CN104678395B - MIMO-OFDM radar imaging method based on cyclic prefix - Google Patents

Abstract

The invention discloses an MIMO-OFDM radar imaging method based on cyclic prefix, and mainly aims to solve the problem of distance unit interference in the prior art. The MIMO-OFDM radar imaging method comprises the following steps: designing a Zadoff-Chu sequence based on cyclic shift as discrete time domain waveforms transmitted from different antennas of discrete time domain; inserting the cyclic prefix into the heads of the discrete time domain waveforms; performing digital/analog conversion on signals with the cyclic prefix, and adding radar carrier frequency so as to generate transmission signals of the transmitting antennas; dividing full wide swath into a plurality of sub-wide swaths through a plurality of spatial filters, thereby obtaining baseband discrete echo signals of the sub-wide swaths, and performing distance reconstruction free of distance unit interference for the signals, thereby achieving imaging. By adopting the MIMO-OFDM radar imaging method, the influence of distance unit interference can be avoided, distance images can be relatively effectively reconstructed on the premise that the high distance resolution and spatial diversity are ensured, and the MIMO-OFDM radar imaging method can be applied to the detecting and imaging process of a synthetic aperture radar.

Description

MIMO-OFDM radar imaging method based on cyclic prefix

Technical Field

The invention belongs to the technical field of radars, and particularly relates to an imaging method of a multi-input multi-output orthogonal frequency division multiplexing MIMO-OFDM synthetic aperture radar SAR.

Background

With the development of modern radar technology, MIMO radar has been widely researched and becomes an important research direction of modern radar systems. The diversity MIMO radar has space diversity and can effectively improve the space resolution. However, in order to ensure spatial diversity of the diversity MIMO radar, the signal waveforms transmitted by the multiple transmit antennas must be orthogonal to each other, which is generally difficult to design for a synthetic aperture radar with high range and azimuth resolution. Therefore, how to design the waveform of the MIMO SAR system is a key issue of the current research.

In the existing waveform design of the MIMO SAR system, in order to ensure space diversity, frequency bands which are not overlapped with each other are adopted among a plurality of waveforms, and the method can cause distance ambiguity due to the reduction of distance resolution. If the distance resolution is not reduced, the same frequency band is needed to be adopted among a plurality of waveforms, but the time domain delay forms of different waveforms are not mutually orthogonal, and the full space diversity cannot be obtained for the MIMO SAR system.

Orthogonal frequency division multiplexing, OFDM, waveforms have been used in SAR systems in recent years. In order to obtain a set of orthogonal OFDM waveforms suitable for MIMO SAR imaging, researchers have proposed an interactive framework structure in the frequency domain that divides the effective bandwidth into several sub-bands that do not overlap with each other. However, these SAR imaging methods all use a conventional matched filter, which may generate inter-range-unit interference IRCI, affecting the imaging performance.

Disclosure of Invention

The invention aims to provide a MIMO-OFDM radar imaging method based on cyclic prefix aiming at the defects of the prior art, so as to avoid the generation of interference IRCI between distance units and improve the imaging performance.

In order to achieve the purpose, the technical scheme of the invention comprises the following steps:

(1) according to the requirement that the MIMO radar needs to transmit orthogonal waveforms, a cyclic shift Zadoff-Chu sequence is designed to serve as a discrete time domain waveform s transmitted by each antenna of the MIMO-OFDM radar_m(n)，m＝1,…,M_TN is 0, …, N-1, wherein M_TThe number of transmitting antennas is N, and the number of sub-bands is N;

(2) discrete time domain waveform s at each transmit antenna_m(n) inserting a cyclic prefix with the length of L at the beginning of the signal to obtain a signal after the cyclic prefix is inserted:

(3) for the signal u inserted with the cyclic prefix_m(n) performing digital-to-analog conversion to obtain a continuous-time signal u_m(t) and in u_m(t) adding the radar carrier frequency f_cGenerating a transmission signal of each transmission antenna;

(4) the receiving array antenna divides the full mapping band into Q sub mapping bands through a plurality of spatial filters, and obtains a baseband discrete echo signal r of each sub mapping band_p(n)，0≤n<N+L_p+ L-1, 1. ltoreq. p. ltoreq.Q, where L_pThe number of distance units of the pth sub-swath;

(5) for each sub mapping band, the base band discrete echo signal r_p(n) reconstructing the distance without interference between distance units to obtain the RCS coefficient of the radar scattering sectional area of each antenna full surveying and mapping band as follows: h is_m(n)＝[h_1,m(n),…,h_p,m(n),…,h_Q,m(n)]，m＝1,…,M_T，0≤n<L_pThe RCS coefficient is the distance of the radarAnd (4) separating the image.

