A method for calculating target distance-direction information for MIMO radar

Abstract

The present invention discloses a method for calculating target distance-direction information for MIMO radar, including: obtaining a one-way delay and a receiving signal of a certain array element through a detection system model of the MIMO radar; calculating the total normalized delay to obtain a receiving signal in discrete form; expressing the radar transmitted orthogonal signal in discrete form, and writing the receiving signals of multiple array elements in matrix form; obtaining a joint probability density function between the receiving signal and the distance and direction according to the noise probability density function and the received signal in matrix form; deriving the posterior probability density function of the distance and direction; and obtaining the distance-direction mutual information of the target. The present invention defines the spatial information in the MIMO radar as the mutual information between the distance, DOA, scattering characteristics and the received signal, and the information content includes two types of distance information and direction information. The theoretical formula of the distance-direction information of the target is derived, providing theoretical guidance for system designers.

Description

Technical Field

[0001] The present invention belongs to the technical field of information transmission and processing, relates to a multiple-input multiple-output (MIMO) radar technology, and in particular to a method for calculating target distance-direction information for a MIMO radar. Background Art

[0002] MIMO technology was first widely used in the field of communications. By placing multiple antennas at the transmitting and receiving ends for transmission and reception, spatial diversity and spatial multiplexing are achieved, which improves channel capacity and channel transmission reliability. Inspired by this technology, relevant scholars later proposed the concept of MIMO radar. This radar transmits unrelated or orthogonal signals at the same time, generating multiple independent channels between the transmitting and receiving ends. According to the antenna position and signal processing method, MIMO can be divided into two categories: distributed and centralized. Among them, the array structure of the centralized MIMO radar is similar to that of an ordinary phased array radar. The spacing between its array elements is small, the transmitting end sends mutually orthogonal signals, and then receives the echo signals through multiple array elements, and the transmission pattern is formed at the receiving end. By observing the echo signal, the information of the target can be obtained, such as the distance of the target, the direction of arrival (DOA), and the scattering characteristics.

[0003] From the perspective of information theory, mutual information can be interpreted as the reduction of the prior uncertainty of an object. This shows that mutual information can also be applied to the radar field to evaluate the performance of the system. The application of information theory ideas and methods to radar detection systems has been explored at home and abroad. Shortly after the establishment of Shannon information theory, Woodward and Davies began to study the problem of mutual information of distance of targets in radar detection systems. They used the inverse probability principle to obtain the approximate relationship between the mutual information of distance and the time-band product and signal-to-noise ratio of a single constant modulus scattering target. Subsequent scholars also studied the use of information theory to derive the distance-direction information of phased array radars and their closed expressions. At present, there is no theoretical analysis of the application of information theory to MIMO radar systems for distance-direction information. Therefore, it is of great significance to study the calculation method of spatial information of MIMO radars on the basis of the original theory. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for calculating target range-direction information for MIMO radar is provided. The spatial information in the MIMO radar is defined as the mutual information between the distance, DOA, scattering characteristics and the received signal. The information content includes two types of distance information and direction information. A theoretical formula for the range-direction information of the target is derived, which provides theoretical guidance for system designers.

[0005] Technical solution: To achieve the above object, the present invention provides a method for calculating target range-direction information for a MIMO radar, including the following steps:

[0006] S1: Obtain the one-way delay through the established detection system model of the MIMO radar.

[0007] S2: Obtain the received signal of a certain array element according to the one-way delay.

[0008] S3: Perform down-conversion, sampling, and normalization processing on the received signal. According to the narrowband hypothesis, calculate the total normalized delay to obtain the received signal in discrete form.

[0009] S4: Express the radar transmitted orthogonal signal in discrete form according to the received signal in discrete form, and write the received signals of multiple array elements in matrix form.

[0010] S5: Obtain the joint probability density function between the received signal and range and direction according to the noise probability density function and the received signal in matrix form.

[0011] S6: Deduce the posterior probability density function of range and direction according to the joint probability density function.

[0012] S7: Based on the definition of mutual information in information theory, obtain the range-direction mutual information of the target through the posterior probability density function.

[0013] Further, the method for establishing the detection system model of the MIMO radar in step S1 is as follows:

[0014] Establish the detection system model of the MIMO radar using polar coordinates, with the first antenna as the origin, the distance from the target to the reference origin as r p , and the angle with the polar coordinate normal as θ;

[0015] The distance from the target to the array element is

[0016]

[0017] where: r p is the distance from the target to the array element, d is the distance between array elements, m is the serial number of the transmitting antenna, and θ is the range and direction of arrival.

[0018] Further, the method for obtaining the one-way delay in step S1 is as follows:

[0019] Approximate the distance from each array to the target to obtain the corresponding one-way delay:

[0020]

[0021] where c represents the propagation speed of electromagnetic waves.

