Waveform optimization method for integrated communication and perception of UAV in marine environment

Abstract

The present invention relates to the field of maritime wireless communication technology, and more specifically, to an integrated waveform optimization method for communication and perception of unmanned aerial vehicles (UAVs) in a marine environment, which has both good communication performance and good perception performance. The method is characterized in that, for a maritime UAV ISAC system, in order to enable the integrated waveform to simultaneously have both target detection and communication functions, it is necessary to optimize the communication sum rate while constraining radar performance. The present invention models the wireless propagation channel of the UAV in a marine environment, and proposes an integrated waveform weighted optimization design method. The communication sum rate and radar beam pattern error are weighted, and a convex approximation solution is obtained using an SCA algorithm. The weight r is within the interval of [0.2, 0.5], which can ensure that the integrated system has good communication performance while still having good perception performance.

Description

Technical field:

[0001] The present invention relates to the field of marine wireless communication technology, and more specifically to a waveform optimization method for integrating communication and perception of unmanned aerial vehicles (UAVs) in a marine environment, which not only has good communication performance but also good perception performance. Background technology:

[0002] The future of 6G will usher in a new era of intelligent interconnection and the integration of virtual and real life. This is inseparable from the development of communication and perception technologies. However, due to the scarcity of frequency resources, sharing these resources between the two is a pressing issue. Integrated Communication and Perception (ISAC) technology offers a new approach to addressing this issue. It allows communication and perception to share equipment and frequency resources, enabling simultaneous target detection and information communication by transmitting an integrated waveform. It is considered a key technology for 6G. my country is also a major maritime nation with a coastline exceeding 32,600 km and abundant marine resources. With the increasing frequency of ocean exploration activities, the demand for marine communications and maritime target perception is increasing significantly.

[0003] Existing research has focused on terrestrial wireless communications. With the growing demand for ocean exploration and the development of the marine economy, maritime wireless communications are also gaining increasing attention. Currently, there is limited research on ISAC technology for maritime wireless communications. Compared to terrestrial wireless channels, the marine wireless channel environment is more complex and harsh, characterized by high attenuation and significant influences from temperature and humidity.

[0004] According to data from the Ministry of Industry and Information Technology, by March 2024, my country had built a total of 3.647 million 5G base stations. Compared to 4G base stations, 5G base stations offer wider coastal coverage, enabling 5G network coverage within 40 kilometers. However, compared to land-based base stations, the number of base stations located along the coast, on islands, or on the sea surface remains relatively small, due to the difficulty and high cost of constructing base stations on the sea surface. Drones, with their lightness, flexibility, and portability, are suitable for use as nodes in maritime wireless communications. Drones can communicate wirelessly via air-to-sea and near-sea wireless channels. The maritime communication environment dictates unique properties for these two channels: 1. Sparsity: This is primarily reflected in the fact that obstructions in the maritime wireless propagation environment are sparsely distributed, primarily over vast expanses of sea. It is also reflected in the scattered distribution of receiving users at sea, primarily on ships and islands. This is significantly different from the densely populated and bustling conditions on land. Sparsity means that the direct line-of-sight (LOS) path for electromagnetic wave propagation is generally unobstructed. Furthermore, the large sea surface area provides a propagation path for sea surface reflection. This sparsity makes both direct and sea surface reflection propagation paths extremely important in maritime channel modeling. 2. Instability: This is primarily caused by the undulating motion of ocean waves. The vertical motion of ocean waves causes the height of antennas onboard ships above the ocean surface to fluctuate accordingly. Actual measurements have shown that changes in antenna height will cause variations in signal strength. Furthermore, for sea surface reflection propagation paths, the wave-induced surface motion causes random variations in the reflecting surface, which in turn alters the signal propagating along the reflection path, leading to multipath fading. 3. Evaporation Duct Phenomenon: In coastal and marine environments, a sharp drop in the atmospheric refractive index caused by fluctuations in atmospheric pressure, humidity, and temperature creates a nearly permanent atmospheric duct. Signals transmitted through this duct do not diffuse isotropically but are trapped between the ocean surface and the duct. Signals propagating via evaporation ducting can achieve beyond-line-of-sight (B-LOS) transmission, thus attracting considerable attention. Humidity is the most critical factor in the formation of atmospheric ducting, and evaporation ducting, caused by evaporation from sea surface water, plays a key role in atmospheric ducting. Evaporation ducting is more likely to occur in tropical ocean regions. This means that in addition to the LOS path and the sea surface reflection path, a third path, caused by evaporation ducting, may also be present in near-sea wireless signal propagation. Summary of the invention:

[0005] In view of the shortcomings and deficiencies in the existing technology, the present invention proposes a waveform optimization method for integrated communication and perception of unmanned aerial vehicles in marine environments, which not only has good communication performance but also good perception performance.

