A Design Method for a Waveform Complementary Mismatch Filter Bank for Integrated Radar and Communication
By designing a complementary mismatch filter group in the integrated radar communication system, the problem of distance fuzzy problems and unreasonable noise assumptions at high pulse repetition frequency is solved, and better radar performance and adaptability are achieved.
Patent Information
- Application Number
- CN202310113495.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-02-14
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2043-02-14
AI Technical Summary
The existing radar communication integrated system is prone to distance blurring at high pulse repetition frequency, resulting in the degradation of the performance of traditional mismatch filters. Most studies assume that the received noise is Gaussian white noise, and the actual noise is colored noise is not considered.
A radar communication integrated waveform complementary mismatch filter group was designed. By constructing an IRC system model, CMFG performance indicators under color noise were established, and the optimization problem was used to deal with the Lagrangian function, the final mismatch filter was obtained.
While maintaining the system communication performance, the radar performance is enhanced, especially in the case of blurred distances, and is suitable for common color noise environments in practice.
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Figure CN116305821B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the cross - technical field of radar and communication, and particularly relates to a design method of a waveform complementary mismatch filter bank for integrated radar and communication. Background Art
[0002] Due to the advantages of the integrated radar and communications (IRC) system, such as reducing the mutual interference between radar and communication systems and improving the spectrum utilization rate, the research on the IRC system has become a hot topic.
[0003] The most important point in realizing IRC lies in designing an IRC waveform that can simultaneously realize radar and communication functions. To improve the signal - to - noise ratio (SNR) of the IRC echo signal at the radar receiver, the matched filters (MFs) are often used to process the echo signal. However, the output of the matched filtering usually has a relatively high sidelobe level (SLL), which will reduce the radar target detection performance. To solve this problem, existing researchers have replaced the matched filter with a mismatch filter, which not only improves the radar performance but also maintains the communication performance of the system. Among them, C. Sahin and J. G Metcalf proposed a design method of a mismatch filter based on the maximum SNR metric. M. Jiang and G. Liao et al. proposed a design method of a tunable mismatch filter. However, neither of these two methods considered the existence of range ambiguity. When the pulse repetition frequency (PRF) of the IRC system is relatively high, range ambiguity will occur, resulting in false detection. At this time, the performance of the traditional mismatch filter will drop significantly. In addition, the mismatch filters designed in these two methods were studied under the premise that the received noise is Gaussian white noise, but this assumption has low feasibility in practice. Therefore, it is necessary to consider the case where the received noise is colored noise. Summary of the Invention
[0004] To solve the above problems existing in the prior art, the present invention provides a design method of a waveform complementary mismatch filter bank for integrated radar and communication. The technical problems to be solved by the present invention are realized through the following technical solutions:
[0005] A design method of a waveform complementary mismatch filter bank for integrated radar and communication, the design method includes:
[0006] Step 1: Construct an IRC system model, where the IRC system model includes an IRC system transmitted signal model, an IRC system received signal model, and a CMFG output signal model;
[0007] Step 2: Under the conditions of the IRC system model, establish CMFG performance indicators under colored noise, where the CMFG performance indicators include a first SNR improvement factor, a first normalized sidelobe energy of the unambiguous output, and a first normalized energy of the CMFG range-ambiguous output;
[0008] Step 3: Obtain a first CMFG optimization problem according to the CMFG performance indicators, where the first CMFG optimization problem is a non-convex optimization problem;
[0009] Step 4: Obtain a second CMFG optimization problem according to the first CMFG optimization problem, where the second CMFG optimization problem is a convex optimization problem;
[0010] Step 5: Use the Lagrangian function to process the second CMFG optimization problem to obtain the final mismatch filter.
