CN112986924A - OFDM radar communication integrated range and speed fast super-resolution estimation method - Google Patents
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Abstract
The invention discloses a method for estimating the distance speed and the super resolution of OFDM radar communication integration, which comprises the following steps: constructing an OFDM radar communication integrated signal model, and inputting relevant parameters for the OFDM radar communication integrated signal model; carrying out communication information compensation on the OFDM radar communication integrated signal model to obtain a communication information compensation model; carrying out frequency smoothing processing on the communication information compensation model to obtain a target signal model of the distance and the speed to be estimated; and performing distance estimation and speed estimation on the target signal model based on a super-resolution method to obtain a distance estimation result and a speed estimation result with super-resolution. The invention utilizes the OFDM radar communication integrated waveform to carry out distance and speed super-resolution estimation, and has lower calculation complexity compared with the prior method under the condition of equal estimation precision.
Description
Technical Field
The invention belongs to the field of radar and communication interdisciplinary science, and particularly relates to a range speed fast super-resolution estimation method integrating OFDM radar communication.
Background
Orthogonal Frequency Division Multiplexing (OFDM) waveforms have been widely used in digital television broadcasting, digital video broadcasting, digital audio broadcasting, and Wireless Local Area Network (WLAN). In addition, OFDM has also attracted a great deal of attention in radar applications. Such as Synthetic Aperture Radar (SAR) imaging, Space-time adaptive Processing (STAP), Radar target parameter estimation, and Radar target detection. Therefore, it is reasonable to use the OFDM waveform as a radar communication integrated waveform. In addition, many scholars have conducted intensive research on OFDM radar communication integrated waveforms.
In the intelligent transportation system, the intelligent vehicles need to communicate with other vehicles, and at the same time, need to estimate their distances, speeds, and the like, in order to improve driving safety. Because the OFDM radar communication integrated waveform is the traditional OFDM communication waveform, the OFDM communication waveform is widely applied in practical application, and the communication function can be realized by utilizing the existing processing method. In contrast, the distance and speed of other vehicles cannot be estimated directly using the conventional radar parameter estimation method because the OFDM radar communication integrated waveform is different from the OFDM waveform in the radar. The OFDM radar waveform is generally a pulse waveform, and although researchers have studied the radar communication integration waveform of the pulse OFDM, it is found that the data transmission rate is low. On the other hand, the OFDM radar communication integrated waveform contains communication information, and each OFDM symbol is usually different, whereas the OFDM radar waveform does not need to transmit communication information, and each transmitted pulse is the same. Due to these differences, the range and speed estimation method of the OFDM radar cannot be directly applied to the radar communication integration system.
In order to estimate the distance and speed using an OFDM radar communication integrated waveform, c.sturm and w.wisebeck propose a method of dividing a received modulation symbol by a transmitted modulation symbol and then using Inverse Discrete Fourier Transform (IDFT) and Discrete Fourier Transform (DFT). In this method, the range resolution is determined by the signal bandwidth and the velocity resolution is determined by the Coherent Processing Interval (CPI). However, to improve distance and speed resolution, the signal bandwidth and CPI need to be increased, respectively. However, increasing the signal bandwidth increases the hardware implementation cost and the consumption of frequency resources, while increasing CPI decreases the update rate. In addition, the CPI may not be increased due to fluctuations in the target.
Disclosure of Invention
In order to estimate the distance and the speed by utilizing an OFDM radar communication integrated waveform, the invention provides a method for quickly estimating the distance and the speed based on OFDM radar communication integration.
The technical problem to be solved by the invention is realized by the following technical scheme:
an OFDM radar communication integrated range speed fast super-resolution estimation method comprises the following steps:
step A: constructing an OFDM radar communication integrated signal model, and inputting relevant parameters for the OFDM radar communication integrated signal model;
and B: carrying out communication information compensation on the OFDM radar communication integrated signal model to obtain a communication information compensation model;
and C: carrying out frequency smoothing processing on the communication information compensation model to obtain a target signal model of the distance and the speed to be estimated;
step D: and performing distance estimation and speed estimation on the target signal model based on a super-resolution method to obtain a distance estimation result and a speed estimation result with super-resolution.
