A signal detection method based on distributed multi-antenna sensors

Abstract

This invention relates to the field of signal detection technology and discloses a signal detection method based on distributed multi-antenna sensors. It applies multi-antenna wireless sensors and massive MIMO technology to a distributed detection network. Each sensor observes and senses the presence or absence of a target signal within its coverage area; each sensor makes a local decision; each sensor transmits its local decision information to a fusion center to calculate the global detection probability; the calculated global detection probability is then simulated and verified to obtain the detection result of whether the target signal exists. The beneficial effect of this invention is that it enables a method to improve signal detection performance in complex environments.

Description

Technical Field

[0001] This invention relates to the field of signal detection technology, and specifically to a signal detection method based on a distributed multi-antenna sensor. Background Technology

[0002] Distributed sensor networks based on local sensor signals exhibit excellent detection performance. In decision fusion within wireless sensor networks operating in fading channels, likelihood ratio-based fusion rules can be used, requiring only channel statistics and eliminating reliance on instantaneous channel state information. Further considering a general orthogonal channel model between local sensors and the fusion center, the likelihood ratio test (LRT) method can be employed for local sensor decisions. However, while the above research demonstrates good detection performance in ideal environments, in complex low signal-to-noise ratio environments, the detection performance deteriorates drastically due to channel interference affecting transmission results.

[0003] With the widespread application of massive MIMO (Multiple Input Multiple Output) technology in 5G communication, research on distributed detection networks based on massive MIMO has gradually begun. These studies not only focus on cellular communication, but also consider the use of multi-antenna technology in distributed wireless sensor detection networks. For massive MIMO wireless sensor networks, in the literature [Chawla A, Patel A, Jagannatham AK, et al. Robust Distributed Detection in Massive MIMO Wireless Sensor Networks Under CSI Uncertainty[C], 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall). IEEE, 2018: 1-5.], the authors proposed an optimal distributed detection framework based on the Neyman-Pearson (NP) criterion. The literature [Ding G, Gao X, Xue Z, et al. Massive MIMO for Distributed Detection with Transceiver Impairments[J]. IEEE Transactions on Vehicular Technology, vol. 67, no. 1, pp. 604-617, Jan. 2018.] studies a distributed detection network consisting of multiple single-antenna sensors and a large multi-antenna fusion center, further considering the impact of transceiver hardware impairments on detection performance. However, these studies only consider the use of multi-antenna arrays at the fusion center, without considering the role of multiple antennas on the sensors. Furthermore, unlike 5G communication, detection networks require further consideration of data fusion so that the fusion center can make correct global decisions. That is, the communication objective focuses more on improving channel throughput, while signal detection focuses more on improving detection probability to make accurate decisions.

[0004] In summary, the existing technology has the following problems:

[0005] (1) Although single-antenna detection research has good detection performance in ideal environments, the detection performance will deteriorate sharply in complex low signal-to-noise ratio environments due to the influence of the channel on the transmission results.

[0006] (2) There are few existing studies on multi-antenna signal detection, and existing studies only consider the use of multi-antenna arrays in the fusion center, without considering the role of multi-antennas on the sensor. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a signal detection method based on a distributed multi-antenna sensor, which can improve signal detection performance in complex environments.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A signal detection method based on a distributed multi-antenna sensor includes the following steps:

[0010] In a distributed detection network, N wireless sensors with K antennas are set up. The N wireless sensors with K antennas and a fusion center with M antennas form a virtual MIMO channel. The N wireless sensors with K antennas observe and sense the presence or absence of target signals within their coverage area. Here, N, K and M are all natural numbers greater than or equal to 1.

[0011] Each wireless sensor, which includes K antennas, detects the presence or absence of a target signal and makes a local decision.

[0012] N wireless sensors, including K antennas, transmit their local decision information to the fusion center to calculate the global detection probability;

[0013] The power of the sensor is iteratively optimized to obtain the detection result of whether the target signal exists.

