A method for estimating direction of arrival of coherent signals

Abstract

The present invention discloses a method for estimating the direction of arrival of a coherent signal, belonging to the field of ship radar and communication signal processing. The method comprises: a transmitting end sends a pilot signal of a target power to a receiving end, and the receiving end obtains the multipath delay structure of the channel based on the pilot signal; the transmitting end sends a normal pilot signal to the receiving end, and calculates the cross-correlation function between the received signal and the transmitted signal; the peak values ​​of the cross-correlation function are sorted in descending order to determine the candidate possibilities of the first delay, and the cross-correlation function after the composite path is calculated to determine the shortest delay; a cost function for the delay is constructed, and the cost function is differentiated with respect to two independent variables to obtain an estimated value of the arrival time difference; the direction of arrival is calculated from the estimated value of the arrival time difference, completing the one-dimensional direction of arrival estimation of the coherent signal applied to a uniform linear array. This method can improve the detection accuracy of passive radar and sonar equipment for targets and enhance the comprehensive detection capability of surface ships.

Description

Technical Field

[0001] The present invention belongs to the field of ship radar and communication signal processing, and in particular relates to a one-dimensional direction-of-arrival estimation method for coherent signals applied to a uniform linear array. Background Art

[0002] Estimating the direction of arrival of correlated signals under complex noise or interference is one of the core issues in array antenna processing that deserves in-depth study.

[0003] In practical applications, the signals received by the receiving sensor may come from multiple transmitting targets, resulting in multi-source signals; or the received signals may be non-stationary, with time-frequency characteristics changing over time; or the signals may be blocked by buildings during propagation, resulting in multipath transmission effects; or the signals may encounter complex noise interference, such as non-Gaussian noise and correlated signals. These situations lead to significant gaps in the accuracy, robustness, and complexity of the applied direction of arrival estimation algorithms, making it difficult to simultaneously achieve high accuracy, strong robustness, and low complexity. Therefore, studying the problem of direction of arrival estimation for real signals in such complex environments is not only of great theoretical research significance, but also of great practical application value.

[0004] Currently, there are two common DOA estimation algorithms: one is the DOA estimation algorithm based on feature structure, and the other is the angle estimation technology based on cost function.

[0005] Direction of Arrival (DOA) estimation based on eigenstructures is an important application of spatial spectrum estimation within DOA estimation. Classic high-resolution spectrum estimation methods include the Multiple Signal Classification (MUSIC) algorithm and the Signal Parameter Estimation via Spatial Rotation Invariance (ESPRIT) algorithm. The MUSIC algorithm constructs orthogonal signal and noise subspaces to obtain the spatial spectrum and estimates parameters by searching for peaks in the spatial spectrum. The ESPRIT algorithm constructs a new substeering matrix from the two signal subspaces and uses eigenvalue decomposition to estimate parameters, leveraging the relationship between the subarray transformation matrix and the estimated parameters. DOA estimation algorithms based on eigenstructures are significantly affected by search range, search accuracy, and the number of array elements. When the search range is large, the search accuracy is high, and the number of array elements is large, these DOA estimation algorithms achieve good angular resolution, high estimation performance, and a certain degree of noise immunity, even performing well in high signal-to-noise ratio (SNR) regions. However, their drawbacks are particularly pronounced: they cannot compute coherent signals, and the large number of matrices involved leads to high computational complexity.

[0006] The basic concept of the cost-based DOA estimation algorithm is to establish a cost function and use minimization as a technical criterion. This optimization criterion, such as minimum mean square error, maximum likelihood, and nonlinear least squares, is then used to minimize time delay through iteration. Cost-based DOA estimation algorithms offer extremely high performance. For example, maximum likelihood-based DOA estimation performance metrics often serve as the optimal performance line in simulation comparisons. However, because the algorithm involves iterative operations and has exponential computational complexity, current hardware is unlikely to meet this computational power requirement in practical applications. Summary of the Invention

[0007] Aiming at the limitation that traditional direction-of-arrival estimation algorithms based on characteristic structures cannot be used for coherent signals, and the problem of high computational complexity of current direction-of-arrival estimation algorithms, a direction-of-arrival estimation algorithm is proposed that estimates the shortest delay based on a quasi-static structure with a fixed delay structure, minimizes the cost function related to the delay, and solves the direction of arrival. This algorithm can be applied to coherent signals of uniform linear arrays, overcoming the problem of high computational complexity in existing methods.