Compared with the prior art, the invention has the following advantages:

firstly, because the cyclic prefix is inserted into the transmitted OFDM signal and a new distance reconstruction algorithm is adopted in the echo processing, the influence of IRCI on the imaging performance can be avoided;

secondly, the invention adopts the Zadoff-Chu sequence as the transmitting pulse signal of the MIMO-OFDM radar, a plurality of transmitting waveforms adopt the same frequency band, and the peak-to-side lobe ratio of the transmitting waveforms is 1, thereby ensuring high distance resolution and transmitting power efficiency, and ensuring space diversity because the transmitting waveforms are mutually and completely orthogonal.

Drawings

FIG. 1 is a general flow chart of an implementation of the present invention;

FIG. 2 is a schematic diagram of a MIMO-OFDM SAR signal transmission process in the present invention;

FIG. 3 is a schematic diagram of a MIMO-OFDM SAR signal receiving process using a spatial filter according to the present invention;

FIG. 4 is a schematic diagram of distance reconstruction in the present invention;

FIG. 5 is a graph of imaging performance using the method of the present invention;

fig. 6 is a graph comparing the imaging performance of the conventional MIMO chirp waveform and OFDM chirp waveform in a noise-free environment by using the method of the present invention;

fig. 7 is a diagram of the reconstructed range profile rms error using the method of the present invention and using the conventional MIMO chirp method.

Detailed Description

Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

Referring to fig. 1, the imaging of the present invention is divided into three parts: a first part for generating the transmitting signals of each antenna, wherein the generation process is as shown in figure 2; a second part, dividing the full mapping band into a plurality of sub mapping bands at the receiving end to obtain baseband discrete echo signals of each sub mapping band, as shown in fig. 3; and in the third part, distance reconstruction without interference between distance units is carried out on the baseband discrete echo signals, as shown in figure 4.

The first part generates a transmission signal for each antenna.

As shown in fig. 2, the implementation steps of this part are as follows:

step 1, according to the requirement that the MIMO radar needs to transmit orthogonal waveforms, a Zadoff-Chu sequence based on cyclic shift is designed to be used as discrete time domain waveforms transmitted by each antenna of the MIMO-OFDM.

1a) The frequency domain waveform of the first antenna is generated by using a Zadoff-Chu sequence:

wherein N is the number of sub-bands, μ is an integer less than and coprime to N,<N>₂denotes the remainder of N divided by 2, j denotes the imaginary unit;

1b) to S₁(k) Performing N-point Inverse Discrete Fourier Transform (IDFT) to obtain S₁(k) The discrete time domain waveform of (a) is:

wherein (·)^*Denotes taking the complex conjugate, s₁(0) The time domain waveform at time 0 is shown, N being 0, …, N-1. It can be seen that for each n there is s₁(n)|＝|s₁(0) Where | represents a modulus value, i.e. s₁(n) is a constant modulus value sequence;

1c) the frequency domain waveform for the second antenna is designed as:

wherein β is exp (-j pi. mu.N/4), S₁(<k-N/2>_N)＝βS₁(k) exp (j π k) is S with a displacement of N/2₁(k) The cyclic shift expression of (c). According to the zero period correlation characteristic of the Zadoff-Chu sequence, S₁(k) And S₂(k) Are orthogonal. The advantage of discrete frequency domain orthogonality is that it is not affected by time delays in the time domain, while discrete time domain orthogonality is delay sensitive;

1d) to S₂(k) Performing N-point IDFT to obtain S₂(k) The discrete time domain waveform of (a) is:

s₂(n)＝β^*s₁(n)exp(jπn)，n＝0,…,N-1，

s₂(n) is also a constant modulus sequence;

1e) s is obtained by the design method used in steps 1c) and 1d)_m(k)，m＝2,3,…,M_TThe discrete time domain waveform of (a) is:

s_m(n)＝β^*s_m-1(n)exp(jπn)，m＝2,3,…,M_T，n＝0,…,N-1，

wherein M is_TIs the number of transmitting antennas. s_mAnd (n) are constant modulus value sequences.