[0022] Furthermore, the expression of the received signal in step S2 is:

[0023]

[0024] Where: m represents the serial number of the transmitting array element, q represents the serial number of the receiving array element, α is the amplitude of the target complex scattering coefficient, is the initial phase, f c is the carrier frequency, τ(r p , θ, m, q) represents the round-trip time delay, w q (t) represents additive complex Gaussian white noise with mean 0 and bandwidth B / 2.

[0025] Furthermore, the total normalized delay in step S3 is:

[0026]

[0027] Where: K = B / f c , represents the ratio of signal bandwidth to carrier frequency;

[0028] The effect of narrowband on the transmitted signal is:

[0029] ψ m (n-τ mq )≈ψ m (n-Kr)

[0030] The final discrete received signal is:

[0031]

[0032] Furthermore, the discrete form of the orthogonal signal transmitted by the radar in step S4 is expressed as:

[0033] The time domain expression of the transmitted multi-carrier signal is:

[0034]

[0035] Where: k represents the subcarrier number, a mk represents the Chu sequence value carried by the kth subcarrier of the mth array element, and N represents the number of sampling points;

[0036] Discrete form ψ m (n-Kr) is:

[0037]

[0038] Furthermore, the matrix form of the received signal in step S4 is:

[0039]

[0040] in: is the transmission steering vector about the angle θ; S(r) is a matrix about the normalized distance r, representing the delayed baseband signal; is the transmission steering vector about the angle θ, and W represents the noise matrix.

[0041] Furthermore, the probability density function of the noise in step S5 is:

[0042]

[0043] The joint probability density function is:

[0044]

[0045] Furthermore, the posterior probability density function in step S6 is:

[0046]

[0047] Furthermore, the distance-direction mutual information of the target in step S7 is:

[0048] I(ZR, Θ) = log 2 DΩ+E z [∫∫p(r,θ|z)log 2 p(r,θ|z)drdθ]

[0049] Beneficial effects: Compared with the prior art, the present invention uses mutual information in Shannon information theory to quantify and reduce the prior uncertainty of transmitted information. The present invention defines the spatial information in MIMO radar as the mutual information between distance, arrival direction, scattering characteristics and received signals. By using the properties of probability distribution function, Bayesian criterion and Zadoff-Chu sequence to generate orthogonal signals, the theoretical formula of the distance-direction information of MIMO radar is derived. This formula has a specific calculation formula and measurement standard for the amount of information that can be obtained by MIMO radar. The law of information change reflects the information acquisition efficiency of the radar system and provides guidance for system designers. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of the method of the present invention;

[0051] Figure 2 This is a model diagram of the MIMO radar polar coordinate system in the present invention;

[0052] Figure 3 This is the simulation result diagram of the posterior probability density function of the MIMO radar;

[0053] Figure 4The simulation results of the distance-direction information of MIMO radar when the number of antennas is different. DETAILED DESCRIPTION

[0054] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0055] The present invention provides a method for calculating target distance-direction information for MIMO radar, such as Figure 1 As shown, the following steps are included:

[0056] Step 1: Since there is no specific restriction on the spacing between antenna elements of MIMO radar, it can be dense or sparse. In this embodiment, the spacing d between adjacent antenna elements is set to half the wavelength, that is, d = λ / 2, where λ is the wavelength of the transmitted signal. At the same time, it is assumed that the detection target is a far-field point target, the transmitted signal is a narrowband signal, and it is assumed that each array can independently transmit and receive waveforms.

[0057] The detection system model of MIMO radar is established using polar coordinate system, such as Figure 2 As shown. Taking the first antenna as the origin, the distance from the target to the reference origin is r p , and the angle between it and the polar coordinate normal is θ. According to the trigonometric theorem, the distance from the point target to the mth transmitting array element is:

[0058]

[0059] Considering the far-field assumption, the distance between the target and the radar is much larger than the array aperture width of the MIMO radar, that is, md / r p <<1.

[0060] The corresponding one-way delay can be approximated as

[0061]

[0062] Where: c represents the propagation speed of electromagnetic waves.

[0063] Step 2: Use ψ m (t) represents the transmission signal of the mth antenna array element. After the signal of each array element is transmitted by the transmitter, it reaches the far-field target and is reflected, and finally superimposed at the receiving array element. The receiving signal of the qth receiving array element can be expressed as

[0064]

[0065] Where: m represents the serial number of the transmitting array element, q represents the serial number of the receiving array element. Since the receiving and transmitting elements share the same array, the value ranges of m and q are the same, both 0, ..., M-1, α is the amplitude of the target complex scattering coefficient, is the initial phase, f c is the carrier frequency, τ(r p , θ, m, q) represents the round-trip time delay of the detection signal sent from the mth transmitting array element to the target and then reflected by the target and returned to the qth receiving array element, w q (t) represents additive complex Gaussian white noise with mean 0 and bandwidth B / 2;.