[0011] In an embodiment of the present invention, the IRC system model transmits L groups of IRC waveforms with a fixed pulse repetition interval T throughout the coherent processing interval, where each group of IRC waveforms includes K IRC waveforms;
[0012] The IRC system received signal model:
[0013]
[0014] where g l,k represents the received signal at the x l,k th PRI, M l,k = min{x l,k - 1, M}, M represents the maximum range-ambiguous sequence, 0 ≤ m ≤ M, β m represents the complex scattering coefficient in the range cell, represents the complex number space, n l,k represents the zero-mean colored noise at the receiving end, S represents the transmitted signal sampling sequence, S = [s 1,1 , s 1,2 ,..., s l,k ,..., s L,K , s l,k = [s l,k (1), s l,k (2),..., s l,k (N)] T s l,k represents the x l,kThe sampling sequence of the transmitted signal at a PRI, x l,k =(l - 1)K + k, N represents the sequence length, s l,k (N) represents the transmitted signal of the Nth sequence at the x l,k th PRI, 1 ≤ l ≤ L, 1 ≤ k ≤ K, (·) T denotes transpose;
[0015] The output signal model of the CMFG is:
[0016]
[0017]
[0018] Wherein, represents the output signal of the lth group of CMFG, h l,k represents the kth mismatch filter in the lth group of CMFG, denotes the convolution matrix.
[0019] In an embodiment of the present invention, the first SNR improvement factor of the lth group of CMFG is:
[0020]
[0021]
[0022]
[0023] Wherein, represents the first SNR improvement factor of the lth group of CMFG, P l S represents the signal power of the lth group of CMFG, P l N represents the noise power of the lth group of CMFG, v l,k represents the K-point discrete Fourier transform at h l,k point, (·) H denotes conjugate transpose, u l,k is the K-point discrete Fourier transform of n l,k , p l,k is the power spectral density of n l,k , ⊙ represents the exclusive NOR operation, (·) * denotes conjugate;
[0024] The first normalized sidelobe energy of the unambiguous output of the lth group of CMFG is:
[0025]
[0026] Among them, represents the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG;
[0027] The first normalized energy of the range ambiguity output of the l-th group of CMFG is:
[0028]
[0029] Among them, represents the first normalized energy of the range ambiguity output of the l-th group of CMFG.
[0030] In an embodiment of the present invention, the first CMFG optimization problem is:
[0031]
[0032]
[0033] Among them, h l,k represents the k-th mismatched filter in the l-th group of CMFG, w s and w n are weights that satisfy the condition of w s + w n = 1, represents the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, represents the first normalized energy of the range ambiguity output of the l-th group of CMFG, represents the first SNR improvement factor of the l-th group of CMFG, s l,k represents the transmitted signal sampling sequence at the x l,k -th PRI, represents the complex space, N represents the sequence length, and K represents the number of mismatched filters in each group of CMFG.
[0034] In an embodiment of the present invention, step 4 includes:
[0035] Step 4.1, according to the constraint conditions, when the effective power of the signal in the l-th group of CMFG is 1, obtain the output of the l-th group of CMFG;
[0036] Step 4.2: When the signal power of the l-th group of CMFG is 1, convert the first SNR improvement factor of the l-th group of CMFG, the first normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG, and the first normalized energy of the range-ambiguous output of the l-th group of CMFG into the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG, and the second normalized energy of the range-ambiguous output of the l-th group of CMFG according to the output of the l-th group of CMFG;
[0037] Step 4.2: Convert the first CMFG optimization problem into the second CMFG optimization problem according to the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG, and the second normalized energy of the range-ambiguous output of the l-th group of CMFG.
[0038] In an embodiment of the present invention, the constraint condition is:
[0039]
[0040] wherein,
[0041] The output of the l-th group of CMFG is:
[0042]
[0043] wherein,
[0044] The second SNR improvement factor of the l-th group of CMFG is:
[0045]
[0046] wherein, represents the second SNR improvement factor of the l-th group of CMFG, v l,k represents the K-point discrete Fourier transform at h l,k , and
[0047] The second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG is:
[0048]
[0049] wherein, represents the second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG.
[0050] The second normalized energy of the range-ambiguous output of the l-th group of CMFG is:
[0051]
[0052] Among them, represents the second normalized energy of the range ambiguity output of the l-th group of CMFG.
[0053] In an embodiment of the present invention, the second CMFG optimization problem is:
[0054]
[0055]
[0056] where T represents transpose.