[0014] Furthermore, the local decision is obtained through a likelihood ratio test, specifically through the following steps:

[0015] In the case of ideal hardware, assuming H0 and H1 represent the absence and presence of the target signal, respectively, the sensing information of the i-th sensor is modeled as a binary hypothesis problem, with the following model:

[0016]

[0017] Where θ represents the target signal emitted by the target radiation source to be detected, and s i v represents the measurement signal received by the i-th sensor. i The measurement noise of the i-th sensor, That is, v i It follows a mean of 0 and a variance of σ. v,i The set of standard complex Gaussian random variables, σ v,i Let be the variance of the Gaussian distribution of the measurement noise of the i-th sensor; model the target signal as a zero-mean cyclic complex Gaussian vector, i.e. The mean is 0, and the variance σ0 θ .

[0018] Furthermore, the modeling of the above formula (1) is simplified, specifically as follows:

[0019] The k-th antenna of the i-th sensor has a gain of g. i,k Amplify its measurement signal s i The signal is then forwarded through the channel to a fusion center with M antennas. The signal received by the m-th antenna at the fusion center is:

[0020]

[0021] Among them, g ik h is the gain of the k-th antenna of the i-th sensor. i,m The channel gain between the i-th sensor and the m-th antenna of the fusion center is represented by: The wireless fading channel is modeled as follows:

[0022]

[0023] in, It is a complex Gaussian vector, d i It is the distance from the i-th sensor to the fusion center, and α represents the path loss exponential factor. Substituting formula (2) into formula (1) yields formula (4):

[0024]

[0025] Based on the received signal y m The presence or absence of the target signal is determined by what is called the Likelihood Ratio Test (LRT) of the optimal fusion rule to distinguish between H0 and H1.

[0026] Furthermore, the method for calculating the global detection probability is as follows:

[0027] The detection probability P, which describes the local detection performance of the i-th sensor, is... D,i And the false alarm probability P FA,i Defined as:

[0028]

[0029] Based on the obtained formula (4), the detection probability P is defined and calculated. D And the false alarm probability P FA The detection performance of the fusion center is evaluated; specifically, the global detection probability P of the target signal existing and being successfully detected by the sensor is evaluated. D Defined as:

[0030]

[0031] Among them, the symbol g = [g] is introduced. 1,1,...,g i,k ] T H represents the amplification gain of each antenna of the sensor, H = [h 1,1 ,...,h i,k [ ] is the channel gain matrix composed of instantaneous channel state information between each sensor and the fusion center, y represents the received signal, and C w Let y be the covariance under H0. Indicates the signal detection threshold;

[0032] Rewrite formula (6) as follows:

[0033]

[0034] Among them, substitution variables substitution variables C w +C s C is the covariance of y under H1. s It is the covariance of y under H0; and It follows a distribution I M The eigenvalues ​​of W, representing the identity matrix, are defined as follows:

[0035] W = UGU H (8)

[0036] Where G represents the singular value diagonal matrix, and f(g) represents the probability density function of the Gaussian distribution. Formula (6) is converted to

[0037]

[0038] Where U represents the orthogonal matrix of the decomposition, and (a) is a function where the unitary transformation does not change U. The distribution, (b) because A scaled chi-square distribution with two degrees of freedom;

[0039] Similarly, the false alarm probability P of a wireless signal being detected as present when it does not exist is... FA for:

[0040]

[0041] According to the Neyman-Pearson lemma, by adjusting the detection threshold Given a false alarm probability P FA Maximize detection probability P under ε D Where ε is a randomly given constant value for the false alarm probability, according to formula (6) we have Will Substituting into formula (9), we get:

[0042]

[0043] Furthermore, the method for optimizing the power of sensors at different positions is as follows:

[0044]

[0045] Where, P = [p 1,1 ,...,p i,k ], p i,k Let be the power of the k-th antenna of the i-th sensor.

[0046] To further optimize, in formula (12), it is assumed that M becomes infinite under wireless channel fading. Then, f(g) is transformed and asymptotically analyzed to obtain the objective function:

[0047]

[0048] From formula (13), we know that as long as If σ remains constant, f(g) will remain asymptotically constant; where σ v,ik This represents the variance of the noise received by the sensor. d i It is the distance from the i-th sensor to the fusion center. α is the path loss exponent factor, σ n This represents the noise variance of the fusion center.

