A Method for Designing Orthogonal Waveforms in MIMO Radar Based on Noise Signals

Abstract

This invention belongs to the field of radar technology, specifically relating to a method for designing orthogonal waveforms for MIMO radar based on noise signals. The method involves: establishing an orthogonal waveform signal model for MIMO radar; generating independent and identically distributed complex Gaussian sample sequences using a pseudo-random number generator; setting the peak-to-average power ratio (PAPR) and L2 norm of the waveforms to specified values ​​using an alternating projection algorithm; obtaining the autocorrelation and cross-correlation functions of the waveform set; establishing optimization models for the autocorrelation and cross-correlation functions of the waveform set; and using a sequential quadratic programming method to obtain a waveform set with excellent autocorrelation and cross-correlation performance. By generating orthogonal waveform sets using alternating projection and sequential quadratic programming, each waveform possesses the same PAPR and L2 norm while ensuring orthogonality and low sidelobes. This method can be applied to scenarios with high power constraints, such as vehicle-mounted MIMO radar.

Description

Technical Field

[0001] This invention belongs to the field of automotive millimeter-wave radar technology, specifically relating to a method for designing orthogonal waveforms for MIMO radar based on noise signals. Background Technology

[0002] Compared to sensors like cameras and lidar, millimeter-wave radar is unaffected by dust, rain, snow, or other adverse weather conditions, enabling all-weather operation and making it an indispensable core sensor for advanced driver assistance systems (ADAS) in automobiles. However, the explosive growth in the number of millimeter-wave radar systems installed in vehicles has increased the probability of frequency overlap, leading to increasingly severe interference between vehicle radars. Interference from other vehicle radars causes decreased sensitivity, missed alarms, and false alarms in one's own radar, seriously threatening driving safety and becoming a bottleneck in the application of automotive radar.

[0003] To mitigate interference between vehicle-mounted millimeter-wave radars, scholars both domestically and internationally have proposed various interference suppression methods based on antenna polarization, time domain, frequency domain, spatial domain, and coding. Spatiotemporal frequency domain and polarization-based interference suppression methods utilize, or create, the differences between the active and interfering signals in the correlation domain to suppress interference. Coding domain methods modulate the radar waveform through coding, giving the active radar different signal characteristics from other interfering radars, thereby reducing interference between radar systems.

[0004] With limited bandwidth allocation, the compatibility issues between numerous radars are difficult to resolve using time, frequency, spatial, or polarization diversity. Compared to limited resources such as space-time-frequency and polarization domains, waveform diversity holds promise for mitigating this increasingly serious problem of mutual interference between automotive radars. While random noise signals offer good orthogonality, their random autocorrelation sidelobes and high peak-to-peak sidelobe ratio severely limit their application in energy-efficient scenarios. Therefore, we propose a MIMO radar orthogonal waveform design method based on noise signals, which can alleviate the mutual interference problem between automotive radars. Summary of the Invention

[0005] The purpose of this invention is to provide a MIMO radar orthogonal waveform design method based on noise signals, which can alleviate the mutual interference problem between automotive radars.

[0006] The specific technical solution adopted by this invention is as follows:

[0007] A method for designing orthogonal waveforms for MIMO radar based on noise signals includes the following steps:

[0008] Step 1: Establish a MIMO radar orthogonal waveform signal model;

[0009] Step 2: Use a pseudo-random number generator to generate independent and identically distributed complex Gaussian sample sequences;

[0010] Step 3: Use the alternating projection algorithm to set the waveform peak-to-average power ratio and L2 norm to the specified values;

[0011] Step 4: Obtain the autocorrelation function and cross-correlation function of the waveform set;

[0012] Step 5: Establish optimization models for the autocorrelation and cross-correlation functions of the waveform set;

[0013] Step 6: Use the sequential quadratic programming method to obtain an optimized waveform set with excellent autocorrelation and cross-correlation performance.

[0014] Further, step 1 includes the following steps:

[0015] The orthogonal waveform signal model for MIMO radar is established as follows, where S = {s1, ..., s} m ,…,s M} is a waveform set containing M orthogonal signals, where the s of the m-th waveform signal is... m for

[0016] s m =[s m (1),…,s m (n),…,s m (N)] T

[0017] Where m = 1, 2, ..., M, n = 1, 2, ..., N, N = f s ·T represents the total number of signal samples, f s and T represent the sampling frequency and signal duration, respectively, s m (n) is the nth sample of the mth transmitted signal.

[0018]

[0019] Among them, a mn and φ mn They are signals s m The amplitude and phase of the nth sequence.

[0020] Furthermore, in step 2, a pseudo-random number generator is used to generate M independent and identically distributed complex Gaussian sample sequences S.

