Robust opportunistic spectrum sensing and communication co-optimization method for mobile antenna full duplex

Abstract

The present application relates to the field of communication technology, and discloses a movable antenna full-duplex robust opportunistic spectrum sensing communication cooperative optimization method, wherein a secondary base station is equipped with a transmitting movable antenna array and a receiving movable antenna array; a primary base station and the secondary base station estimate channel parameters of each link, calculate a detection statistic, calculate a spectrum detection probability and a false alarm probability, and solve a minimum sensing signal-to-noise ratio that meets spectrum detection probability threshold and false alarm probability threshold requirements; an average interference power constraint for primary users is constructed; and a BCD-SCA-SPGA algorithm is used to solve optimal sensing and communication beamforming and optimal transmitting and receiving movable antenna positions. The transmitting movable antenna array is used for sensing the spectrum of the primary base station and secondary base station transmission; the receiving movable antenna array is used for secondary base station communication; through optimization of the antenna position, the sensing and communication performance is simultaneously improved; and when channel information is inaccurate, a robust beam is designed to protect the communication quality of the primary users.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a method for collaborative optimization of full-duplex, robust, opportunistic spectrum-aware communication using a movable antenna. Background Technology

[0002] The Internet of Things (IoT) in the 6G era, such as intelligent transportation and smart factories, will lead to a dramatic increase in data traffic, resulting in expanded bandwidth demands, which contradicts the current limited bandwidth. To address this issue, Opportunistic Spectrum Access (OSA) has emerged as a promising potential technology. Furthermore, with the spatial freedom and channel reconfiguration advantages of Movable Antenna Array (MA) technology, applying MA to OSA can significantly improve the communication and sensing performance of OSA systems. However, when applying MA to OSA systems, using the same MA to simultaneously improve communication and sensing performance is ineffective because the MA suitable for sensing may not be communication-optimal. Moreover, due to the generally short sensing time constrained by communication in OSA systems, frequently adjusting the MA within a short period to simultaneously improve communication and sensing performance is impractical. Furthermore, in OSA systems, because the primary and secondary systems lack coordination (belonging to different operators), it is difficult to accurately obtain interference channel information. Summary of the Invention

[0003] The purpose of this invention is to address the problem that existing methods using mobile antenna arrays (MA) in OSA systems cannot simultaneously improve communication and sensing performance. This invention provides a robust opportunistic spectrum sensing and communication collaborative optimization method using movable antenna full-duplex arrays (MA). The secondary base station has two sets of movable antenna arrays (MA): one set is used for sensing the spectrum of the primary base station and for secondary base station transmission; the other set is used for secondary base station communication. By optimizing the potential for positional changes in the movable antenna arrays, both sensing and communication performance can be improved simultaneously. Furthermore, considering channel imperfections, robust beamforming is designed to effectively protect the communication quality of the primary user even when channel information is inaccurate.

[0004] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0005] A robust, opportunistic spectrum-aware communication cooperative optimization method with a movable antenna in full-duplex mode includes the following steps:

[0006] Step 1: The secondary base station is equipped with a transmit mobile antenna array and a receive mobile antenna array that operate in full-duplex mode and can move within a given area;

[0007] Step 2: The primary base station and secondary base station estimate the channel parameters of each link through pilot signals, and calculate the detection statistics of the received signal based on the channel parameters; calculate the spectrum detection probability and false alarm probability based on the detection statistics, and solve for the minimum perceived signal-to-interference-plus-noise ratio that meets the requirements of the spectrum detection probability threshold and the false alarm probability threshold.

[0008] Step 3: Calculate the amplitude gain of the interference channel based on the Gaussian distribution, and construct the average interference power constraint for the primary user. The average interference power constraint has a deterministic convex quadratic constraint condition.

[0009] Step 4: Based on the channel parameters of each link, the minimum perceived signal-to-interference-plus-noise ratio, and the average interference power constraint, the BCD-SCA-SPGA algorithm is used to solve the effective data rate optimization problem of the secondary base station, and the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position are obtained.

[0010] Furthermore, step 1 specifically includes:

[0011] remember Let be the position vector of the transmitting mobile antenna array, where For the nth t The positions of n transmitting mobile antennas t =1,2,...,N t ;remember Let be the position vector of the receiving mobile antenna array, where For the nth r The location of the receiving mobile antenna, n r =1,2,...,N r ;

[0012] The guide vector is represented as:

[0013] ;

[0014] ;

[0015] Where k is the user index; l is the path index; a k,l (x) is the steering vector of the transmitting mobile antenna of the k-th user on the l-th path; b k,l (y) is the steering vector of the receiving mobile antenna for the k-th user on the l-th path; e is the Euler number; j is the imaginary number; The carrier wavelength; Let be the departure angle of the l-th path for the k-th user; Let be the departure angle of the l-th path of the k-th user; T is the matrix transpose; It is the set of complex numbers.

[0016] Furthermore, in step 2, the step of the primary base station and the secondary base station estimating the channel parameters of each link through pilot signals includes:

[0017] The sensing channel h(y) between the receiving mobile antennas of the primary base station and the secondary base station is:

[0018] ;

[0019] in, The first free space path loss coefficient; L represents the channel gain coefficient for the l-th path of the k-th user; p Let l be the number of ray paths, l=1,2,...,L p ; b are complex channel coefficients; l (y) is the steering vector of the receiving mobile antenna for the l-th path;

[0020] Full-duplex self-interference channel h between the transmitting and receiving mobile antennas of the secondary base station I (x,y) is:

[0021] ;

[0022] in, The second free space path loss coefficient; Let a be the channel gain coefficient for a full-duplex self-interference channel; when there is only one user and only one path, a I (x)=a k,l (x), b I (y)=b k,l (y); the superscript H indicates the conjugate transpose of the vector.

[0023] Furthermore, step 2, the step of calculating the detection statistics of the received signal based on the channel parameters, includes:

[0024] Let the amplitude y[k] of the received signal after sensing beamforming at the receiving mobile antenna be:

[0025] ;

[0026] Where N is the number of perceived samples, N=f s T,f s P is the sampling rate, T is the sensing duration; p v is the primary user's transmit power; w is the secondary base station's sensing beamforming; n[k] is the noise superimposed on the k-th sample; s[k] is the normalized power complex Gaussian signal transmitted by the primary user. It conforms to a Gaussian distribution. For noise variance;

[0027] Sensing signal-to-interference-plus-noise ratio for;

[0028] ;

[0029] Based on the amplitude y[k] of the received signal, calculate the detection statistic:

[0030] ;

[0031] Where Y is the detection statistic.