[0006] The present invention is achieved by the following measures:

[0007] A method for optimizing the integrated waveform of UAV communication and perception in marine environments is proposed. The method is characterized by the fact that for a marine UAV ISAC system, in order to make the integrated waveform have both target detection and communication functions, it is necessary to optimize the communication rate while constraining the radar performance. Therefore, there is a problem (P2):

[0008]

[0009] where ||·||2 is the 2-norm of the matrix, α k is the weight of the kth communication user, R1 is the solution to the problem (P1), and Γ is the threshold, that is, the error between the covariance matrix of the integrated waveform and R1 must be less than this threshold to ensure radar performance;

[0010] Transform the problem (P2) and let Then problem (P2) is equivalent to problem (P3):

[0011]

[0012]

[0013]

[0014]

[0015] The feasibility of problem (P3) is expressed as the following question (FP1):

[0016] (FP1): find{w k}

[0017] st(17a),(17b),(17c) and (17d)

[0018] The inequality constraint (17a) is equivalent to the following equation:

[0019] Where Z is the error matrix, The difference between R1 and R2, then constraints (17a) and (17b) are expressed as:

[0020] ||Z||2≤Γ(19a),tr(R1)+tr(Z)≤P max (19b),

[0021] Since R1 is the solution to problem (P1), the trace of R1 is equal to P max , and the elements on the diagonal of R1 are all equal to P max / N, Γ is generally very small, so when Z satisfies constraint (19a), the elements in Z are very small. To make constraint (19b) hold, the elements on the diagonal of Z must be less than or equal to 0, and to make (17d) meet, the matrix after R1+Z is still a semi-positive definite matrix. It is believed that constraints (17a), (17b) and (17d) must have a non-empty feasible domain. Finally, constraint (17c) is satisfied using singular value decomposition (SVD) or Gaussian randomization after satisfying other constraints.

[0022] The objective function in problem (P3) is non-concave, and the constraint (17c) is non-convex. If the perception performance constraint (17a) is strict, that is, the error threshold Γ between the integrated waveform covariance matrix and the radar beam covariance matrix is ​​required to be extremely small, the feasible domain of the optimization problem will be greatly reduced, which may lead to poor communication performance. Therefore, the following weighted optimization problem (P4) is considered:

[0023]

[0024] Where 0≤ρ is the weighting coefficient, which means the ratio of communication power to perception power, r k ({W k}) is the communication rate of the kth communication user,

[0025] The objective function and constraints of problem (P4) are still non-convex. The continuous convex approximation SCA and semi-definite relaxation SDR methods are used to solve problem (P4).

[0026] The method of using continuous convex approximation SCA and semi-definite relaxation SDR described in the present invention to solve problem (P4) is specifically: the non-concave objective function is approximated as a concave function through the SCA method, and the original problem is iteratively approximated. During the approximation, the approximate function to be found must have the same first-order derivative as the original objective function and must be the lower bound of the original objective function.

[0027] Consider the p≥1th iteration in the SCA algorithm, and the iteration point is set to Observe the objective function of problem (P4). The first sum is a non-concave function, and the second subtracted term is a convex function, that is, the total form is a non-concave plus concave form. Transform one of the first sums and perform a first-order Taylor expansion, and we have:

[0028]

[0029] in:

[0030]

[0031] yes At the iteration point The first-order Taylor expansion at , because It can be expanded into a concave-minus-concave form, so we only need to The second term of can be expanded by the first order Taylor. The first order Taylor expansion of the concave function must be greater than or equal to the concave function itself, so

[0032] Therefore, the p-th SCA approximation iteration of problem (P4) can be expressed as problem (P5.p):

[0033]

[0034] The rank-one constraint (17c) in problem (P5.p) is still non-convex. Using the idea of ​​SDR, we relax the rank-one constraint and express the relaxed problem as problem (SDR5.p):

[0035]

[0036] Problem (SDR5.p) is a convex semidefinite program (SDP) that can be solved with the help of convex optimization solvers such as CVX. The solution to problem (SDR5.p) is If it satisfies the rank-one constraint (17c), then it is the optimal solution to the problem (P5.p). If it does not satisfy the rank-one constraint (17c), then use SVD or Gaussian randomization to obtain a rank-one solution. In the next SCA iteration, the iteration point is updated to γ∈(0,1] is the iteration step size.