Step 2, discrete time domain waveform s of each transmitting antenna_m(n) inserting a cyclic prefix with the length of L at the beginning of the signal to obtain a signal after the cyclic prefix is inserted:

the length L of the cyclic prefix should be at least equal to the maximum range bin number of one sub-swath, so that range side lobes can be suppressed.

Step 3, for the signal u inserted with the cyclic prefix_m(n) performing digital-to-analog conversion to obtain a continuous-time signal u_m(t) and in u_m(t) adding the radar carrier frequency f_cAnd generating a transmission signal of each transmission antenna.

And a second part, dividing the full mapping band into a plurality of sub mapping bands at a receiving end to obtain baseband discrete echo signals of each sub mapping band.

As shown in fig. 3, the implementation steps of this part are as follows:

and 4, dividing the full mapping band into Q sub mapping bands by the receiving array antenna through a plurality of spatial filters, and obtaining baseband discrete echo signals of the sub mapping bands.

4a) The receiving array antenna divides the full mapping band into Q sub mapping bands through a plurality of spatial filters, and the maximum distance units L of all the sub mapping bands_oSatisfy L_o≤NM_TWherein L is_o＝max(L₁,…,L_p,…,L_Q) Max (. cndot.) denotes the maximum value, L_pThe number of distance units for the pth sub-swath, and the cyclic prefix length L of each transmitted OFDM waveform_o；

4b) Sampling the echo signal by analog/digital conversion with a sampling frequency f_sB, where B is the bandwidth of the transmitted waveform, Δ f is the frequency difference between two adjacent sub-carrier frequencies, and the baseband discrete echo signal of the pth sub-swath is obtained as:

wherein h is_p,m(l)＝g_p(l)h_m(l)，Represents the p-th spatial filter response, rect (-) represents a rectangular window function, h_m(l) And (v) represents the radar scattering cross section RCS coefficient of the l-th distance unit corresponding to the m-th emission waveform, and v (n) represents the noise of the n-th sampling point. g_p(l) At intervals ofThe internal value is 1, and the other values are 0, g_p(l) If the sidelobe of the actual spatial filter is lower than-35 dB, the influence of the noise v (n) on the imaging performance is larger than that of the non-ideal spatial filter, and g is adopted at the moment_p(l) Is reasonable.

And a third part, performing distance reconstruction without interference between distance units on the baseband discrete echo signals.

As shown in fig. 4, the implementation steps of this part are as follows:

step 5, the baseband discrete echo signal r of each sub mapping band_p(n) distance reconstruction without interference among distance units is carried out to obtain the RCS coefficient of the radar scattering cross section of each antenna full surveying and mapping band.

5a) From r_pStarting to sample N points at the L-th sampling point in (N) to obtain a removed r_pTime domain signal after cyclic prefix portion in (n):

5b) to z_p(N) performing N-point Discrete Fourier Transform (DFT) to obtain a frequency domain signal corresponding to the time domain signal:

wherein S is_m(k) And V(k) Are respectively s_mN-point DFTs of (N) and v (N + L);

is thatThe N-point DFT of (1),

5c) using frequency-domain waveforms S transmitted by the antennas_m(k)，m＝1,…,M_TTo Z_p(k) Performing discrete frequency domain matched filtering to obtain a result after matched filtering:

wherein,

5d) for Y_p,m(k) And (3) carrying out N-point discrete inverse Fourier transform (IDFT) on two sides to obtain an original sub-swath RCS coefficient as follows:

5e) the RCS coefficient h of each original sub mapping band_p,m(n) combining into a vector to obtain the RCS coefficient of the radar scattering sectional area of each antenna full surveying and mapping band as follows:

h_m(n)＝[h_1,m(n),…,h_p,m(n),…,h_Q,m(n)]，m＝1,…,M_T，0≤n<L_p，

the RCS coefficient is the range profile of the radar.

