Multi-antenna OFDM system beam forming method based on GLQSP covariance matrix reconstruction

Abstract

The invention discloses a multi-antenna OFDM (Orthogonal Frequency Division Multiplexing) system beam forming method based on GLQSP covariance matrix reconstruction, which realizes low-complexity reconstruction of an interference and noise covariance matrix through covariance matrix reconstruction and a steering vector correction mechanism, and is applied to a multi-antenna OFDM system, so that the multi-antenna OFDM system beam forming method has the advantages that the interference and noise covariance matrix can be effectively reconstructed, and the beam forming efficiency is improved. The anti-interference capability of a wireless ad hoc network system in an interference scene is improved. According to the method, efficient and accurate reconstruction of the steering vector is realized through approximate calculation of angle domain discrete integration and subspace alternate projection, and relatively high calculation accuracy can be ensured while the calculation complexity of integral operation is reduced. Through covariance matrix reconstruction and a steering vector correction mechanism, low-complexity reconstruction of an interference and noise covariance matrix is realized, and the interference and noise covariance matrix is applied to a multi-antenna OFDM system, so that the anti-interference capability of a wireless ad hoc network system in an interference scene is improved.

Description

TECHNICAL FIELD

[0001] The application relates to a multi-antenna OFDM system beam forming method based on GLQSP covariance matrix reconstruction, and belongs to the technical field of communication. BACKGROUND

[0002] At present, new progress is continuously made in wireless communication technology, and meanwhile, market demand is increasingly diversified. Under the joint promotion of the two, the wireless ad hoc network architecture has achieved remarkable development through decentralization, intelligent scheduling of resources, and device collaborative transmission. However, due to the adoption of a multi-hop transmission mechanism and a wireless link connection and the facing of a dynamic network topology transformation environment, the network architecture has high sensitivity to external interference. Therefore, under a complex electromagnetic interference environment, the reliability of the wireless ad hoc network communication system will face severe challenges. In order to cope with this challenge, by adopting a high-precision DOA estimation algorithm, the system can accurately locate the direction of an interference source and a target signal, and then, in combination with an adaptive beam forming algorithm, dynamically adjusts the weight values of an antenna array, so that interference suppression and signal enhancement are cooperatively optimized in a multipath channel. This technical system not only significantly improves the communication reliability under a complex electromagnetic environment, but also provides application support for efficient resource scheduling and anti-interference of the ad hoc network node, and becomes one of the key technologies for promoting the development of the wireless ad hoc network system in the direction of high reliability and anti-interference.

[0003] As one of the key algorithms of array signal processing, adaptive beam forming plays an important role in improving the detection capability of a signal or the communication quality, and is widely applied to scenes such as radars, sonars and satellite communications. The basic principle is to calculate a steering vector by using the angle of arrival of a signal received by an array antenna, and then adaptively adjust the weight values of each array element, so as to form an optimal weight vector adapting to the current environment. How can the algorithm realize the alignment of a main lobe to a desired signal in an array directivity diagram to enhance the receiving gain according to the direction information of the desired signal and interference signals, how to form a null in the direction of interference while enhancing the desired signal, and how to effectively suppress interference and improve the signal-to-interference-and-noise ratio of the system. SUMMARY

[0004] The application aims at the problem that the traditional adaptive beam forming has strong sensitivity to steering vector error and insufficient robustness in a complex interference environment in actual application, and proposes a multi-antenna OFDM system beam forming method based on GLQSP covariance matrix reconstruction. The covariance matrix reconstruction beam forming algorithm based on Gaussian-Legendre integral subspace projection realizes low-complexity reconstruction of an interference and noise covariance matrix through a covariance matrix reconstruction and steering vector correction mechanism, and applies the matrix to a multi-antenna OFDM system, so as to improve the anti-interference capability of the wireless ad hoc network system in an interference scenario.

[0005] The technical scheme adopted by the present application to solve its technical problems is: a multi-antenna OFDM system beam forming method based on GLQSP covariance matrix reconstruction, comprising: the signal sending end and the interference source sending end are single antennas, the receiving end adopts a uniform linear antenna array composed of N r rth receiving antenna in the interference environment receives the time domain OFDM signal as follows:

[0006]

[0007] In the formula, r = 1, 2,..., N r h r (t) is the expected signal channel impulse response of the rth receiving antenna, h jr (t) is the interference signal channel impulse response of the rth receiving antenna, Convolution calculation is represented. After signal sampling, removing the cyclic prefix and fast Fourier transform, the corresponding frequency domain OFDM signal Y is obtained, and the dimension of Y is N r ×sc, sc is the number of subcarriers and its size is equal to the DFT point number, that is, sc = nFFT. Generally, in a wireless communication system, MIMO technology significantly improves the system performance through spatial diversity and spatial multiplexing, and an adaptive beam forming algorithm enhances the signal quality and suppresses the interference through spatial filtering.

