) the u-th antenna sends out signal at n time, x_v(n) for the v-th antenna sending out signal at time n, X_u(k) For the kth QPSK symbol at the u antenna for OFDM modulation, X_s(l) For the l-th QPSK symbol at the s-th antenna for OFDM modulation, beta_ukFor the weight at the k information-bearing subcarrier of the u antenna, β_vlFor the weight at the l information-carrying subcarrier of the v antenna, β_slFor 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 time_t＝P_r-P_lWhen 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 P_t＝P_r-P_l。

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:

wherein min (. cndot.) is the minimum value, P (. theta.)_c)＝a^H(θ_c)Ra(θ_c) P is the radiation characteristic spectrum of the radar, theta_cAngle 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);

where p is the number of the detection target, θ_pAn 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 instep 1.

∑diag(R)＝P_tCondition (c)

Wherein: diag (-) denotes the diagonal element of the extraction matrix, P_tIs 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:

u, v diagonal elements R_uu、R_vvThe calculation formula of (2) is as follows:

in the formula: n is a radical of_cIs the number of sub-carriers actually carrying the information. Beta is a_ukFor the weight at the k information-bearing subcarrier of the u antenna, β_vkFor the weight at the kth information-bearing subcarrier of the vth antenna, denotes the conjugate.

As is apparent from the formula (6),

as can be seen from the basic inequality,

then

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 a_okFor the weight at the kth information-bearing subcarrier of the mth antenna,β_gkthe 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):

therefore, it is

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 embodiment_tThe specific method is as follows:

(1) determining the number of subcarriers actually carrying information

Taking the number N of discrete Fourier transform (i.e. the total number of OFDM sub-carriers, including virtual sub-carriers) as the nearest N_cPower 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

This position is the parent node carrying the QPSK symbol and the second node

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

Weight beta of the position of the corresponding child node_ms＝conj(β_is) Wherein

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 beta_nWhether or not to equal P_tIf not, multiplying all values of the beta matrix by the scale factor mu,

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 P_mThen P is_Δ＝P_l-P_m；

The total number of nodes marked in step 3 should be N_t(N_c-N_t+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

Is equally distributed to each mark position beta_markObtaining:

the total transmission power is P_t+P_ΔThe power value is necessarily less than the transmitting power limit of the radar, and is limited to P_rAnd 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 N_G(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:

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 max_δ(. 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 antenna_s(n) there are:

in the formula:

for the convolution symbols, h_is(n) is a time domain representation of the channel, z_is(n) is the channel noise and (n),

for transmitting signal x of ith antenna_i(n) multiplied by the value of the steering vector.

Is defined as equation 12, which has no meaning in itself,

is x_i(n) deriving y_s(n) an intermediate amount in the process.

The two sides of the equation are simultaneously used for the discrete Fourier transform of N2048

Wherein: y is_s(k)、

H_is(k)、Z_is(k) Are each the above-mentioned y_s(n)、

h_is(n)、z_is(n) fourier transform form.

Neglecting noise, writing into a matrix form, and obtaining:

noting that the channel matrix at the k point is H, the frequency domain at the k point is equalized by X^a(k) The formula of (1) is:

X^a(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 period^a(k) Then carrying out discrete Fourier transform to obtain x^a(n) according to formula (12), mixing x^aThe 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

Comprises the following steps:

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 a_i,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:

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 antenna_w,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)b^c(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 N_tX N transmitting signal matrix, the radar receiving array and the transmitting array using the same antenna, so that Y is N_tX N matrix of received signals, Z being N_tAn 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

min_w,ψ||w^*Y-ψ(θ)a^*(θ)X||² s.t.w^*b^c(θ)＝1 (20)

In the formula: w is N_tThe purpose of thex 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

In the formula:

for the observation data sample covariance matrix:

the optimization problem in equation (20) can be simplified as follows:

wherein

The optimization problem in equation (23) is given by the APES beamformer giving a weight vector estimate of

APES with formula (25) taken into formula (21) with easy ψ (θ) was estimated as

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)

