A multi-target detection-oriented intelligent metasurface assisted radar-communication integrated system transmission waveform and reflection beam forming joint design method

Abstract

This invention discloses a joint design method for the transmitted waveform and reflected beamforming of a smart metasurface (RIS)-assisted radar-communication integrated (DFRC) system for multi-target detection. This method aims to solve the problem of line-of-sight link interruption between the base station and the target caused by obstacles in practical multi-target detection scenarios. A mathematical model is established to maximize the minimum radar illumination power in multiple target directions while satisfying clutter interference constraints, communication constraints, constant modulus constraints of the transmitted waveform, and passive / active RIS constraints. A symbol-level precoding system based on beneficial interference is introduced. The multi-target detection performance is verified by jointly designing the transmitted waveform and passive / active RIS reflection coefficients of the DFRC system. Addressing the challenge of non-convex joint optimization of the transmitted waveform and RIS reflection coefficients, this invention uses an alternating optimization algorithm combined with first-order Taylor expansion and successive convex approximation techniques to solve the problem, effectively achieving the joint design of the transmitted waveform and passive / active RIS reflection coefficients.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically a joint design method for transmitted waveform and reflected beamforming of an intelligent metasurface-assisted radar communication integrated system for multi-target detection. Background Technology

[0002] As is well known, radar systems and wireless communication systems play an indispensable role in ensuring the operation of critical social infrastructure and the upgrading of emerging technologies. However, with the evolution of fifth-generation and subsequent advanced communication technologies, the throughput demand of communication services on wireless spectrum resources is constantly increasing. Due to the scarcity of available spectrum resources, the originally independent radar and communication systems are increasingly overlapping in the frequency domain, and the resulting co-channel interference has become a key factor restricting the performance of both systems. Against the backdrop of increasingly complex electromagnetic environments and highly limited frequency band resources, radar-communication integrated (DFRC) systems have emerged. Through deep integration at the hardware architecture and waveform resource levels, these systems not only effectively alleviate spectrum conflicts but also achieve synergistic enhancement of the functions of radar and communication systems.

[0003] From a radar perspective, the detection performance of a radar system is related to the energy of the detection waveform transmitted by the transmitter. This energy is reflected from the target and captured by the receiver, forming the basis for target detection. Therefore, evaluating the detection performance of a radar system with radar illumination power as the core has significant physical implications. From a communication perspective, traditional block-level precoding treats multi-user interference as interference, resulting in a significant performance degradation when there are many users. In contrast, symbol-level precoding (SLP) technology can transform multi-user interference into beneficial interference and fully utilize the waveform's degrees of freedom, thus better ensuring multi-user communication performance. SLP optimizes the transmitted signal at the symbol level, enabling accurate decoding of the received signal and guaranteeing the quality of service for multiple users. Simultaneously, SLP allows for designing the transmitted signal within each snapshot, providing greater degrees of freedom (DoF) for radar detection system waveform design.

[0004] In practice, due to the complexity of urban environments, the line-of-sight path between radar and the target can be obstructed by obstacles, severely impacting target detection performance. Intelligent metasurfaces (RIS), as a novel antenna system, can flexibly adjust the reflection characteristics of electromagnetic waves, including amplitude, frequency, and phase. Therefore, the emergence of RIS provides a new approach to better addressing such problems. RIS can reconstruct the wireless propagation environment by adjusting the phase of the reflecting elements. Furthermore, due to its low cost, high efficiency, and high flexibility, RIS plays a crucial role in modern wireless communication and radar systems. RIS can be divided into two basic types: passive and active. Both are widely used in DFRC systems. Compared to passive RIS, active RIS, with its signal amplification capability, can effectively compensate for the multiplicative fading caused by two-way path propagation, thus significantly improving the performance of the DFRC system.

[0005] In practical applications, multi-target detection has become a critical task. Modern communication scenarios demand higher quality of service, and the emergence of SLP technology provides a new technical solution for RIS-assisted DFRC systems. Therefore, this invention designs a RIS-assisted DFRC system for multi-target detection by introducing SLP technology and customizes a specialized method to solve the joint design problem of transmitted waveform and reflected beamforming. Summary of the Invention

[0006] The purpose of this invention is to propose a joint design method for transmit waveform and reflected beamforming in an intelligent metasurface-assisted radar-communication integrated system for multi-target detection. The technical solution employed in this invention is based on processing algorithms such as alternating optimization, introduction of auxiliary variables, first-order Taylor expansion, and successive convex approximation, used for the joint design of transmit waveform and reflected beamforming in a RIS-assisted DFRC system. Results show that the design of this invention outperforms traditional DFRC systems. The specific steps of the joint design method for transmit waveform and reflected beamforming in a RIS-assisted DFRC system for multi-target detection are as follows:

[0007] Step 1: Establish a non-line-of-sight multi-target detection problem model for the RIS-assisted DFRC system. The radar optimization adopts the criterion of maximizing the minimum radar illumination power in multiple target directions, and the communication constraint adopts the SLP criterion to improve the user's received SINR. Each user's received signal consists of two parts: line-of-sight and non-line-of-sight transmission signals.

[0008] Step 2: Decouple the coupled variables based on the alternating optimization framework to obtain the transmit waveform optimization subproblem and the RIS reflection coefficient optimization subproblem.

[0009] Step 3: By introducing auxiliary variables, first-order Taylor expansion, and successive convex approximation, the emission waveform optimization subproblem is transformed into a convex optimization problem, which is then effectively solved using existing convex optimization techniques.