[0008] Advantages:

[0009] 1. The present application adopts a direct matrix reconstruction mechanism to realize directional elimination of the expected signal in the covariance matrix, a covariance matrix reconstruction beam forming algorithm based on Gaussian-Legendre integral subspace projection, efficient and accurate reconstruction of the steering vector is realized through approximate calculation of the angle domain discrete integral and subspace alternating projection, which can reduce the calculation complexity of the integral operation while ensuring high calculation accuracy.

[0010] 2. The present application realizes low complexity reconstruction of the interference and noise covariance matrix through the covariance matrix reconstruction and steering vector correction mechanism, and applies it to the multi-antenna OFDM system to improve the anti-interference ability of the wireless ad hoc network system in the interference scenario. DETAILED DESCRIPTION

[0011] Figure 1 It is a receiving end anti-interference system model diagram of the multi-antenna OFDM system of the present application.

[0012] Figure 2 It is a wireless ad hoc network space anti-interference system model diagram of the present application.

[0013] Figure 3 It is a beam forming spatial spectrum diagram of the present application.

[0014] Figure 4 This is the MRC constellation diagram under single-tone interference according to the present invention.

[0015] Figure 5 This is the constellation diagram after beamforming under single-tone interference according to the present invention.

[0016] Figure 6 The graph shows the variation of MSE with SNR for the LS channel estimation of this invention under interference conditions.

[0017] Figure 7 This is a diagram showing the system bit error rate of each algorithm under single-tone interference in this invention.

[0018] Figure 8 The graph shows the relationship between the bit error rate of each algorithm and the interference-to-signal ratio.

[0019] Figure 9 The graph shows the relationship between the bit error rate of each algorithm and the steering vector mismatch angle.

[0020] Figure 10 The graph shows the relationship between the bit error rate of each algorithm and the number of multipaths. Detailed Implementation

[0021] The invention will now be described in further detail with reference to the accompanying drawings.

[0022] This invention presents an anti-interference architecture based on a multi-antenna OFDM system. This architecture achieves spatial diversity through multi-antenna reception. For each subcarrier signal in the OFDM system, an adaptive beamforming algorithm is used to construct the main lobe pointing to the desired signal in the spatial domain, while simultaneously generating null suppression interference signals. Finally, a zero-forcing equalization algorithm is used to eliminate frequency-selective fading caused by multipath channels. This system deeply integrates pilot channel estimation, spatial filtering, and frequency equalization, providing a high signal-to-noise ratio for subsequent signal demodulation. The receiver anti-interference system model based on the multi-antenna OFDM system is as follows: Figure 1 As shown:

[0023] Assuming both the signal transmitter and the interference source transmitter are single antennas, and the receiver uses an N-type antenna... r A uniform linear antenna array composed of n elements receives the following time-domain OFDM signal from the r-th receiving antenna under interference conditions:

[0024]

[0025] In the formula, r = 1, 2, ..., N r h r (t) represents the desired signal channel impulse response of the r-th receiving antenna, h jr (t) represents the interference signal channel impulse response of the r-th receiving antenna. This represents convolution computation. After signal sampling, removal of the cyclic prefix, and Fast Fourier Transform, the corresponding frequency domain OFDM signal is Y, with dimension N. r ×sc dimension, where sc is the number of subcarriers and its size is equal to the number of DFT points, i.e., sc = nFFT. Typically, in wireless communication systems, MIMO technology significantly improves system performance through spatial diversity and spatial multiplexing, while adaptive beamforming algorithms enhance signal quality and suppress interference through spatial filtering. Research shows that beamforming after FFT can provide lower bit error rate (BER) performance and is superior to anti-interference schemes when adaptive beamforming is performed before FFT. Furthermore, in flat fading channels, in diversity receiving antenna systems, post-FFT beamforming, through the optimization objective of maximizing the signal-to-noise ratio on each subcarrier, is mathematically equivalent to Maximum Ratio Combining (MRC) in the frequency domain. Specifically, N r The ×1D beamforming weight vector w is spatially filtered to transform the original N-dimensional beamforming weight vector at the receiver. r The ×sc-dimensional signal is compressed into a 1×sc-dimensional space, as shown in Equation (4.2). When the weight vector equals the channel response conjugate, the signal-to-noise ratio of the output signal reaches the theoretical upper limit. At this point, the beamforming system is equivalent to MRC. To simplify the analysis, only one transmit antenna is selected, avoiding the need for joint design of precoding and complex signal detection algorithms for multi-stream transmission. Although spatial multiplexing gain is sacrificed, it can be compensated for by subsequent frequency domain equalization techniques, and the improvement of the system bit error rate by the beamforming algorithm can be analyzed more clearly. This architecture can further improve diversity gain through space-time coding extension, but as the number of transmit and receive antennas increases, the complexity of the system will inevitably increase.