The effect of the invention is further illustrated by the following simulation experiment:

1. simulation conditions are as follows:

the simulation experiment adopts an optimal spatial filter, namely an antenna is ideal, the angle and distance unit of the target is completely contained, and the sidelobe signal is inhibited. Transmitting antenna is M_T2, the number of sub-bands is N1024. Both channels had 8 strong scatter points, which were randomly generated. The SNR before range reconstruction is 0dB, where SNR is defined as the ratio of the power of the strongest scattering point to the receiver noise power. The carrier frequency and the signal bandwidth of the MIMO radar are respectively 6GHz and 100 MHz. Maximum distance unit number L of all sub-swaths₀Is 200, and satisfies less than N/2. The length L of the cyclic prefix is 200. The amplitudes of all scattering points in the swath are subject to a uniform distribution and the maximum amplitudes of the scattering points are normalized.

2. Simulation content:

simulation 1, adopting the method of the present invention to reconstruct the range profile of two transmitting antennas under the noise-free and noise-containing conditions, the result is shown in fig. 5, wherein fig. 5(a) and 5(b) are the range profile reconstruction results of two channels under the noise-free condition, respectively, and fig. 5(c) and 5(d) are the range profile reconstruction results of two channels under the noise-containing condition;

simulation 2, comparing the imaging performance of the method with that of the conventional MIMO chirp waveform and OFDM chirp waveform in a noise-free environment, and obtaining a result as fig. 6, where fig. 6(a) and 6(b) are distance images reconstructed by the method of the present invention for two channels, fig. 6(c) and 6(d) are reconstructed distance images obtained by the conventional MIMO chirp waveform for the two channels, and fig. 6(c) and 6(d) are reconstructed distance images obtained by the conventional OFDM chirp waveform for the two channels, respectively;

simulation 3, the root mean square error RMSE of the reconstructed range profile of the channel 1 is calculated by using the method of the present invention and the conventional MIMO chirp method, and the result is shown in fig. 7.

3. And (3) simulation result analysis:

as can be seen from fig. 5(a) and 5(b), the range images of both channels can be completely reconstructed without noise.

As can be seen from fig. 5(c) and 5(d), the distance reconstruction method of the present invention has good imaging performance in a noisy environment without IRCI.

As can be seen from fig. 6(a) and 6(b), the distance image can be completely reconstructed using the method of the present invention because the scattering points between different range bins in the method of the present invention have no IRCI.

As can be seen from fig. 6(c), 6(d), 6(e) and 6(f), the reconstructed range images obtained by using the conventional MIMO chirp waveform and OFDM chirp waveform have inaccurate peak amplitudes and invisible weak scattering points, which both impair the performance of the range images, because neither method is IRCI-free, so that there is interaction between the side lobes and the main lobe of the adjacent spatial scattering points.

As can be seen from fig. 7, the RMSE for reconstructing the range profile using the method of the present invention decreases with increasing SNR until the RMSE decreases to the minimum error value, whereas the RMSE for reconstructing the range profile using the conventional MIMO chirp method does not decrease with increasing SNR when the SNR is large to a certain extent. This is because the method of the present invention is IRCI-free, while the conventional MIMO chirp method has IRCI, the interaction between the side lobe and the main lobe of the adjacent spatial scattering point exists, the reconstructed range image has false peaks, and some weak scattering points are submerged.

Claims (4)

1. A MIMO-OFDM radar imaging method based on cyclic prefix includes the following steps:

(1) according to the requirement that the MIMO radar needs to transmit orthogonal waveforms, a cyclic shift Zadoff-Chu sequence is designed to serve as a discrete time domain waveform s transmitted by each antenna of the MIMO-OFDM radar_m(n)，m＝1,…,M_TN is 0, …, N-1, wherein M_TThe number of transmitting antennas is N, and the number of sub-bands is N;

(2) discrete time domain waveform s at each transmit antenna_m(n) inserting a cyclic prefix of length L at the beginning of the sequence to obtain an insertionSignal after cyclic prefix:

$u_m\left(n\right)=\left\{\begin{array}{cc}{s}_m(n+N-L),& 0\&le;n<L\\ s_m(n-L),& L\&le;n<L+N-1\end{array}\right.;$