[0010] Step 4: By introducing auxiliary variables, first-order Taylor expansion, and successive convex approximation, the RIS reflection coefficient optimization subproblem is transformed into a convex optimization problem, which is then effectively solved using existing convex optimization techniques.

[0011] The RIS-assisted DFRC system of the present invention can effectively detect multiple targets while significantly improving multi-user communication performance. Attached Figure Description

[0012] To more clearly illustrate this technical solution, the accompanying drawings used in the prior art description below are briefly introduced.

[0013] Figure 1 Convergence Analysis of Passive RIS-Assisted DFRC System

[0014] Figure 2 Convergence Analysis of Active RIS-Assisted DFRC System

[0015] Figure 3 Relationship between minimum radar illumination power and transmit power

[0016] Figure 4 Relationship between minimum radar illumination power and the number of RIS units

[0017] Figure 5 Relationship between minimum radar illumination power and RIS unit amplification factor

[0018] Figure 6 Relationship between minimum radar illumination power and communication user quality

[0019] Figure 7 Relationship between minimum radar illumination power and number of communication users Detailed Implementation

[0020] The present invention, namely a joint design method for transmit waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection, is further described below with reference to the accompanying drawings and examples.

[0021] This invention presents a joint design method for the transmit waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection. The invention aims to maximize the minimum radar illumination power in multiple target directions, with the communication service quality of each user as a constraint. It verifies the performance of RIS-assisted DFRC in multi-target detection scenarios by jointly designing the DFRC transmit waveform and passive / active RIS reflection coefficients. For the constructed transmit waveform and RIS joint design problem, methods such as alternating optimization, introducing auxiliary variables, first-order Taylor expansion, and successive convex approximation are used to effectively solve the problem model. The specific implementation steps are as follows:

[0022] Step 1: Consider a RIS-assisted DFRC system multi-target detection model architecture. This architecture consists of five parts: DFRC base station (BS), passive / active RIS, user terminals, a group of targets to be detected, and several clutter interference sources near the target group. Specifically, the BS adopts a uniform linear array design with consistent array element structure, with N transmit and receive antennas, and has both signal transmission and reception functions. The DFRC system completes the detection task of T targets while ensuring the communication quality of U users. The RIS constructs a uniform linear array through M one-dimensionally arranged programmable units, and all user terminals adopt a single-port antenna design.

[0023] In the design of a RIS-assisted DFRC system, the MIMO radar transmit waveform matrix is ​​as follows: in, Let x be the transmitted signal vector in the l-th snapshot, L be the total number of snapshots, and let x = vec(X), where vec(·) is the vectorization operator. The phase shift vector of RIS is... And there are This is the channel matrix from BS to RIS. This represents the guidance vector from RIS to the t-th target, and its specific expression is:

[0024]

[0025] at the same time This represents the channel between RIS and the t-th target, where β t This represents the path loss coefficient. Since the direct connection between the BS and the target is obstructed, the BS instead utilizes a path from the BS to the RIS and then to the target to transmit signals to the detection target. In this case, when the transmitted waveform reaches the target t, it becomes the illumination signal on target t, and its mathematical expression is:

[0026]

[0027] Since one of the key factors affecting radar detection performance is the illumination power of the radar signal, the illumination power of the radar signal on the t-th target can be expressed by the following formula:

[0028]

[0029] Considering the influence of clutter interference near the target, the radar signal illumination power to it can be expressed in the following form:

[0030]

[0031] The number of clutter interference sources is Q. This represents the channel between the passive RIS and the q-th clutter interference.

[0032] Where β q This is the path loss coefficient. The steering vector expression from RIS to the q-th clutter interference is:

[0033]

[0034] In radar systems, the efficiency of the transmitter power amplifier is crucial to the overall system performance. To maximize the power amplifier's efficiency, the amplitude of the transmitted signal must remain constant throughout the entire signal period. Therefore, the designed radar waveform should satisfy the constant modulus constraint:

[0035]

[0036] Here, E0 represents the transmit power of the BS transmitter.

[0037] From a radar detection perspective, the key to improving target detection performance is to increase the radar signal's illumination power on the target while reducing the illumination power against clutter interference. Therefore, a clutter interference constraint is introduced as follows:

[0038]

[0039] Where, η q This represents the threshold power at which the radar signal is illuminated by clutter interference.

[0040] In multi-user MIMO communication, the SLP (Simultaneous Phase Logic) system is used for transmit waveform design. By accurately controlling the amplitude and phase of each transmitted symbol, interference between users is minimized, thus ensuring the communication performance of each user. Therefore, the received signal of the u-th user at time l is:

[0041]

[0042] Where, n u_lThe received noise of the communication user at time l follows the law of... distributed; This refers to the channel from the BS to the user. This refers to the channel from the RIS to the user.

[0043] Assume that at time l, the symbol s to be transmitted is... l The waveform is independently and identically distributed from a phase constellation diagram, which is known in advance at both the base station and the user end. To improve the demodulation performance of the signal at the receiver, a CI-based precoding scheme is used to design the transmitted waveform. Its core constraints can be expressed as follows:

[0044]

[0045] Where, γ u θ represents the minimum SNR that the u-th user needs to guarantee, and θ is the phase of the received signal.