[0026]

[0027] Figure 2 This system model for spatial interference mitigation is based on an array-based signal processing framework. Addressing signal transmission scenarios under complex interference, it first silences all nodes during the node detection time slot. Then, the Turbo-based variational Bayesian DOA estimation algorithm extracts information such as the DOA of the interference signal and the number of interference sources. Next, during the normal node reception time slot, covariance matrix interference cancellation technology is used to estimate the DOA of the desired signal. Subsequently, a beamforming algorithm is reconstructed based on the covariance matrix, utilizing the DOA information to perform spatial filtering. This suppresses interference while directing the beam towards the desired signal, ultimately achieving optimized reception under interference conditions. This system, through a joint architecture of DOA estimation and beamforming algorithms, constructs a closed-loop architecture of dynamic interference sensing and adaptive spatial filtering, achieving the goal of interference suppression.

[0028] In multi-antenna OFDM systems, interference significantly degrades the accuracy of channel estimation and the performance of signal detection. First, strong interference contaminates pilot symbols, causing a non-linear increase in the mean square error of traditional least-squares channel estimation, which is further aggravated in multi-antenna scenarios. Second, the condition number of the equivalent channel matrix in the zero-forcing detector deteriorates due to interference, leading to a multiplied noise amplification effect and significantly suppressing improvements in the bit error rate (BER). Even with further reductions in noise power, system performance cannot be effectively improved. Furthermore, non-stationary interference disrupts the orthogonality of OFDM subcarriers, exacerbating frequency domain estimation bias and inter-symbol interference. These issues highlight the necessity of designing anti-interference algorithms for multi-antenna OFDM ad hoc wireless networks. Taking BPSK signals as an example, its BER formula under additive white Gaussian noise interference is:

[0029]

[0030] In the formula, Q(·) is the complementary error function, and E b Let N be the average energy per bit of the signal, and N0 be the power spectral density of Gaussian white noise. J Let be the power spectral density of the interference signal. The formula for the bit error rate of a BPSK signal in a Ricean interference channel is:

[0031]

[0032] In the formula, K r This is the Rice factor. Therefore, beamforming anti-interference technology can significantly suppress interference and reduce the bit error rate. However, traditional adaptive beamforming anti-interference algorithms have two drawbacks [ 75 First, there's the issue of guide vector mismatch, which mainly stems from several factors: inaccurate DOA estimation, array position displacement, or amplitude-phase deviations within element channels. Guide vector mismatch causes main lobe shift in the beam pattern, directly leading to a decrease in the system's output signal-to-interference-plus-noise ratio (SIR). Secondly, the optimization objectives of traditional MVDR beamforming algorithms are as follows:

[0033]

[0034] stw H a(θ1)=1

[0035] In the formula, R is the covariance matrix of the received signal. When the covariance matrix contains the desired signal, then... R i The covariance matrix of the interference signal. Let be the desired signal power, and a(θ1) be the desired signal steering vector. Especially in high signal-to-noise ratio (SNR) scenarios, traditional beamforming algorithms may misclassify it as interference because the optimization objective is to minimize... The beamforming algorithm causes a deep null in the direction of the desired signal, resulting in a "self-cancellation" phenomenon, which poses a serious threat to the system's anti-interference capability. As the signal-to-noise ratio increases, the proportion of the desired signal in the covariance matrix will increase significantly, which will also cause the output signal-to-interference-and-noise ratio to decrease.

[0036] Meanwhile, high-precision signal and interference direction vector estimation is realized by combining Capon spectrum search and neighborhood optimization strategy, and the accuracy of the interference plus noise covariance matrix is significantly improved by reconstructing the noise covariance matrix through least squares solution. By integrating and eigenvalue decomposition of the angle of the desired signal, the signal and noise and interference subspaces are separated, and the estimation accuracy of the direction vector is constrained by convex optimization. Through linear integration and maximum entropy power spectrum estimation, the direction of the interference is dynamically estimated and the interference plus noise covariance matrix is reconstructed, the interference area is accurately located through iterative spatial spectrum sampling, and the calculation complexity is significantly reduced by combining the conjugate gradient optimization algorithm to avoid direct matrix inversion. Similarly, a ring-shaped uncertainty set is proposed to replace the conventional linear integration interval to improve robustness, which improves the performance of the algorithm while increasing the computational complexity.

[0037] The application can perform eigenvalue decomposition on the covariance matrix according to the array signal model, and has:

[0038]

[0039] In the formula, The eigenvalues after eigenvalue decomposition, in general communication scenarios, the power of the desired signal and the interference signal is usually significantly higher than the noise power. Therefore, in the case of one signal source and M interference sources, the first M+1 eigenvalues corresponding to the signal subspace composed of the desired signal and the interference signal, and the last N r -M-1 eigenvalues belong to the noise subspace, and their values are approximately equal and close to the noise power level.e i The ith eigenvalue λ i corresponding to the eigenvector, E s =[e1,e2,...,e M+1 ] is the signal plus interference subspace, E n =[e M+2 ,e M+3 ,...,e N ] is the noise subspace. Σ s represents a diagonal matrix composed of signal plus interference eigenvalues, and Σ n represents a diagonal matrix composed of noise eigenvalues. When there is one desired signal and M interference sources, the received signal covariance matrix after eigenvalue decomposition will have M+1 eigenvalues of a significantly larger order of magnitude, and the remaining residual eigenvalues correspond to the eigenvalues of the noise subspace. Based on this characteristic, the noise power can be estimated by the mean of all eigenvalues in the noise subspace.