[0032] Furthermore, step 2, which involves calculating the spectrum detection probability and false alarm probability based on detection statistics, and solving for the minimum perceived signal-to-interference-plus-noise ratio (SNR) that satisfies the requirements of the spectrum detection probability threshold and the false alarm probability threshold, includes:

[0033] ;

[0034] ;

[0035] in, P is the energy detection threshold. f P represents the probability of a false alarm. d For spectrum detection probability; This indicates that the primary user is in an idle state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability of; This indicates that the primary user is in an occupied state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability; Q(.) is the Gaussian Q-function;

[0036] Given a false alarm probability threshold P f0 Spectrum detection probability threshold P d0 Requires P to be satisfied f ≤P f0 and P d ≥P d0 And satisfy the perceived signal-to-interference-plus-noise ratio. Greater than or equal to the minimum perceived signal-to-interference-plus-noise ratio ;

[0037] Solve :

[0038] ;

[0039] in, This represents the minimum energy detection threshold. This means defining the expression on the left as the expression on the right;

[0040] Solve :

[0041] ;

[0042] Given P d0 P f0Under the constraints, the perceived signal-to-interference-plus-noise ratio The above constraints must be met.

[0043] Furthermore, step 3, which involves calculating the interference channel amplitude gain based on a Gaussian distribution and constructing an average interference power constraint for the primary user, includes:

[0044] The estimated amplitude gain of the interference channel is:

[0045] ;

[0046] Among them, g sp (x) represents the actual amplitude gain of the interfering channel; e is the error vector, which follows a Gaussian distribution. , Let I be the variance of the channel estimation error, and I be the identity matrix.

[0047] The average interference power constraint for primary users is:

[0048] ;

[0049] in The average interference power threshold allowed by the system. , This represents the worst-case leakage power threshold. w represents calculating the statistical average. max This is the maximum value of w.

[0050] Furthermore, in step 4, the effective data rate optimization problem of the secondary base station is as follows:

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, R represents the effective data rate of the secondary system. eff Optimization of R; max This indicates the highest data rate of secondary users when the primary user is idle; R prot This indicates the data rate of secondary users when the primary user is in an occupied state and the primary user is protected. For the ellipsoidal error set; w prot Guard beamforming of secondary base stations during primary user idle state; P max P is the maximum transmit power; prot To protect beamforming power; D0 is the minimum antenna spacing; X min X max These represent the lower and upper limits of the movable position of the transmitting mobile antenna on the parallel line segment, respectively. min Y max These are the lower and upper limits of the movable position of the receiving mobile antenna on the parallel line segment, respectively.

[0062] ;

[0063] ;

[0064] Among them, h ss (x) represents the channel amplitude gain between the secondary base station and the secondary user; h ps (x) represents the channel amplitude gain between the primary base station and the secondary user; s p Signals sent by the master system; This represents Gaussian noise superimposed on the secondary user.

[0065] Furthermore, the BCD-SCA-SPGA algorithm includes the BCD-SCA algorithm and the SPGA algorithm;

[0066] Step 4, which uses the BCD-SCA-SPGA algorithm to solve the effective data rate optimization problem of the secondary base station and obtains the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position, includes:

[0067] Step 4-1: Under the conditions of fixed transmit mobile antenna position vector x, receive mobile antenna position vector y, and transmit beamforming, solve for the optimal sensing beamforming using the SCA-BCD algorithm.

[0068] Step 4-2: Under the conditions of fixed transmitting mobile antenna position vector x, receiving mobile antenna position vector y, and optimal sensing beamforming v, the optimal communication beamforming is solved using the SCA-BCD algorithm.

[0069] Step 4-3: Under the conditions of fixed optimal sensing beamforming and optimal communication beamforming, use the SPGA algorithm to solve for the optimal transmitting mobile antenna position and the optimal receiving mobile antenna position.

[0070] Furthermore, step 4-1 specifically includes:

[0071] Update Sensing Beamforming v:

[0072] ;

[0073] ;

[0074] definition and ;

[0075] Optimal sensing beamforming v is The main eigenvectors, For the carrier wavelength; first calculate B. -1 A is the eigenvector corresponding to its largest eigenvalue, which is the main eigenvector v.

[0076] Furthermore, step 4-2 specifically includes:

[0077] Given the transmitted beamforming w max Protect beamforming w prot The update objective function is:

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] Among them, c and H I I s All are intermediate parameters, , , .

[0083] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0084] (1) This invention innovatively proposes a full-duplex robust opportunistic spectrum access (OSA) system enhanced by a movable antenna array (MA). This system can improve sensing and communication performance by combining the advantages of full-duplex mode and MA, while also improving spectrum utilization efficiency by taking advantage of OSA.

[0085] (2) This invention proposes a new transmission protocol. When the secondary base station detects that the primary user is occupied, it uses a protected lower transmission power and beam to transmit signals, which will not cause unacceptable interference to the primary user. This is different from the traditional spectrum sharing system (SS). When the primary user is detected to be busy, the SS remains silent and does not transmit information, which will cause spectrum waste, especially in scenarios where the primary user has a high tolerance for communication quality. When the secondary base station detects that the primary base station is idle, the invention uses the optimal transmission power and beam to transmit information. At this time, the power is larger, which can increase the communication capacity of the secondary base station, while not causing interference to the primary base station.

[0086] (3) This invention proposes a full-duplex mechanism and proposes for the first time to use two sets of movable antenna array (MA) systems, one set for spectrum sensing and the other set for communication, which can simultaneously improve sensing and communication performance without frequently changing the antenna position.

[0087] (4) The present invention proposes the BCD-SCA-SPGA algorithm, which improves the sensing performance by optimizing the sensing beamforming and moving antenna position of the MA, and improves the communication capacity of the secondary base station while protecting the primary user by optimizing the transmitting beamforming and protection beamforming of the communication MA and the antenna position of the communication MA.

[0088] (5) In view of the uncertainty of the interference channel, the present invention designs a robust beamforming. In the optimization problem, the uncertainty of the channel is modeled as a Gaussian variable. The beamforming designed in the case of channel error can effectively protect the primary user under any circumstances.

[0089] (6) The proposed scheme of this invention was simulated and compared with five similar baseline schemes. The simulation results show that the effective data rate of this scheme is about 30% higher than that of other similar baseline algorithms. At the same time, it has been greatly improved in terms of protecting the primary user and suppressing self-interference (a drawback of full-duplex systems). The system's spectrum sensing accuracy has also been improved by using MA. Attached Figure Description

[0090] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0091] Figure 1 The effective data rate R in Embodiment 2 of the present invention eff A schematic diagram showing the change in the number of iterations as the block coordinates decrease (BCD) decreases.

[0092] Figure 2 The effective data rate R in Embodiment 2 of the present invention eff With maximum transmit power P max A diagram illustrating the changes.