In one embodiment, the communication information compensation model is expressed as:
wherein N istTo point target number, xiiIs the attenuation factor due to the propagation loss, scattering and radar cross-sectional area of the ith target, i is 0,1, …, Nt-1; Is a Gaussian noise vector; j is the imaginary symbol, e is the natural base number, Δ f is the subcarrier spacing, fcIs the carrier frequency, RiIs the distance of the ith target, viIs the relative velocity of the ith target, c is the signal propagation velocity; t issFor the length of a complete OFDM symbol, TgIs the length of the cyclic prefix CP in the complete OFDM symbol, Tp=NsTs,NsFor the number of complete OFDM symbols, NcIs the number of subcarriers; n is the number of valid OFDM symbols in the complete OFDM symbol, p is the number of pulses,the superscript T in the expression of (a) denotes a matrix transposition.
In one embodiment, the target signal model collects column vectors for the kth through (k + M-1) th received signals;
the expression of the target signal model is as follows;
In one embodiment, the step D includes:
step D3: computing the covariance matrix estimateTo obtain a signal subspace Us(ii) a The signal subspace UsTo be estimated from said covariance matrixObtained NtThe characteristic vector corresponding to the maximum characteristic value is formed; the signal subspace UsIs one MNp×NtOrder matrix, NpIs the number of pulses;
step D4: constructing a selection matrix;
step D5: based on the signal subspace UsAnd the selection matrix, calculate the distance-related eigenvalue decomposition and velocity-related eigenvalue decomposition;
step D6: a distance estimation result is computed based on the distance-related eigenvalue decomposition and a velocity estimation result is computed based on the velocity-related eigenvalue decomposition.
In one embodiment, step D4 includes:
constructing a selection matrix J, selecting the matrix JRAnd a selection matrix Jv;
Wherein,nI0=[In,0n×1];0Im=[0m×1,Im],0m×nrepresents an m × n zero matrix, ImDenotes an m × m identity matrix, InRepresenting an n x n identity matrix.
In one embodiment, step D5 includes:
Step E5-3: computingEigenvalue decomposition G of-1ΛRG, decomposing as a distance-dependent characteristic value, and calculatingEigenvalue decomposition G of-1ΛvG, decomposing as a speed-related characteristic value;
wherein,the superscript H of (a) represents the matrix transposition conjugate; dRAnd DvAre all diagonal matrices;
In one embodiment, step D6 includes:
step E6-1: calculating a distance estimation result using a distance estimation formula based on the distance-dependent eigenvalue decomposition
Step E6-2: calculating a velocity estimation result using a velocity estimation formula based on the velocity-related eigenvalue decomposition
The distance estimation formula is as follows:
the velocity estimation formula is:
where angle () denotes the angle of a complex scalar,is ΛRThe (c) th element of (a),is ΛvThe ith element in (1).
In one embodiment, the length T ═ T of the effective OFDM symbols-TgSatisfy the requirement ofWherein,is the maximum detectable distance.
In one embodiment, the length T of the pulsepSatisfies the following conditions:
According to the OFDM radar communication integrated distance and speed fast super-resolution estimation method, the interference of communication information on distance and speed estimation is eliminated through communication information compensation; through frequency smoothing, the correlation among the received signals is reduced; moreover, distance estimation and speed estimation are carried out on the target signal model subjected to frequency smoothing processing based on a super-resolution method, and a translation invariance structure of the signal model in a frequency domain and a pulse domain is utilized; thus, the present invention can improve the resolution of distance and velocity estimation without increasing the signal bandwidth and CPI. Moreover, the method has lower calculation complexity under the condition of equal estimation accuracy.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic flow chart of a method for fast super-resolution estimation of range and speed integrated with OFDM radar communication according to an embodiment of the present invention;
FIGS. 2(a) and 2(b) show waveforms of an OFDM radar communication integration signal utilized by embodiments of the present invention;
FIGS. 3(a), 3(b), 3(c) and 3(d) illustrate the distance and velocity estimation comparison of an embodiment of the present invention to a prior method;
FIGS. 4(a) and 4(b) show the results of a resolution comparison of the present invention with a prior method;
fig. 5(a) and 5(b) show the rms error versus signal-to-noise ratio for the distance and velocity estimates of the present invention versus the prior method.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
In order to estimate the distance and the speed by utilizing an OFDM radar communication integrated waveform, an embodiment of the present invention provides an OFDM radar communication integrated distance and speed fast super-resolution estimation method, which is shown in fig. 1 and includes the following steps:
step A: and constructing an OFDM radar communication integrated signal model, and inputting relevant parameters for the OFDM radar communication integrated signal model.