[0049] To reduce the complexity of subsequent formula derivations, the following symbols are defined: The optimization problem of formula (13) can then be rewritten as:

[0050]

[0051] To find an efficient solution to formula (16), and to simplify the formula, we define a substitution variable t. ik :

[0052]

[0053] Then the equivalent transformation of formula (16) is:

[0054]

[0055] An efficient solution to the problem was found using the augmented Lagrange function; Equation (18) was rewritten using a partial augmented Lagrange function as follows:

[0056]

[0057] Where L1 represents the augmented Lagrangian function, {λ ik}, (i=1,...,N,k=1,...,K) represent the Lagrange multipliers, {ρ ik}, (i = 1, ..., N, k = 1, ..., K) represent the penalty parameter; μ is used. ik =λ ik / ρ ik As a scaling factor describing the relationship between them, formula (19) can be rewritten in proportional form:

[0058]

[0059] Formula (20) can be further written as:

[0060]

[0061] Furthermore, the Alternating Multiplier Method (ADMM) algorithm is used to further optimize the sensor's reporting power. The specific method is as follows:

[0062] Through the original variable {x ik},{t ik} and bivariate {ρ ik},{μ ik The ADMM algorithm solves equation (21) through continuous iterations. For the (j+1)th iteration, the ADMM algorithm includes the following steps:

[0063] S1: Update fixed

[0064]

[0065] in, Indicates the penalty parameter. For the original variables, where To simplify substitution variables, It is a scaling factor;

[0066] By decomposing and optimizing the variables in formula (22), the vertex of the parabola is found, and the solution to the closed expression is obtained as follows:

[0067]

[0068] S2: Update fixed

[0069]

[0070] To simplify understanding, the following symbols are introduced: and The equivalent transformation of formula (24) is:

[0071]

[0072] For optimization, define the symbol x = [x 11 ,...,x ik ] T , r = [r 11 ,...,r ik ] T ,

[0073] The optimization problem in the above text is equivalently represented by the above notation:

[0074]

[0075] S3: Update fixed

[0076]

[0077] S4: Update

[0078]

[0079] The value of τ determines whether the penalty function is constant or variable. The initial choice of the penalty parameter is to use τ > 1 to improve convergence performance and reduce loss.

[0080] Furthermore, the stopping iteration condition for continuously iterating through formula (21) using the ADMM algorithm is:

[0081]

[0082] Where, ε obj and ε con It is the convergence tolerance, which is a constant threshold.

[0083] Furthermore, the detection probability of multi-antenna sensors was analyzed and optimized. This also included using the Monte Carlo method to simulate and verify the calculated global detection probability. Specifically, the sensor positions were randomly generated, and the detection probability was improved by combining the given sensor power and a sensor fusion algorithm.

[0084] The signal detection method of this invention first derives a closed-form expression for the optimal detector detection probability based on the Neyman-Pearson criterion and the likelihood ratio test criterion, thereby improving the signal detection probability through multiple antennas. Then, considering the energy constraints of the sensor, the power of the sensor is optimized using the alternating direction multiplier method. Finally, simulation results show that the power-optimized multi-antenna sensor has better detection performance, and a trade-off between the number of antennas and the reported total power P is discovered.

[0085] When the number of antennas in the fusion center is fixed, using multi-antenna sensors can improve the detection performance of the detector. When the number of antennas of the sensor is fixed, using different antennas in the fusion center will also affect the detection performance. That is, as the number of antennas increases, the detection performance will be better, eventually reaching the performance limit.

[0086] Compared with the prior art, the present invention provides a signal detection method based on a distributed multi-antenna sensor, which has the following advantages:

[0087] (1) The signal detection method of the present invention can improve the signal detection performance in complex environments and overcome the channel fading effect when the sensor sends back to the fusion center, thereby improving the signal detection probability.

[0088] (2) The signal detection method of the present invention has discovered a trade-off between the number of antennas and the total reported power P, namely, using more antennas to compensate for the loss under limited power, and vice versa.

[0089] (3) For large-scale distributed sensor networks, the faster the convergence speed of the algorithm, the faster the detection speed of the signal detection method of the present invention. Attached Figure Description

[0090] Figure 1 This is a flowchart of the signal detection method based on a distributed multi-antenna sensor according to the present invention;

[0091] Figure 2 This is a schematic diagram of signal detection for the distributed multi-antenna sensor of the present invention;

[0092] Figure 3 The detection probability P in the multi-antenna sensor network of this invention when the number of sensor antennas K = 1, 2, and 4 D With the false alarm probability P FA Resulting graph;

[0093] Figure 4 The graph shows the detection probability results as the number of fusion center antennas M changes when the number of sensor antennas K = 1, 2, and 4 respectively in this invention.