[0057] In an embodiment of the present invention, the Lagrangian function is:
[0058]
[0059] where λ l represents the Lagrange multiplier, and Re represents the real part.
[0060] Advantages of the present invention:
[0061] The integrated radar-communication waveform complementary mismatch filter bank provided by the present invention introduces the principle of complementary sequences into the CMFG design of IRC waveforms, enhancing the radar performance of the system while maintaining the communication performance of the IRC system.
[0062] The present invention considers the influence of range ambiguity in the CMFG design; for the CMFG design, the present invention considers a more general situation in reality, that is, the noise is colored noise rather than white noise in traditional research. The present invention proposes a design method for a complementary mismatch filter bank based on the principle of complementary sequences, and the present invention has better range ambiguity echo suppression and better detection performance compared with traditional methods under the same conditions. Description of the Drawings
[0063] Figure 1 is a schematic flowchart of a design method for an integrated radar-communication waveform complementary mismatch filter bank provided by an embodiment of the present invention;
[0064] Figure 2 is the transmitted signal and received signal of the IRC radar-communication integrated signal used in an embodiment of the present invention;
[0065] Figure 3 is a schematic flowchart of the signal processing of the radar receiver provided by an embodiment of the present invention;
[0066] Figure 4It is a schematic diagram of the performance comparison result between PSLR (Peak-to-sidelobe ratio) and SNR-IF provided by an embodiment of the present invention;
[0067] Figure 5 It is a schematic diagram of the performance comparison result between AF (Attenuation factor) and SNR-IF provided by an embodiment of the present invention;
[0068] Figure 6 It is a schematic diagram of the comparison result between the detection probability and the false alarm probability in the present invention and the existing methods provided by an embodiment of the present invention. Detailed implementation manners
[0069] The following further describes the present invention in detail with specific embodiments, but the implementation manners of the present invention are not limited thereto.
[0070] Embodiment 1
[0071] In order to improve the processing performance of the radar-communication integrated waveform under colored noise, an embodiment of the present invention utilizes the principle of complementary sequences and proposes a design method for a complementary mismatch filter bank of the radar-communication integrated waveform. Please refer to Figure 1 , Figure 1 It is a schematic flowchart of a design method for a complementary mismatch filter bank of a radar-communication integrated waveform provided by an embodiment of the present invention. The design method for the complementary mismatch filter bank of the radar-communication integrated waveform proposed by the present invention includes steps 1-step 5, where:
[0072] Step 1: Construct an IRC system model, which includes an IRC system transmitted signal model, an IRC system received signal model, and a CMFG (Complementary mismatch filter group) output signal model.
[0073] In an example of the present invention, it is assumed that the IRC system will transmit L groups of IRC waveforms with a fixed pulse repetition interval (PRI) T during the entire coherent processing interval (CPI), where each group of IRC waveforms includes K IRC waveforms. The IRC waveforms use traditional communication waveforms, such as binary phase shift keying (BPSK) waveforms, and the transmitted waveform is as shown in Figure 2 Figure (a) in. In Figure 2 Figure (a) in, s l,k represents the transmitted signal sampling sequence at the x l,k th PRI, where xl,k = (l - 1)K + k. When 1 ≤ k ≤ K and 1 ≤ l ≤ L, s l,k can be expressed as:
[0074] s l,k = [s l,k (1), s l,k (2),..., s l,k (N)] T (1)
[0075] where N represents the sequence length, s l,k (N) represents the transmitted signal of the Nth sequence at the x l,k th PRI, and T represents the transpose.