In the embodiment of the present invention, the used OFDM radar communication integrated waveform is shown in fig. 2(a), and the OFDM radar communication integrated waveform is composed of a plurality of complete OFDM symbols. As shown in fig. 2(b), each complete OFDM symbol is composed of an effective OFDM symbol and a Cyclic Prefix (CP), and the CP is a repetition of an end portion of the effective OFDM symbol. Each complete OFDM symbol may contain different communication information, with a length TsThe length of CP contained therein is TgThe length of the effective OFDM symbol is T, T is equal toΔ f is the subcarrier spacing. As can be seen from FIG. 2(b), Ts=T+Tg。
Firstly, from NsNpThe baseband of the OFDM radar communication integrated waveform composed of the OFDM symbols can be expressed as:
wherein,introduced by CP, NsFor the number of complete OFDM symbols, NpIs the number of pulses; t isp=NsTsIs represented by NsLength of one complete OFDM symbol, NcIs the number of subcarriers, rect [ T/T ]s]Is a rectangular window function, when T is more than or equal to 0 and less than TsIts value is equal to 1; for T is more than or equal to 0 and less than Ts,The communication information modulated on the mth subcarrier, the nth OFDM symbol, and the pth pulse is represented. Wherein, thetam,n,pIs the m-th subcarrier, the n-th OFDM symbolThe sign and the information phase on the p-th pulse, j is the imaginary sign, e is the natural base number, and the rest of the parameters can be referred to above.
Further, based on the baseband expression, the finally transmitted narrowband OFDM radar communication integrated waveform may be represented as:
wherein f iscIs the carrier frequency, j is the imaginary sign, and the remaining parameters are as described above.
Assuming a sampling frequency fs=NcΔ f, i.e. obtaining N-N from each valid OFDM symbolcTime samples of (a). After removing the CP, the CP is expressed by the equation Δ t 1/(N)cΔf)=T/NcThen, the received signal of the p-th pulse, the n-th OFDM symbol and the k-th time sample can be represented as:
wherein N istIs the point target number; in an actual intelligent traffic system, the targets are vehicles, namely the number of point targets is the number of vehicles; the distance of the ith target is RiThe relative velocity of the i-th target is vi,i=0,1,…,Nt1, c is the signal propagation speed, n (t) represents noise, ξiIs the attenuation factor due to propagation loss, scattering and radar cross-sectional area of the ith target;substituting t in the formula by (k delta t + nT)s+pTp) The last term of the above formula (3) can be obtainedk is 0,1, …, N-1, and the rest of the parameters can be referred to above.
And (3) is the signal model of the OFDM radar communication integration constructed in the step a.
Then, the model is input with relevant parameters including Nt、Ns、Np、NcAnd M, etc. Where M is the number of subcarriers.
And B: and carrying out communication information compensation on the OFDM radar communication integrated signal model to obtain a communication information compensation model.
Specifically, the communication information compensation is performed on the OFDM radar communication integrated signal model shown in the above formula (3) to obtain a received signal vectorObtaining a communication information compensation model; the expression of the communication information compensation model is as follows:
wherein, is a Gaussian noise vector; n is the number of valid OFDM symbols in the complete OFDM symbol, p is the number of pulses,the superscript T in the expression of (a) denotes the matrix transpose, and the remaining parameters can be referred to above.
And C: and carrying out frequency smoothing treatment on the communication information compensation model to obtain a target signal model of the distance and the speed to be estimated.
Here, the frequency smoothing process is performed on the communication information compensation model, and the obtained target signal model of the distance and the speed to be estimated may be represented as:
Step D: and performing distance estimation and speed estimation on the target signal model based on a super-resolution method to obtain a distance estimation result and a speed estimation result with super-resolution.