[0093] Figure 3 This is a schematic diagram comparing the mobile antenna layout and the uniform antenna layout in Embodiment 2 of the present invention. Figure 3 (a) in the text is X max Comparison when =4λ Figure 3 (b) in the text is X max Comparison when =6λ.

[0094] Figure 4 This is the transmission beam diagram of Embodiment 2 of the present invention.

[0095] Figure 5 The effective data rate R in Embodiment 2 of the present invention eff With aperture X max A diagram illustrating the changes.

[0096] Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0097] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0098] It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, the terms "first," "second," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance, or suggesting any such actual relationship or order between these entities or operations.

[0099] Example 1:

[0100] This invention is achieved through the following technical solution: a mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method, such as... Figure 6 As shown, it includes the following steps:

[0101] Step 1: The secondary base station is equipped with a transmit mobile antenna array and a receive mobile antenna array that operate in full duplex mode and can move within a given area.

[0102] This design proposes a full-duplex (FD) monobase secondary base station (SBS) equipped with two movable antenna arrays (MA), one of which is N... t One is a transmit mobile antenna array (Tx-MAs) consisting of 1 transmit mobile antenna, and the other is an N-type transmit mobile antenna array. r A receive mobile antenna array (Rx-MAs) consisting of several receiving mobile antennas. This secondary base station serves a single-antenna downlink secondary user while simultaneously sensing signals from the primary base station (PT). The positions of the transmitting and receiving mobile antennas can be determined via a flexible cable connected to the RF link, at two parallel line segments [X]. min ,X max ] and [Y min ,Y max [Internal flexible adjustment, X] min X max These represent the lower and upper limits of the movable position of the transmitting mobile antenna on the parallel line segment, respectively. min Y max These represent the lower and upper limits of the movable position of the receiving mobile antenna on the parallel line segment, respectively. Furthermore, this scheme assumes the communication channel is a narrowband quasi-static channel; therefore, the time overhead required to adjust the positions of the transmitting and receiving mobile antennas is acceptable compared to the longer channel coherence time for primary and secondary users.

[0103] remember Let be the position vector of the transmitting mobile antenna array, where For the nth t The positions of n transmitting mobile antennas t =1,2,...,N t ;remember Let be the position vector of the receiving mobile antenna array, where For the nth r The location of each receiving mobile antenna, n r =1,2,...,N r This scheme adopts a channel model based on field response, with the secondary base station along the direction... The steering vectors of the transmitting mobile antenna array and the receiving mobile antenna array are respectively expressed as:

[0104] ;

[0105] ;

[0106] Where k is the user index; l is the path index; a k,l (x) is the steering vector of the transmitting mobile antenna of the k-th user on the l-th path; b k,l (y) is the steering vector of the receiving mobile antenna for the k-th user on the l-th path; e is the Euler number; j is the imaginary number; The carrier wavelength; Let be the departure angle of the l-th path for the k-th user; Let be the departure angle of the l-th path of the k-th user; T is the matrix transpose; It is the set of complex numbers.

[0107] Step 2: The primary base station and secondary base station estimate the channel parameters of each link through pilot signals, and calculate the detection statistics of the received signal based on the channel parameters; calculate the spectrum detection probability and false alarm probability based on the detection statistics, and solve for the minimum perceived signal-to-interference-plus-noise ratio that meets the requirements of the spectrum detection probability threshold and the false alarm probability threshold.

[0108] definition This is the first free space path loss coefficient. Let L be the channel gain coefficient for the k-th user and the l-th path. p Let l be the number of ray paths, l=1,2,...,L p Then the sensing channel h(y) between the receiving mobile antennas of the primary base station and the secondary base station is:

[0109] ;

[0110] in, b are complex channel coefficients; l (y) is the steering vector of the receiving mobile antenna for the l-th path.

[0111] Full-duplex self-interference channel h between the transmitting and receiving mobile antennas of the secondary base station I (x,y) is:

[0112] ;

[0113] in, The second free space path loss coefficient; Let a be the channel gain coefficient for a full-duplex self-interference channel; when there is only one user and only one path, a I (x)=a k,l (x), b I (y)=b k,l(y); the superscript H denotes the conjugate transpose of the vector. It is assumed that the channel state information (CSI) of the above channel is fully known at the secondary base station. Although perfect channel state information is obtained in practice, this assumption still establishes an upper bound for performance analysis.

[0114] Let the amplitude y[k] of the received signal after sensing beamforming at the receiving mobile antenna be:

[0115] ;

[0116] Where N is the number of perceived samples, N=f s T,f s P is the sampling rate, T is the sensing duration; p v is the primary user's transmit power; w is the secondary base station's sensing (receiving) beamforming; n[k] is the noise superimposed on the k-th sample; s[k] is the normalized power complex Gaussian signal transmitted by the primary user. It follows a Gaussian distribution. This represents the noise variance.

[0117] The perceived signal-to-interference-plus-noise ratio (SINR) is defined as follows: .

[0118] Based on the amplitude y[k] of the received signal, the detection statistic is calculated. The detection statistic is represented by the received signal energy Y and is defined as follows:

[0119] ;

[0120] If the primary user is in an idle state Y follows a central chi-square distribution with 2N degrees of freedom; if the primary user is in an occupied state. Y follows a rule with 2N degrees of freedom. The non-central chi-square distribution.

[0121] When N is sufficiently large (e.g., N>10), according to the approximation of the Central Limit Theorem (CLT), the distribution of Y is as follows: In the idle state of the primary user... Below, Y approximately follows In primary user-occupied state Below, Y approximately follows ,in Therefore, we have:

[0122] ;

[0123] ;

[0124] in, The energy detection threshold can be adjusted according to sensing requirements; Pf P represents the probability of a false alarm. d For spectrum detection probability; This indicates that the primary user is in an idle state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability of a false alarm; This indicates that the primary user is in an occupied state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability of detection is the probability of the spectrum; Q(.) is the Gaussian Q function.

[0125] Given a false alarm probability threshold P f0 Spectrum detection probability threshold P d0 Requires P to be satisfied f ≤P f0 and P d ≥P d0 Furthermore, this embodiment must satisfy the perceived signal-to-interference-plus-noise ratio during the optimization process. Greater than or equal to the minimum perceived signal-to-interference-plus-noise ratio By P f and P f ≤P f0 We can obtain:

[0126] ;

[0127] Since Q(.) is monotonically decreasing, therefore we have To make P f ≤P f0 Solve for the energy detection threshold for:

[0128] ;

[0129] in, This represents the minimum energy detection threshold. This means defining the expression on the left as the expression on the right. In formula P... d In the middle, P d Follow Monotonically decreasing, therefore, while simultaneously satisfying P f0 and P d0 When both requirements are met, the energy detection threshold optimal value equal Applying requirement P d ≥P d0 Then, we can obtain:

[0130] ;

[0131] Using the monotonically decreasing property of Q(.) again, we can obtain:

[0132] ;

[0133] Will Substituting, we get:

[0134] ;

[0135] Solve We can obtain:

[0136] ;

[0137] From this formula, we can see that, given P d0 P f0 Under the constraints, the perceived signal-to-interference-plus-noise ratio The above constraints must be met.