[0008] To achieve the above object, the present invention provides a method for estimating the direction of arrival of a coherent signal, comprising:

[0009] The transmitter first sends a pilot signal with the target power to the receiver. The receiver obtains the multipath delay structure of the channel based on the received pilot signal.

[0010] The transmitting end sends a normal pilot signal to the receiving end and calculates the cross-correlation function between the received signal and the transmitted signal;

[0011] Sort the peak values ​​of the cross-correlation function in descending order to determine the candidate possibility of the first time delay, and calculate the cross-correlation function after the synthesis path to determine the shortest time delay;

[0012] Construct a cost function for time delay. To minimize the cost function, take the derivative of the cost function with respect to the two independent variables to obtain an estimated value of the arrival time difference.

[0013] The direction of arrival (DOA) is obtained from the estimated value of the arrival time difference, completing the one-dimensional DOA estimation of the coherent signal applied to the uniform linear array.

[0014] In some optional embodiments, Determine the multipath delay structure of device u Among them, t u,i =τ u,i -τ u,1 represents the delay τ of the i-th path u,i The delay τ with the first path u,1 The delay difference, P u Indicates the number of propagation paths.

[0015] In some optional embodiments, Calculate the cross-correlation function R between the received signal and the transmitted signal cc [m], x[n] represents the signal size at the nth moment, n, m belong to the set [0, N-1], N is the signal length, x + [n] is the conjugate of x[n], and y[n+m] represents the received signal at the n+mth moment.

[0016] In some optional embodiments, Calculate the cross-correlation function sum(v after the synthesis path u,i ), where v u,i represents the sum of all path cross-correlation functions corresponding to the i-th candidate possibility of device u, t u,j =τ u,j -τ u,1 represents the delay τ of the jth path u,j The delay τ with the first path u,1 The delay difference, q u,i represents the delay corresponding to the i-th peak.

[0017] In some optional embodiments, Determine the shortest delay estimate q u,Iu Indicates the first u The delay corresponding to the peak is the shortest delay, V u represents the composite path cross-correlation function, and

[0018] In some optional embodiments, Construct the cost function J about the delay, where Δτ u,i is the arrival time difference between adjacent antennas on the i-th path of device u, represents the estimated delay time of the i-th path from device u to antenna l, τ u,i,1 represents the delay of the i-th path from device u to antenna 1, L represents the number of antenna arrays receiving the signal, Δτ i,p It represents the arrival time difference between adjacent antennas on the i-th path of device p.

[0019] In some optional embodiments, Get an estimate of the time difference of arrival It represents the estimated delay time of the i-th path from device u to antenna L.

[0020] In some optional embodiments, Get the estimated value of the direction of arrival of the i-th path of device u d is the distance between antennas, and c is the speed of light.

[0021] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0022] The one-dimensional direction of arrival estimation of coherent signals provided by the present invention is a coherent signal direction of arrival estimation algorithm based on a uniform antenna array. The algorithm is simple and efficient. First, the shortest delay is obtained by path synthesis, and then the direction of arrival is solved by constructing a delay cost function and minimizing it.

[0023] The present invention can avoid the complicated eigenvalue decomposition process, reduce the computational complexity, and under the condition of very low signal-to-noise ratio, the method still has good estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a wireless communication channel model established in an embodiment of the present invention. The transmitter uses multiple antennas and multiple devices for transmission, and the signals reach the receiver via a wireless multipath channel. The receiver uses a uniform antenna array. Under far-field conditions, the arrival time of signals along the same path to the antenna array elements is determined by the antenna spacing and the direction of arrival.