Specifically, the step D may include a plurality of sub-steps as follows:
Step D3: computing covariance matrix estimatesTo obtain a signal subspace Us(ii) a The signal subspace UsCorresponding covariance matrix estimates are collectedN of (A)tA feature vector of the largest feature value; the signal subspace UsIs one MNp×NtOrder matrix, NpIs the number of pulses.
Step D4: a selection matrix is constructed.
Specifically, a selection matrix J is constructed and constructedRAnd a selection matrix Jv;
Wherein,nI0=[In,0n×1];0Im=[0m×1,Im],0m×nrepresents an m × n zero matrix, ImDenotes an m × m identity matrix, InRepresenting an n x n identity matrix.
It will be appreciated that in selecting the expression of matrix J, the sign of the kronecker product is evaluatedTaking N from the left and right sides N respectivelyp-1 and M-1; in the selection matrix JRIn the expression ofLeft N is Np-1, inTaking M-1 as the right M; in the selection matrix JvIn the expression ofLeft m is Np-1, inThe right M is M-1.
Step D5: based on signal subspace UsAnd selecting a matrix, calculating a distance-related eigenvalue decomposition and a velocity-related eigenvalue decomposition.
Specifically, the step D5 may include the following sub-steps:
Step D5-3: computingEigenvalue decomposition G of-1ΛRG, decomposing as a distance-dependent characteristic value, and calculatingEigenvalue decomposition G of-1ΛvG, as a velocity-related eigenvalue decomposition.
Wherein,the superscript H of (1) represents matrix conjugate transpose; dRAnd DvAre all diagonal matrices;
Step D6: a distance estimation result is computed based on the distance-related eigenvalue decomposition, and a velocity estimation result is computed based on the velocity-related eigenvalue decomposition.
Specifically, the step D6 may include the following sub-steps:
e6-1: calculating a distance estimation result using a distance estimation formula based on the distance-dependent eigenvalue decomposition
E6-2: calculating a velocity estimation result using a velocity estimation formula based on the velocity-related eigenvalue decomposition
In practical application, the step E6-1 and the step E6-2 are not executed sequentially, or executed in parallel.
Wherein, the distance estimation formula used in step E6-1 is:
the velocity estimation formula used in step E6-2 is:
where angle () represents a complex scalar quantityAnd scalar quantityThe angle of (a) is determined,is ΛRThe (c) th element of (a),is ΛvThe ith element in (1).
In addition, in the intelligent transportation system, in order to ensure that the distance estimation result is unambiguous, the length T of the effective OFDM symbol should satisfyWherein,is the maximum detectable distance. While the length T of each pulse is such as to ensure that the estimated velocity result is unambiguouspIt should satisfy:
wherein,is the maximum speed of the target, i.e. the maximum possible speed of the vehicle in the intelligent transportation system. It will be appreciated that the parameter N in this formulasAnd TgIs designed to meet the above maximum unambiguous distance and maximum unambiguous speed, or the parameter T and the parameter TpTogether satisfy the requirements of the formula.
According to the OFDM radar communication integrated distance and speed fast super-resolution estimation method provided by the embodiment of the invention, through communication information compensation, the interference of communication information on distance and speed estimation is eliminated; through frequency smoothing, the correlation among the received signals is reduced; moreover, distance estimation and speed estimation are carried out on the target signal model subjected to frequency smoothing processing based on a super-resolution method, and a translation invariance structure of the signal model in a frequency domain and a pulse domain is utilized; thus, the present invention can improve the resolution of distance and velocity estimation without increasing the signal bandwidth and CPI.
In addition, compared with the existing algorithm, the method and the device have lower calculation complexity under the condition of the same estimation precision. Specifically, in the embodiment of the present invention, the total computation complexity is about when expressed by using a large O-notation:
the total computational complexity of the existing R-V-MUSIC algorithm, when expressed using large O-notation, is approximately:
the total computational complexity of the existing R-V-Capon algorithm, when expressed using large O notation, is about:
wherein N isvIs the number of divided velocity grids in the R-V-MUSIC algorithm, NRIs the number of distance grids divided in the R-V-MUSIC algorithm. Due to NvNRTypically compared to MNpTherefore, compared with the existing R-V-MUSIC algorithm and R-V-Capon algorithm, the OFDM radar communication integrated range-speed fast super-resolution estimation method provided by the embodiment of the invention has much lower computational complexity.