[0138] In spectrum-sharing systems, because the constraints on detection performance are stricter than the constraints on false alarm tolerance, there is usually P d0 >1-P f0 This reflects the priority of protecting primary users in perceptual radio networks. In practice, the target detection probability threshold P... d0 The value is typically close to but less than 1, especially in low signal-to-noise ratio (SNR) scenarios. For example, in IEEE 802.22 WRAN, for a SNR of 20 dB, a value of P can be taken. d0 =0.9. It should be noted that if the primary user requests 100% protection for its frequency band, then secondary users will not be allowed to use that band. This scheme also assumes that the primary user is in an occupied state. The probability P1 is relatively small, for example, less than 0.3. Therefore, from an economic perspective, exploring secondary user usage in this frequency band is reasonable. It should be noted that primary users are currently in a pre-emptive state. The probability P1 is that the primary user is in an idle state. The sum of the probabilities P0 is 1.

[0139] Step 3: Calculate the amplitude gain of the interference channel based on the Gaussian distribution, and construct the average interference power constraint for the primary user. The average interference power constraint has a deterministic convex quadratic constraint condition.

[0140] Since there is no cooperation between the primary base station and the secondary base station, the interference channel amplitude gain g between the secondary base station and the primary user... sp (x) is difficult to estimate accurately, therefore there is an error between the estimated channel state information and the true channel state information. This scheme uses the estimation of the interference channel amplitude gain. , where e is the error vector and follows a Gaussian distribution. , Let g be the variance of the channel estimation error, and I be the identity matrix. sp(x) represents the true channel state information (CSI), defined as ,in For complex channel gain; L is the path loss coefficient in the third free space; sp Let l be the number of interfering paths, where l = 1, 2, ..., L sp ;a sp,l (x) is the steering vector of the transmitting moving antenna of the master user sp in the l-th interference path. Therefore, the amplitude gain of the interference channel is estimated. Follows the mean g sp (x), variance is The circularly symmetric complex Gaussian distribution, i.e. .

[0141] To provide statistical protection in the event of a missed detection, this scheme introduces an average interference power constraint. ,in The average interference power threshold allowed by the system is typically... , This represents the worst-case leakage power threshold, reflecting stricter controls on high-risk missed detection events; w max The maximum value of the transmit beamforming w for a base station; This indicates the calculation of the statistical average over a random variable or vector. The value of is determined by the following process.

[0142] First, consider the probability interference constraint. This probabilistic disturbance constraint represents the worst-case leakage power threshold for primary users. The probability does not exceed , The threshold is set as a preset value. Then, the Markov inequality is used to transform this probabilistic disturbance constraint into a deterministic convex quadratic constraint type, suitable for optimization modeling. For any non-negative random variable X and a>0, the Markov inequality gives... Accordingly, this probabilistic disturbance constraint can be replaced with: Further calculations yield the following:

[0143] ;

[0144] Therefore, we have:

[0145] ;

[0146] Based on the above derivation, the original probabilistic disturbance constraint can be approximated as the following deterministic convex quadratic constraint type:

[0147] ;

[0148] Therefore, there is This approximation is simple to calculate, but because Markov inequalities usually cannot provide a bound that closely approximates the actual situation, they are often conservative.

[0149] Step 4: Based on the channel parameters of each link, the minimum perceived signal-to-interference-plus-noise ratio, and the average interference power constraint, the BCD-SCA-SPGA algorithm is used to solve the effective data rate optimization problem of the secondary base station, and the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position are obtained.

[0150] The effective data rate optimization problem for secondary base stations, as defined in this scheme, aims to balance the ideal throughput gain obtained when the primary user is correctly detected to be idle with the protected transmission when the primary user is occupied. This optimization problem does not reward missed detection events, as missed detections are inherently suppressed by security constraints; simultaneously, it implicitly penalizes false alarms by not incentivizing wasted spectrum opportunities. Based on the above analysis, the effective data rate optimization problem for secondary base stations is defined as follows:

[0151] ;

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] ;

[0161] in, R represents the effective data rate of the secondary system. eff Optimization; R max This indicates the highest data rate of secondary users when the primary user is idle; R prot This indicates the data rate of secondary users when the primary user is in an occupied state and the primary user is protected. For the ellipsoidal error set; w prot During the idle state of the primary user, the secondary base station performs protection beamforming; P maxP is the maximum transmit power; prot To protect beamforming power; D0 is the minimum antenna spacing.

[0162] have:

[0163] ;

[0164] ;

[0165] Among them, h ss (x) represents the channel amplitude gain between the secondary base station and the secondary user. ,in For complex channel gain, L c Let l = 1, 2, ..., L be the number of communication paths between the secondary base station and the secondary user. c ;a l (x) represents the steering vector of the transmitting mobile antenna under the l-th communication path; h ps (x) represents the channel amplitude gain between the primary base station and the secondary user; s p The signal sent by the primary base station; This represents Gaussian noise superimposed on the secondary user.

[0166] C1 guarantees that the perceived signal-to-interference-plus-noise ratio (SINR) from the primary base station to the secondary user is higher than the minimum perceived SINR. , Depends on the target detection probability threshold P d0 And the target false alarm probability threshold P f0 This is a Quality of Service (QoS) constraint on the secondary link. C2 restricts the protection beamforming of the secondary base station. prot The maximum interference power to primary users does not exceed the threshold, and the ellipsoidal error set is taken into account. The worst-case channel uncertainty within the range is a robust interference constraint. C3 is used to control missed detection events (P). d ≤1) Probabilistic constraints on the degree of harm, shaping the transmit beam of the secondary base station w max The average interference power caused to primary users, based on the probability of missed detection. Weighted constraint at threshold The following constraint is also robust, but focuses on average interference power rather than worst-case interference power. C4 to C8 represent the original constraints regarding power budget, beamforming normalization, and possible spatial or spectral spacing between users or channels.