[0046] Considering that equation (9) contains both real and imaginary parts of the function, to facilitate the solution, the imaginary part of the function is transformed into the real part form, i.e. Therefore, equation (9) can be further expressed as:

[0047]

[0048] To simplify the representation, the following variables can be defined:

[0049]

[0050] Based on equation (8), the ideal noise-free signal received by the user can be further derived as follows:

[0051]

[0052] Among them, e l This represents the identity matrix I. L The l-th column vector. Therefore, the CI constraint can be concisely expressed as:

[0053]

[0054] In practical applications, the reflection coefficient of passive RIS typically satisfies the constant modulus constraint, expressed as:

[0055]

[0056] In summary, the objective function is to maximize the minimum radar illumination power in multiple target directions, while satisfying clutter interference constraints, CI constraints, constant mode constraints of the transmitted waveform, and constant mode constraints of the passive RIS. This allows for the joint design of the DFRC system's transmitted waveform and the reflection coefficient of the RIS. Therefore, the overall optimization model can be expressed as:

[0057]

[0058] Step 2: A method based on an alternating optimization framework is adopted to transform the non-convex problem (15), which is difficult to handle directly, into two relatively easy sub-problems, to alternately optimize the emission waveform and the passive RIS reflection coefficient.

[0059] Since the objective function in equation (15) is a max-min problem, it is difficult to solve directly. In order to solve it effectively, an auxiliary variable R1 is first introduced, and terms that are not related to x are removed. The optimization problem of the transmitted waveform x can be expressed as:

[0060]

[0061] Next, because And there are Therefore, it can be restated. Similarly, And there are Therefore, P q It can be restated as At this time, it can be ordered Then there is Given a set of L snapshots, the matrix representation P of the transmitted waveform is... t It can be represented as Considering the variable to be optimized, x = vec(X), to achieve dimensional matching, the following operation can be performed: Let as well as Again Then we can eventually obtain P. t =x H D t x. Similarly, because Can make Then there is Defineable as well as Again Then P q =x H D q Therefore, the optimization problem concerning the transmitted waveform x can be expressed in the following form:

[0062]

[0063] Due to matrix Dt It is positive semi-definite, which shows that the constraint x is... H D t x≥R1 is nonconvex. To facilitate the solution, we relax it to a convex constraint. Using a first-order Taylor expansion, we can obtain:

[0064]

[0065] in, c1=-(x (s) ) H D t x (s) Then constraint x H D t x≥R1 can be replaced with:

[0066]

[0067] Therefore, problem (17) can be transformed into the following form:

[0068]

[0069] Next, the non-convex constant modulus waveform constraint is also equivalently replaced, as follows:

[0070]

[0071] In the transformed expression, only equality constraints exist. It is non-convex. Because the intersection of the two types of constraints is very small, it is difficult to handle. The following relaxes the equality constraint as follows: Here, ρ is an auxiliary variable whose value approaches zero. At this point, the inequality on the right-hand side... It is convex, but the inequality on the left... It is non-convex. To convert a non-convex constraint into a convex constraint, we can use a successive convex approximation technique based on a first-order Taylor expansion to transform the inequality on the left into the following form:

[0072]

[0073] In summary, by introducing the penalty relaxation variable ρ into the objective function, the problem of minimizing the emitted waveform can be ultimately updated to:

[0074]

[0075] Among them, κ1 is the introduced penalty parameter, which is mainly used to adjust the impact of the penalty term on the system. It can be found that problem (23) is a convex optimization problem, so it can be solved effectively by interior point method or convex optimization toolboxes such as CVX.

[0076] The specific process for solving problem (16) is as follows:

[0077] S1: Input parameter x (0) , v, Dt, D q h d，u h r，u E0, η q ,κ1,δ th ;

[0078] S2: Initialization settings: s = 0, x (s) =x (0) ;

[0079] S3: Iteratively solve problem (23) to obtain x (s+1) ;

[0080] S4: Determine if the iteration termination condition is met. If it is met, ||x (s+1) -x (s) ||2≤δ th If x > 0, then stop the loop; otherwise, x > 0. (0) ←x (s+1) s = s + 1, return to step S2;

[0081] S5: Output x (s+1) .

[0082] Step 3: Next, remove terms unrelated to the passive RIS reflection coefficient v, and transform the problem description using a similar approach to Step 2. First, introduce the auxiliary variable R2, then the optimization problem regarding v can be expressed in the following form:

[0083]

[0084] in, And there are Therefore, it can be restated. Similarly, And there are Therefore, P q It can be restated as Similarly, if there are L snapshots, then P t It can be restated as Where x = vec(X), to simplify the expression, we can let Then P t =v H D t2 v, similarly, make Then P q =v H D q2 v. Therefore, problem (24) can be redefined as follows:

[0085]

[0086] Because of v H D t2 The constraint v≥R² is non-convex; we will relax it to a convex constraint below. Using a first-order Taylor expansion, we can obtain the following relationship:

[0087]

[0088] in c2=-(v (n) ) H D t2 v (n) Therefore, the non-convex constraint v H D t2 v≥R2 can be transformed into:

[0089]

[0090] Therefore, problem (25) can be transformed into the following form:

[0091]

[0092] Next, the expression of the CI constraint will be modified so that it can explicitly express the variable v:

[0093]

[0094] in, And there are in

[0095] For the non-convex monotony constraint of v, it can be equivalently expressed as follows:

[0096]

[0097] for It can be relaxed to Here, 'b' is an auxiliary variable whose value approaches zero. It's easy to observe that the inequality on the right-hand side... It is convex, and the inequality on the left is... It is non-convex. To transform the non-convex part into a convex constraint, a successive convex approximation method based on first-order Taylor expansion can be used to perform the following transformation:

[0098]

[0099] In summary, by introducing the penalty slack variable b into the objective function, the optimization problem of solving the passive RIS reflection coefficient v can be ultimately expressed as:

[0100]

[0101] Wherein, κ2 is the penalty parameter introduced by the system, which can be used to adjust the influence of the penalty term. Obviously, problem (32) is a convex optimization problem, which can be effectively solved by the interior point method or the convex optimization toolbox.