Translated fromChinese

1.一种基于MIMO-OFDM的雷达通讯一体化波形设计方法，其特征在于，包括如下步骤：1. a radar communication integrated waveform design method based on MIMO-OFDM, is characterized in that, comprises the steps:步骤1，确定天线规模和数字调制方法，并计算雷达的导向矢量，计算当所有天线发送互不相关信号时的均匀雷达辐射特性谱；Step 1, determine the antenna scale and digital modulation method, calculate the steering vector of the radar, and calculate the uniform radar radiation characteristic spectrum when all antennas transmit mutually uncorrelated signals;步骤2：确定通讯目标的角度距离位置信息，限定雷达发射的总功率为定值，限定发射信号在探测方向的辐射特性谱与步骤1中的均匀雷达辐射特性谱之差的Frobenius范数小于某个阈值，通过凸优化方法，最小化通讯方向上天线的辐射功率，获得相应的发射信号自协方差矩阵；Step 2: Determine the angular distance position information of the communication target, limit the total power emitted by the radar to a fixed value, and limit the Frobenius norm of the difference between the radiation characteristic spectrum of the transmitted signal in the detection direction and the uniform radar radiation characteristic spectrum in step 1 to be less than a certain value. A threshold is used to minimize the radiated power of the antenna in the communication direction through the convex optimization method, and the corresponding auto-covariance matrix of the transmitted signal is obtained;步骤3：计算发射端所使用的承载信息的OFDM子载波的数量，并以此确定离散傅里叶变换点数，根据步骤2中得到的发射信号自协方差矩阵，将待发送的信号顺次填入不同天线的子载波中并赋予相应的权重，保证不同天线之间有且仅有一个子载波所承载的信号是相同的，每个天线未与其他天线有相关性的子载波承载的信号权重置为0并进行标记；Step 3: Calculate the number of OFDM subcarriers used by the transmitting end to carry information, and determine the number of discrete Fourier transform points. According to the auto-covariance matrix of the transmitted signal obtained in step 2, fill in the signals to be sent in sequence. Enter the sub-carriers of different antennas and assign corresponding weights to ensure that the signals carried by one and only one sub-carrier between different antennas are the same, and the weight of the signals carried by the sub-carriers that each antenna has no correlation with other antennas reset to 0 and mark;步骤4：用步骤2中得到的自协方差矩阵计算天线的辐射功率谱，找到此辐射功率谱在通讯方向拐点的3dB处的辐射功率值，并计算此值和通讯功率限制的差值，并将此能量差值均匀分配到步骤3中标记的子载波位置处；Step 4: Calculate the radiated power spectrum of the antenna with the autocovariance matrix obtained in step 2, find the radiated power value of the radiated power spectrum at 3dB of the inflection point of the communication direction, and calculate the difference between this value and the communication power limit, and Evenly distribute this energy difference to the subcarrier positions marked in step 3;步骤5：对排列好并加上权重的符号进行离散反傅里叶变换，得到OFDM符号，并对每个周期的OFDM符号加上CP窗；Step 5: Perform discrete inverse Fourier transform on the arranged and weighted symbols to obtain OFDM symbols, and add a CP window to the OFDM symbols of each cycle;步骤6：根据雷达的探测范围，计算出合适的发射信号脉冲宽度和脉冲周期，对于同一个天线，将多个相邻周期的OFDM符号顺次排列在一起组合成一个脉冲，持续时间等于脉冲宽度；等待一个脉冲周期后发送下一个由OFDM符号组成的脉冲信号，重复此操作直至所有OFDM信号发送完毕；Step 6: Calculate the appropriate pulse width and pulse period of the transmitted signal according to the detection range of the radar. For the same antenna, arrange the OFDM symbols of multiple adjacent periods in sequence to form a pulse with a duration equal to the pulse width ; After waiting for one pulse period, send the next pulse signal composed of OFDM symbols, and repeat this operation until all OFDM signals are sent;步骤7：设通讯信道已知，在通讯接收端，对接收到的信号进行同步；同步完成后去除CP端，并将相邻脉冲内的信号连接起来；对此信号频域均衡，将均衡后的信号除以步骤1中计算的导向矢量；Step 7: Assuming that the communication channel is known, at the communication receiving end, the received signal is synchronized; after the synchronization is completed, the CP end is removed, and the signals in the adjacent pulses are connected; the frequency domain of this signal is equalized, and the equalized The signal of is divided by the steering vector calculated in step 1;步骤8：在通讯接收端，对步骤7中的信号进行离散傅里叶变换，根据步骤3调制信号的填充顺序和步骤4中不同天线不同载波位置处的权重大小，对还原出来的调制信号进行最大似然估计；Step 8: At the communication receiving end, the discrete Fourier transform is performed on the signal in step 7, and according to the filling order of the modulated signal in step 3 and the weights at different carrier positions of different antennas in step 4, the restored modulated signal is processed. maximum likelihood estimation;步骤9：在雷达接收端，对接收到的信号进行同步，计算出探测信号从发射到接收所经历的时间，从而计算出探测目标与雷达之间的距离；对同步后的信号使用振幅相位估计获得复振幅谱，谱的极大值位置即为探测目标与天线阵形成的角度。Step 9: At the radar receiving end, synchronize the received signal, calculate the time elapsed from the transmission to the reception of the detection signal, and then calculate the distance between the detection target and the radar; use the amplitude phase estimation for the synchronized signal The complex amplitude spectrum is obtained, and the position of the maximum value of the spectrum is the angle formed by the detection target and the antenna array.2.根据权利要求1所述基于MIMO-OFDM的雷达通讯一体化波形设计方法，其特征在于：所述步骤2中，凸优化方法由Matlab凸优化工具箱CVX完成，此处的凸优化变量为发射信号x(n)的自协方差矩阵R，优化目标具体为：2. The integrated waveform design method for radar communication based on MIMO-OFDM according to claim 1, characterized in that: in the step 2, the convex optimization method is completed by the Matlab convex optimization toolbox CVX, and the convex optimization variable here is The auto-covariance matrix R of the transmitted signal x(n), the optimization objective is specifically:

式中，min(·)为求最小值，

P即雷达的辐射特性谱，θ_c为通讯目标所在的角度，a(θ_c)为雷达的导向矢量，上标H为共轭转置变换；In the formula, min( ) is the minimum value,

P is the radiation characteristic spectrum of the radar, θ_c is the angle of the communication target, a(θ_c ) is the steering vector of the radar, and the superscript H is the conjugate transpose transformation;限制条件具体为：The restrictions are specifically:条件①：R为半正定埃尔米特矩阵；Condition ①: R is a positive semi-definite Hermitian matrix;

其中，p为探测目标的序号，θ_p为雷达发送的探测信号的角度；L为步骤2中所述阈值，可人为设定；φ(θ_p)为步骤1中的均匀雷达辐射特性谱；Wherein, p is the sequence number of the detection target, θ_p is the angle of the detection signal sent by the radar; L is the threshold value described in step 2, which can be set manually; φ(θ_p ) is the uniform radar radiation characteristic spectrum in step 1;∑diag(R)＝P_t 条件③∑diag(R)=P_t condition③其中：diag(·)表示提取矩阵的对角线元素，P_t为发射信号的总功率限制；Where: diag( ) represents the diagonal elements of the extraction matrix, and P_t is the total power limit of the transmitted signal;

其中：R_uv表示R中第u行第v列个元素，条件④由基本不等式推导出。Among them: R_uv represents the element in the uth row and the vth column in R, and the condition ④ is derived from the basic inequality.3.根据权利要求1所述基于MIMO-OFDM的雷达通讯一体化波形设计方法，其特征在于：所述步骤3中，OFDM承载信息的子载波总数为

其中：N_t为发射端天线数量；填充数字调制符号的具体方法为：对于第i个天线的第s个承载信息的子载波而言，若

则此位置称为父节点，其搭载的QPSK符号与第

个天线的第s个承载信息的子载波搭载的QPSK符号相同，此位置称为子节点；若某位置为父节点，则顺次取出一个调制符号填入此位置；若某位置为子节点，则追溯其父节点的调制符号填入，若某位置非父节点也非子节点，则顺次取出一个调制符号填入此位置。3. The integrated waveform design method for radar communication based on MIMO-OFDM according to claim 1, characterized in that: in the step 3, the total number of sub-carriers of OFDM bearing information is

Among them: N_t is the number of antennas at the transmitting end; the specific method of filling digital modulation symbols is: for the s-th information-carrying sub-carrier of the i-th antenna, if

Then this position is called the parent node, and the QPSK symbol carried by it is the same as the first node.

The QPSK symbols carried by the s-th information-carrying subcarrier of each antenna are the same, and this position is called a child node; if a certain position is a parent node, a modulation symbol is taken out and filled in this position in turn; if a certain position is a child node, Then trace back the modulation symbol of its parent node and fill it in. If a certain position is neither a parent node nor a child node, then take out a modulation symbol and fill in this position in turn.4.根据权利要求3所述基于MIMO-OFDM的雷达通讯一体化波形设计方法，其特征在于：所述步骤3中，分配权重的具体方法为：第一步，若第i个天线的第s个承载信息的子载波是一个父节点，那么权重

β_ms＝conj(β_is)，其中：

即子节点所在的天线位置，N_c为每个天线的承载信息的子载波总数，P_x为调制信号的平均符号功率，conj(·)表示求共轭，β_is为第i个天线的第s个承载信息的子载波处的权重，β_ms是第m个天线的第s个承载信息的子载波处的权重，R_im为R在第i行第m列的值；若某位置非父节点也非子节点，标记这个位置并将此权重暂时置为零；第二步，计算当前的权重矩阵β所对应的发射符号总功率P_n是否等于总功率限制P_t，若不等则β矩阵所有值乘以比例因子μ，

4. The integrated waveform design method for radar communication based on MIMO-OFDM according to claim 3, characterized in that: in the step 3, the specific method for assigning weights is: the first step, if the s th of the i th antenna A subcarrier carrying information is a parent node, then the weight

β_ms = conj(β_is ), where:

That is, the antenna position where the child node is located, N_c is the total number of sub-carriers that carry information for each antenna, P_x is the average symbol power of the modulated signal, conj( ) represents the conjugation, and β_is the ith antenna. The weights at the s information-bearing subcarriers, β_ms is the weight at the s-th information-bearing subcarrier of the mth antenna, and_Rim is the value of R at the ith row and mth column; if a position is not the parent The node is also not a child node, mark this position and temporarily set the weight to zero; the second step is to calculate whether the total power P_n of the transmitted symbols corresponding to the current weight matrix β is equal to the total power limit P_t , if not, then β All values of the matrix are multiplied by the scale factor μ,

5.根据权利要求4所述基于MIMO-OFDM的雷达通讯一体化波形设计方法，其特征在于：所述步骤4中，均匀分配权重的具体方法为：将步骤3中得到的所有标记位置处的权重全部改为

其中：P_Δ为步骤4中所述差值。5. The integrated waveform design method for radar communication based on MIMO-OFDM according to claim 4, characterized in that: in the step 4, the specific method for evenly distributing the weights is: All weights are changed to

Where: P_Δ is the difference described in step 4.

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