[0167] The effective data rate optimization problem for secondary base stations is nonconvex because the effective data rate involves the product of optimization variables (e.g., it typically depends on R). max and R prot ) and probability Pf and P d Therefore, it is generally not a convex function. C1 is non-convex because it includes... The quadratic form of this term with respect to v. C2 and C3 contain the form... The worst-case quadratic constraint is a robust quadratic constraint. Even without maximization operations, when e is fixed... Regarding w prot It is convex; however, maximizing e usually makes the constraint non-convex, unless It has a special structure (such as an ellipsoidal error set) and can be reconstructed using an S-process. This reconstruction may give convex constraints, but is not necessarily equivalent to the original constraints. The effective data rate optimization problem of secondary base stations, along with bilinear or trilinear terms in the constraints (such as beamforming, the product of power and probability), further increases the complexity of convexity analysis. If the original constraints C4 to C8 only involve norm, power constraints, or spatial constraints, they may each be convex, but due to the above factors, the overall problem remains non-convex.

[0168] The non-convexity of the effective data rate optimization problem for secondary base stations stems from the non-concave objective function, the worst-case robust quadratic constraint, and the joint optimization of beamforming and power variables. If a global solution is required, specialized non-convex optimization methods are needed, such as successive convex approximations, semidefinite relaxations with rank constraints, or branch-and-bound methods. In practical applications, convex approximations or iterative algorithms are typically used to find suboptimal but feasible solutions. This proposal suggests a BCD-SCA-SPGA algorithm for globally solving the non-convex optimization problem of the effective data rate for secondary base stations. The BCD-SCA-SPGA algorithm includes a block coordinate descent (BCD) algorithm based on successive convex approximation (SCA) and a sequential projection gradient ascent (SPGA) algorithm.

[0169] First, this scheme proposes a block coordinate descent (BCD) algorithm based on successive convex approximation (SCA), hereinafter referred to as the SCA-BCD algorithm, and iteratively solves for optimal sensing beamforming and optimal communication beamforming. Then, this scheme proposes a sequential projection gradient ascent (SPGA) algorithm, hereinafter referred to as the SPGA algorithm, and iteratively solves for optimal transmit mobile antenna position and optimal receive mobile antenna position. Therefore, the steps of the BCD-SCA-SPGA algorithm in solving the effective data rate optimization problem of the secondary base station mainly include steps 4-1 to 4-3, ultimately obtaining the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position.

[0170] Step 4-1: Under the conditions of fixed transmit mobile antenna position vector x, receive mobile antenna position vector y, and transmit beamforming, solve for the optimal sensing beamforming using the SCA-BCD algorithm.

[0171] First, there's the update of the perceived beamforming v. Given a fixed transmit moving antenna position vector x, a receive moving antenna position vector y, and a transmit beamforming w... max Protective beamforming w prot Update perception beamforming v:

[0172] ;

[0173] ;

[0174] This is a generalized Rayleigh quotient problem, defined as follows: and The optimal sensing beamforming v is The principal eigenvectors are normalized to the unit norm. Let be the carrier wavelength. Solution method: This can be efficiently solved using standard numerical linear algebra tools, such as MATLAB's `eig` function. Since B is a positive definite matrix, we can first calculate B. -1 A is given by matrix inversion and eigenvalue decomposition. The eigenvector corresponding to its largest eigenvalue is then obtained, which is the principal eigenvector v. The computational complexity of matrix inversion and eigenvalue decomposition is O(n log n). .

[0175] Step 4-2: Under the conditions of fixed transmitting mobile antenna position vector x, receiving mobile antenna position vector y, and optimal sensing beamforming v, the optimal communication beamforming is solved using the SCA-BCD algorithm.

[0176] Secondly, there is the update to communication beamforming. Communication beamforming includes transmit beamforming (w) max and protection beamforming w prot Given fixed x, y, and optimal v, w max With w prot The optimization problem is non-convex.

[0177] 1) Transmit beamforming w max Update.

[0178] Given a protective beamforming w prot Regarding transmitted beamforming w max The update objective function is:

[0179] ;

[0180] ;

[0181] Where M is an intermediate parameter, we have Because P in the update objective function dSince the constraint is fixed, it is convex. To handle the non-concavity of the update objective function, this scheme employs semi-definite relaxation (SDR), defining... and The relaxation problem is:

[0182] ;

[0183] ;

[0184] ;

[0185] ;

[0186] Here, Tr(.) represents finding the trace of a matrix.

[0187] Solution Method: The relaxation problem described above is a standard semidefinite programming problem (SDP), which can be efficiently solved using the interior-point method and convex optimization solvers such as CVX, MOSEK, or SeDuMi. For an SDP with a K×K matrix of variables and m constraints, it achieves... The iteration complexity of the optimal solution is typically O(n log n). In this embodiment, K=N t If the solution is... If w is a rank-one matrix, then it can be obtained through Cholesky decomposition. max , The conjugate matrix of W is given; otherwise, Gaussian randomization is used to extract high-quality feasible solutions. This Gaussian randomization process involves extracting solutions from a Gaussian distribution. Generate multiple random vectors, and select the vector with the highest value of the updated objective function while satisfying the constraints.

[0188] 2) Protective beamforming w prot Update.

[0189] Given the optimal transmit beamforming w max Regarding the protection of beamforming w prot The update objective function is:

[0190] ;

[0191] ;

[0192] ;

[0193] ;

[0194] Among them, c and H I I s All are intermediate parameters, , , Due to the existence of the objective function and constraints, this problem is non-convex. The proposed solution at the current iteration number t... The successive convex approximation (SCA) is applied at this point.

[0195] right The process of applying the successive convex approximation (SCA) is as follows: Let , , There is an objective function , d (a) indicates that the spectral detection probability is a function of a, according to the aforementioned definition. Therefore, it also means that the probability of spectrum detection is a function of the perceived signal-to-interference-plus-noise ratio.

[0196] In the t-th iteration, the objective function f at the point (a (t) ,s (t) The first-order Taylor expansion at () is approximated as:

[0197] ;

[0198] Among them, f (t) For f in the t-th iteration, we have ; f (t) The gradient of a; a (t) Let a be the value of 'a' in the t-th iteration. f (t) The gradient with respect to s; s (t) Let s be the value of s in the t-th iteration.

[0199] The gradient is:

[0200] ;

[0201] ;

[0202] Construct lower bounds for a and s respectively. Since... Since u is a convex function, therefore in u (t) The first-order approximation at a gives a lower bound for a:

[0203] ;

[0204] Among them, u (t) Let u represent the value in the t-th iteration; It is the lower bound of a.

[0205] For s, through By linearizing the quadratic function to the first order, we obtain a lower bound for s:

[0206] ;

[0207] in, w in the t-th iteration prot Re represents the real part of a complex number; It is the lower bound of s.

[0208] The lower realm and Substituting into the objective function f, we obtain the lower bound of f. :

[0209] ;

[0210] use and The lower realm It can be further simplified to:

[0211] ;

[0212] To simplify the parameters, define Therefore, it can be Abbreviated as:

[0213] ;

[0214] Therefore, it is necessary to find the lower bound of the objective function f. It can be solved directly using the successive convex approximation (SCA).