[0102] The specific process for solving problem (24) is as follows:

[0103] S1: Input parameter v (0) , X, D t2 D q2 , g u，l η q ,κ2,δ th ;

[0104] S2: Initialization settings: n = 0, v (n) =v (0) ;

[0105] S3: Iteratively solve problem (32) to obtain v (n+1) ;

[0106] S4: Determine if the iteration termination condition is met. If it is met, ||v (n+1) -v (n) ||2≤δ th If the loop stops, then stop; otherwise, v (0) ←v (n+1) If n = n + 1, return to step S2;

[0107] S5: Output v (n+1) .

[0108] In summary, the complete process for solving problem (15) of the joint design method for transmit waveform and reflected beamforming of a passive RIS-assisted DFRC system for multi-target detection based on the alternating optimization framework is as follows:

[0109] S1: Input parameter K max ,θ,γ u , G,h d，u h r，u A t A q ,κ1,κ2,η q δ th ,t;

[0110] S2: Initialization settings: Set k = 0, x (0) v (0) And calculate

[0111] S3: Solve problem (16) according to the method in step 2 and update x (k+1) ;

[0112] S4: Solve problem (24) according to the method in step 3 and update v (k+1) ;

[0113] S5: Determine if the iteration termination condition is met. If the maximum number of iterations is reached, the loop stops; otherwise, k = k + 1, and the process returns to step S3.

[0114] S6: Output x (k+1) v (k+1) .

[0115] Step 4: Referring to the design and solution of the multi-target detection model for the DFRC system assisted by a passive RIS, in practical applications, the emission waveform and reflection coefficient of an active RIS are usually limited by hardware conditions. Due to power limitations, the power of the active RIS in the l-th snapshot is constrained as follows:

[0116]

[0117] Among them, P max This represents the maximum power of the active RIS. Furthermore, the signal amplification performance of an active RIS is constrained by its implementation architecture; therefore, the amplification factor of each RIS unit must meet the following conditions:

[0118] |v m |≤τ,m=1,...,M (34)

[0119] Where τ is the maximum amplification factor of the active RIS unit.

[0120] The problem model for the multi-target detection part of the active RIS-assisted DFRC system can be formalized as follows:

[0121]

[0122] Step 5: Since the optimization variables x and v in equation (35) are coupled in the objective function and constraints, and there is a constant modulus non-convex constraint, problem (35) is a non-convex problem. In order to deal with this complex optimization problem, the following method is to use the alternating optimization algorithm and introduce auxiliary variables to solve it.

[0123] First, remove terms irrelevant to the emitted waveform x. Then, introduce an auxiliary variable R3 to transform problem (35) into a max problem, resulting in:

[0124]

[0125] Next, similar to the transformation processing method used in step 2 to solve the transmitted waveform part, for P... t P q The constant modulus constraint is then subjected to equivalent simplification and substitution transformations, as well as convexity transformations, the specific processes of which will not be elaborated here. Therefore, by introducing the penalty relaxation variable μ into the objective function, the problem of optimizing the transmit waveform of the active RIS-assisted DFRC system can be ultimately expressed as:

[0126]

[0127] Wherein, κ3 represents the penalty parameter, which is mainly used to adjust the influence of the penalty factor. It can be found that problem (37) is a convex optimization problem, so it can be solved effectively using the interior point method or convex optimization toolboxes such as CVX.

[0128] The specific process for solving problem (36) is as follows:

[0129] S1: Input parameter x (0) , v, D t D q h d，u h r，u E0, P max η q ,κ3,δ th ;

[0130] S2: Initialization settings: s = 0, x (s) =x (0) ;

[0131] S3: Iteratively solve problem (37) to obtain x (s+1) ;

[0132] S4: Determine if the iteration termination condition is met. If it is met, ||x (s+1) -x (s) ||2≤δ th If x > 0, then stop the loop; otherwise, x > 0. (0) ←x (s+1) s = s + 1, return to step S2;

[0133] S5: Output x (s+1) .

[0134] Step 6: Remove terms irrelevant to v and introduce auxiliary variable R4. The optimization problem regarding the reflection coefficient of the active RIS can then be expressed in the following form:

[0135]

[0136] To explicitly represent the optimization variable v, the energy constraint update of the active RIS can be further expressed in the following form:

[0137]

[0138] in,

[0139] Next, similar to the relevant transformation processing method for solving the passive RIS reflection coefficient part in step 3, we will perform simplified representation by substitution function and convex transformation processing, etc. The specific process will not be described here.

[0140] In summary, the optimization problem for solving the reflection coefficient of an active RIS can be ultimately expressed as:

[0141]

[0142] Obviously, problem (40) is a convex optimization problem, which can be solved globally using the interior point method or the convex optimization toolbox.

[0143] The specific process for solving problem (38) is as follows:

[0144] S1: Input parameter v (0) , X, D t2 D q2 , g u，l , P max ,∏,η q δ th ;

[0145] S2: Initialization settings: n = 0, v (n) =v (0) ;

[0146] S3: Iteratively solve problem (40) to obtain v (n+1) ;

[0147] S4: Determine if the iteration termination condition is met. If it is met, ||v (n+1) v (n) ||2≤δ th If the loop stops, then stop; otherwise, v (0) ←v (n+1) If n = n + 1, return to step S2;

[0148] S5: Output v (n+1) .