[0066] Down-convert the received signal to baseband, and we get

[0067]

[0068] And sampling the signal at the Nyquist sampling rate B, we can get

[0069]

[0070] In order to generalize the model, the Nyquist sampling rate is further used in this embodiment to normalize the delay, that is, let τ mq =Bτ(r p , θ, m, q). The normalized delay can be divided into two parts: the transmission propagation delay τ m and receiving propagation delay τ q , we can get

[0071] τ mq =τ m +τ q

[0072] The normalized polar diameter r = r p Substituting / d and d = λ / 2, we get the transmission propagation delay as

[0073]

[0074] Where: K = B / f c , represents the ratio of signal bandwidth to carrier frequency;

[0075] So the total normalized delay is

[0076]

[0077] The value of the second term in the above formula will not be greater than KM. Under the narrowband assumption, KM < < 1. Then the difference caused by this term on the signal envelope at each array element can be ignored, that is,

[0078] ψ m (n-τmq ) ≈ ψ m (n - Kr)

[0079] The received signal in the final discrete form can be expressed as

[0080]

[0081] where: represents the scattering phase introduced by the target position; β θ = πsinθ represents the spatial frequency.

[0082] Step 3: OFDM is an orthogonal multi - carrier modulation signal, which can be used as the transmitted signal of the MIMO radar. The present invention considers the following transmitted multi - carrier signal

[0083]

[0084] where: k represents the serial number of the sub - carrier; a mk represents the Chu sequence value carried by the k - th sub - carrier of the m - th array element, and its time - domain expression is

[0085]

[0086] where: y is an arbitrary integer relatively prime to N; q is an arbitrary integer. After sampling the transmitted signal, the sampling sequence can be obtained as

[0087]

[0088] where: N represents the number of sampling points, Δf = B / K = 1 / T is the sub - carrier interval, T s = T / N is the sampling period, so

[0089]

[0090] When dealing with the subsequent processing noise term, using the matrix form will bring certain convenience to the problem analysis and at the same time retain the spatial characteristics of the radar system. Therefore, the matrix expression form of the received sequences of different receiving array elements is introduced below. Assuming the number of sampling points is N, the N×M - dimensional observation data matrix can be obtained as:

[0091]

[0092] where: is the transmitting steering vector, is the receiving steering vector, and W represents the noise matrix. For more concise expression later, in this embodiment, let

[0093] U = S(r)a(θ)b T (θ)

[0094] Where: U represents the sampling result after the product operation of the transmit steering vector, the receive steering vector and the delayed baseband signal. Then,

[0095]

[0096] Step 4: For any element w in the noise matrix ij , that is, the noise sampling point with sequence number j received by the i-th receiving array element has a mean value of 0 and a power spectrum density of N 0 Because under the Nyquist sampling condition, the noise samples of different array elements and at different times are independent of each other, then each noise element in the matrix is ​​an independent and identically distributed one-dimensional complex Gaussian random variable. From this, the probability density function of the noise matrix can be written as

[0097]

[0098] Where: tr(·) means finding the trace of the matrix; (·) H represents the conjugate transposed matrix. The PDF of the received signal Z can be obtained under the given target distance, direction and scattering conditions. For the constant mode scattering model, the amplitude of the scattered signal is a constant α 0 ,but

[0099]

[0100] Where: Re(·) represents the real part of a complex number. Since the random variables R, Θ and Z are independent of each other, we can get

[0101]

[0102] Then, for a given phase Φ, the joint density between R, Θ and Z is

[0103]

[0104] Step 5: For tr(U H U), substitute the relevant formula, and due to the linear property of matrix trace, we get tr(U H U)=tr(b * (θ)a H (θ)S H (r)S(r)a(θ)b T (θ)

[0105] For any two antennas numbered i and j, the transmitted signals

[0106]

[0107] then

[0108] SH (r)S(r)=NI M

[0109] so

[0110]

[0111] From this we can calculate

[0112] tr(U H U)=NM 2

[0113] According to the Bayesian formula, we can get the posterior PDF

[0114]

[0115] Since tr(Re(·))=Re(tr(·)), then

[0116]

[0117] Where: I 0 (·) represents the first kind of zero-order modified Bessel function. Therefore, for a single target scene, assuming that the target distance and direction are uniformly distributed in the observation interval and are independent of each other, then the distance and direction information of the target is

[0118] I(Z;R,Θ)=log 2 DΩ+E z [∫∫p(r,θ|z)log 2 p(r,θ|z)drdθ].

[0119] In order to verify the effectiveness of the method of the present invention, a simulation test was carried out on the method of the present invention. The specific simulation results are as follows: Figure 3-4 shown.