[0215] Constrained convexity:

[0216] C1: Convertable to u max Let u be the maximum value. This is a convex quadratic constraint, which can be represented as a second-order cone constraint. .

[0217] C2: For the ellipsoidal error set C is the Hermitian positive definite matrix, e is the error vector, and Ce is the covariance. Using the S-process, robust constraints are equivalent to the existence of parameters. , so that:

[0218] ;

[0219] in, This is a real number greater than 0 generated during the S-process; it is an intermediate variable that needs optimization. This equation is a linear inequality (LMI).

[0220] Power constraints: linearizing norm constraints into And add trust region constraints To ensure approximate accuracy, we obtain information about w. prot The convex part problem is:

[0221] ;

[0222] ;

[0223] ;

[0224] ;

[0225] ;

[0226] ;

[0227] in, This indicates that the lower bound of the objective function f is w. prot The function is such that w can be optimized. prot To maximize .

[0228] Solution Method: The above is a convex optimization problem, including linear objective, second-order cone constraints, LMI constraints, and linear equality or inequality constraints. This convex optimization problem can be treated as a hybrid second-order cone and semidefinite programming problem, and can be efficiently solved using the interior-point method of solvers such as MOSEK. Its computational complexity mainly consists of a time complexity of (N... t +1)×(N t The LMI constraint (+1) determines that the complexity of each iteration is O(n). .

[0229] Step 4-3: Under the conditions of fixed optimal sensing beamforming and optimal communication beamforming, use the SPGA algorithm to solve for the optimal transmitting mobile antenna position and the optimal receiving mobile antenna position.

[0230] Next, the optimal transmit moving antenna position is updated. The optimal sensing beamforming v and the optimal transmit beamforming w are fixed. max And optimal protection beamforming w prot Under this assumption, the optimization problem of the effective data rate of the secondary base station degenerates into a subproblem of optimizing the position vectors x and y of the transmitting and receiving mobile antennas.

[0231] 1) Simplified position optimization subproblem.

[0232] With fixed v and w max and w prot Under these conditions, the effective data rate R eff (x,y) can be represented as:

[0233] ;

[0234] ;

[0235] ;

[0236] The perceived signal-to-interference-plus-noise ratio (SINR) is:

[0237] ;

[0238] Therefore, the simplified optimization problem for the position vectors x and y is expressed as:

[0239] ;

[0240] ;

[0241] ;

[0242] ;

[0243] ;

[0244] ;

[0245] ;

[0246] ;

[0247] Due to the coupled SINR expression, robust leakage constraint, and minimum spacing constraint, the above problem remains highly non-convex, and local optima can be obtained efficiently.

[0248] 2) Augment the objective function.

[0249] To achieve gradient-based updates, sensing and interference constraints are incorporated into the effective data rate optimization of the secondary base station as a quadratic penalty term. Specifically, the following definition is used:

[0250] ;

[0251] ;

[0252] ;

[0253] ;

[0254] ;

[0255] Therefore, the augmented objective function is defined as:

[0256] ;

[0257] in, To broaden the objective function; ; All values ​​are greater than 0, serving as penalty factors. The SPGA algorithm is used to iteratively maximize the augmented objective function, while simultaneously satisfying box constraints and spacing constraints through a projection step.

[0258] 3) Initialization and gradient update.

[0259] First, generate a feasible or nearly feasible initial point (x) within the movable region. (0) ,y (0) In practice, it can be done in the region [X]. min ,X max ] and [Y min ,Y max Discrete search is used to select a... A suitable initial point with a relatively large value.

[0260] To simplify the parameters, define: , , , ,therefore .

[0261] At the same time, define: , , The augmented objective function with respect to the position vector , The gradient is denoted as:

[0262] ;

[0263] ;

[0264] Introducing activation indicator functions:

[0265] ;

[0266] ;

[0267] ;

[0268] in, The first activation exponential function, This is the second activation indicator function. This is the third activation indicator function. Therefore, Regarding x i The gradient is:

[0269] ;

[0270] and Regarding y m The gradient is: ;

[0271] The detailed derivatives can be obtained directly from the steering vector-based channel model used, as follows:

[0272] ;

[0273] ;

[0274] ;

[0275] ;

[0276] ;

[0277] ;

[0278] Among them, superscript Indicates conjugate.

[0279] ;

[0280] ;

[0281] ;

[0282] ;

[0283] ;

[0284] ;

[0285] ;

[0286] ;

[0287] ;

[0288] ;

[0289] ;

[0290] ;

[0291] Where [.]n represents the nth element in the matrix or vector.

[0292] Subsequently, the position variables are updated according to the projection gradient ascent rule:

[0293] ;

[0294] ;

[0295] in, Let be the position variable of the i-th transmitting mobile antenna in the (t+1 / 2)-th iteration, i.e., the midpoint; Let be the position variable of the i-th transmitting mobile antenna in the t-th iteration; Let be the position variable of the m-th receiving mobile antenna in the t-th iteration; Let be the position variable of the m-th receiving mobile antenna in the (t+1 / 2)-th iteration, i.e., the midpoint; This represents the step size in the t-th iteration.

[0296] 4) Projection of feasible region.

[0297] After gradient update, intermediate points may violate movable region or spacing constraints. Therefore, a feasible region projection step is required. First, box projection is performed:

[0298] ;

[0299] ;

[0300] Subsequently, the minimum spacing constraint is satisfied through sequential mapping. The elements are arranged in ascending order as follows The projection value is:

[0301] ;

[0302] ;

[0303] for A similar (or identical) process is also used. Finally, the repaired position vector is mapped back to the original antenna index to obtain the position vector x of the transmitting moving antenna in the (t+1)th iteration. (t+1) and the position vector y of the receiving mobile antenna (t+1) .

[0304] The above SPGA algorithm framework is as follows This paper presents an efficient local search method for non-convex location optimization problems. By combining gradient ascent on the augmented objective function with feasible region projection, the proposed method can improve the effective data rate while maintaining the feasibility of antenna array location.

[0305] Example 2:

[0306] Example 2 presents the simulation results and analysis of the method proposed in Example 1, and provides the results to verify the effectiveness of the proposed BCD-SCA-SPGA algorithm and evaluate its performance. In addition to the proposed BCD-SCA-SPGA algorithm with a moving antenna array, this example also uses five baseline schemes for performance comparison. The five baseline schemes are: (1) fixed antenna position + optimized beamforming only; (2) fixed antenna position + w prot The maximum ratio combining (MRT) calculation is adopted; (3) fixed sensing beamforming + optimization of only other variables; (4) assuming perfect channel and not considering estimation error, i.e., no robust design; (5) heuristic method of MRT / MRC (ratio of maximum ratio combining to maximum ratio transmission). For arrays with fixed antenna positions, the initial configuration is a uniform linear array (ULA) with adjacent element spacing of λ / 2.