[0037] The present invention provides a maritime UAV ISAC system, wherein the UAV is fixed at a height H above the sea surface. To simplify the design, it is assumed that the UAV is equipped with a uniform linear array with N vertically arranged antennas, with an antenna spacing of d. t , so the transmitted signal has nothing to do with the direction of the drone. The N transmitting antennas are used for target detection and information communication at the same time. The drone acts as an aerial node near the sea surface to communicate with K single receiving antenna users on the sea surface, and detects M targets near the sea surface at the same time. With the drone as the origin, a three-dimensional rectangular coordinate system is established. The horizontal coordinate set of the K communication users is represents the horizontal coordinate of the kth communication user, and the horizontal coordinate set of M detection targets is It represents the horizontal coordinate of the mth detection target. The target position is obtained through the detection task previously scheduled by the UAV, such as omnidirectional search detection. After that, the UAV performs directional detection on the predetermined target. The duration of one working cycle of the UAV is T. One working cycle is divided into L time slots, and the duration of each time slot is Δ = T / L. During one working cycle, the UAV transmits an integrated waveform to perform directional detection on the target area of ​​interest and complete communication with the communication user at the same time.

[0038] Assume that the communication signal sent to the kth user in the lth time slot is s k [l], and The communication signals of different users are independent of each other. is the corresponding beamforming vector, then the transmitted signal vector of the lth time slot can be expressed as:

[0039]

[0040] Then the covariance matrix of the transmitted signal is:

[0041]

[0042] in represents the mathematical expectation of time, (·) H , (·) * denote conjugate transpose and conjugate respectively,

[0043] The average transmission power of the drone is:

[0044]

[0045] Among them||·|| 2 represents the square of the vector 2 norm,

[0046] Assume that the maximum transmission power of the UAV is P max , so there are the following power constraints:

[0047]

[0048] The signal transmitted by the drone reaches the receiving antenna of the communication user after passing through the near-sea wireless channel. Assuming that the channel state is known and the distance between the transmitting and receiving antennas is close, considering the double-ray path loss model, the channel vector between the transmitting antenna and the kth user is expressed as:

[0049] h k =βa(θ k ) (9),

[0050] Where β=(λ / (4πd k ))(2sin((2πh t hr ) / (λd k ))) is the two-ray path loss, where λ is the operating wavelength of the transmitted signal, is the horizontal distance between the UAV and the kth user, h t and h r are the transmitting antenna height and the receiving antenna height respectively, a(θ k ) is the direction vector between the UAV and the kth user, which is specifically expressed as:

[0051] a(θ k )=[1 exp(j2πd t sinθ k / λ)…exp(j2π(N-1)d t sinθ k / λ)] T (10),

[0052] where θ k is the elevation angle from the kth user to the UAV, that is

[0053] Assume that the received signal vector of the kth communication user in the lth time slot is y k [l], then:

[0054]

[0055] Where n k [l] is the noise received by the kth communication user in the lth time slot, and Therefore, the Signal to Interference plus Noise Ratio (SINR) of the kth communication user in the lth time slot is:

[0056]

[0057] Where |·| represents the modulo operation. It can be seen that within a working cycle, since the channel vector and the beamforming vector do not change with time, γ k It also does not change with time, that is, γ k [l] = γ k , then the communication rate achievable by the kth communication user in the lth time slot is:

[0058] r k =log2(1+γ k ) (13),

[0059] The integrated signal transmitted by the UAV performs target detection while communicating, and its transmission beam pattern is expressed as:

[0060]

[0061] Where θ is the detection azimuth,

[0062] The classic MIMO radar beamforming problem can be formulated as Problem (P1):

[0063]

[0064] in is a set of detection angles, which divides the entire detection angle into M blocks. α is a weight coefficient, P d (θ m ) is the ideal transmit beam pattern at θ m The value in the direction, diag(·) means taking the diagonal vector, 1 is a vector with all elements 1, P t is the transmit power, N t is the number of transmitting antennas.

[0065] This paper studies an integrated communication and perception system for unmanned aerial vehicles (UAVs) operating in marine environments. The wireless propagation channel for UAVs in marine environments is modeled. A weighted integrated waveform optimization design method is proposed. This method weights the communication sum rate and radar beam pattern error, and uses the SCA algorithm to perform a convex approximation. Simulation results show that a weight ρ value in the range [0.2, 0.5] ensures good communication performance while maintaining good perception performance for the integrated system. Description of the drawings:

[0066] Figure 1 This is a schematic diagram of the wireless channel at sea.

[0067] Figure 2 Schematic diagram of the ISAC system of the maritime UAV in the present invention.

[0068] Figure 3 This is the UAV transmitting antenna model in the present invention.

[0069] Figure 4 These are the two-ray path loss model and the three-ray path loss model at different operating frequencies in the present invention, (a) is the two-ray model, and (b) is the three-ray model.