[0094] Figure 5 The graph shows the detection probability results of the number of fusion center antennas M and the total sensor reporting power P when the number of sensor antennas is K=1, 2, and 4 respectively.

[0095] Figure 6 This is a schematic diagram showing the convergence performance of the ADMM iterative algorithm for each sensor when the number of antennas K=1 in this invention;

[0096] Figure 7This is a schematic diagram showing the convergence performance of the ADMM iterative algorithm for each sensor when the number of antennas K=2 in this invention;

[0097] Figure 8 This is a schematic diagram showing the convergence performance of the ADMM iterative algorithm for each sensor when the number of antennas K=4 in this invention. Detailed Implementation

[0098] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0099] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may include different values. 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 need not be further discussed in subsequent figures.

[0100] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "upper", "lower", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only used to facilitate the description of the present invention and to simplify the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of the present invention.

[0101] This invention relates to a signal detection method based on a distributed multi-antenna sensor, comprising the following steps:

[0102] like Figure 1 As shown, the signal detection method based on a distributed multi-antenna sensor of the present invention comprises the following steps:

[0103] The first step involves applying multi-antenna wireless sensors and massive MIMO technology to a distributed detection network. N multi-antenna sensors (with K antennas) and a fusion center with M antennas form a "virtual" MIMO channel. Multiple sensors observe and sense phenomena within their coverage area, and then send their local assessments to the fusion center for global evaluation. For example... Figure 2 The diagram shows a distributed multi-antenna sensor.

[0104] The second step involves local decision-making by the multi-antenna sensors. In ideal hardware, assuming H0 and H1 represent the absence and presence of the target signal, respectively, the sensing information from the i-th sensor is modeled as a binary hypothesis problem, with the following model:

[0105]

[0106] Where θ represents the target signal emitted by the target radiation source to be detected, and s i v represents the measurement signal received by the i-th sensor. i The measurement noise of the i-th sensor, That is, v i It follows a mean of 0 and a variance of σ. v,i The set of standard complex Gaussian random variables, σ v,i Let be the variance of the Gaussian distribution of the measurement noise of the i-th sensor; model the target signal as a zero-mean cyclic complex Gaussian vector, i.e. The mean is 0, and the variance σ0 θ .

[0107] The k-th antenna of the i-th sensor has a gain of g. ik Amplify its measurement signal s i The signal is then forwarded through the channel to a fusion center with M antennas. The signal received by the m-th antenna at the fusion center is...

[0108]

[0109] Among them, g i,k It can be abbreviated as g ik Let h be the gain of the k-th antenna of the i-th sensor. i,km h represents the channel gain between the k-th antenna of the i-th sensor and the m-th antenna of the FC. i,m The channel gain between the i-th sensor and the m-th antenna of the fusion center is represented by: The wireless fading channel is modeled as follows:

[0110]

[0111] in, It is a complex Gaussian vector, d ih is the distance from the i-th sensor to the fusion center. Since the different antennas of the same sensor (or fusion center FC) are located close to each other and much lower than the distance between the sensor and the FC, for simplification, the channel between different antennas of the same sensor and the fusion center is approximated as two points. Therefore, h... i,km ≈h i,m , where α is the path loss exponential factor.

[0112] Substituting formula (32) into formula (31) yields formula (34):

[0113]

[0114] Based on the received signal y m The method of determining the presence or absence of the target signal to distinguish between H0 and H1 is called the Likelihood Ratio Test (LRT).

[0115] The third step involves transmitting information to the fusion center via multiple antennas to calculate the global detection probability. The detection probability P, which describes the local detection performance of the i-th sensor, is then used. D,i And the false alarm probability P FA,i Defined as:

[0116]

[0117] Based on the obtained LRT detector expression, the detection probability P is defined and calculated. D And the false alarm probability P FA The detection performance of the fusion center is evaluated. Specifically, the detection probability P of the wireless signal being present and successfully detected by the sensor is considered. D Defined as

[0118]

[0119] For ease of derivation and memorization, the symbol g = [g] is introduced. 1,1 ,...,g i,k ] T H represents the amplification gain of each antenna of the sensor, H = [h 1,1 ,...,h i,k [ ] is the channel gain matrix composed of instantaneous channel state information between each sensor and the fusion center, y represents the received signal, and C w Let y be the covariance under H0. This indicates the signal detection threshold.