[0307] Table 1 shows all the options in X max Feasibility under {3λ, 4λ, 5λ, 6λ}. All optimization-based designs, including fixed antenna position schemes and non-robust schemes, remained feasible throughout the range, while the baseline scheme (5) violated constraints in all test channel implementations, regardless of aperture size. Figure 4 As can be seen from the transmit beam diagram, the baseline scheme (5) radiates too much power towards the primary user, thus failing to simultaneously meet the sensing and secondary user protection requirements, and even the maximum movable area cannot restore feasibility. This indicates that in the two movable antenna array-enhanced full-duplex OSA systems considered in this scheme, a dedicated joint design of the transmit beamformer, sensing beamforming, and antenna position vector is indispensable.

[0308] Table 1. Variation X under different schemes max Feasibility Comparison Table

[0309]

[0310] Figure 1 This demonstrates R under this scheme, baseline scheme (2), and baseline scheme (3). eff The evolution of the curves with the number of iterations of the block coordinate descent (BCD) is shown. All curves are basically monotonically constant, verifying the convergence characteristics of the SCA-BCD algorithm. This scheme converges to 7.43 bits / s / Hz in about four iterations; the baseline scheme (3) requires about seven iterations to reach 7.40 bits / s / Hz; and the baseline scheme (2) requires about ten iterations to converge, with a significantly lower final value of 7.21 bits / s / Hz. Therefore, this scheme, by jointly updating all blocks, not only accelerates convergence but also improves the target value after convergence; the fewer outer iterations also indicate that the computational cost of this scheme is moderate.

[0311] Figure 2 This demonstrates the R-values ​​of this scheme compared to five baseline schemes. eff With maximum transmit power P max The changes in R for all schemes. eff All follow P max As P increases, this scheme consistently outperforms other baseline schemes, from P max The speed increased from 6.97 bits / s / Hz at 0.5W to P. max The gain of this scheme relative to other baseline schemes remains almost constant throughout the range, at approximately 0.87 bits / s / Hz; correspondingly, this scheme requires less than 0.7W to achieve the rate obtained by the baseline scheme (1) at 2.5W, i.e., a power saving of approximately 6dB. The difference between the baseline scheme (3) and this scheme remains within 0.05 bits / s / Hz; the baseline scheme (2) loses approximately 0.2 bits / s / Hz; the baseline scheme (4) incurs a sustained loss of approximately 0.8 bits / s / Hz by sacrificing robustness, highlighting the importance of considering CSI imperfections. The power-independent performance gap further indicates that the gain of this scheme comes from the utilization of spatial degrees of freedom and robust interference management, rather than additional transmit power.

[0312] Figure 3 This paper presents a comparison between the mobile antenna layout optimized using the SPGA algorithm and the uniform antenna layout (linspace). Figure 3 (a) in the text is X max Comparison at λ=4, data rate R under mobile antenna layout prot =7.53, data rate R under uniform antenna layout lin =6.52; Figure 3 (b) in the text is X max Comparison at =6λ, data rate R under mobile antenna layout prot =7.79, data rate R under uniform antenna layout lin =6.52. The optimized mobile antenna layout of this scheme exhibits significant non-uniformity. The SPGA algorithm sets several antennas in close pairs while pushing other antennas towards the aperture boundary, thereby adjusting the array geometry according to the specific channel and constraint direction. This geometric flexibility of the mobile antenna layout allows the effective data rate to reach X. max At =4λ, the bit rate improved from 6.52 to 7.53 bits / s / Hz (approximately 15.5%), in X max At 6λ, the efficiency improves to 7.79 bits / s / Hz (approximately 19.5%). Notably, a uniform antenna layout does not benefit at all from the increased aperture, confirming that the additional spatial freedom offered by a larger movable area can only be utilized through antenna placement optimization.

[0313] Figure 4 The transmit beamforms of this scheme and the baseline scheme (5) are shown. The beamforming of this scheme focuses the main lobe in the direction of the secondary user (90°), while forming deep spatial nulls in the directions of the interference source (approximately 60°) and the primary user (approximately 120°); this provides an additional 25 dB of suppression in these directions compared to the baseline scheme (5). In contrast, the baseline scheme (5) exhibits a wide quasi-omnidirectional pattern that leaks near-peak power to the primary user, which directly explains the infeasibility reported in Table 1. These results intuitively demonstrate that this scheme can protect primary user communications and suppress interference with almost no loss of main lobe gain in the direction of the secondary user.

[0314] Figure 5 The effective data rate R is shown. eff With aperture X max The variation. Both this scheme and the baseline scheme (2) achieve 7.1-7.3 bits / s / Hz, with this scheme maintaining a slight but stable advantage and being about 1 bit / s / Hz higher (about 16%) than the baseline scheme (1) (about 6.24 bits / s / Hz) at each aperture. Baseline schemes (2) and (3) cluster around 6.24-6.30 bits / s / Hz and are largely unaffected by X. max Impact. Furthermore, the position optimization gain in X max At λ = 3λ, the system is close to saturation, and the remaining fluctuations (within 0.15 bits / s / Hz) stem from the non-convexity of the position subproblem. Therefore, a compact movable region of only a few wavelengths is sufficient to obtain most of the spatial degrees of freedom gain, which is attractive for practical implementation.