[0025] Figure 2 This is a graph showing the root mean square error (RMSE) of direction of arrival estimation versus signal-to-noise ratio, provided by an embodiment of the present invention. The horizontal axis represents the signal-to-noise ratio, and the vertical axis represents the root mean square error. The proposed algorithm is the algorithm proposed in the present invention, and the existing algorithm is the existing PC-MUSIC algorithm (an improved traditional MUSIC algorithm).

[0026] Figure 3 The figure is a flow chart of a method for estimating a direction of arrival provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0028] The present invention provides a method for estimating the direction of arrival of a coherent signal, which includes the following techniques:

[0029] (1) System model establishment

[0030] Considering the system model as a multi-antenna multi-device communication system model, it is assumed that there are L antenna arrays for receiving signals, U transmitting devices for transmitting signals, the propagation channel is a wireless multipath signal propagation channel and the number of propagation paths is P u , then at any receiving antenna, the discrete model of the received signal can be expressed as:

[0031]

[0032] Among them, y[n] represents the received signal at the nth moment, x u [n] represents the transmission (pilot) signal of device u at the nth moment, w[n] represents the mean value of 0 and the variance of σ 2 Additive Gaussian white noise (Gaussian white noise refers to noise with amplitude obeying Gaussian distribution and power spectrum density obeying uniform distribution, which is a stationary random process), * represents convolution operation, h u [n] represents the multipath wireless channel transfer function of device u.

[0033] Considering that the wireless channel is a multipath time-invariant channel, which is affected by different signal attenuation coefficients and delay factors, the impact response function of the multipath time-invariant channel can be expressed as:

[0034]

[0035] Among them, δ represents the impulse function, α u,i and τ u,i Denote the amplitude attenuation coefficient and signal delay time of the i-th path of device u respectively. Substituting equation (2) into equation (1), we can obtain the time domain relationship between the transmitted signal and the received signal:

[0036]

[0037] It can be seen that in the set communication system model, although the signals on each path have different delays and attenuations, they are clearly coherent signals. The received signal is the superposition of multiple coherent signals. However, the traditional direction of arrival estimation algorithm based on characteristic structures can only be used to obtain the direction of arrival of multiple incoherent signal sources. Therefore, it cannot be directly applied to the multipath wireless communication system model. Therefore, a new direction of arrival estimation algorithm is proposed.

[0038] (2) Multipath delay estimation

[0039] Preprocessing: First, the transmitter sends a high-power pilot signal (referring to the unmodulated direct sequence spread spectrum signal continuously transmitted by the base station) to the receiver. The receiver obtains the multipath delay structure of the channel based on the received pilot signal and expresses the multipath delay structure of device u as follows:

[0040]

[0041] Among them, t u,i =τ u,i -τ u,1 represents the delay difference between the i-th path and the first path. Using the multipath delay structure, the multipath delay of device u can be expressed as:

[0042]

[0043] Delay estimation: The transmitter sends a normal signal to the receiver. The receiver calculates the cross-correlation function based on the received signal y and the transmitted signal x:

[0044]

[0045] Among them, x[n] represents the signal size at the nth moment, n, m belong to the set [0, N-1], N is the signal length, x + [n] is the conjugate of x[n].

[0046] From formula (3), we can observe that the received signal is actually a distorted replica of the transmitted signal after delay and attenuation. Then, the cross-correlation function of the received signal and the transmitted signal obtained from formula (6) has a peak value corresponding to the delay, which is the delay of the received signal. However, as the noise increases, the peak value of the cross-correlation function is increasingly susceptible to noise, or the number of peaks may be greater than the number of multipaths, causing errors in the estimation results.