[0021]

[0022] Here, randn(N,M) is a function that generates an array of random normal distributions. Each sampling point of each waveform signal in S follows a complex Gaussian distribution with a mean of 0 and a variance of 1.

[0023] s m (n)~CN(0,1).

[0024] Furthermore, step 3 includes the following steps:

[0025] Step 301: Using frame theory, perform L2 norm approximation on the waveform set obtained in Step 2.

[0026] S Tight =α*(SS) H ) -12 S

[0027] Where α = Mc / N, It is the square of the L2 norm of each waveform sequence, which is determined by the power of the radar platform.

[0028] Step 302: Place S Tight Each waveform sequence is normalized to have a unit norm;

[0029]

[0030] Step 303: Set k = 0, s m The index of the (Nk) minimum amplitude is Q, and if Q is not unique, it is incremented by k; the following updates s m If each updated sample s in Q m (q) all satisfy |s m If (q)|>η, then increment k and continue updating s. m ;

[0031]

[0032] in, is the peak-to-average power ratio of the sequence.

[0033] Step 303: Based on the alternating projection method, repeat operations 301 to 303 until the F-norm of the waveform set difference obtained from two adjacent operations is less than the threshold.

[0034] ||S j+1 -S j || F ≤ε

[0035] Furthermore, step 4 includes the following steps:

[0036] Step 401: According to the definition of the aperiodic autocorrelation function, signal s p The aperiodic autocorrelation function is

[0037]

[0038] Where p = 1, 2, ..., M.

[0039] Step 402: According to the definition of the aperiodic cross-correlation function, signal s p With signal s q The aperiodic correlation function between them can be written as

[0040]

[0041] Where p = 1, 2, ..., M, q = 1, 2, ..., M.

[0042] Furthermore, step 5 establishes an optimization model for the autocorrelation function and cross-correlation function of the waveform set:

[0043]

[0044] st|C p,p (k)|·σ,k=1,…,N-1,p=1,2,…,M

[0045] w|C p,q (k)|·σ,k=-N+1,…1,…,N-1,

[0046] p≠q=1,2,…,M

[0047] φ mn ∈[-π,π],m=1,2,…,M; n=1,2,…,N

[0048] Furthermore, step 6 utilizes a sequential quadratic programming method to optimize each sampling phase of the waveform set in order to obtain a waveform set with excellent autocorrelation and cross-correlation performance.

[0049] The technical effects achieved by this invention are as follows:

[0050] (1) The present invention provides a method for designing orthogonal waveforms for MIMO radar based on noise signals. The method sets the peak-to-average power ratio and L2 norm of the waveform by alternating projection and optimizes the waveform phase by using a sequential quadratic programming method. This generates a waveform set with good orthogonality and cross-correlation, which can be applied to scenarios with high power limitation requirements, such as MIMO vehicle radar. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0052] Figure 2 This is the phase of the orthogonal waveform set generated by the present invention;

[0053] Figure 3 This is the phase of the orthogonal waveform set generated by the present invention;

[0054] Figure 4 This is a comparison diagram of the autocorrelation function of the orthogonal waveform set generated by this invention and the autocorrelation function of random noise signal;

[0055] Figure 5 This is a comparison diagram of the cross-correlation function of the orthogonal waveform set generated by this invention and the cross-correlation function of random noise signal. Detailed Implementation

[0056] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0057] Figure 1-5 As shown, a method for designing orthogonal waveforms for MIMO radar based on noise signals is proposed. The method involves: establishing an orthogonal waveform signal model for MIMO radar; generating independent and identically distributed complex Gaussian sample sequences using a pseudo-random number generator; setting the peak-to-average power ratio (PAPR) and L2 norm of the waveforms to specified values ​​using an alternating projection algorithm; obtaining the autocorrelation and cross-correlation functions of the waveform set; establishing optimization models for the autocorrelation and cross-correlation functions of the waveform set; and using a sequential quadratic programming method to obtain a waveform set with excellent autocorrelation and cross-correlation performance. This method generates orthogonal waveform sets using alternating projection and sequential quadratic programming, ensuring orthogonality and low sidelobes while maintaining the same PAPR and L2 norm for each waveform. This approach can be applied to scenarios with high power constraints, such as MIMO vehicle-mounted radar.

[0058] Please see Figure 1 This paper details a method for designing orthogonal waveforms for MIMO radar based on noise signals. The method includes the following steps:

[0059] Step 1: Establish a MIMO radar orthogonal waveform signal model.