[0149] In summary, the complete process for solving problem (35) of the joint design method for transmit waveform and reflected beamforming of an active RIS-assisted DFRC system for multi-target detection based on the alternating optimization framework is as follows:

[0150] S1: Input parameter K max P max ,θ,γ u , G,h d,u h r，u A t A q ,κ3,η q ,τ,t;

[0151] S2: Initialization settings: Set k = 0, x (0) v (0) And calculate

[0152] S3: Solve problem (36) according to the method in step 5 and update x. (k+1) ;

[0153] S4: Solve problem (38) according to the method in step 6 and update v (k+1) ;

[0154] S5: Determine if the iteration termination condition is met. If the maximum number of iterations is reached, the loop stops; otherwise, k = k + 1, and the process returns to step S3.

[0155] S6: Output x (k+1) v (k+1) .

[0156] Example

[0157] The invention further illustrates the joint design method of transmit waveform and reflected beamforming for a RIS-assisted DFRC system for multi-target detection through Matlab simulation.

[0158] 1) Simulation system parameter settings

[0159] In the simulation design of this invention, the experimental baseline parameters are set as follows: number of users U = 3, number of transmit signal snapshots L = 32, number of transmit antennas N = 12, number of RIS array elements M = 160, transmit power E0 = 16dBW, and communication user service quality γ. u =10dB, clutter interference illumination power threshold η q =10 -3 The active RIS unit amplification factor τ = 5, and the maximum power P of the active RIS is... max =30dBmW, the radar detection scene contains two main targets (θ)t (∈{-30°, 30°}) and three interference sources (θ) q ∈{-60°, 0°, 60°}). The link loss model for the channel is uniformly adopted as follows:

[0160]

[0161] Where C0 = -30dB is the baseline loss value at a reference distance d0 = 1m, σ represents the path loss exponent, and d represents the spacing between different components in the model. The path distances from BS to user, BS to RIS, and RIS to target / user are set to 30m, 30m, and 3m, respectively, with corresponding path loss exponents of 2.6, 2.2, and 2.3. The channel G from base station to RIS uses a Ricean fading model with a Ricean factor of 3. Other channels use Rayleigh fading channels following a complex Gaussian distribution. The channel between RIS and target / interference uses a line-of-sight attenuation model with a noise power of [missing information].

[0162] 2) Experimental Analysis System Setup

[0163] To better analyze the multi-target detection performance of passive / active RIS-assisted DFRC systems, this invention constructs six types of experimental analysis systems: (1) an active RIS-assisted DFRC system; (2) an active RIS-assisted radar-only system; (3) a passive RIS-assisted DFRC system; (4) a passive RIS-assisted radar-only system; (5) a conventional DFRC system; and (6) a conventional radar-only system. Considering the presence of line-of-sight and non-line-of-sight links and to ensure fairness in performance comparison, this section sets the loss gain from the BS to the target to be the same for both line-of-sight and non-line-of-sight links. This means that the attenuation of the non-line-of-sight link can be added to the line-of-sight link, and the minimum radar illumination power among multiple targets is used as the evaluation index.

[0164] 3) Simulation Experiments and Result Analysis

[0165] pass Figure 1 and Figure 2 The convergence characteristics of the minimum radar illumination power with the number of iterations can be observed in both passive RIS-assisted DFRC systems and active RIS-assisted DFRC systems. The active RIS, with its ability to actively amplify signals, demonstrates a performance difference compared to the passive RIS, which only reflects signals, indicating that the active RIS is superior to the passive RIS in assisting and improving the DFRC system. In both design scenarios, the minimum radar illumination power converges to a stable value after a finite number of iterations, thus verifying the convergence performance of the proposed algorithm.

[0166] pass Figure 3It can be seen that as the transmit power gradually increases, the minimum radar illumination power of all systems shows a gradual upward trend. Specifically, when the transmit power is 16 dBW, the minimum radar illumination power achieved by the active RIS-assisted DFRC system is -38.18 dB, which is about 26.7% higher than the minimum radar illumination power of -52.11 dB achieved by the passive RIS-assisted DFRC system; while the minimum radar illumination power achieved by the passive RIS-assisted DFRC system is about 45.1% higher than the minimum radar illumination power of -95 dB achieved by the conventional DFRC system. It can also be noted that the performance of the radar system alone in all three scenarios is about 0.4 dB higher than the DFRC system in the corresponding three scenarios on average. This is because the communication system diverts some of the energy from the DFRC system. When the transmit power is 20 dBW, the active RIS-assisted DFRC system achieves a minimum radar illumination power of -34.06 dB, which is approximately 29.1% higher than the -48.03 dB minimum radar illumination power achieved by the passive RIS-assisted DFRC system. Furthermore, the passive RIS-assisted DFRC system achieves approximately 47.2% higher minimum radar illumination power than the conventional DFRC system, which reaches -90.95 dB. Therefore, this fully verifies that both active and passive RIS-assisted DFRC systems outperform traditional DFRC systems in multi-target detection, and that the active RIS provides superior assistance to the DFRC system compared to the passive RIS.

[0167] pass Figure 4 It can be seen that as the number of RIS units gradually increases, the minimum radar illumination power of both the RIS-assisted DFRC system and the radar-only system gradually increases. Specifically, when the number of RIS units is 64, the minimum radar illumination power of the active RIS-assisted DFRC system is improved by approximately 23.8% compared to the passive RIS-assisted DFRC system, and by approximately 51.5% compared to the conventional DFRC system, while the passive RIS-assisted DFRC system only improves the performance by approximately 36.3% compared to the conventional DFRC system. However, when the number of RIS units increases to 256, the active RIS-assisted DFRC system improves the performance by approximately 64.3% compared to the passive RIS-assisted DFRC system, and by approximately 64.3% compared to the conventional DFRC system, while the passive RIS-assisted DFRC system improves the performance by approximately 49.4% compared to the conventional DFRC system.