[0315] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method, characterized in that, Includes the following steps: Step 1: The secondary base station is equipped with a transmit mobile antenna array and a receive mobile antenna array that operate in full duplex mode and can move within a given area; Step 2: The primary base station and the secondary base station estimate the channel parameters of each link through pilot signals, and calculate the detection statistics of the received signal based on the channel parameters; The probability of spectrum detection and the probability of false alarm are calculated based on the detection statistics, and the minimum perceived signal-to-interference-plus-noise ratio that meets the requirements of the probability of spectrum detection and the probability of false alarm is solved. Step 3: Calculate the amplitude gain of the interference channel based on the Gaussian distribution, and construct the average interference power constraint for the primary user. The average interference power constraint has a deterministic convex quadratic constraint condition. Step 3, which involves calculating the interference channel amplitude gain based on a Gaussian distribution and constructing an average interference power constraint for the primary user, includes: The estimated amplitude gain of the interference channel is: ； Among them, g sp (x) represents the actual amplitude gain of the interfering channel; e is the error vector, which follows a Gaussian distribution. , Let I be the variance of the channel estimation error, and I be the identity matrix. The average interference power constraint for primary users is: ； in The average interference power threshold allowed by the system. , This represents the worst-case leakage power threshold. w represents calculating the statistical average. max The maximum value of w; Step 4: Based on the channel parameters of each link, the minimum perceived signal-to-interference-plus-noise ratio, and the average interference power constraint, the BCD-SCA-SPGA algorithm is used to solve the effective data rate optimization problem of the secondary base station, and the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position are obtained. In step 4, the effective data rate optimization problem of the secondary base station is as follows: ； ； ； ； ； ； ； ； ； ； in, R represents the effective data rate of the secondary system. eff Optimization of R; max This indicates the highest data rate of secondary users when the primary user is idle; R prot This indicates the data rate of secondary users when the primary user is in an occupied state and the primary user is protected. For the ellipsoidal error set; w prot Guard beamforming of secondary base stations during primary user idle state; P max P is the maximum transmit power; prot To protect beamforming power; D0 is the minimum antenna spacing; X min X max These represent the lower and upper limits of the movable position of the transmitting mobile antenna on the parallel line segment, respectively. min Y max These are the lower and upper limits of the movable position of the receiving mobile antenna on the parallel line segment, respectively. ； ； Among them, h ss (x) represents the channel amplitude gain between the secondary base station and the secondary user; h ps (x) represents the channel amplitude gain between the primary base station and the secondary user; s p Signals sent by the master system; This represents Gaussian noise superimposed on the secondary user. The BCD-SCA-SPGA algorithm includes the BCD-SCA algorithm and the SPGA algorithm; Step 4, which uses the BCD-SCA-SPGA algorithm to solve the effective data rate optimization problem of the secondary base station and obtains the optimal sensing beamforming, optimal communication beamforming, optimal transmit mobile antenna position, and optimal receive mobile antenna position, includes: Step 4-1: Under the conditions of fixed transmit mobile antenna position vector x, receive mobile antenna position vector y, and transmit beamforming, solve for the optimal sensing beamforming using the SCA-BCD algorithm. Step 4-2: Under the conditions of fixed transmitting mobile antenna position vector x, receiving mobile antenna position vector y, and optimal sensing beamforming v, the optimal communication beamforming is solved using the SCA-BCD algorithm. Step 4-3: Under the conditions of fixed optimal sensing beamforming and optimal communication beamforming, use the SPGA algorithm to solve for the optimal transmit mobile antenna position and the optimal receive mobile antenna position.

2. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 1, characterized in that, Step 1 specifically involves: remember Let be the position vector of the transmitting mobile antenna array, where For the nth t The positions of n transmitting mobile antennas t =1,2,...,N t ;remember Let be the position vector of the receiving mobile antenna array, where For the nth r The location of each receiving mobile antenna, n r =1,2,...,N r ; The guide vector is represented as: ； ； Where k is the user index; l is the path index; a k,l (x) is the steering vector of the transmitting mobile antenna of the k-th user on the l-th path; b k,l (y) is the steering vector of the receiving mobile antenna for the k-th user on the l-th path; e is the Euler number; j is the imaginary number; The carrier wavelength; Let be the departure angle of the l-th path for the k-th user; Let be the departure angle of the l-th path of the k-th user; T is the matrix transpose; It is the set of complex numbers.

3. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 2, characterized in that, Step 2, the step of the primary base station and the secondary base station estimating the channel parameters of each link through pilot signals, includes: The sensing channel h(y) between the receiving mobile antennas of the primary base station and the secondary base station is: ； in, The first free space path loss coefficient; L represents the channel gain coefficient for the l-th path of the k-th user; p Let l be the number of ray paths, l=1,2,...,L p ; b are complex channel coefficients; l (y) is the steering vector of the receiving mobile antenna for the l-th path; Full-duplex self-interference channel h between the transmitting and receiving mobile antennas of the secondary base station I (x,y) is: ； in, The second free space path loss coefficient; Let a be the channel gain coefficient for a full-duplex self-interference channel; when there is only one user and only one path, a I (x)=a k,l (x), b I (y)=b k,l (y); the superscript H indicates the conjugate transpose of the vector.

4. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 3, characterized in that, Step 2, the step of calculating the detection statistics of the received signal based on the channel parameters, includes: Let the amplitude y[k] of the received signal after sensing beamforming at the receiving mobile antenna be: ； Where N is the number of perceived samples, N=f s T,f s P is the sampling rate, T is the sensing duration; p v is the primary user's transmit power; w is the secondary base station's sensing beamforming; n[k] is the noise superimposed on the k-th sample; s[k] is the normalized power complex Gaussian signal transmitted by the primary user. It follows a Gaussian distribution. For noise variance; Sensing signal-to-interference-plus-noise ratio for: ； Based on the amplitude y[k] of the received signal, calculate the detection statistic: ； Where Y is the detection statistic.

5. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 4, characterized in that, Step 2, which involves calculating the spectrum detection probability and false alarm probability based on detection statistics, and then determining the minimum perceived signal-to-interference-plus-noise ratio (SNR) that satisfies the requirements of the spectrum detection probability threshold and the false alarm probability threshold, includes: ； ； in, P is the energy detection threshold. f P represents the false alarm probability. d For spectrum detection probability; This indicates that the primary user is in an idle state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability of; This indicates that the primary user is in an occupied state, and the detection statistic Y is greater than or equal to the energy detection threshold. The probability; Q(.) is the Gaussian Q-function; Given a false alarm probability threshold P f0 Spectrum detection probability threshold P d0 Requires P to be satisfied f ≤P f0 and P d ≥P d0 And satisfy the perceived signal-to-interference-plus-noise ratio. Greater than or equal to the minimum perceived signal-to-interference-plus-noise ratio ; Solve : ； in, This represents the minimum energy detection threshold. This means defining the expression on the left as the expression on the right; Solve : ； Given P d0 P f0 Under the constraints, the perceived signal-to-interference-plus-noise ratio The above constraints must be met.

6. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 1, characterized in that, Step 4-1 specifically involves: Update Sensing Beamforming v: ； ； definition and ; Optimal sensing beamforming v is The main eigenvectors, Let B be the carrier wavelength; first calculate B. -1 A is the eigenvector corresponding to its largest eigenvalue, which is the main eigenvector v.

7. The mobile antenna full-duplex robust opportunistic spectrum-aware communication cooperative optimization method according to claim 6, characterized in that, Step 4-2 specifically involves: Given a protective beamforming w prot Transmit beamforming w max The update objective function is: ； ； Where M is an intermediate parameter, we have ; Given the transmitted beamforming w max Protect beamforming w prot The update objective function is: ； ； ； ； Among them, c and H I I s All are intermediate parameters, , , .

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