[0060] Specifically, step 1 includes the following steps:

[0061] The orthogonal waveform signal model for MIMO radar is established as follows, where S = {s1, ..., s} m ,…,s M} is a waveform set containing M orthogonal signals, where the s of the m-th waveform signal is... m for

[0062] s m =[s m (1),…,s m (n),…,s m (N)] T

[0063] Where m = 1, 2, ..., M, n = 1, 2, ..., N, N = f s ·T represents the total number of signal samples, f sand T represent the sampling frequency and signal duration, respectively, s m (n) is the nth sample of the mth transmitted signal.

[0064]

[0065] Among them, a mn and φ mn They are signals s m The amplitude and phase of the nth sequence.

[0066] Step 2: Use spatial smoothing to decohere the array-received data X(t) to obtain the decorrelation covariance matrix R. f ;

[0067] Specifically, in step 2, a pseudo-random number generator is used to generate M independent and identically distributed complex Gaussian sample sequences S.

[0068]

[0069] Here, randn(N,M) is a function that generates an array of random normal distributions. Each sampling point of each waveform signal in S follows a complex Gaussian distribution with a mean of 0 and a variance of 1.

[0070] s m (n)~CN(0,1);

[0071] Step 3: Use the alternating projection algorithm to set the waveform peak-to-average power ratio and L2 norm to the specified values;

[0072] Specifically, step 3 includes the following steps:

[0073] Step 301: Using frame theory, perform L2 norm approximation on the waveform set obtained in Step 2.

[0074] S Tight =α*(SS) H ) -12 S

[0075] Where α = Mc / N, It is the square of the L2 norm of each waveform sequence, which is determined by the power of the radar platform.

[0076] Step 302: Place S Tight Each waveform sequence is normalized to have a unit norm;

[0077]

[0078] Step 303: Set k = 0, s m The index of the (Nk) minimum amplitude is Q, and if Q is not unique, it is incremented by k; the following updates sm If each updated sample s in Q m (q) all satisfy |s m If (q)|>η, then increment k and continue updating s. m ;

[0079]

[0080] in, is the peak-to-average power ratio of the sequence.

[0081] Step 304: Based on the alternating projection method, repeat operations 301 to 303 until the F-norm of the waveform set difference obtained from two adjacent operations is less than the threshold.

[0082] ||S j+1 -S j || F ≤ε

[0083] Step 4: Obtain the autocorrelation function and cross-correlation function of the waveform set.

[0084] Specifically, step 4 includes the following steps:

[0085] Step 401: According to the definition of the aperiodic autocorrelation function, signal s p The aperiodic autocorrelation function is

[0086]

[0087] Where p = 1, 2, ..., M.

[0088] Step 402: According to the definition of the aperiodic cross-correlation function, signal s p With signal s q The aperiodic correlation function between them can be written as

[0089]

[0090] Where p = 1, 2, ..., M, q = 1, 2, ..., M.

[0091] Step 5: Establish optimization models for the autocorrelation and cross-correlation functions of the waveform set.

[0092] Specifically, step 5 establishes an optimization model for the autocorrelation function and cross-correlation function of the waveform set:

[0093]

[0094] st|C p,p (k)|·σ,k=1,…,N-1,p=1,2,…,M

[0095] w|C p,q (k)|·σ,k=-N+1,…1,…,N-1,

[0096] p≠q=1,2,…,M

[0097] φ mn ∈[-π,π],m=1,2,…,M; n=1,2,…,N

[0098] Where σ is the objective function, which physically represents the upper bound of the autocorrelation sidelobe, and w is a parameter that adjusts the proportion of autocorrelation sidelobe and cross-correlation level.

[0099] Step 6: Use the sequential quadratic programming method to obtain an optimized waveform set with excellent autocorrelation and cross-correlation performance.

[0100] Specifically, step 6 includes the following steps:

[0101] By using a quadratic programming method, the sampling phases of the waveform set are optimized to minimize the autocorrelation sidelobes and cross-correlation levels, thereby obtaining a waveform set with excellent autocorrelation and cross-correlation performance. The optimization model is then calculated. Specifically, the orthogonal waveform set generated by the above scheme has the same peak-to-average power ratio and L2 norm, as well as low sidelobes, and can be applied to scenarios with high power constraints, such as MIMO vehicle radar.

[0102] To more clearly illustrate the effects of the present invention, the following simulation experiments are disclosed herein;

[0103] Simulation parameter settings:

[0104] The design includes an orthogonal waveform set with three member sequences. Each waveform has a time-bandwidth product of 400, 400 sampling points, a peak-to-average power ratio (PAPR) of ρ = 1.5, a waveform L2 norm of 1, and an alternating projection algorithm termination threshold of ε = 10. -7 The cross-correlation and autocorrelation weighting coefficients were set to w = 0.3162.

[0105] In this embodiment, an experiment on waveform set amplitude and phase is conducted:

[0106] Based on the parameter settings, generate a waveform set according to this technical solution.