[0070] Figure 5 These are the integrated beam pattern, the MIMO radar beam pattern, and the ideal beam pattern under different communication weights in the embodiment of the present invention.

[0071] Figure 6 1 is the reachability and rate curve under different noise powers when the maximum transmission power of the UAV in the embodiment of the present invention is 10W.

[0072] Figure 7 1 and 2 are curves showing the communication reachability and rate as well as the error between the integrated beam and the radar beam in an embodiment of the present invention. (a) is the communication reachability and rate curve, and (b) is the error between the integrated beam and the radar beam. Specific implementation method:

[0073] UAV transmission signals propagate through air-to-sea and near-sea wireless channels. Compared to inland propagation environments, the sparseness of the ocean environment results in sparser scattering of transmitted signals. In most cases, only two propagation paths are considered: line-of-sight transmission and reflection from the sea surface. The air-to-sea channel is dependent on elevation angle, and path loss models with varying degrees of accuracy are proposed. A single logarithmic distance model is used to approximate path loss over the entire link distance range, with reference to the free-space path loss model. The expression for this is as follows:

[0074]

[0075] Where d is the link distance, d min is the reference distance, A0 is the constant at the minimum effective link distance, n A is the path loss exponent, X A is the shadow fading, F A is an adjustment, variable ζ = -1 or +1, depending on the movement of the drone. +1 means the drone is moving towards the receiver, and -1 means the drone is moving away from the receiver. Here we assume that the drone is at a fixed height and does not move, so this term can be ignored.

[0076] In addition, there are two-ray models and three-ray models that are more accurate than the single logarithmic distance model to describe wireless propagation loss in marine environments. The two-ray model is expressed as follows:

[0077]

[0078] Where d is the link distance, λ is the operating wavelength, h t is the transmitting antenna height, h r is the receiving antenna height.

[0079] When there is a path transported by evaporation ducts, the two-ray model is no longer applicable and the three-ray model is used instead:

[0080] L threee-ray (d) = -10log 10 ((λ / (4πd)) 2 (2(1+Δ)) 2 ) (3)

[0081] Where Δ=2sin(2πh t h r / (λd))sin(2π(he -h t )(h e -h r ) / (λd)),h e is the effective height of the evaporation duct.

[0082] The two-ray model and the three-ray model have different applicable conditions, which are mainly affected by the link distance d, such as Figure 1 As shown in the figure: when d is small, the angle between the LOS path and the sea level is large, no third path appears, and the double-ray model is applicable; d gradually increases, and when it is greater than the threshold d break =4h t h r / λ, a third path appears, which is transmitted by the evaporation duct. The three-ray model is applicable. When d continues to increase and exceeds the maximum range of LOS transmission d LOS When the signal is transmitted beyond the horizon only by the evaporation duct, d LOS It is given by the following formula:

[0083]

[0084] in is the radius of the Earth.

[0085] Consider Figure 2 The maritime UAV ISAC system is shown in FIG. , where the UAV is fixed at a height H from the sea surface. To simplify the design, it is assumed that the UAV is equipped with a Figure 3 The vertical arrangement shown is a uniform linear array with N antennas, with an antenna spacing of d t Therefore, the transmitted signal has nothing to do with the direction of the drone. These N transmitting antennas are used for target detection and information communication at the same time. The drone acts as an aerial node near the sea surface to communicate with K single receiving antenna users on the sea surface, and detects M targets near the sea surface at the same time. With the drone as the origin, a three-dimensional rectangular coordinate system is established, and the horizontal coordinate set of the K communication users is represents the horizontal coordinate of the kth communication user, and the horizontal coordinate set of M detection targets is represents the horizontal coordinate of the mth detected target. The target's location is determined by the drone's pre-determined detection mission, such as omnidirectional search. The drone then performs directional detection of the target. Each UAV operation cycle lasts T and is divided into L time slots, each with a duration of Δ = T / L. During each operation cycle, the drone transmits an integrated waveform to perform directional detection of the target area of ​​interest while simultaneously communicating with the user.

[0086] Assume that the communication signal sent to the kth user in the lth time slot is sk [l], and The communication signals of different users are independent of each other. is the corresponding beamforming vector, then the transmitted signal vector of the lth time slot can be expressed as:

[0087]

[0088] Then the covariance matrix of the transmitted signal is:

[0089]

[0090] in represents the mathematical expectation of time, (·) H , (·) * denote conjugate transpose and conjugate, respectively.

[0091] The average transmission power of the drone is:

[0092]

[0093] where ||·|| 2 Represents the square of the 2-norm of a vector.