[0047] At this time, the multipath delay structure can be used to perform multipath synthesis to enhance the peak of the cross-correlation function, thereby more accurately calculating the delay. The peak values ​​of the cross-correlation functions of the received signal and the transmitted signal are sorted in descending order. The peak sorting can be expressed as:

[0048]

[0049] Among them, q u,i is the delay corresponding to the i-th peak, that is, the index corresponding to the i-th peak. Assuming the delay corresponding to the i-th peak is the delay corresponding to the first path, the i-th candidate possibility of the delay of device u is:

[0050]

[0051] Add up all the path cross-correlation functions corresponding to the i-th candidate possibility:

[0052]

[0053] v u,i It represents the sum of all path cross-correlation functions corresponding to the i-th candidate possibility of device u.

[0054] The cross-correlation function vector of the composite path can be obtained as:

[0055]

[0056] Finally, the index corresponding to the first path is found by finding the maximum value of the cross-correlation vector of the composite path, and the multipath delay time of the device u is obtained.

[0057]

[0058] After path synthesis, the cross-correlation function of the first path is improved. u,i ≠τ u,1 , then after using the delay structure, q u,i +t u,i ≠τ u,i , R[q u,i +t u,i ] represents the cross-correlation function signal corresponding to the i-th candidate possibility of device u, and R[q u,i +t u,i ] is likely to correspond to a smaller noise term in the cross-correlation function, so the probability that the delay corresponding to the maximum value of the cross-correlation function after path synthesis is the delay of the first path increases. Therefore, the first path can be judged more accurately, and the probability of generating an erroneous integer delay estimate is reduced.

[0059] (3) Direction of Arrival Estimation

[0060] The direction of arrival (DOA) is estimated using the estimated delay as follows, assuming the receiving array is a uniform antenna array with L elements and d antenna spacing. In the far field, signals from a given path arrive at each antenna in the antenna array at nearly identical angles, and the signal wavefront from any path arrives at the antenna array in a planar form. Therefore, the arrival time difference of signals from the same path at adjacent antennas is determined by the antenna spacing and DOA. Therefore, the delay difference between adjacent antennas on the i-th path of device u can be expressed as:

[0061]

[0062] Where Δτ u,i is the arrival time difference between adjacent antennas on the i-th path of device u, θ u,i is the arrival direction of the i-th path of device u, and c is the speed of light.

[0063] Given the delay of device u to antenna 1 along the i-th path, the delay of device u to antenna 1 along the i-th path is:

[0064] τ u,i,l =τ u,i,1 +(l-1)Δτ u,i (13)

[0065] According to the estimated delay time of the antenna array i-th path Given a cost function, a linear fit is performed on the estimated delay to determine the difference in delay estimates for all antennas in the antenna array:

[0066]

[0067] In order to minimize the cost function, the cost function is differentiated with respect to the two independent variables, and the operation expression is:

[0068]

[0069] in, Indicates the partial derivative operation. Substituting formula (14) into formula (15), we get:

[0070]

[0071] This gives the estimated time difference of arrival between adjacent antennas on the i-th path of device u:

[0072]

[0073] According to formula (12), and substituting formula (17) into it, we can get the estimated value of the direction of arrival of the i-th path of device u:

[0074]

[0075] Thus, the one-dimensional direction of arrival estimation of coherent signals applied to uniform linear array is completed.

[0076] like Figure 1 As shown, at the transmitter: select a random signal as the input signal, set the signal length to N = 1000, and the sampling frequency f s =1Hz, set the channel to multipath transmission channel P u =5, the attenuation of each transmission path is -4dB, -2dB, -6dB, -3dB, and -5dB respectively, and the delay time of each path is 30ns, 10ns, 50ns, 20ns, and 40ns respectively. (Channel parameter settings are only for pure research and simulation use. Actual parameter acquisition should be based on fitting the channel model with large data to ultimately determine the channel auxiliary parameters.)