In order to verify the effectiveness of the method for quickly estimating the range and speed of the OFDM radar communication integration provided by the embodiment of the invention, the beneficial effects of the embodiment of the invention are explained by adopting a simulation verification and a CRB (Cram é -Rao, Cramer-Rao bound) calculation mode.
First, CRB of the distance estimation result and the velocity estimation result in the embodiment of the present invention is calculated. Specifically, the CRB of the velocity estimation result v may be expressed as:
and the CRB of the distance estimation result may be obtained by calculating the CRB of the time delay τ, which may be expressed as:
in the above two calculation formulas of CRB:
in addition, N0Is the power spectral density of the noise, where λ represents the carrier wavelength and Re {. cndot.) represents the real part of the complex scalar.
The above Jττ、Jτv、JvτAnd JvvIn the expression of (a):
wherein,is the Fourier transform of (t- τ) s (t, τ), S (jw) isFourier transform of (1)*Represents the conjugate operator, |, represents the absolute value of the scalar,and D, representing the OFDM radar communication integrated waveform of the baseband mentioned in the step A at the time delay of tau.
Using the CRB of the time delay τ, the CRB of the resulting distance estimation structure is:
then, the beneficial effects of the present invention are further explained by the simulation verification results. Wherein, the simulation environment is MATLAB R2016 a. The simulation parameters comprise: the noise adopts complex Gaussian noise with the mean value of zero, the length of an effective OFDM symbol is T-10, and the length of a CP is Tg4 mus, subcarrier spacing Δ f 0.1MHz, carrier frequency fcThe modulation scheme is BPSK (Binary Phase Shift Keying) at 1GHz, and is used for transmitting communication information.
FIG. 3(a), FIG. 3(b), FIG. 3(c) and FIG. 3(d) are the prior R-V-MUSIC algorithm of the present invention, respectivelyDistance estimation and velocity estimation of existing R-V-Capon algorithms and existing R-V-FFT algorithms. Wherein the number of subcarriers is Nc128, the number of complete OFDM symbols is Ns64, pulse number N p15. A total of 4 targets are set: target 1, target 2, target 3 and target 4; their respective distance and speed parameters are (80m, 30m/s), (90m, 30m/s), (30m, -7m/s), (30m, 0m/s), respectively. The Signal-to-Noise Ratio (SNR) is 0 dB. By comparison, the invention can obtain super-resolution distance and speed estimation equivalent to R-V-MUSIC and R-V-Capon algorithms. And the result of the R-V-FFT algorithm has only two peak values, and the four targets can not be effectively distinguished.
Fig. 4(a) and 4(b) are resolution comparison results of the present invention and the prior art method. FIG. 4(a) shows the distance estimation result of 30m/s, and the distance estimation of the targets 1 and 2 can be obtained with a small estimation error by the R-V-MUSIC and R-V-Capon algorithm. But the R-V-FFT algorithm can only obtain a range estimate with a higher estimation error for one target. Fig. 4(b) shows a velocity image of 30m, the present invention can directly obtain a velocity estimate. The R-V-MUSIC and R-V-Capon algorithms obtain two peak values at corresponding target speeds. Whereas the R-V-FFT algorithm can only get one peak, a longer CPI is needed to distinguish between targets 3 and 4 using the R-V-FFT algorithm.
Based on the simulation results, it can be understood that: to achieve super-resolution range and velocity estimation, the invention does not need to search the whole range and velocity space, which is needed by the R-V-MUSIC and R-V-Capon algorithms. Therefore, the R-V-MUSIC and R-V-Capon algorithms have higher computational complexity. Furthermore, to achieve the same range and velocity resolution, the R-V-FFT algorithm requires a larger signal bandwidth and a longer CPI, which is not required by the present invention.