[0120] Formula (36) can be rewritten as

[0121]

[0122] Among them, substitution variables substitution variables C w +C s C is the covariance of y under H1. s It is the covariance of y under H0; and It follows a distribution I M The eigenvalues ​​of W, representing the identity matrix, are defined as follows:

[0123] W = UGU H (38)

[0124] Where G represents the singular value diagonal matrix, and f(g) represents the probability density function of the Gaussian distribution. Formula (36) is converted to

[0125]

[0126] Where U represents the orthogonal matrix of the decomposition, and (a) is a function where the unitary transformation does not change U. The distribution, (b) because A scaled chi-square distribution with two degrees of freedom;

[0127] Similarly, the false alarm probability P of a wireless signal being detected as present when it does not exist is... FA for

[0128]

[0129] According to the NP criterion, by adjusting the decision threshold Given a false alarm probability P FA Maximize detection probability P under ε D Where ε is a randomly given constant value for the false alarm probability, according to formula (36) we have Will Substituting into formula (39), we get:

[0130]

[0131] The fourth step derives the detection probability of a multi-antenna sensor network given a false alarm probability. In practical applications, due to the small size, low cost, and limited energy carried by sensors, it is necessary to optimize the reporting power of sensors at different locations to improve the working time of the sensor network.

[0132]

[0133] Where, P = [p 1,1 ,...,p i,k ], p i,kLet be the power of the k-th antenna of the i-th sensor.

[0134] According to formula (41), (Because 0 < ε < 1), based on the fact that the exponential function is an increasing function, that is, under the total constraint of the reporting power of all sensors, in order to maximize the detection probability, the objective function f(g) needs to be maximized. Since the power reported by the sensors is limited, it is necessary to consider improving the detection performance of the entire network under the premise of power constraint. However, since this is a nonlinear and nonconvex optimization problem, it is not easy to obtain the optimal g. In addition, obtaining the optimal detection requires a channel matrix H composed of a large amount of instantaneous channel state information between the sensors and the fusion center. When M becomes large, only CSI needs to be counted. In order to further optimize, in formula (42), it is assumed that M becomes infinite under wireless channel fading, and then f(g) is transformed and asymptotically analyzed to obtain the objective function:

[0135]

[0136] From formula (43), we can see that as long as If σ remains constant, then f(g) will remain asymptotically constant, where σ v,ik This represents the variance of the noise received by the sensor. d i It is the distance from the i-th sensor to the fusion center. α is the path loss exponent factor, σ n This represents the noise variance at the fusion center. Asymptotically constant detection performance can be achieved if any reduction in sensor transmit power is balanced by a corresponding increase in the number of antennas at the fusion center.

[0137] As M→∞, the optimization problem in equation (43) can be reformulated as follows:

[0138]

[0139] Before solving the optimization problem in formula (44), we first analyze the detection probability P. D The upper bound is as follows

[0140]

[0141] As M→∞ and P→∞, formula (45) gives the condition for a given false alarm probability P. FA Under certain conditions, the LRT detector can achieve the upper limit of detection performance.

[0142] The preceding derivation provides important insights for improving detection performance. When the number of antennas is large, the upper limit of the system's detection performance is finite and depends on the signal variance. Variance of received noise in the sensor And the number of sensors, N. It can be seen that the prerequisite for reaching the upper limit of detection performance is infinite M and P, at which point the distribution of sensing and reporting power becomes irrelevant. However, for practical systems, the values ​​of M and P cannot be infinite, therefore optimization... This will bring significant benefits to the performance of formula (44).

[0143] To reduce the complexity of subsequent formula derivations, new notations are used for definition: Therefore, formula (44) can be simplified as:

[0144]

[0145] This equation-constrained optimization problem is difficult to solve as a non-convex programming problem and has been proven to be a nondeterministic problem of polynomial complexity. To find an efficient solution to equation (46), we first define...