[0094] Assume that the maximum transmission power of the UAV is P max , so there are the following power constraints:

[0095]

[0096] The signal transmitted by the drone reaches the receiving antenna of the communication user after passing through the near-sea wireless channel. Assuming that the channel state is known and the distance between the transmitting and receiving antennas is close, considering the double-ray path loss model, the channel vector between the transmitting antenna and the kth user is expressed as:

[0097] h k =βa(θ k ) (9)

[0098] Where β=(λ / (4πd k ))(2sin((2πh t h r ) / (λd k ))) is the two-ray path loss, where λ is the operating wavelength of the transmitted signal, is the horizontal distance between the UAV and the kth user, h t and h r are the transmitting antenna height and the receiving antenna height respectively, a(θ k ) is the direction vector between the UAV and the kth user, which is specifically expressed as:

[0099] a(θk )=[1 exp(j2πd t sinθ k / λ)…exp(j2π(N-1)d t sinθ k / λ)] T (10)

[0100] where θ k is the elevation angle from the kth user to the UAV, that is

[0101] Assume that the received signal vector of the kth communication user in the lth time slot is y k [l], then:

[0102]

[0103] Where n k [l] is the noise received by the kth communication user in the lth time slot, and

[0104] Therefore, the Signal to Interference plus Noise Ratio (SINR) of the kth communication user in the lth time slot is:

[0105]

[0106] Where |·| represents the modulo operation. It can be seen that in one working cycle, because the channel vector and the beamforming vector do not change with time, γ k It also does not change with time, that is, γ k [l] = γ k , then the communication rate achievable by the kth communication user in the lth time slot is:

[0107] r k =log2(1+γ k ) (13)

[0108] The integrated signal transmitted by the UAV performs target detection while communicating, and its transmission beam pattern is expressed as:

[0109]

[0110] Where θ is the detection azimuth.

[0111] The classic MIMO radar beamforming problem can be formulated as Problem (P1):

[0112]

[0113] in is a set of detection angles, which divides the entire detection angle into M blocks. α is a weight coefficient, P d (θ m ) is the ideal transmit beam pattern at θ m The value in the direction, diag(·) means taking the diagonal vector, 1 is a vector with all elements 1, P t is the transmit power, N t is the number of transmitting antennas.

[0114] In order to make the integrated waveform have both target detection and communication functions, we need to optimize the communication rate while constraining the radar performance. Therefore, there is a problem (P2):

[0115]

[0116]

[0117] where ||·||2 is the 2-norm of the matrix, α k is the weight of the kth communication user, R1 is the solution to the problem (P1), and Γ is the threshold, that is, the error between the covariance matrix of the integrated waveform and R1 must be less than this threshold to ensure radar performance.

[0118] Transform the problem (P2) and let Then problem (P2) can be equivalent to problem (P3):

[0119]

[0120]

[0121]

[0122]

[0123] For problem (P3), its feasibility can be expressed as the following problem (FP1):

[0124] (FP1): find{w k}

[0125] st(17a),(17b),(17c) and (17d)

[0126] For the inequality constraint (17a), we can express it as follows:

[0127]

[0128] Where Z is the error matrix, The difference between R1 and R2, then constraints (17a) and (17b) can be expressed as:

[0129] ||Z||2≤Γ (19a)

[0130] tr(R1)+tr(Z)≤P max (19b)

[0131] Since R1 is the solution to problem (P1), the trace of R1 is equal to P max , and the elements on the diagonal of R1 are all equal to P max / N, Γ is generally very small. Therefore, when Z satisfies constraint (19a), the elements in Z are very small. To satisfy constraint (19b), all elements on the diagonal of Z must be less than or equal to 0. To satisfy (17d), the matrix after R1 + Z remains positive semidefinite. Therefore, we can assume that constraints (17a), (17b), and (17d) must have a nonempty feasible region. Finally, constraint (17c) can be satisfied using singular value decomposition (SVD) or Gaussian randomization after satisfying the other constraints.

[0132] The objective function in problem (P3) is non-concave, and the constraint (17c) is non-convex. If the perception performance constraint (17a) is strict, that is, the error threshold Γ between the integrated waveform covariance matrix and the radar beam covariance matrix is ​​required to be extremely small, the feasible domain of the optimization problem will be greatly reduced, which may lead to poor communication performance. Therefore, the following weighted optimization problem (P4) is considered:

[0133]

[0134] Where 0≤ρ is the weighting coefficient, which means the ratio of communication power to perception power. k ({W k}) is the communication rate of the kth communication user,

[0135] Problem (P4) relaxes the constraints on perception performance by adding a user-determined weighting coefficient ρ. A larger ρ favors communication performance, while a smaller ρ favors perception performance. The objective function and constraints of Problem (P4) are still non-convex. We will now use the methods of continuous convex approximation (SCA) and semidefinite relaxation (SDR) to solve Problem (P4).