[0168] pass Figure 5It can be seen that the minimum radar illumination power of both the active RIS-assisted DFRC system and the radar-only system increases with the increase of the active RIS unit amplification factor. Specifically, for the active RIS-assisted DFRC system, the minimum radar illumination power at a RIS unit amplification factor of 8 is approximately 30.5% higher than that at a amplification factor of 2, fully verifying that the active RIS unit's signal amplification capability grants the DFRC system more degrees of freedom. Specifically, when the RIS unit amplification factor is 2, the radar performance of the active RIS-assisted DFRC system is improved by approximately 11.8% compared to the passive RIS system and by approximately 51.6% compared to the conventional DFRC system. It can also be noted that when the RIS unit amplification factor increases to 8, the radar performance of the active RIS system is improved by approximately 38.6% compared to the passive RIS-assisted DFRC system and by approximately 66.3% compared to the conventional DFRC system. This means that the multi-target detection performance of the active RIS-assisted DFRC system is effectively improved with the increase of the active RIS amplification factor.

[0169] pass Figure 6 It can be seen that as the user's communication service quality gradually increases, the minimum radar illumination power of both the active / passive RIS-assisted DFRC system and the conventional DFRC system gradually decreases. This means that as the requirements for communication service quality increase, the radar performance of the DFRC system will also weaken to some extent. However, when the communication user quality requirement reaches 35dB, the performance of the active RIS-assisted DFRC system is still about 26.6% higher than that of the passive RIS-assisted system, and it also maintains a performance advantage of about 59.5% higher than that of the conventional DFRC system without RIS assistance. Therefore, this further verifies that the RIS-assisted DFRC system can effectively mitigate the loss of radar performance while improving multi-user communication quality, thus effectively enabling multi-target detection.

[0170] pass Figure 7It can be seen that as the number of communication users increases, the minimum radar illumination power of both active / passive RIS-assisted DFRC systems and conventional DFRC systems gradually decreases. This means that as the number of users in the system increases, the radar performance of the DFRC system also weakens accordingly. This is because the spectrum resources of a DFRC system are limited. When multiple users share spectrum resources, mutual interference between signals occurs, thereby reducing radar signal quality and multi-target detection performance. However, when the number of communication users increases to 10, the performance of the active RIS-assisted DFRC system is still about 28.2% higher than that of the passive RIS-assisted system, and about 58.2% higher than that of the conventional DFRC system without RIS assistance. At this point, the performance of the passive RIS-assisted DFRC system is also about 41.7% higher than that of the conventional DFRC system. In summary, this further verifies that RIS-assisted DFRC systems significantly enhance the overall performance of DFRC systems, effectively detecting multiple targets while also significantly improving multi-user communication performance.

Claims

1. A joint design method for transmitted waveform and reflected beamforming of a smart metasurface (RIS)-assisted radar-communication integrated (DFRC) system for multi-target detection, characterized in that: A non-line-of-sight multi-target detection problem model for a RIS-assisted DFRC system is established. Radar optimization employs maximizing the minimum radar illumination power in multiple target directions as the criterion, while communication constraints utilize a symbol-level precoding (SLP) criterion based on beneficial interference (CI) to improve the user's received SINR. The performance of the RIS-assisted DFRC in multi-target detection scenarios is verified by jointly designing the DFRC system's transmit waveform and passive / active RIS reflection coefficients. For the constructed transmit waveform and RIS joint design problem, methods such as alternating optimization, introducing auxiliary variables, first-order Taylor expansion, and successive convex approximation are used to effectively solve the problem model. Specifically, the following steps are included: Step 1: In the RIS-assisted DFRC system design, the base station (BS) is defined as a uniform linear array with consistent array element structure. The number of transmit and receive antennas is N. The RIS constructs the uniform linear array using M one-dimensionally arranged programmable units. The MIMO radar transmit waveform matrix is ​​as follows: in, Let x be the transmitted signal vector in the l-th snapshot, L be the total number of snapshots, and let x = vec(X), where vec(·) is the vectorization operator; the phase shift vector of RIS is... And there are The channel matrix from BS to RIS is defined as Q, P. t Let P be the illumination power of the radar signal on the t-th target. q E0 represents the illumination power of the radar signal against the q-th clutter interference, and E0 represents the transmit power of the BS transmitter. q This represents the radar signal illumination power threshold against clutter interference. The expected received signal for the u-th user at time l is s. u，l， The signal-to-noise ratio requirement of the u-th user is γ u The variance of the received signal is Then the symbol-level precoding parameters of the u-th user at time l. It can be represented as: Where θ = π / M represents the phase of the received signal. It reflects the distance between the noise-free signal received by the user and the decision boundary of the expected received symbol, which can determine the performance of the user's communication symbol detection. For the joint design problem of transmit waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection, the objective function is to maximize the minimum radar illumination power in multiple target directions, while satisfying clutter interference constraints, CI constraints, constant mode constraints of the transmit waveform, and constant mode constraints of the passive RIS. The specific optimization model is as follows: In the above formula, e l This represents the identity matrix I. L The l-th column vector, This refers to the channel from the BS to the user. This refers to the channel from the RIS to the user; Step 2: Based on the alternating optimization framework, decouple the coupled variables and transform problem (2) into two relatively easy-to-solve subproblems to alternately optimize the transmission waveform and RIS reflection coefficient. At the same time, introduce auxiliary variables to transform the complex max-min problem into an easy-to-handle max problem. First, remove the terms that are not related to the transmission waveform x and introduce the auxiliary variable R1. Then, the subproblem of optimizing the transmission waveform can be expressed as: This invention transforms subproblem (3) into a convex problem that is easy to solve by using first-order Taylor expansion and successive convex approximation method; Step 3: Remove terms unrelated to the passive RIS reflection coefficient v, and introduce the auxiliary variable R2. Then the optimization problem regarding v can be expressed as: This invention transforms subproblem (4) into a convex problem that is easy to solve by using first-order Taylor expansion and successive convex approximation method; Step 4: Similar to the passive RIS-assisted DFRC system multi-target detection optimization model design in Step 1, redefine P. max Let τ be the maximum power of the active RIS and τ be the maximum amplification factor of the active RIS unit. Then, the optimization model for multi-target detection in an active RIS-assisted DFRC system can be expressed as: Step 5: Similar to the solution method in Step 2. First, remove terms unrelated to the emitted waveform x, and introduce auxiliary variable R3 to transform problem (5) into a max problem, resulting in: This invention transforms subproblem (6) into a convex problem that is easy to solve by using first-order Taylor expansion and successive convex approximation method; Step 6: Remove terms irrelevant to v and introduce auxiliary variable R4. Then, the optimization problem regarding the reflection coefficient of the active RIS can be expressed as: This invention uses a first-order Taylor expansion technique to transform the subproblem (7) into a convex problem that is easy to solve.

2. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that: Consider a passive RIS-assisted DFRC system multi-target detection model architecture; the architecture consists of five parts: DFRC BS, passive RIS, user terminals, target group to be detected, and several clutter interference sources near the target group; specifically, the BS adopts a uniform linear array design with consistent array element structure, with N transmit and receive antennas, and has the functions of signal transmission and reception. The DFRC system completes the detection task of T targets while ensuring the communication quality of U users. The RIS constructs a uniform linear array through M one-dimensional programmable units, and all user terminals adopt a single-port antenna design; Let be the guidance vector from RIS to the t-th target, and its specific expression is: at the same time This represents the channel between PIS and the t-th target, β t This represents the path loss coefficient. Since the direct connection between the BS and the target is obstructed, the BS instead utilizes the path from the BS to the RIS and then to the target to transmit signals to the detection target. In this case, when the transmitted waveform reaches the target t, it becomes the illumination signal on target t, and its mathematical expression is: Since one of the key factors affecting radar detection performance is the illumination power of the radar signal, the illumination power of the radar signal on the t-th target can be expressed by the following formula: Considering the influence of clutter interference near the target, the radar signal illumination power to it can be expressed in the following form: in, Let β represent the channel between the passive RIS and the q-th clutter interference, where β q This is the path loss coefficient; the steering vector expression from RIS to the qth clutter interference is: In radar systems, the efficiency of the transmitter power amplifier is crucial to the overall system performance. To maximize the efficiency of the power amplifier, it is necessary to ensure that the amplitude of the transmitted signal remains constant throughout the entire signal period. Therefore, the designed radar waveform should satisfy the constant modulus constraint. From a radar detection perspective, the key to improving target detection performance is to increase the radar signal's illumination power on the target while reducing the illumination power against clutter interference. Therefore, the clutter interference constraint is introduced as follows: In multi-user MIMO communication, the SLP (Simultaneous Phase Logic) system is used for transmit waveform design. By accurately controlling the amplitude and phase of each transmitted symbol, interference between users is minimized, thereby ensuring the communication performance of each user. The received signal of the u-th user at time l is: Where, n u，l The received noise of the communication user at time l follows the law of... distributed; This refers to the channel from the BS to the user. This refers to the channel from the RIS to the user; Assume that at time l, the symbol s to be transmitted is... l It is selected independently and identically distributed from a phase constellation diagram, and this constellation diagram is known in advance at both the base station and the user end; to improve the demodulation performance of the signal at the receiver, a CI-based precoding scheme is used to design the transmitted waveform, and its core constraints can be expressed as follows: Where, γ u θ represents the minimum SNR that the u-th user needs to guarantee, and θ is the phase of the received signal; Considering that equation (16) contains both real and imaginary parts of the function, to facilitate the solution, the imaginary part of the function is transformed into the real part form, i.e. Therefore, equation (16) can be further expressed as: Based on equation (15), the ideal noise-free signal received by the user can be further derived as follows: Among them, e l This represents the identity matrix I. L The l-th column vector; therefore, the CI constraint can be concisely expressed as: In practical applications, the reflection coefficient of passive RIS typically satisfies the constant modulus constraint, expressed as:

3. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that, The objective function is a max-min problem, which is difficult to solve directly. To solve it effectively, we first introduce an auxiliary variable R1 to fix the passive RIS reflection coefficient and remove terms that are irrelevant to the transmitted waveform x. Then, the subproblem of problem (2) with respect to the transmitted waveform x can be expressed as problem (3). Next, since And there are Therefore, it can be restated. Similarly, And there are Therefore, P q It can be restated as At this time, it can be ordered Then there is Given a set of L snapshots, the matrix representation P of the transmitted waveform is... t It can be represented as Considering the variable to be optimized, x = vec(X), to achieve dimensional matching, the following operation can be performed: Let as well as Again Then we can eventually obtain P. t =x H D t x; Similarly, due to Can make Then there is Defineable as well as Again Then P q =x H D q Therefore, the optimization problem (3) concerning the transmitted waveform x can be further expressed in the following form: Due to matrix D t It is positive semi-definite, which shows that the constraint x is... H D t x≥R1 is non-convex; for ease of solution, it is relaxed to a convex constraint; by using a first-order Taylor expansion technique, we can obtain: in, c1=-(x (s) ) H D t x (s) Then constrain x H D t x≥R1 can be replaced with: Therefore, problem (21) can be transformed into the following form: Next, the non-convex constant modulus waveform constraint is also equivalently replaced, as follows: In the transformed expression, only equality constraints exist. It is non-convex; since the intersection of the two types of constraints is very small, it is difficult to handle; below, the equality constraint is relaxed to Here, ρ is an auxiliary variable whose value approaches zero; at this point, the inequality on the right side... It is convex, but the inequality on the left... The constraint is non-convex; to convert a non-convex constraint into a convex constraint, we can use a successive convex approximation technique based on a first-order Taylor expansion to transform the inequality on the left into the following form: In summary, by introducing the penalty relaxation variable ρ into the objective function, the problem of optimizing the emission waveform (3) can be finally expressed as: Among them, κ1 is the introduced penalty parameter, which is mainly used to adjust the impact of the penalty term on the system; it can be found that problem (27) is a convex optimization problem, so it can be solved effectively by interior point method or convex optimization toolbox such as CVX.

4. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that, Remove terms irrelevant to the passive RIS reflection coefficient v, and transform the problem description using a method similar to that in claim 3; first, introduce the auxiliary variable R2, then the subproblem of problem (2) regarding the passive RIS reflection coefficient v can be expressed as problem (4); next, since And there are Therefore, it can be restated. Similarly, And there are Therefore, P q It can be restated as Similarly, if there are L snapshots, then P t It can be restated as Where x = vec(X), to simplify the expression, we can let Then P t =v H D t2 v, similarly, make Then P q =v H D q2 v; Therefore, problem (4) can be redefined as the following expression: Because of v H D t2 v≥R2 is a non-convex constraint, which we will relax to a convex constraint below; using the first-order Taylor expansion technique, we can obtain the following relationship: in c2=-(v (n) ) H D t2 v (n) Therefore, the non-convex constraint v H D t2 v≥R2 can be transformed into: Therefore, problem (28) can be transformed into the following form: Next, the expression of the CI constraint will be modified so that it can explicitly express the variable v: in, And there are in For the non-convex monotony constraint of v, it can be equivalently expressed as follows: for It can be relaxed to Here, b is an auxiliary variable whose value approaches zero; it is easy to observe that the inequality on the right side... It is convex, and the inequality on the left is... It is non-convex; in order to transform the non-convex part into a convex constraint, a successive convex approximation method based on first-order Taylor expansion can be used to perform the following transformation: In summary, by introducing the penalty relaxation variable b into the objective function, the optimization problem (4) for solving the passive RIS reflection coefficient v can be finally expressed as: Wherein, κ2 is the penalty parameter introduced by the system, which can be used to adjust the influence of the penalty term; obviously, problem (35) is a convex optimization problem, which can be effectively solved by the interior point method or the convex optimization toolbox.

5. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that: Consider a multi-target detection model architecture for a DFRC system assisted by an active RIS. This architecture consists of five parts: a DFRC BS, an active RIS, a user terminal, a group of targets to be detected, and several clutter interference sources near the target group. The design is similar to the passive RIS-assisted DFRC system multi-target detection model in claim 2, and the specific process will not be elaborated here. In particular, in practical applications, the transmission waveform and reflection coefficient of the active RIS are usually limited by hardware conditions. Due to power limitations, the power of the active RIS in the l-th snapshot is constrained as follows: Among them, P max This represents the maximum power of the active RIS; furthermore, the signal amplification effect of the active RIS is constrained by its implementation architecture. Therefore, the amplification factor of each RIS unit needs to meet the following conditions: |in m |≤τ, m=1,..., M (37) Where τ is the maximum amplification factor of the active RIS unit.

6. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that: The objective function is a max-min problem, which is difficult to solve directly. To solve it effectively, we first introduce an auxiliary variable R3, fix the active RIS reflection coefficient, and remove terms that are not related to the transmitted waveform x. Then, the subproblem of problem (5) with respect to the transmitted waveform x can be expressed as problem (6). Next, similar to the transformation processing method in claim 3, we process P... t P q The constant modulus constraint is subjected to equivalent simplification and substitution transformation and convex transformation respectively. The specific process will not be elaborated here. Therefore, by introducing the penalty relaxation variable μ into the objective function, the problem of optimizing the emission waveform of the active RIS-assisted DFRC system (6) can be finally expressed as: Among them, κ3 represents the penalty parameter, which is mainly used to adjust the influence of the penalty factor; it can be found that problem (38) is a convex optimization problem, so it can be solved effectively by interior point method or convex optimization toolbox such as CVX.

7. The method for jointly designing the transmitted waveform and reflected beamforming of a RIS-assisted DFRC system for multi-target detection according to claim 1, characterized in that: By removing terms irrelevant to the reflection coefficient v of the active RIS and introducing an auxiliary variable R4, problem (5) can be expressed as problem (7) regarding the reflection coefficient v of the passive RIS. Next, a related transformation processing method similar to that used in claim 4 is adopted to simplify the representation of the passive RIS reflection coefficient and perform convex transformation processing, etc. The specific process will not be described here. In particular, in order to explicitly express the optimization variable v, the energy constraint update of the active RIS can be further expressed in the following form: in, In summary, the optimization problem (7) for solving the reflection coefficient of the active RIS can be finally expressed as: Obviously, problem (40) is a convex optimization problem, which can be solved globally using the interior point method or the convex optimization toolbox.

Images