[0146]

[0147] Therefore, the equivalent transformation of formula (46) is:

[0148]

[0149] An efficient solution to the problem was found using the augmented Lagrange function. First, equation (48) is rewritten using a partial augmented Lagrange function as follows:

[0150]

[0151] Where L1 represents the augmented Lagrangian function, {λ ik}, (i=1,...,N,k=1,...,K.) represents the Lagrange multiplier, {ρ ik}, (i = 1, ..., N, k = 1, ..., K.) represents the penalty parameter. μ is used. ik =λ ik / ρ ik As a proportional factor describing the relationship between them, formula (49) can be rewritten in proportional form:

[0152]

[0153] After these simplification preparations, formula (50) can be further written as:

[0154]

[0155] For multiple optimization variables, traditional convex optimization algorithms struggle to find the optimal solution. Alternating Direction Method of Multipliers (ADMM) is an important technique for parallel processing and multivariate optimization, particularly suitable for solving complex optimization problems. Therefore, we propose using ADMM to solve the following problem. Subsequent simulations will demonstrate that this is a highly effective algorithm for equation (51). Specifically, the process involves using the original variable {x}... ik},{t ik} and bivariate {ρ ik},{μ ik The algorithm solves equation (51) through continuous iterations. For the (j+1)th iteration, the algorithm can be summarized into four steps:

[0156] Step 1: Update fixed

[0157]

[0158] in, Indicates the penalty parameter. For the original variables, where To simplify substitution variables, It is a scaling factor;

[0159] Clearly, this is a multivariate quadratic programming problem, which is quite complicated to solve. However, we find that t is not coupled with other variables. Therefore, by decomposing and optimizing the variables in formula (52), we can find the vertex of the parabola and obtain the solution of the closed expression.

[0160]

[0161] Step Two: Update fixed

[0162]

[0163] To simplify understanding, the following symbols are introduced: and The equivalent transformation of formula (54) can be obtained as:

[0164]

[0165] Furthermore, the notation x = [x] is introduced. 11 ,...,x ik ] T , r = [r 11 ,...,rik ] T ,

[0166] The optimization problem in [the context of the problem] can be equivalently represented by the above notation:

[0167]

[0168] Quadratic programming (QP) problems can be solved effectively using existing mathematical tools, such as the CVX software package or the MATLAB Optimization Toolbox.

[0169] Step 3: Update fixed

[0170]

[0171] Step 4: Update

[0172]

[0173] The value of τ determines whether the penalty function is constant or variable. It is recommended to use τ > 1 for the initial selection of the penalty parameter to improve convergence performance and reduce loss.

[0174] Because the algorithm involves a large number of iterations, its convergence must be a primary concern. The timeliness of the algorithm is crucial for collaborative sensing, especially in scenarios involving natural disaster detection and hazard information detection. The algorithm's convergence was guaranteed under different parameters.

[0175] In addition, the following stopping conditions are given: during continuous iterations, the constraint fluctuations of the objective function are small; specifically, the following conditions are simultaneously established.

[0176]

[0177] Where ε obj and ε con It is the convergence tolerance, which can be a smaller constant threshold.

[0178] Table 1 shows the ADMM algorithm used to optimize sensor reporting power.

[0179]

[0180]

[0181] The method for verifying the calculated global detection probability through simulation is as follows:

[0182] Assume that N = 10 sensors are distributed around the M antenna fusion centers, at a distance d.i To compare the impact of multi-antenna and single-antenna sensors on detection performance under the same environment, a set of uniformly distributed random distance vectors was selected for subsequent simulations within the range [2,20]. The set of random distance vectors is [17.5024,3.3541,19.4117,6.4284,5.9324,14.0173,8.3763,8.6594,19.7629,11.0626]. The sum of the power reported by all sensors is P = 400mW, and the signal variance is... noise variance The false alarm probability is tentatively set as P. FA =ε=0.05. Additionally, the path loss exponential factor α=2, and the measurement noise of the i-th sensor... Randomly distributed in the region [0.25, 0.5].