[0076] Assume that the maximum range ambiguity sequence is known as M (M ≤ LK - 1). The received signal at the radar receiver includes an unambiguous echo, first - order and second - order range - ambiguous echoes, as shown in Figure (b) of Figure 2 . For simplicity, only consider the target echo in the range cell where 0 ≤ m ≤ M, and c represents the speed of light. The received signal at the x l,k th PRI is denoted by g l,k as shown in Figure 2 . g l,k contains the echo of the IRC waveform with range ambiguity and colored noise, which is expressed as:
[0077]
[0078] where β m represents the complex scattering coefficient in the range cell, including path loss, target scattering, and the phase introduced due to delay during propagation. M l,k = min{x l,k - 1, M}, S represents the transmitted signal sampling sequence, S = [s 1,1 , s 1,2 ,..., s l,k ,..., s L,K , only the (l - 1)K + k - mth element is 1 and the rest are 0, n l,k represents the zero - mean colored noise at the receiving end, represents the complex space. β 0 s l,k represents the unambiguous echo, represents the range - ambiguous echo.
[0079] In this embodiment, the following assumptions are made:
[0080] Assume nl,k The power spectrum density (PSD) of u is known. l,k is n l,k The K-point discrete Fourier transform (DFT) of n, where K = 2N - 1. Therefore, the power spectrum density of n can be expressed as: l,k The power spectrum density of n can be expressed as:
[0081]
[0082] where ⊙ represents the exclusive NOR operation, and (·) * represents the conjugate.
[0083] Assume that the received n l,k are independent of each other in different PRIs.
[0084] Let We can obtain Then Equation (2) is transformed into:
[0085]
[0086] where g l,k represents the received signal at the x l,k th PRI.
[0087] In a radar receiver, assume there are L groups of CMFGs, as Figure 3 shown. Each CMFG contains K mismatched filters. The kth mismatched filter in the lth group of CMFGs is expressed as:
[0088] h l,k = [h l,k (1), h l,k (2),..., h l,k (N)] T (5)
[0089] where h l,k (1), h l,k (2),..., h l,k (N) represent the N sampling points of the kth mismatched filter in the lth group of CMFGs.
[0090] As Figure 3 shown, the sum of the outputs of all mismatched filters is the output signal of the CMFG, denoted by r l r. The output signal of the lth group of CMFGs is expressed as:
[0091]
[0092] where Represents the output noise of the filter. When m = 0, β 0 r l,0 is the unambiguous output of the l-th group of CMFG; when m > 0, represents the range-ambiguous output of the l-th group of CMFG, where: represents the convolution matrix,
[0093] Step 2: Under the conditions of the IRC system model, establish the performance metrics of the CMFG under colored noise. The performance metrics of the CMFG include the first SNR improvement factor, the first normalized sidelobe energy of the unambiguous output, and the first normalized energy of the CMFG range-ambiguous output.
[0094] Step 2.1: Derive the output SNR of the l-th CMFG, which can be expressed as:
[0095]
[0096] where, is the input SNR, and the expression is
[0097] P l S represents the signal power of the l-th group of CMFG, P l S The expression is as follows:
[0098]
[0099] where,
[0100] P l N represents the noise power of the l-th group of CMFG, and the expression is as follows:
[0101]
[0102] where, represents the K-point discrete Fourier transform at h l,k .
[0103] Step 2.2: Since it is assumed that the noises received in different pulse repetition intervals are independent of each other, Equation (9) can be simplified to:
[0104]
[0105] Therefore, Equation (11) is the noise power of the l-th group of CMFG after simplification.
[0106] The first SNR improvement factor obtained according to Equation (10) is:
[0107]
[0108] wherein, represents the first SNR improvement factor of the l-th group of CMFG.
[0109] Step 2.4, the first normalized sidelobe energy of the unambiguous output of the l-th CMFG is expressed as:
[0110]
[0111] wherein, represents the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG.
[0112] Step 2.5, the first normalized energy of the range ambiguous output of the l-th CMFG is defined as:
[0113]
[0114] wherein, represents the first normalized energy of the range ambiguous output of the l-th group of CMFG.
[0115] Step 3, obtain the first CMFG optimization problem according to the CMFG performance index, and the first CMFG optimization problem is a non-convex optimization problem.
[0116] Specifically, to make the CMFG have a low-sidelobe unambiguous output, a low-energy range ambiguous output, and a high SNR-IF characteristic, a CMFG weighted optimization problem, that is, the first CMFG optimization problem, is established according to the CMFG performance index. The model of this first CMFG optimization problem is:
[0117]
[0118]
[0119] wherein, l = 1, 2,..., L, w s and w n are weights that satisfy the condition w s + w n = 1,
[0120] Step 4, obtain the second CMFG optimization problem according to the first CMFG optimization problem, and the second CMFG optimization problem is a convex optimization problem.