[0136] The non-concave objective function is approximated to a concave function using the SCA method, and the original problem is iteratively approximated. During the approximation, the approximate function to be found must have the same first-order derivative as the original objective function and be a lower bound of the original objective function.

[0137] Consider the p≥1th iteration in the SCA algorithm, and the iteration point is set to Observe the objective function of problem (P4). The first sum is a non-concave function, and the second subtracted term is a convex function, that is, the total form is a non-concave plus concave form. Transform one of the first sums and perform a first-order Taylor expansion, and we have:

[0138]

[0139] in:

[0140]

[0141] yes At the iteration point The first-order Taylor expansion at . Because It can be expanded into a concave-minus-concave form, so we only need to The second term of can be expanded by the first order Taylor. The first order Taylor expansion of the concave function must be greater than or equal to the concave function itself, so

[0142] Therefore, the p-th SCA approximation iteration of problem (P4) can be expressed as problem (P5.p):

[0143]

[0144] The rank-one constraint (17c) in problem (P5.p) is still non-convex. Using the idea of ​​SDR, we relax the rank-one constraint and express the relaxed problem as problem (SDR5.p):

[0145]

[0146] Problem (SDR5.p) is a convex semidefinite program (SDP) that can be solved using convex optimization solvers such as CVX. The solution to problem (SDR5.p) is If it satisfies the rank-one constraint (17c), then it is the optimal solution to the problem (P5.p). If it does not satisfy the rank-one constraint (17c), then use SVD or Gaussian randomization to obtain a rank-one solution. In the next SCA iteration, the iteration point is updated to γ∈(0,1] is the iteration step size.

[0147] The pseudo code for the entire solution process of problem (P4) is given below:

[0148] Algorithm 1 UAV communication perception weighted waveform optimization algorithm based on continuous convex approximation

[0149]

[0150]

[0151] Example:

[0152] The settings of key parameters of the simulation experiment are shown in Table 1.

[0153] Table 1 Simulation parameter settings

[0154]

[0155] Figure 4 It is a two-ray path loss model and a three-ray path loss model under the operating frequencies of 200MHz and 1GHz. Figure 4 (a) is the dual-ray path loss model at two operating frequencies when the transmit and receive antenna heights are 40.8m and 50.7m respectively. The smooth curve is the L-band single logarithmic model, and its parameter values ​​are: A0 = 100.7dB, n A =1.9,d min =2.6km, X A =18.5dB. Figure 4 (b) Transmitting and receiving antenna height and Figure 4 (a) is the same, the three-ray path loss model at two operating frequencies. It can be seen that no matter which operating frequency the two-ray model or the three-ray model, its path loss curve has a clear concave tip compared to the single logarithmic model. This is because the sparsity of the ocean environment causes the signal propagation to be mainly transmitted through three paths: LOS, reflection, and evaporation duct. This is different from the fading formed by the superposition of a large number of multipath signals in the terrestrial wireless environment. The superposition of three sparse multipaths at the receiving end may produce a large attenuation at certain link distances, that is, a concave tip. At the same time, it can be found that when the operating frequency is 1GHz, the path attenuation of the two-ray model or the three-ray model is generally greater than that when the operating frequency is 200MHz, but there are also some link distances where the attenuation is smaller than that when the operating frequency is 200MHz. This is caused by the two path loss models: both models contain the first term (λ / (4πd)) 2 , the greater the operating frequency, the smaller the wavelength. Although the second item is also related to the wavelength, its influence is smaller and is mainly affected by the first item.

[0156] This example is attached Figure 5 As shown, when ρ = 0, 0.5, 1, the noise power The integrated beam pattern, MIMO radar beam pattern, and ideal radar beam pattern for a target orientation of θ = π / 4 and an operating frequency of 50 MHz. It can be seen that the ideal radar beam pattern is a rectangular window located at the target orientation. Of course, such a steep change in the ideal rectangle is impossible to achieve in practice. The MIMO radar beam pattern is an approximation of the ideal radar beam pattern. Its main lobe is prominent at the target orientation, and its side lobes fluctuate somewhat compared to the ideal beam pattern, which is completely zero. The integrated waveform for ρ = 0 considers only perception performance, and its beam pattern essentially overlaps with the MIMO radar beam pattern. For ρ = 0.5 and 1, the integrated beam pattern has two larger lobes: one located at the target orientation and the other at the communication user orientation. As ρ increases, the lobe at the communication user orientation increases, but the lobe at the target orientation shifts toward the target.