[0120] Figure 3 The following are the two-dimensional simulation results of the posterior probability density function on distance and DOA when the signal-to-noise ratio is 15 dB. It can be seen that when the signal-to-noise ratio is high, the posterior probability function is distributed at the actual position of the target with a very high probability, and the MIMO radar can obtain the position of the target.

[0121] Figure 4 The simulation results of the distance-direction information of MIMO radar with different numbers of antennas are shown in Figure 2. It can be seen that when the signal-to-noise ratio is the same, the amount of information obtained increases with the increase in the number of antennas; for a specific number of antennas, the higher the signal-to-noise ratio, the more information is obtained.

Claims

1. A method for calculating target distance-direction information for MIMO radar, It is characterized in that The steps include: S1: Obtain the one-way delay by building a good MIMO radar detection system model; S2: Obtain the receiving signal of a certain array element according to the one-way delay; S3: down-converting, sampling and normalizing the received signal, and according to the narrowband assumption, calculating the total normalized delay to obtain a discrete received signal; S4: According to the received signal in discrete form, the radar transmitted orthogonal signal is expressed in discrete form, and the received signals of multiple array elements are written in matrix form; S5: obtaining a joint probability density function between the received signal and the distance and direction according to the noise probability density function and the received signal in matrix form; S6: derive the posterior probability density function of distance and direction based on the joint probability density function; S7: Based on the definition of mutual information in information theory, the distance-direction mutual information of the target is obtained through the posterior probability density function.

2. A method for calculating target distance-direction information for MIMO radar according to claim 1, It is characterized in that The method for establishing the detection system model of the MIMO radar in step S1 is: The detection system model of MIMO radar is established using the polar coordinate system, with the first antenna as the origin and the distance from the target to the reference origin as r. p , the angle between it and the polar coordinate normal is θ; The distance between the target and the array element is Where: r p is the distance from the target to the array element, d is the distance between the array elements, m is the serial number of the transmitting antenna, and θ is the distance and the direction of arrival.

3. A method for calculating target distance-direction information for MIMO radar according to claim 2, It is characterized in that The method for obtaining the one-way delay in step S1 is: Approximate the distance from each array to the target and obtain the corresponding one-way delay: Among them, c represents the propagation speed of electromagnetic waves.

4. A method for calculating target distance-direction information for MIMO radar according to claim 3, It is characterized in that The expression of the received signal in step S2 is: Where: m represents the serial number of the transmitting array element, q represents the serial number of the receiving array element, α is the amplitude of the target complex scattering coefficient, is the initial phase, f c is the carrier frequency, τ(r p , θ, m, q) represents the round-trip time delay, w q (t) represents additive complex Gaussian white noise with mean 0 and bandwidth B / 2.

5. A method for calculating target distance-direction information for MIMO radar according to claim 4, It is characterized in that The step S3 is specifically as follows: Down-convert the received signal to baseband, and we get And sample the signal at the Nyquist sampling rate B, and get The delay is normalized using the Nyquist sampling rate, that is, τ mq =Bτ(r p ,θ,m,q), the normalized delay is divided into two parts, namely the transmission propagation delay τ m and receiving propagation delay τ q ,get t mq =t m +t q The normalized polar diameter r = r p Substituting / d and d = λ / 2, we get the transmission propagation delay as Where: K = B / f c , represents the ratio of signal bandwidth to carrier frequency; The total normalized delay is: The effect of narrowband on the transmitted signal is: ψ m (n-τ mq )≈ψ m (n-Kr) The final discrete received signal is: Where: represents the scattering phase introduced by the target position; β θ =πsinθ represents the spatial frequency.

6. A method for calculating target distance-direction information for MIMO radar according to claim 5, It is characterized in that The discrete form of the orthogonal signal transmitted by the radar in step S4 is expressed as: The time domain expression of the transmitted multi-carrier signal is: Where: k represents the subcarrier number, a k represents the Chu sequence value carried by the kth subcarrier of the mth array element, and N represents the number of sampling points; Discrete form ψ m (n-Kr) is:

7. A method for calculating target distance-direction information for MIMO radar according to claim 6, It is characterized in that The matrix form of the received signal in step S4 is: in: is the transmission steering vector about the angle θ; S(r) is a matrix about the normalized distance r, representing the delayed baseband signal; is the transmission steering vector about the angle θ; W represents the noise matrix.

8. A method for calculating target distance-direction information for MIMO radar according to claim 7, It is characterized in that The method for acquiring the distance-direction mutual information of the target in step S7 is: Since tr(Re(·))=Re(tr(·)), then Where: I 0 (·) represents the first kind of zero-order modified Bessel function. For a single target scene, assuming that the target distance and direction are uniformly distributed in the observation interval and are independent of each other, the distance-direction mutual information of the target is I(Z(R,Θ))log 2 DΩ+E x [∫∫p(r,θ|z)log 2 p(r,θ|z)drdθ]

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