[0121] Specifically, since the first CMFG optimization problem is a non-convex optimization problem, it is necessary to convert it into a convex optimization problem.
[0122] Step 4.1: When the effective signal power of the l-th group of CMFG is 1 according to the constraint conditions, obtain the output of the l-th group of CMFG.
[0123] Specifically, when the constraint conditions are met, P l S is always equal to 1, such that Then the output of the l-th CMFG can be written as:
[0124]
[0125] The constraint conditions are:
[0126]
[0127] Among them,
[0128] Step 4.2: When the signal power of the l-th group of CMFG is 1, according to the output of the l-th group of CMFG, convert the first SNR improvement factor of the l-th group of CMFG, the first normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG, and the first normalized energy of the range-ambiguous output of the l-th group of CMFG into the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG, and the second normalized energy of the range-ambiguous output of the l-th group of CMFG.
[0129] Specifically, the second SNR improvement factor of the l-th group of CMFG is:
[0130]
[0131] Among them, represents the second SNR improvement factor of the l-th group of CMFG,
[0132] The second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG is:
[0133]
[0134] Among them, represents the second normalized sidelobe energy of the non-ambiguous output of the l-th group of CMFG.
[0135] The second normalized energy of the range-ambiguous output of the l-th group of CMFG is:
[0136]
[0137] Among them, represents the second normalized energy of the range-ambiguous output of the l-th group of CMFG.
[0138] Step 4.2. Transform the first CMFG optimization problem into a second CMFG optimization problem according to the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, and the second normalized energy of the range-ambiguous output of the l-th group of CMFG. The model of the second CMFG optimization problem is:
[0139]
[0140]
[0141] That is, formula (21) is the transformed convex optimization problem.
[0142] Step 5. Process the second CMFG optimization problem using the Lagrange multiplier function to obtain the final mismatched filter.
[0143] Specifically, solve the second CMFG optimization problem using the Lagrange multiplier function, which is expressed as:
[0144]
[0145] where λ l represents the Lagrange multiplier, and Re represents the real part.
[0146] The optimization problem needs to satisfy The solution can be obtained as:
[0147]
[0148] where represents the finally obtained optimal mismatched filter, D = [I N , 0 N×(N-1) , and F J represents the J-point DFT matrix.
[0149] For the integrated radar and communication waveform complementary mismatched filter bank provided by the present invention, the principle of complementary sequences is introduced into the CMFG design of the IRC waveform, enhancing the radar performance of the system while maintaining the communication performance of the IRC system.
[0150] The present invention considers the influence of range ambiguity in the CMFG design; for the CMFG design, the present invention considers a more general situation in reality, that is, the noise is colored noise rather than white noise in traditional research. The present invention proposes a design method for a complementary mismatched filter bank based on the principle of complementary sequences, and the present invention has better range-ambiguous echo suppression and better detection performance compared with traditional methods under the same conditions.
[0151] Simulation analysis
[0152] To verify the effectiveness of the designed complementary mismatched filter bank for radar-communication integration waveforms under colored noise provided by the embodiments of the present invention, simulation verification is adopted to illustrate the beneficial effects of the embodiments of the present invention.
[0153] To evaluate the performance of the designed CMFG, the peak-to-sidelobe ratio (PSLR), the attenuation factor (AF), and the SNR improvement factor (SNR-IF) defined above are adopted.
[0154] 1) Peak-to-sidelobe ratio.
[0155] The peak-to-sidelobe ratio is used to measure the SLL of the unambiguous output of the CMFG, and its definition is as follows:
[0156]
[0157] In the formula, P sl represents the maximum sidelobe value of the unambiguous output of the CMFG, and P ml represents the peak value.
[0158] 2) Attenuation factor.