[0183] Figure 3 This describes the detection probability P of the detector when the number of sensor antennas K = 1, 2, and 4 in a multi-antenna sensor network. D With the false alarm probability P FA The relationship between them is as follows: When the number of antennas in the fusion center is fixed, using a multi-antenna sensor can improve the detector's detection performance. When the number of sensor antennas is fixed, using different antennas in the fusion center will also affect the detection performance; that is, as the number of antennas increases, the detection performance will be better, eventually reaching a performance limit. Figure 4 As shown.

[0184] exist Figure 5 In this paper, the impact of the number of sensor antennas, the number of fusion center antennas, and the total sensor reporting power on detection performance in multi-antenna sensor networks is more clearly demonstrated. Simulation results show that using multi-antenna sensors can achieve better detection performance. The simulation results show that as the number of FC antennas increases, when M reaches a certain number of antennas (e.g., 200-250), the detection performance of the proposed solution is very close to its performance limit. With the increase in the number of antennas, the signal reception capability of the fusion center will be stronger, and the ability to overcome transmission channel fading during detection will be greatly improved. However, when it reaches a certain level, the detection performance depends on other factors such as receiver noise; that is, the value of M depends on the number of sensor antennas and other variables, such as... Furthermore, as the number of antennas or the transmit power at the fusion center increases infinitely, the system's detection performance will reach its limit. If the number and power of antennas at the fusion center were infinite, no power optimization would be necessary. However, in practice, the number of antennas cannot be too large, and the power is finite. Therefore, considering power optimization is crucial. In the use of multi-antenna sensors, to achieve good detection performance, this invention has discovered a trade-off between the number of antennas and the total reported power P. In other words, more antennas can be used to compensate for losses with limited power, and vice versa.

[0185] Figures 6 to 8 The convergence performance of the ADMM iterative algorithm under different antenna sensors is shown. It can also be seen that the algorithm reaches a relatively stable state after 30 iterations. The timeliness of the algorithm is crucial for collaborative sensing, and several dozen iterations are acceptable for practical applications. For large-scale distributed sensor networks, the faster the convergence speed of the algorithm, the faster the detection speed.

[0186] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0187] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A signal detection method based on distributed multi-antenna sensors, characterized in that, The method comprises the following steps: N wireless sensors including K antennas are arranged in a distributed detection network, the N wireless sensors including K antennas and a fusion center including M antennas form a virtual MIMO channel, and the N wireless sensors including K antennas perform observation and perception on the presence or absence of a target signal in a coverage range of the N wireless sensors including K antennas, wherein N, K, and M are natural numbers greater than or equal to 1; Each wireless sensor including K antennas performs signal detection perception on the presence or absence of the target signal, and obtains a local decision; The N wireless sensors including K antennas transmit information of the local decisions to the fusion center, and calculate a global detection probability; Power iterative optimization is performed on the sensors, and a detection result of the presence or absence of the target signal is obtained; The specific steps of the local decision are as follows: It is assumed that H0 and H1 represent the absence and presence of the target signal respectively, and perception information of an i-th sensor is modeled as a binary hypothesis problem, and the model is as follows: where θ denotes the target signal emitted by the target radiating source to be detected, s i represents the measurement signal received by the i-th sensor, v i is the measurement noise of the i-th sensor, i.e. v i obeys a set of complex Gaussian random variables with mean 0 and variance σ v,i σ v,i is the variance of the Gaussian distribution of the measurement noise of the i-th sensor; the target signal is modeled as a zero-mean circular complex Gaussian vector, i.e. with mean 0 and variance σ θ ; The calculation method of the global detection probability is as follows: The detection probability P D,i and the false alarm probability P FA,i is defined as: The global detection probability P that the target signal exists and is successfully detected by the sensor D is defined as: wherein the symbol g = [g 1,1 ,...,g i,k ] T represents the amplification gain of each antenna of the sensor, H = [h 1,1 ,...,h i,k ] is a channel gain matrix composed of the instantaneous channel state information between each sensor and the fusion center, y represents the received signal, C w is the covariance of y under H0, represents the signal detection threshold; The formula (6) is rewritten as: where the substitution variable substitution variable C w + C s is the covariance of y under H1, C s is the covariance of y under H0; and is distributed as I M denotes the identity matrix, and the eigen decomposition of W is defined as: W = UGU H (8) where G denotes a singular value diagonal matrix, f(g) denotes a probability density function of a Gaussian distribution, Equation (6) is converted to Where U represents the orthogonal matrix of the decomposition, and (a) is a function where the unitary transformation does not change U. The distribution, (b) because A scaled chi-square distribution with two degrees of freedom; By the same token, the false alarm probability P that a wireless signal is not present but is detected as being present FA is: According to Neyman-Pearson lemma, by adjusting the detection threshold At a given false alarm probability P FA = ε, the detection probability P D is maximized, where ε is a random given false alarm probability constant value, according to formula (6) Substituting into formula (9) gives 2. The signal detection method based on distributed multi-antenna sensors according to claim 1, wherein, The modeling of the formula (1) is simplified, and the specific method is as follows: The kth antenna of the ith sensor with gain g i,k Amplify its measurement signal s i And forwarded through the channel to the fusion center with M antennas, the signal received by the mth antenna of the fusion center is: where g ik is the gain of the kth antenna of the ith sensor, h i,m denotes the channel gain between the ith sensor and the mth antenna of the fusion center, and the wireless fading channel is modeled as: wherein is a complex Gaussian vector, d i is the distance of the ith sensor to the fusion center, and a represents the path loss exponent factor. Bringing equation (2) into equation (1) gives equation (4): The target signal is determined based on the received signal y m The presence or absence of the target signal is determined to distinguish H0 and H1.