[0157] Figure 6 The communication achievable rate of the integrated waveform under different noise powers is given when the maximum transmission power of the UAV is fixed at 10W and the operating frequency is 6MHz, 50MHz and 100MHz. Where N0 is the noise power, that is, The communication reachable sum rate is given by Equation (12). It can be seen that when the noise power increases, the communication reachable sum rate of the integrated waveform first decreases gently, and then decreases rapidly when the noise power is greater than about 80dBW. Moreover, the higher the operating frequency, the lower the communication reachable sum rate under the same signal-to-noise ratio. This is mainly because the higher the frequency, the greater the path loss of the dual-ray model.

[0158] Figure 7 The communication reachability and rate curves and the error curves between the integrated beam pattern and the MIMO radar beam pattern (hereinafter referred to as error curves) are shown when the maximum transmission power of the drone is fixed at 10W, the operating frequency is 50MHz and 100MHz, and the noise power is -80dBW and -50dBW. It can be seen that the communication reachability and rate curves and the error curves are similar to steps. Figure 7 As shown in (a), when the noise power is fixed and the operating frequency increases, the communication reachable sum rate decreases; when the operating frequency power is fixed and the noise power increases, the communication reachable sum rate decreases; and under certain noise power and operating frequency, as the weight ρ increases, the reachable sum rate first increases rapidly and then tends to be flat. Figure 7As shown in (b), when the noise power is -80dBW, the error curves at 50MHz and 100MHz basically coincide; when the noise power is -50dBW, the error curve at 100MHz is significantly higher than the error curve at 50MHz. And under a certain noise power and operating frequency, as the weight ρ increases, the error first increases slowly, then rises rapidly, and finally tends to be flat. The communication reachability and rate curves and the error curves eventually tend to be flat because when ρ is greater than a certain value, the maximum power of the drone is limited to 10W. Even if ρ continues to increase, due to power limitations, the communication rate is difficult to increase, and the error will basically not increase. Figure 7 It can be seen that when the weight ρ is in the interval [0.2, 0.5], the communication reachability and rate are large while the error is also small, that is, the communication and perception of the integrated waveform show good performance.

[0159] This paper studies an integrated communication and perception system for unmanned aerial vehicles (UAVs) operating in marine environments. The wireless propagation channel for UAVs in marine environments is modeled. A weighted integrated waveform optimization design method is proposed. This method weights the communication sum rate and radar beam pattern error, and uses the SCA algorithm to perform a convex approximation. Simulation results show that a weight ρ value in the range [0.2, 0.5] ensures good communication performance while maintaining good perception performance for the integrated system.

Claims

1. A waveform optimization method for integrated communication and perception of unmanned aerial vehicles in marine environments, characterized in that: For maritime UAV ISAC systems, in order to enable the integrated waveform to simultaneously perform both target detection and communication functions, it is necessary to optimize communication speed while also constraining radar performance. This leads to the following problems (P2): (16a), (16b), where is the 2-norm of the matrix, It is The weight of each communication user, is the solution to problem (P1), is the threshold, that is, the covariance matrix of the integrated waveform and The error of must be less than this threshold to ensure the radar performance; transform the problem (P2) and let , then problem (P2) is equivalent to problem (P3): , （17a）， （17b）， （17c）， （17d）， The feasibility of problem (P3) is expressed as the following question (FP1): For the inequality constraint (17a), it is equivalent to the following equation: (18), where is the error matrix, representing and The difference between , then constraints (17a) and (17b) are expressed as: (19a), (19b), because is the solution to problem (P1), so The trace is equal to ,and The elements on the diagonal are equal to , The value of is generally small. Under the condition that constraint (19a) is satisfied, The elements in are all small. To make constraint (19b) hold, The elements on the diagonal must be less than or equal to 0, and in order to satisfy (17d), The matrix after is still a semi-positive definite matrix. It is considered that constraints (17a), (17b) and (17d) must have a non-empty feasible region. Finally, constraint (17c) is satisfied using singular value decomposition (SVD) or Gaussian randomization after satisfying other constraints. In problem (P3), the objective function is non-concave, and the constraint (17c) is non-convex. If the perception performance constraint (17a) is strict, it requires the error threshold of the integrated waveform covariance matrix and the radar beam covariance matrix to be If is extremely small, the feasible domain of the optimization problem will be greatly reduced, which will lead to poor communication performance. Therefore, the following weighted optimization problem (P4) is considered: ， in is the weighting coefficient, which means the ratio of communication power to perception power. It is The communication rate of each communication user, , The objective function and constraints of problem (P4) are still non-convex. The continuous convex approximation SCA and semi-positive relaxation SDR method are used to solve problem (P4); Assume that The time slot is sent to The communication signal of a user is ,and , the communication signals of different users are independent of each other, is the corresponding beamforming vector, then The transmitted signal vector of a time slot is expressed as: （5）， Then the covariance matrix of the transmitted signal is: （6）， in It represents the mathematical expectation of time. , denote conjugate transpose and conjugate respectively, The average transmission power of the drone is: （7）， in represents the square of the vector 2 norm, Assume that the maximum transmission power of the UAV is , so there are the following power constraints: （8）， The signal transmitted by the UAV reaches the receiving antenna of the communication user after passing through the near-sea wireless channel. Assuming that the channel state is known and the distance between the transmitting and receiving antennas is close, considering the double-ray path loss model, the distance from the transmitting antenna to the first The channel vector between users is expressed as: （9）， In the formula is the two-ray path loss, where is the operating wavelength of the transmitted signal, For drones and The horizontal distance between users, and are the transmitting antenna height and the receiving antenna height respectively, For drones and The direction vector between users is specifically expressed as: (10), in For the The elevation angle from the user to the drone is ; Set up the first Time slot The received signal vector of a communication user is , then: （11）， In the formula For the Time slot The noise received by each communication user, and , so the Time slot The signal-to-interference-and-noise ratio (SINR) of a communication user is: （12）， in Indicates the modulo operation. In one working cycle, since the channel vector and beamforming vector do not change with time, It also does not change with time, that is, , then Time slot The achievable communication rate of each communication user is: （13）， The integrated signal transmitted by the UAV performs target detection while communicating, and its transmission beam pattern is expressed as: （14）， in is the detection azimuth, The classic MIMO radar beamforming problem is formulated as Problem (P1): （15）， in Is a set of detection angles, which divides the entire detection angle into piece, is a weight coefficient, is the ideal transmit beam pattern at The value in the direction, It means taking the diagonal vector, is a vector whose elements are all 1. is the transmit power, is the number of transmitting antennas.