(3) for the signal u inserted with the cyclic prefix_m(n) performing digital-to-analog conversion to obtain a continuous-time signal u_m(t) and in u_m(t) adding the radar carrier frequency f_cGenerating a transmission signal of each transmission antenna;

(4) receiving arrayThe antenna divides the full mapping band into Q sub mapping bands through a plurality of spatial filters, and obtains a baseband discrete echo signal r of each sub mapping band_p(n)，0≤n<N+L_p+ L-1, 1. ltoreq. p. ltoreq.Q, where L_pThe number of distance units of the pth sub-swath;

(5) for each sub mapping band, the base band discrete echo signal r_p(n) reconstructing the distance without interference between distance units to obtain the RCS coefficient of the radar scattering sectional area of each antenna full surveying and mapping band as follows: h is_m(n)＝[h_1,m(n),…,h_p,m(n),…,h_Q,m(n)]，m＝1,…,M_T，0≤n<L_pAnd the RCS coefficient is the range profile of the radar.

2. The method of claim 1, wherein the designing of step (1) is based on a cyclically shifted Zadoff-Chu sequence as discrete time domain waveforms s transmitted by antennas of the MIMO-OFDM radar_m(n) the method comprises the following steps:

1a) the frequency domain waveform of the first antenna is generated by using a Zadoff-Chu sequence:

$S_1\left(k\right)=\exp \left(\frac{-j\mathrm{\&pi;}\mathrm{\&mu;}k(k+<N{>}_2)}{N}\right),k=0,...,N-1$

wherein μ is oneAn integer less than and coprime to N,<N>₂denotes the remainder of N divided by 2, j denotes the imaginary unit;

1b) to S₁(k) Performing N-point Inverse Discrete Fourier Transform (IDFT) to obtain S₁(k) The discrete time domain waveform of (a) is:

$\begin{array}{c}{s}_1\left(n\right)=\frac{1}{\sqrt{N}}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{S}_1\left(k\right)\exp \left(\frac{j2\mathrm{\&pi;}nk}{N}\right)\\ =S_1^{*}\left({\mathrm{\&mu;}}^{-1}n\right)\exp \left(\frac{-j2\mathrm{\&pi;}n<N{>}_2}{N}\right)s_1\left(0\right)\end{array},$

wherein (·)^*Denotes taking the complex conjugate, s₁(0) A time domain waveform representing time 0, N being 0, …, N-1;

1c) the frequency domain waveform for the second antenna is designed as:

$S_2\left(k\right)={\mathrm{\&beta;}}^{*}{S}_1(<k-\frac{N}{2}{>}_N)=S_1\left(k\right)\exp \left(j\mathrm{\&pi;}k\right),$

wherein β is exp (-j pi. mu.N/4), S₁(<k-N/2>_N)＝βS₁(k) exp (j π k) is S with a displacement of N/2₁(k) The cyclic shift expression of (a);

1d) to S₂(k) Performing N-point IDFT to obtain S₂(k) The discrete time domain waveform of (a) is:

s₂(n)＝β^*s₁(n)exp(jπn)，n＝0,…,N-1；

1e) s is obtained by the design method used in steps 1c) and 1d)_m(k) The discrete time domain waveform of (a) is:

s_m(n)＝β^*s_m-1(n)exp(jπn)，m＝2,3,…,M_T，n＝0,…,N-1。

3. the method according to claim 1, wherein the receiving array antenna of step (4) divides the full mapping band into Q sub mapping bands by a plurality of spatial filters, and obtains the baseband discrete echo signal r of each sub mapping band_p(n) the method comprises the following steps:

4a) the receiving array antenna divides the full mapping band into Q sub mapping bands through a plurality of spatial filters, and the maximum distance units L of all the sub mapping bands_oSatisfy L_o≤N/M_TWherein L is_o＝max(L₁,…,L_p,…,L_Q) Max (. cndot.) denotes the maximum value, L_pThe number of distance units for the pth sub-swath, and the cyclic prefix length L of each transmitted OFDM waveform_o；

4b) Sampling the echo signal by adopting analog/digital conversion to obtain a baseband discrete echo signal of the pth sub mapping band as follows:

$r_p\left(n\right)=\underset{m=1}{\overset{M_T}{\&Sigma;}}\underset{l=0}{\overset{L_p-1}{\&Sigma;}}{h}_{p,m}\left(l\right)u_m(n-l)+v\left(n\right),0\&le;n<N+L_p+L-1,1\&le;p\&le;Q,$

wherein h is_p,m(l)＝g_p(l)h_m(l)，Represents the p-th spatial filter response, rect (-) represents a rectangular window function, h_m(l) And (v) represents the radar scattering cross section RCS coefficient of the l-th distance unit corresponding to the m-th emission waveform, and v (n) represents the noise of the n-th sampling point.

4. The method of claim 1, wherein the baseband discrete echo signal r for each sub-swath of step (5)_p(n) performing distance reconstruction without interference between distance units to obtainRadar scattering sectional area RCS coefficient h of each antenna full surveying and mapping zone_m(n) the method comprises the following steps:

5a) from r_pStarting to sample N points at the L-th sampling point in (N) to obtain a removed r_pTime domain signal after cyclic prefix portion in (n):

$\begin{array}{c}{z}_p\left(n\right)=r_p\left(n+L\right)\\ =\underset{m=1}{\overset{M_T}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}{h}_{p,m}\left(l\right)u_m\left(n+L-l\right)+v\left(n+L\right)\\ =\underset{m=1}{\overset{M_T}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L_p-1}{\mathrm{\&Sigma;}}}{h}_{p,m}\left(l\right)s_m\left(n-l\right)+v\left(n+L\right)\end{array},0\&le;n<N;$

5b) to z_p(N) performing N-point Discrete Fourier Transform (DFT) to obtain a frequency domain signal corresponding to the time domain signal:

$Z_p\left(k\right)=\frac{1}{\sqrt{N}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{z}_p\left(n\right)\exp \left(\frac{-j2\mathrm{\&pi;}nk}{N}\right)=\sqrt{N}\underset{m=1}{\overset{M_T}{\mathrm{\&Sigma;}}}{H}_{p,m}\left(k\right)S_m\left(k\right)+V\left(k\right),$

wherein S is_m(k) And V (k) are each s_mN-point DFTs of (N) and v (N + L);

is thatThe N-point DFT of (1),

5c) using frequency-domain waveforms S transmitted by the antennas_m(k)，m＝1,…,M_TTo Z_p(k) Performing discrete frequency domain matched filtering to obtain a result after matched filtering:

$\begin{array}{c}{Y}_{p,m}\left(k\right)=\frac{1}{\sqrt{N}}{S}_m^{*}\left(k\right)Z_p\left(k\right)=S_m^{*}\left(k\right)\underset{i=1}{\overset{M_T}{\mathrm{\&Sigma;}}}{H}_{p,i}\left(k\right)S_i\left(k\right)+\frac{1}{\sqrt{N}}{S}_m^{*}\left(k\right)V\left(k\right)\\ =H_{p,m}\left(k\right)+S_m^{*}\left(k\right)\underset{i\&NotEqual;m}{\overset{M_T}{\underset{i=1}{\mathrm{\&Sigma;}}}}{H}_{p,i}\left(k\right)S_i\left(k\right)+{\stackrel{\&OverBar;}{V}}_m\left(k\right)\end{array},$

wherein,

5d) for Y_p,m(k) The two sides adopt N-point discrete inverse Fourier transform (IDFT) to obtain an original sub mapping band RCSThe coefficients are:

$h_{p,m}\left(n\right)=\frac{1}{\sqrt{N}}\underset{k=0}{\overset{N-1}{\&Sigma;}}{Y}_{p,m}\left(k\right)\exp \left(\frac{j2\mathrm{\&pi;}nk}{N}\right),0\&le;n<L_p,1\&le;p\&le;Q;$

5e) the RCS coefficient h of each original sub mapping band_p,m(n) combining into a vector to obtain the RCS coefficient of the radar scattering sectional area of each antenna full surveying and mapping band as follows:

h_m(n)＝[h_1,m(n),…,h_p,m(n),…,h_Q,m(n)]，m＝1,…,M_T，0≤n<L_p，

the RCS coefficient is the range profile of the radar.