[0040] The DOA of the desired signal and the interference signal is input into the beamforming algorithm as known information. According to formula (2.33), the essence of the Capon power spectrum is the minimum power of the array output when the beamformer achieves distortionless reception in the direction θ, so the spectrum value includes the real power of the input signal and the residual noise power suppressed to the lower limit by the array. Based on the sparse characteristics of the spatial array signal, the desired signal power is concentrated in a narrow area adjacent to the real arrival angle, and the covariance matrix can be reconstructed by integral operation of the power spectrum:

[0041]

[0042] In the formula, Θ represents the interval containing the desired signal arrival angle θ1, and the smaller the interval, the less the amount of redundant information in the area, so that the reconstructed covariance matrix is more accurate, and the signal steering vector estimation is also more accurate. In view of the problem that the continuous integral in formula (4.7) is difficult to solve, L s discrete angle sampling points are uniformly selected in the target angle coverage interval Θ The original integral operation is converted to a finite item summation form as follows:

[0043]

[0044] The approximation accuracy of the method depends on the discretization parameter L s , and the computational complexity of the method is The third-order Gauss-Legendre quadrature method is used to effectively approximate the integral operation of the power spectrum, and this method can further reduce the computational complexity to while ensuring high calculation accuracy. A generalized interpolation-type Gauss quadrature formula with N g nodes can be expressed as:

[0045]

[0046] In the formula, a and b are the upper and lower limits of the integral, x n is the Gauss integral node, e(f) is the integral residual term (residual), N g is a positive integer, A n is the calculation weight, and when constructing GLQ, the integral node x n is taken as the root of the Legendre polynomial , which ensures the highest algebraic accuracy of the integral formula for polynomial integral functions. The Legendre polynomial sequence is as follows:

[0047]

[0048] For the third order Legendre polynomial, there is P3(x) = (5x 3 -3x) / 2 = 0, and the three roots are obtained as:

[0049] x1= 0, For the convenience of calculation, the integral interval of formula (4.9) is chosen as [-1, 1]:

[0050]

[0051] The algebraic accuracy of the third order Legendre polynomial is at least 3 order, that is, it can accurately integrate all polynomial functions with the order not more than 3. When f(x) = 1, f(x) = x and f(x) = x 2 , there are:

[0052]

[0053] Solving the above formula, A0=5 / 9, A1=8 / 9, A2=5 / 9, ignoring the integral remainder, formula (4.11) can be approximately expressed as:

[0054]

[0055] In the formula, l n = (a+b) / 2+x n (b-a) / 2 Through a simple linear transformation, the integral on the interval [a, b] can be approximated by the third order Gauss-Legendre integral as:

[0056]

[0057] By formula (4.14) Gauss-Legendre integral calculation formula (4.7), there are:

[0058]

[0059] In the formula, θ a , θ b are the lower bound and the upper bound of the spatial range Θ containing the expected signal arrival angle, and the spatial range is generally selected as the expected signal arrival angle ±5 degrees, l n = (θ a + θ b ) / 2+x n (θ b - θ a ) / 2, the expression of f(θ) is as follows:

[0060]

[0061] The expected signal covariance matrix obtained by formula (4.15) is: Eigenvalue decomposition includes: Where Σ s =diag(λ i (i = 1, 2, ..., b) is an eigenvalue diagonal matrix, and its corresponding eigenvector V s =[V1,V2,...,V b [ξ] represents the principal energy direction within the interval of the desired signal's angle of arrival. To achieve principal energy direction focusing and dimensionality reduction in computation, while ignoring minor eigenvectors to avoid sensitivity to noise and improve algorithm robustness, we retain principal components whose energy percentage exceeds the threshold ξ, i.e., we retain the eigenvectors corresponding to the top α largest eigenvalues. Where α is calculated by the following formula:

[0062]

[0063] Signal subspace C1 = span(E) s ), where E s The covariance matrix in formula (4.6) The signal and interference subspace is constructed simultaneously. An angle constraint subspace is also constructed. The signal-plus-interference subspace and the angle-constraint subspace can be represented by the following formulas:

[0064] C1 = {a:a = E} s α E},(4.18)

[0065]

[0066] The physical meaning of the above equation is that the accurate reconstruction of the steering vector 'a' of the actual signal can be achieved by applying dual subspace constraints, i.e., alternating projections onto the signal subspace and the angle constraint subspace. Essentially, this requires the steering vector to lie within the intersection space C0 = C1∩C2. According to the spatial projection theorem, the intersection of the two constraint sets can be effectively solved using an alternating projection algorithm. If the array steering vector is considered as a vector in a high-dimensional complex space, the optimal solution satisfying the dual constraints can asymptotically converge by iteratively projecting it onto the signal subspace and the angle constraint subspace.