[0159] The AF is used to evaluate the performance of the CMFG in range ambiguity suppression, and its definition is as follows:
[0160]
[0161] In the formula, The larger the AF, the better the performance of the proposed CMFG in range ambiguity suppression.
[0162] The BPSK sequence with a length of N = 64 is used to construct the IRC waveform. In each simulation, 8 different IRC waveforms are randomly generated, and the maximum range ambiguity is set to 1. The designed CMFG with L = 1, K = 1, and M = 0 and the CMFG with L = 1, K = 1, and M = 1 are compared with the traditional matched filter and the mismatched filter. To obtain the simulation results, 500 Monte Carlo experiments are carried out.
[0163] In Figure 4 the performance of the CMFG in terms of the PSLR of the unambiguous output and the SNR-IF (with different weights) is shown. Along the arrow direction, the weight w n increases from 0 to 1. It can be seen that for the designed CMFG, the SNR-IF increases with the increase of w n while the PSLR of the unambiguous output decreases with the increase of w ndeteriorates as it increases. When having the same unambiguous output PSLR, CMFG has a higher SNR-IF at M = 0 than at M = 1. In addition, the SNR-IF performance of the designed CMFG is always greater than that of the other two filters. When w n <5.6×10 -3 is less than <5.6×10 n <0.02, the unambiguous output PSLR of CMFG at M = 0 is lower than that of the matched filter and the mismatched filter.
[0164] Figure 5 shows the AF and SNRIF performance of CMFG. The weight w n increases from 0 to 1 along the arrow direction. It can be seen that the AF of the designed CMFG decreases as w n increases. CMFG at M = 1 always has the largest AF. This indicates that the designed CMFG at M = 1 has the best performance in range ambiguity echo suppression.
[0165] To show the detection performance of the IRC system with different filters, Figure 6 shows the variation of the detection probability and the false alarm probability when the SNR input is -22 dB. Since CMFG has a higher SNR-IF at M = 0 than at M = 1, CMFG has better detection performance at M = 0 than at M = 1, and the detection performance of the designed CMFG is better than that of the other filters.
[0166] In the description of this specification, the descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.
[0167] Although the present application has been described in connection with various embodiments, those skilled in the art will understand and realize other variations of the disclosed embodiments by viewing the accompanying drawings, the disclosure, and the appended claims during the implementation of the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality. A single processor or other unit may implement several functions recited in the claims. Certain measures are recited in mutually different dependent claims, but this does not mean that these measures cannot be combined to produce good results.
[0168] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, and all should be regarded as belonging to the protection scope of the present invention.
Claims
1. A design method for an integrated radar communication waveform complementary mismatched filter bank, characterized in that, the design method includes: Step 1, construct an IRC system model, which includes an IRC system transmitted signal model, an IRC system received signal model, and a CMFG output signal model; Step 2, under the conditions of the IRC system model, establish the CMFG performance indicators under colored noise, and the CMFG performance indicators include the first SNR improvement factor, the first normalized sidelobe energy of the unambiguous output, and the first normalized energy of the CMFG range ambiguous output; Step 3, obtain the first CMFG optimization problem according to the CMFG performance indicators, and the first CMFG optimization problem is a non-convex optimization problem; Step 4, obtain the second CMFG optimization problem according to the first CMFG optimization problem, and the second CMFG optimization problem is a convex optimization problem; Step 5, use the Lagrangian function to process the second CMFG optimization problem to obtain the final mismatched filter.
2. The design method for an integrated radar communication waveform complementary mismatched filter bank according to claim 1, characterized in that, the IRC system model will transmit L groups of IRC waveforms with a fixed pulse repetition interval T throughout the coherent processing interval, where each group of IRC waveforms includes K IRC waveforms; the IRC system received signal model: where, g l,k represents the received signal at the x l,k -th PRI, M l,k = min{x l,k - 1, M}, M represents the maximum range ambiguity sequence, 0 ≤ m ≤ M, β m represents the complex scattering coefficient in the range cell, represents the complex number space, n l,k represents the zero-mean colored noise at the receiving end, S represents the transmitted signal sampling sequence, S = [s 1,1 , s 1,2 ,..., s l,k ,..., s L,K , s l,k = [s l,k (1), s l,k (2),..., s l,k (N)] T , s l,k represents the transmitted signal sampling sequence at the x l,k -th PRI, x l,k = (l - 1)K + k, N represents the sequence length, s l,k (N) represents the transmitted signal of the N-th sequence at the x l,k -th PRI, 1 ≤ l ≤ L, 1 ≤ k ≤ K, T represents the transpose; the CMFG output signal model is: Among them, represents the output signal of the l-th group of CMFG, represents the output noise of the filter, h l,k represents the k-th mismatch filter in the l-th group of CMFG, represents the convolution matrix.