[0107] The amplitude and phase of the three waveform sampling sequences are as follows: Figure 2 and Figure 3 As shown. From Figure 2 As can be seen, the waveform amplitude is strictly limited to meet the peak-to-average power ratio (PAPR) and L2 norm requirements. From... Figure 3 As can be seen, the phase of the waveform is optimized in the range [-π, π] to achieve low autocorrelation sidelobes and low cross-correlation.

[0108] In this embodiment, experiments on waveform set autocorrelation and cross-correlation are conducted:

[0109] Based on the parameter settings, a waveform set is generated according to this technical solution, and the waveform performance is evaluated by the autocorrelation and cross-correlation of the waveform set.

[0110] The waveform before optimization has autocorrelation sidelobes as follows: Figure 4 As shown in (b), not only is the average level high, but the randomness is also strong, which is very unfavorable for detecting weak targets near strong targets. The optimized waveform autocorrelation is as follows: Figure 4 As shown in (a), the optimized peak-to-sidelobe ratio is constrained to below 34.76 dB. Compared with the result before autocorrelation sidelobe optimization, the autocorrelation sidelobe is significantly reduced and smoother. The cross-correlation of the optimized waveform is shown below. Figure 5 As shown, the optimized cross-correlation constraint is below 25dB, and compared with the result before optimization, the cross-correlation is significantly reduced and stabilized.

[0111] In summary, this technical solution constructs an orthogonal waveform set using alternating projection and sequential quadratic programming methods. The peak-to-average power ratio and L2 norm of the waveform are set using alternating projection, and the waveform phase is optimized using sequential quadratic programming, thereby generating a waveform set with good orthogonality and cross-correlation.

[0112] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A method for designing orthogonal waveforms for MIMO radar based on noise signals, characterized in that: Includes the following steps: Step 1: Establish a MIMO radar orthogonal waveform signal model; Step 2: Use a pseudo-random number generator to generate independent and identically distributed complex Gaussian sample sequences; Step 3: Use the alternating projection algorithm to set the waveform peak-to-average power ratio and L2 norm to the specified values; Step 4: Obtain the autocorrelation function and cross-correlation function of the waveform set; Step 5: Establish optimization models for the autocorrelation and cross-correlation functions of the waveform set; Step 6: Use the sequential quadratic programming method to obtain the optimized waveform set; Step 1 includes the following steps: The orthogonal waveform signal model of MIMO radar is established as follows, assuming... It is a collection The waveform set of the nth orthogonal signal, the nth m A waveform signal for in, This represents the total number of signal samples. and These are the sampling frequency and the signal duration, respectively. It is the nth sample of the mth transmitted signal. in, and Signals The The amplitude and phase of each sequence; In step 2, a pseudo-random number generator is used to generate... A sequence of independent and identically distributed complex Gaussian samples in, It is a function that generates an array of random normally distributed data. Each sampling point of each waveform signal follows a complex Gaussian distribution with a mean of 0 and a variance of 1, i.e. 。 2. The method for designing orthogonal waveforms for MIMO radar based on noise signals according to claim 1, characterized in that: Step 3 includes the following steps: Step 301: Using frame theory, perform L2 norm approximation on the waveform set obtained in Step 2. in, It is the square of the L2 norm of each waveform sequence, which is determined by the power of the radar platform; Step 302: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Each waveform sequence is normalized to have a unit norm; Step 303: Settings of The index of the minimum magnitude is ,like If not unique, then increasing. The following updates ,like Each updated sample All meet Then it increases. To be continued ; in, , The peak-to-average power ratio of the sequence; Step 303: Based on the alternating projection method, repeat operations 301 to 303 until the F-norm of the waveform set difference obtained from two adjacent operations is less than the threshold. 。 3. The method for designing orthogonal waveforms for MIMO radar based on noise signals according to claim 2, characterized in that: Step 4 includes the following steps: Step 401: According to the definition of the aperiodic autocorrelation function, the signal... The aperiodic autocorrelation function is in, ; Step 402: According to the definition of the aperiodic cross-correlation function, the signal... With signal The aperiodic correlation function between them can be written as in, .

4. The method for designing orthogonal waveforms for MIMO radar based on noise signals according to claim 3, characterized in that: Step 5 establishes an optimization model for the autocorrelation function and cross-correlation function of the waveform set: in, σ Let be the objective function, and its physical meaning be the upper bound of the autocorrelation sidelobes. w It is a parameter that adjusts the proportion of autocorrelation sidelobes and cross-correlation levels.

5. The method for designing orthogonal waveforms for MIMO radar based on noise signals according to claim 4, characterized in that: Step 6 uses a sequential quadratic programming method to optimize each sampling phase of the waveform set in order to obtain a waveform set with excellent autocorrelation and cross-correlation performance.

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