[33] ,Right now

[0067]

[0068] In the formula, The operator represents the orthogonal projection onto spaces C1 and C2. In the first iteration, a k＝1 =a(θ1), that is, the DOA estimated by the Turbo-OG-VBI algorithm constitutes the steering vector. Through analysis From the eigenvalues, we can obtain:

[0069]

[0070] where represents the largest eigenvalue, the above equation shows that the eigenvalue of is the largest one, which proves that the alternating projection process is convergent. When the iteration number k tends to infinity, a k will converge to the corresponding principal eigenvector, i.e.

[0071]

[0072] where a re is the reconstructed steering vector, the matrix whose largest eigenvalue corresponds to the eigenvector, i.e. the basis vector of the space C1, C2.

[0073] Under low SNR, the sample covariance matrix is dominated by noise, and direct reconstruction of the steering vector will introduce random errors. In addition, the multipath effect will also cause the signal subspace to be ambiguous, resulting in an error in the steering vector of the desired channel. By imposing an energy constraint on the reconstructed steering vector using the covariance matrix and the theory of quadratic constraint quadratic programming convex optimization, we effectively control the model mismatch, noise and multipath interference in physics

[81] . Assuming a = a re + a e , a is the steering vector of the actual desired signal, a e is the steering vector error vector, which can be modeled as the following constrained optimization problem:

[0074]

[0075] The above equation belongs to the category of quadratic constraint quadratic programming, and its convex structure can be efficiently solved by standard convex optimization tools

[82] . The convexity of the QCQP problem is guaranteed by the positive definiteness of the quadratic form of the objective function and the constraint condition. The solution of the modified desired signal steering vector is:

[0076]

[0077] The core requirement of implementing the MVDR beamforming algorithm is to reconstruct the IPNCM containing only interference and noise. In addition, the essence of the covariance matrix is the overall power distribution of the array received signal, while the IPNCM accurately represents the power components of the interference and noise. Therefore, the estimation problem of IPNCM can be equivalent to the joint estimation process of interference power and noise power. According to the definition of IPNCM, it can be expressed as:

[0078]

[0079] In the formula, a(θ) k ) is the steering vector of the k-th interference signal. To correspond to the power of the interference signal, This represents the cross-correlation between signal and noise caused when calculating the sampling covariance matrix with a finite number of snapshots. Currently, there are three mainstream algorithms for reconstructing the IPNCM:

[0080] (1) From the sampling covariance matrix Directly subtract the signal covariance matrix To reconstruct IPNCM

[84] ,Right now However, this method depends on The estimation accuracy ignores the correlation between signal, interference and noise, and the IPNCM estimation bias is significant at high signal-to-noise ratios.

[0081] (2) By interfering angle sector Θ i Within this process, the corrected Capon spectrum is integrated to extract the interference components. Based on the integration result and the noise power estimate, the interference plus noise covariance matrix is ​​reconstructed. 31 ], as shown below:

[0082]

[0083] This method relies on the accuracy of the interference region segmentation and is sensitive to steering vector errors, requiring high-resolution DOA estimation results.

[0084] (3) Directly estimate the power of each interference. and the corresponding interference signal steering vector a(θ) k The IPNCM can be obtained by superimposing the IPNCM and adding it to the noise covariance matrix.

[85] The formula is as follows:

[0085]

[0086] This method relies heavily on prior information about the number of interference signals and is sensitive to the steering vector of the interference signal. Errors in the steering vector will directly lead to inaccurate power estimation.

[0087] Based on the corrected desired signal steering vector obtained in the previous section, the covariance matrix of the desired signal can be calculated as follows:

[0088]

[0089] Performing eigenvalue decomposition on the above equation, and based on spectral analysis, it can be seen that the eigenvectors with larger magnitudes in the covariance matrix carry the main part of the system energy. The subspace spanned by these significant eigenvalues ​​concentrates the main components of the signal energy.

[0090]

[0091] Assume that B = Span{b1, b2, …, b J} is the subspace spanned by the first J (J = 1, 2, …, N s ) eigenvectors of R r , then a re belongs to the subspace B Based on the orthogonal property, the desired signal can be eliminated by constructing a projection matrix Q j , and the received signal of the lth snapshot is given by The received signal of the lth snapshot is processed as follows:

[0092]

[0093] where x s (l), x i (l), x n (l) represent the desired signal, interference signal and noise, respectively. It can be seen from the above equation that the desired signal can be eliminated by the projection matrix. The approximate IPNCM matrix can be obtained by taking the expectation of the residual signal:

[0094]

[0095] The noise power can be estimated by performing eigenvalue decomposition on the sample covariance matrix obtained in equation (4.6):

[0096]

[0097] where is the approximate noise eigenvalue, and the interference signal covariance matrix can be obtained according to equations (4.30) and (4.31):

[0098]

[0099] However, in practical applications, the projection operation cannot perfectly eliminate the desired signal, i.e., the residual signal component cannot be completely suppressed, which limits the accuracy of the interference covariance matrix estimated by the traditional method. To address this problem, an improved GLQ interference covariance matrix reconstruction strategy is adopted: first, the interference covariance matrix is constructed based on the initial estimate, and then it is used as a weight matrix to replace the original inverse covariance matrix for GLQ operation in the interference angle neighborhood. This secondary reconstruction mechanism effectively compensates for the estimation bias caused by the residual signal component through iterative correction, significantly improving the estimation accuracy of the interference covariance matrix. The mathematical representation is the integral operation reconstruction of the interference angle domain:

[0100]

[0101] wherein, is the angle of arrival region of the interference signal, is the spatial range containing the angle of arrival of the interference signal lower and upper bounds. The IPNCM matrix after the second reconstruction is:

[0102]

[0103] GLQSP Covariance Matrix Reconstruction Beamforming Algorithm Flow and Computational Complexity Analysis:

[0104] In summary, the GLQSP Covariance Matrix Reconstruction Beamforming Algorithm flow proposed in the application can be summarized as follows:

[0105]

[0106] The computational complexity of Algorithm 2 mainly depends on the projection matrix construction, the interference plus noise covariance matrix reconstruction based on Gauss-Legendre integral, and the expected signal steering vector estimation. The computational complexity is determined by the following parts: the computational complexity of step 1 for eigenvalue decomposition is In order to calculate the estimated steering vector of the expected signal, the matrix in formula (4.21) needs to be eigenvalue decomposed, and the computational complexity is also Formula (4.22) uses QCQP to impose energy constraints on the steering vector, and the computational complexity is According to formula (4.28), the covariance matrix of the expected signal needs to be eigenvalue decomposed to construct the projection matrix Q j , and the computational complexity is also In summary, the computational complexity of Algorithm 2 is

[0107] Application Steps of GLQSP Covariance Matrix Reconstruction Beamforming Algorithm in OFDM System:

[0108] Figure 1 is the system block diagram of the multi-antenna OFDM system receiver, and the frequency domain OFDM signal after removing the cyclic prefix is Y. The steps of the spatial domain anti-interference performed by the receiver are as follows:

[0109] (1) Estimate the expected signal angle and the interference signal angle using the Turbo-OG-VBI algorithm.

[0110] (2) For each frequency domain subcarrier signal Y(sc), first calculate its sample covariance matrix, then calculate the weight w sc of each subcarrier, and finally input it into formula (4.2) to calculate

[0111] (3) The signal after beamforming The received signal at pilot position can be expressed as:

[0112]

[0113] where h is the time-domain channel impulse response, σ p is the frequency-domain noise vector, and the matrix A is composed of pilot symbols and DFT matrix:

[0114] A = F p diag(P) (4.36) where is the DFT pilot position matrix, k p is the pilot position, and P is the pilot symbol. The time-domain least square channel response is solved by pseudo-inverse:

[0115]

[0116] The time-domain channel response is subjected to nFFT-point fast Fourier transform to obtain the estimated frequency-domain channel response

[0117] (4) Zero-forcing equalization is performed on each frequency-domain subcarrier signal Y(sc)

[86] , and then demodulation is performed to obtain the received signal.

[0118] Simulation experiment analysis

[0119] The channel parameter settings of the application are shown in Table 3.1. In order to verify the performance of the anti-interference algorithm proposed in the application, the subspace projection method (SP) beamforming algorithm

[81] , the diagonal loading (DL) beamforming algorithm

[30] , and the method of directly performing MRC without using beamforming algorithm are compared with the GLQSP covariance matrix reconstruction beamforming algorithm proposed in the application.

[0120] Experiment 1: Beamforming spatial spectrum and signal constellation diagram.

[0121] Figure 3The normalized power spectrum obtained after beamforming of a single subcarrier based on the algorithm of the application is shown, wherein the angles of arrival of the desired signal and the interference signal are obtained by DOA estimation through the Turbo-OG-VBI algorithm. The experimental settings are: signal-to-noise ratio 15 dB, jamming-to-signal ratio 20 dB, channel 3-path Rician channel, BPSK modulated desired signal incident angle 56.5 degrees, single-tone interference source incident angle 88.2 degrees, and DFT point number 2048. According to the power spectrum curve, it is shown that the proposed beamforming algorithm forms a main lobe peak near the incident direction of the desired signal, and the normalized power reaches a maximum value of 0 dB, verifying the spatial focusing ability of the algorithm on the desired signal under high jamming-to-signal ratio conditions and the tolerance ability of the algorithm to DOA estimation errors. At the same time, the beamforming algorithm produces a null of more than -30 dB near the incident angle of the interference signal, reflecting the interference suppression ability of the proposed GLQSP covariance matrix reconstruction beamforming algorithm, which provides a theoretical guarantee for reliable communication in a strong interference scenario. However, due to the small number of receiving antennas, the GLQSP covariance matrix reconstruction beamforming algorithm focuses on improving the tolerance ability to DOA estimation errors in the design, so while achieving interference nulling, it may sacrifice the suppression ability to energy in other non-desired directions, resulting in an increase in the noise floor at some angles, which is manifested as a high sidelobe in the beam pattern.