3. The design method for an integrated radar communication waveform complementary mismatched filter bank according to claim 2, characterized in that, the first SNR improvement factor of the l-th group of CMFG is: Among them, represents the first SNR improvement factor of the l-th group of CMFG, P l S represents the signal power of the l-th group of CMFG, P l N represents the noise power of the l-th group of CMFG, v l,k represents the K-point discrete Fourier transform at h l,k , (·) H represents conjugate transpose, u l,k is the K-point discrete Fourier transform of n l,k , p l,k is the power spectral density of n l,k , ⊙ represents the exclusive NOR operation, (·) * represents conjugate; the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG is: Among them, represents the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG; the first normalized energy of the range ambiguous output of the l-th group of CMFG is: Among them, represents the first normalized energy of the range ambiguity output of the l-th group of CMFG.
4. The design method for an integrated radar communication waveform complementary mismatched filter bank according to claim 1, characterized in that, the first CMFG optimization problem is: where h l,k represents the k-th mismatched filter in the l-th group of CMFG, w s and w n are weights that satisfy the condition w s +w n = 1, represents the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, represents the first normalized energy of the range-ambiguous output of the l-th group of CMFG, represents the first SNR improvement factor of the l-th group of CMFG, s l,k represents the transmitted signal sampling sequence at the x l,k -th PRI, represents the complex space, N represents the sequence length, and K represents the number of mismatched filters in each group of CMFG.
5. The design method for an integrated radar communication waveform complementary mismatched filter bank according to claim 4, characterized in that, Step 4 includes: Step 4.1, according to the constraint conditions, when the signal power of the l-th group of CMFG is 1, obtain the output of the l-th group of CMFG; Step 4.2, when the effective signal power of the l-th group of CMFG is 1, according to the output of the l-th group of CMFG, convert the first SNR improvement factor of the l-th group of CMFG, the first normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, and the first normalized energy of the range ambiguous output of the l-th group of CMFG into the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, and the second normalized energy of the range ambiguous output of the l-th group of CMFG; Step 4.2, according to the second SNR improvement factor of the l-th group of CMFG, the second normalized sidelobe energy of the unambiguous output of the l-th group of CMFG, and the second normalized energy of the range ambiguous output of the l-th group of CMFG, convert the first CMFG optimization problem into the second CMFG optimization problem.
6. The design method of the radar-communication integrated waveform complementary mismatched filter bank according to claim 5, characterized in that, the constraint condition is: Among them, the output of the l-th group of CMFG can be written as: Among them, the second SNR improvement factor of the l-th group of CMFG is: Among them, represents the second SNR improvement factor of the l-th group of CMFG, v l,k represents the K-point discrete Fourier transform at h l,k , the second normalized sidelobe energy of the unambiguous output of the l-th group of CMFG is: Among them, represents the second normalized sidelobe energy of the unambiguous output of the l-th group of CMFG; the second normalized energy of the range-ambiguous output of the l-th group of CMFG is: Among them, represents the second normalized energy of the range ambiguity output of the l-th group of CMFG.
7. The design method of the radar-communication integrated waveform complementary mismatched filter bank according to claim 6, characterized in that, the second CMFG optimization problem is: where (·) T denotes transpose.
8. The design method of the radar-communication integrated waveform complementary mismatched filter bank according to claim 7, characterized in that, the Lagrangian function is: where λ l denotes the Lagrange multiplier, and Re denotes the real part.