3. The method of claim 1, wherein, The method for optimizing the power of the sensors at different positions is as follows: where P = [p 1,1 ,...,p i,k ], p i,k is the power of the kth antenna of the ith sensor. In order to further optimize, in the formula (12), it is assumed that M becomes infinite under wireless channel fading, then f(g) is transformed and asymptotic analysis is performed, and a target function is obtained: By equation (13), f(g) is asymptotically invariant as long as remains unchanged, where σ v,ik represents the variance of the noise received by the sensor, represents d i is the distance from the i-th sensor to the fusion center; a is the path loss exponent factor, σ n represents the noise variance of the fusion center; To reduce the complexity of the subsequent formula derivation, define the symbol: The optimization problem of formula (13) is then re-expressed as: For the effective solution of equation (16), to simplify the equation, define the substitution variable t ik : The equivalent transformation of the formula (16) is as follows: An effective solution of the problem is found by using an augmented Lagrange function; the formula (18) is rewritten as where L1represents an augmented Lagrangian function, {λ ik}, (i = 1,..., N, k = 1,..., K) represent Lagrange multipliers, {ρ ik}, (i = 1,..., N, k = 1,..., K) represent penalty parameters; and μ ik = λ ik / ρ ik is a scale factor describing the relationship between them, formula (19) is rewritten in a proportional form: The formula (20) is further written as 4. The method of claim 3, wherein: An alternating multiplier method ADMM algorithm is used to further optimize and solve the reporting power of the sensors, and the specific method is as follows: by the original variables {x ik}, {t ik} and the bivariate {p ik}, {m ik} through successive iterations, the ADMM algorithm comprises the following steps for the j+1 iteration: S1: update fixed wherein denotes a penalty parameter, is the original variable, wherein is a simplified substitute variable, is a scaling factor; By decomposing and optimizing the variables in the formula (22), the vertex of a parabola is found, and a closed expression solution is obtained as S2: update fixed For simplicity of understanding, the following notations are introduced: The equivalent transformation of equation (24) is obtained as: For optimization, define the symbols x = [x 11 ,...,x ik ] T , r = [r 11 ,...,r ik ] T , E = {e 11 ,...,e ik}, 1 = [1,...,1] T , the optimization problem in equation (25) is equivalently expressed in the above symbols: S3: update fixed S4: Update The value of τ determines whether the penalty function is constant or variable, and the initial selection of the penalty parameter uses τ>1 to improve the convergence performance and reduce the loss.

5. The method of claim 4, wherein: The stop iteration condition of the ADMM algorithm for continuously iterating to solve the formula (21) is as follows: where ε obj and ε con are convergence tolerances, which are constant thresholds.

6. The method of claim 1, wherein: The specific method for simulating and verifying the calculated global detection probability is as follows: the positions of the sensors are randomly generated, the given sensor power is combined, the sensor fusion algorithm is used, and the detection probability is improved.

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