[0122] Figure 4 For the constellation point of the MRC processed frequency domain zero-forcing equalization without using beamforming, the constellation point should be strictly distributed at the (+1, 0) and (-1, 0) positions of the horizontal axis (I axis) in the ideal case. It is found through observation that the signal constellation point after interference presents a significant non-ideal diffusion characteristic, indicating that there is additive noise and phase rotation interference in the channel. Figure 5 The constellation point distribution diagram of the frequency domain equalization after using the GLQSP covariance matrix reconstruction beamforming can be seen from the above figure that the constellation point presents a central symmetric distribution, indicating that the beamforming algorithm significantly eliminates the influence of interference on the signal. However, the constellation point is relatively dispersed, mainly due to the continuous influence of residual interference energy and noise on the amplitude and phase of the signal. Although the beamforming algorithm suppresses most of the interference by reconstructing the interference and noise covariance matrix, in actual scenarios, the direction estimation error of the interference source may cause the null to not accurately align with the interference direction, so that part of the interference energy cannot be completely eliminated. The residual interference component superimposed with the signal destroys the phase consistency of the symbol. In addition, the estimation bias of the covariance matrix under a limited number of snapshots will reduce the calculation accuracy of the beamforming weight, resulting in a weakening of the interference suppression effect.

[0123] Experiment 2: Performance of LS channel estimation under interference environment with respect to signal-to-noise ratio.

[0124] Figure 6The MSE versus SNR curves for LS channel estimation under a three-path Ricean channel with and without single-tone interference (STO) and with STOs of different interference-to-signal ratios are presented. 256 pilots and 1024 DFT points were used. As can be seen from the magnified view, when there is no interference, the performance of LS channel estimation improves significantly with increasing SNR. However, when interference is present, the performance improvement with SNR is smaller. In this case, the estimation performance is mainly limited by the interference power rather than the noise power, thus affecting subsequent frequency domain equalization and demodulation. Therefore, anti-interference strategies must be introduced in interference scenarios to improve communication reliability.

[0125] Experiment 3: Relationship between system bit error rate and SNR of various algorithms under single-tone interference.

[0126] Figure 7 This paper presents the bit error rate (BER) performance of the GLQSP covariance matrix reconstruction algorithm, maximum combining ratio algorithm, subspace projection method, and diagonal loading beamforming algorithm under different SNR conditions. The interference source is a single-tone interference, the interference-to-signal ratio is 15 dB, the multipath number is 3, the DFT number is 1024, and the DOA of the desired signal and the interference signal are estimated using the Turbo-OG-VBI algorithm. Figure 7 It can be seen that the bit error rate (BER) of each algorithm decreases with increasing signal-to-noise ratio (SNR). However, the maximum combining ratio (MBR) algorithm, due to insufficient suppression of single-tone interference, has a significantly higher BER than the GLQSP covariance matrix reconstruction algorithm and the subspace projection beamforming algorithm at high SNR. The subspace projection method relies on a discretized approximation integral method in the subspace estimation of the interference signal, which is susceptible to multipath coherence and noise, leading to bias in the projection matrix. The algorithm of this invention, by introducing the GLQ method, achieves a higher-precision numerical approximation of the continuous angular space when calculating the covariance matrix of the desired signal. This accuracy is more significant at low SNR. Diagonal loading beamforming suffers from poor performance due to steering vector errors. Similarly, at low SNR, noise is the primary influencing factor rather than interference. In this case, beamforming has limited noise suppression capabilities, while MRC, by maximizing signal energy accumulation, is more suitable for noise-dominated scenarios. Furthermore, since adaptive beamforming cannot completely eliminate interference, and channel estimation has errors, the system's BER performance largely depends on factors such as the Rice factor, residual interference power, and channel estimation accuracy.

[0127] Experiment 4: The relationship between the bit error rate of each algorithm and the interference-to-signal ratio.

[0128] Figure 8The curves of the bit error rate of each algorithm changing with the signal-to-interference ratio are described when the signal-to-noise ratio is 30 dB, the multipath number is 3, the DFT point number is 1024, and the DOA of the expected signal and the interference signal is the estimation result of the Turbo-OG-VBI algorithm, and it can be seen from the figure that the algorithm has the lowest bit error rate in high signal-to-interference ratio, which shows that it has the optimal anti-interference ability in a strong interference environment. The core advantage of beamforming is to suppress interference, rather than to eliminate the influence of noise. Therefore, in low signal-to-interference ratio, MRC can adapt to the environmental requirements by integrating the energy of multiple signals through weighting. The diagonal loading beamforming algorithm is sensitive to the estimation error of the steering vector, and the DOA estimation deviation will make the null of the diagonal loading beamforming algorithm no longer accurately point to the interference source, thereby rapidly reducing the anti-interference ability. In addition, improper selection of the diagonal loading factor will also reduce the algorithm performance.

[0129] Experiment 5: Relationship between the bit error rate of the beamforming algorithm and the mismatch angle of the steering vector.