[0077] Receiver: Select a uniform antenna array with L=5 elements and a signal frequency of Antenna spacing is half a wavelength The incident directions corresponding to different paths of the signal sent by the receiving end are 10°, 20°, 30°, 40°, and 50° respectively.

[0078] The noise changes at equal intervals between -10dB and 20dB, and is added to the received signal after normalization. The simulation is performed, and the PC-MUSIC algorithm is used as the comparison algorithm. The comparison results are shown in the figure below. Figure 2 As shown in the implementation flow chart Figure 3 shown.

[0079] (1) The transmitter first sends a high-power pilot signal to the receiver. The receiver obtains the multipath delay structure of the channel (4) based on the received pilot signal.

[0080] (2) The transmitter sends a normal pilot signal to the receiver, and calculates the cross-correlation function between the received signal and the transmitted signal according to formula (6);

[0081] (3) Sort the peak values ​​of the cross-correlation function in descending order to determine the candidate possibility of the first delay, calculate the cross-correlation function after the synthesis path according to formula (9), and then determine the shortest delay according to formula (11);

[0082] (4) Construct a cost function for time delay using formula (14). To minimize the cost function, the cost function is differentiated with respect to the two independent variables to obtain the estimated value of the arrival time difference (formula (17)).

[0083] (5) According to formula (18), the arrival direction is obtained from the arrival time difference estimate, and the one-dimensional arrival direction estimation of the coherent signal applied to the uniform linear array is completed. The specific implementation results are as follows Figure 2 The root mean square error (RMSE) of direction of arrival estimation is shown in the graph as the signal-to-noise ratio changes.

[0084] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0085] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating the direction of arrival of a coherent signal, characterized in that: include: The transmitter first sends a pilot signal with the target power to the receiver. The receiver obtains the multipath delay structure of the channel based on the received pilot signal. The transmitting end sends a normal pilot signal to the receiving end and calculates the cross-correlation function between the received signal and the transmitted signal; Sort the peak values ​​of the cross-correlation function in descending order to determine the candidate possibility of the first time delay, and calculate the cross-correlation function after the synthesis path to determine the shortest time delay; Construct a cost function for time delay. To minimize the cost function, take the derivative of the cost function with respect to the two independent variables to obtain an estimated value of the arrival time difference. The direction of arrival (DOA) is obtained from the estimated value of the arrival time difference, completing the one-dimensional DOA estimation of the coherent signal applied to the uniform linear array. Among them, Calculate the cross-correlation function after the synthesis path ,in, Representation device u No. i The sum of all path cross-correlation functions corresponding to the candidate possibilities is: Indicates the The delay of the path With the The delay of the path The delay difference, Indicates the The delay corresponding to the peak is represents the cross-correlation function between the received signal and the transmitted signal, Indicates the number of propagation paths; Depend on Determine the shortest delay estimate , Indicates the The delay corresponding to the peak is the shortest delay. represents the composite path cross-correlation function, and ; Depend on Constructing a cost function for latency ,in, For devices No. The arrival time difference between adjacent antennas along the path, Representation device Sent to antenna No. The estimated delay time of each path, Representation device Sent to antenna 1 The delay of the path, Indicates the number of antenna arrays receiving signals, Representation device No. The arrival time difference between adjacent antennas along a path.

2. The method according to claim 1, characterized in that Depend on Determine the device Multipath delay structure ,in, Indicates the The delay of the path With the The delay of the path The delay difference.

3. The method according to claim 2, characterized in that Depend on Calculate the cross-correlation function between the received signal and the transmitted signal , Indicates the n The signal size at a moment, n , m Belongs to the set [0, N -1], N is the signal length, for The conjugate of Indicates the The received signal at a moment.

4. The method according to claim 3, characterized in that Depend on Get an estimate of the time difference of arrival , Representation device Sent to antenna No. The estimated delay time of each path.

5. The method according to claim 4, characterized in that Depend on Get the device No. Estimated value of the direction of arrival of each path , Indicates that the antenna spacing is, It's the speed of light.

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