2. The method for optimizing the integrated waveform of UAV communication and perception in marine environment according to claim 1 is characterized in that: The method of using continuous convex approximation SCA and semi-definite relaxation SDR to solve problem (P4) is specifically as follows: the non-concave objective function is approximated as a concave function through the SCA method, and the original problem is iteratively approximated. During the approximation, the approximate function to be found must be the same as the first-order derivative of the original objective function and must be the lower bound of the original objective function.

3. The method for optimizing the integrated waveform of UAV communication and perception in marine environment according to claim 2 is characterized in that: Consider the SCA method Iterations, this iteration point is set to , Problem (P4) The first term of the objective function is a non-concave function, and the second term is a convex function, that is, the total form is a non-concave plus concave form. Transform one of the first terms and perform a first-order Taylor expansion, then we have: （20）， in: （21）， yes At the iteration point The first-order Taylor expansion at , because Expanded into a concave-minus-concave form, so only The second term of can be expanded by the first order Taylor. The first order Taylor expansion of the concave function must be greater than or equal to the concave function itself, so , Therefore, the first The SCA approximation iteration is expressed as problem (P5. ): （22）， Question (P5. ) is still non-convex. Using the idea of ​​SDR, we relax the rank-one constraint and express the relaxed problem as problem (SDR5. ): (23)， Problem (SDR5. ) is a convex semidefinite program (SDP) that is solved with the help of CVX convex optimization solver to obtain the problem (SDR5. ) is solved as , if it satisfies the rank-one constraint (17c), then it is a problem (P5. ), if it does not satisfy the rank-one constraint (17c), then use SVD or Gaussian randomization to obtain a rank-one solution , in the next SCA iteration, the iteration point is updated to , is the iteration step size.

4. The method for optimizing the integrated waveform of UAV communication and perception in a marine environment according to claim 1 is characterized in that: The maritime UAV ISAC system, wherein the UAV is fixed at a height of In order to simplify the design, it is assumed that the UAV is equipped with a vertically arranged A uniform linear array of antennas with an antenna spacing of , so the transmitted signal has nothing to do with the direction of the drone. The transmitting antenna is used for target detection and information communication at the same time. The UAV acts as an aerial node near the sea surface and communicates with the The single receiving antenna users communicate with each other and simultaneously Targets are detected, and a three-dimensional rectangular coordinate system is established with the drone as the origin. The horizontal coordinate set of the communication users is , Indicates the The horizontal coordinates of the communication users, The horizontal coordinate set of the detection target is , Indicates the The horizontal coordinates of the detection target. The target position is obtained through the detection mission previously scheduled by the UAV and omnidirectional search detection. After that, the UAV conducts directional detection on the predetermined target. The duration of one working cycle of the UAV is , a working cycle is divided into time slots, each time slot is ,During a working cycle, the UAV transmits an integrated waveform to ,directedly detect the target area of ​​interest and simultaneously complete ,communication with the communication user.

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