[0130] Figure 9 The relationship diagram of the bit error rate and the angle error of the steering vector of each algorithm is given when the signal-to-noise ratio is 30 dB, the signal-to-interference ratio is 20 dB, and the DFT point number is 1024, and the experimental results show that within an angle error of ±2 degrees, the algorithm and the subspace projection method beamforming algorithm are not sensitive to the mismatch of the steering vector, and the bit error rate increases slowly. Since the diagonal loading beamforming algorithm does not correct the steering vector and the covariance matrix, it is sensitive to the angle error of the steering vector, and its performance rapidly decreases with the increase of the angle error. Even in the ideal condition of no angle error, since the algorithm does not reconstruct the interference and noise covariance matrix, it is still difficult to form a deep null for interference, resulting in that its performance in a high SNR scene is still not as good as other robust beamforming algorithms that reconstruct IPNCM.

[0131] Experiment 6: Relationship between the bit error rate of each algorithm and the multipath number under single-tone interference.

[0132] Figure 10 The curves of the bit error rate changing with the channel multipath number are given for each algorithm when the signal-to-noise ratio is 30 dB, the signal-to-interference ratio is 20 dB, the DFT point number is 1024, and the DOA of the expected signal and the interference signal is the estimation result of the Turbo-OG-VBI algorithm. It can be seen from the figure that when the channel multipath number increases from 1 to 2, the bit error rate of each algorithm increases significantly, because the multipath effect will affect the accuracy of DOA estimation, but the bit error rate of the algorithm still remains the lowest, which reflects that the robustness of the algorithm to the multipath effect is higher than that of other algorithms.

[0133] The application studies the problem of beamforming anti-interference based on multi-antenna OFDM signal receiving end in wireless ad hoc network. Firstly, the angle constraint subspace is constructed by Gauss-Legendre integral, then the reconstructed expected signal steering vector is obtained by alternately projecting the signal subspace of the receiving signal covariance matrix and the angle constraint subspace, the expected signal covariance matrix after eliminating the residual noise is used for eigenvalue decomposition, and then the projection matrix is constructed to eliminate the expected signal and obtain the preliminary IPNCM. In order to further suppress the residual noise, the IPNCM is used to replace the original covariance matrix in the interference area, and combined with the GLQ integral method of Capon power spectrum, a more accurate IPNCM is obtained. Finally, the spatial information is used for beamforming of each subcarrier data of OFDM, and then the signal is demodulated after frequency domain equalization. The experiment simulation proves the effectiveness of the space anti-interference strategy, and the low bit error rate can be ensured in the complex environment.

Claims

1. A method for beamforming in a multi-antenna OFDM system based on GLQSP covariance matrix reconstruction, characterized in that, The method comprises the following steps: The signal sending end and the interference source sending end are single antennas, and the receiving end adopts a uniform linear antenna array composed of N r array elements. In the interference environment, the time domain OFDM signal received by the rth receiving antenna is as follows: where r = 1, 2,..., N r , h r (t) is the desired signal channel impulse response of the rth receiving antenna, h jr (t) is the interference signal channel impulse response of the rth receiving antenna, denotes the convolution operation, and the corresponding frequency domain OFDM signal Y is obtained after signal sampling, removing the cyclic prefix, and fast Fourier transform, with a dimension of N r x sc, where sc is the number of subcarriers and its size is equal to the DFT point number, i.e., sc = nFFT.

2. The method of claim 1, wherein, The method is based on an array receiving signal processing framework, and for a signal transmission scene under complex interference, first, in a node detection time slot, each node is muted, at this time, a Turbo outlier variational Bayesian DOA estimation algorithm is used to extract DOA and the number of interference sources of the interference signal, then, in a normal node receiving time slot, a covariance matrix interference signal elimination technology is used to realize DOA estimation of the expected signal, subsequently, according to a covariance matrix reconstruction beamforming algorithm, spatial domain filtering is completed by using the DOA information, the interference is suppressed, and the beam is pointed to the expected signal, and finally, optimal reception under the interference environment is realized, and through the joint architecture of the DOA estimation and the beamforming algorithm, a closed-loop architecture of dynamic interference perception and adaptive spatial domain filtering is constructed.

3. The method of claim 1, wherein, The method can perform characteristic decomposition on the covariance matrix according to an array signal model, and has the following advantages: wherein, are eigenvalues after eigenvalue decomposition, in general communication scenarios, the power of desired signal and interference signal is usually significantly higher than the noise power, in the case of one signal source and M interference sources, the first M+1 eigenvalues correspond to the signal subspace composed of desired signal and interference signal, the last N r M-1 eigenvalues belong to noise subspace, the values are approximately equal and close to the noise power level, e i The ith eigenvalue λ i corresponds to the eigenvector E s = [e1, e2,..., e M+1 ] is the signal plus interference subspace, E n = [e M+2 , e M+3 ,..., e N ] is the noise subspace, Σ s represents a diagonal matrix composed of signal plus interference eigenvalues, Σ n represents a diagonal matrix composed of noise eigenvalues, when there is one desired signal and M interference sources, the received signal covariance matrix after eigenvalue decomposition will present M+1 eigenvalues of significantly larger order of magnitude, the remaining residual eigenvalues correspond to the eigenvalues of the noise subspace, based on this characteristic, the noise power can be estimated by the average of all eigenvalues in the noise subspace.

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