Fig. 5(a) and 5(b) are plots of Root Mean Square Error (RMSEs) versus SNR for the distance and velocity estimates of the present invention versus the prior art method. Wherein each SNR is subjected to 200 independent Monte Carlo experiments, and in each Monte Carlo experiment, the number of subcarriers is Nc12, the number of OFDM symbols is Ns200 and number of pulses Np=6。
In fig. 5(a), the RMSEs of the distance estimation are shown as a function of SNR. It can be seen that as the SNR increases, the RMSEs of the range estimates and the root CRB on the range estimates decrease. Fig. 5(b) shows the dependence of RMSEs of the velocity estimates on SNR. It can be seen that the RMSEs of the velocity estimates and the root CRB of the velocity estimates decrease as the SNR increases. Compared with the R-V-MUSIC algorithm and the R-V-Capon algorithm, the method has lower calculation complexity and can realize quick estimation compared with the existing algorithm under the same estimation precision.
In the description of the specification, reference to the description of the term "one embodiment", "some embodiments", "an example", "a specific example", or "some examples", etc., means that a particular feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples described in this specification can be combined and combined by those skilled in the art.
While the present application has been described in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the drawings, the disclosure, and the appended claims.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (9)
1. An OFDM radar communication integrated range speed fast super-resolution estimation method is characterized by comprising the following steps:
step A: constructing an OFDM radar communication integrated signal model, and inputting relevant parameters for the OFDM radar communication integrated signal model;
and B: carrying out communication information compensation on the OFDM radar communication integrated signal model to obtain a communication information compensation model;
and C: carrying out frequency smoothing processing on the communication information compensation model to obtain a target signal model of the distance and the speed to be estimated;
step D: and performing distance estimation and speed estimation on the target signal model based on a super-resolution method to obtain a distance estimation result and a speed estimation result with super-resolution.
2. The method of claim 1, wherein the communication information compensation model is expressed as:
wherein N istTo point target number, xiiIs the attenuation factor due to the propagation loss, scattering and radar cross-sectional area of the ith target, i is 0,1, …, Nt-1; Is a Gaussian noise vector; j is the imaginary symbol, e is the natural base number, Δ f is the subcarrier spacing, fcIs the carrier frequency, RiIs the distance of the ith target, viIs the relative velocity of the ith target, c is the signalA propagation speed; t issFor the length of a complete OFDM symbol, TgIs the length of the cyclic prefix CP in the complete OFDM symbol, Tp=NsTs,NsFor the number of complete OFDM symbols, NcIs the number of subcarriers; n is the number of valid OFDM symbols in the complete OFDM symbol, p is the number of pulses,the superscript T in the expression of (a) denotes a matrix transposition.
4. The method of claim 3, wherein step D comprises:
step D3: computing the covariance matrix estimateTo obtain a signal subspace Us(ii) a The signal subspace UsTo be estimated from said covariance matrixObtained NtThe characteristic vector corresponding to the maximum characteristic value is formed; the signal subspace UsIs one MNp×NtOrder matrix, NpIs the number of pulses;
step D4: constructing a selection matrix;
step D5: based on the signal subspace UsAnd the selection matrix, calculate the distance-related eigenvalue decomposition and velocity-related eigenvalue decomposition;
step D6: a distance estimation result is computed based on the distance-related eigenvalue decomposition and a velocity estimation result is computed based on the velocity-related eigenvalue decomposition.
6. The method of claim 5, wherein step D5 comprises:
Step E5-3: computingEigenvalue decomposition G of-1ΛRG, decomposing as a distance-dependent characteristic value, and calculatingEigenvalue decomposition G of-1ΛvG, decomposing as a speed-related characteristic value;
wherein,the superscript H of (a) represents the matrix transposition conjugate; dRAnd DvAre all diagonal matrices;
7. The method of claim 6, wherein step D6 comprises:
step E6-1: calculating a distance estimation result using a distance estimation formula based on the distance-dependent eigenvalue decomposition
Step E6-2: calculating a velocity estimation result using a velocity estimation formula based on the velocity-related eigenvalue decomposition
The distance estimation formula is as follows:
the velocity estimation formula is:
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