Common solution-phase parameter (dry) algorithm for spatial spectra

A general solution of the phase-parameter algorithm

The solution phase parameter (dry) algorithm mainly has the time smoothing class, the Toep class, the Space smoothing Class 3 kinds.

1) The Time smoothing class is based on the fading characteristics of multipath channels, the data of the fast shot is divided into chunks, and the sum average of each block, in order to reduce the correlation of the usual wave, this kind of method needs a large number of fast beats, reduce the utilization of information, and the detection equipment to face the signal pulse is narrow, fast beat number small But the algorithm is suitable for any antenna array.

2) The TOEP algorithm restores the rank of the matrix by changing the structure of the autocorrelation matrix, summing the main diagonal, and then constructing a matrix conforming to the Toeplitz structure, which is only applicable to the uniform linear array .

3) The spatial smoothing algorithm can achieve the restoration of matrix rank by averaging the data received by the sub-array with the same spatial structure, and the algorithm loses the aperture of the antenna in the process of smoothing, and the number of smoothing times needs to be greater than that of the phase parameter (dry) signal; only for homogeneous matrices .

Two, virtual interpolation transform solution phase parameter

A-Principle introduction

It can be found from the algorithm introduction to the solution phase parameter (dry) that the space smoothing algorithm is only applicable to uniform array, but the interval of uniform array needs to be smaller than the minimum wavelength of the signal to be measured. In order to ensure the proper physical aperture of a certain antenna array and the non-uniform array scheme, a virtual interpolation transformation method is used to transform the Nonuniform line array into a uniform line array, or a plurality of translation arrays with the same structure .

Virtual interpolation transform is an approximate fitting of an array manifold with an angle range of two arrays, which can be multiplied by an offline calculation of the transformation matrix within each angular shard and the receiving data matrix. The angular shard size directly influences the precision of fitting.

(a)

(b)

Fig. 1 accuracy of angle slicing transformation

From FIG. 1 (a) It can be seen that the smaller the angle, the smaller the transformation error, the same size of the partition in different angle range of the transformation error, in order to ensure the consistency of the transformation error, usually the different angles of the non-uniform division, the size of the Shard with the increase of the angle range absolute value, 1 (b)

The wave direction of the phase parameter (dry) signal can be obtained by processing the transformed array by the space smoothing algorithm.

B-Simulation Analysis

1- One-dimensional array solution coherence capability simulation comparison

　　The algorithm of the space smoothing of the angle Shard virtual transformation to the homogeneous array is referred to as the virtual slicing method, and the method of transforming the received data into the same array's translation structure is called the virtual translation method. in the simulation of the antenna array in Figure 2, the structure used for example, the incident signal is the center frequency is 6GHz, the bandwidth is 20M, the fast shot number is 16, the incident direction of the random linear FM signal, not as the simulation variable SNR is 10dB, the SNR difference is 6dB, time delay points, The phase delay is subjected to Gaussian distribution random number, and the angle error of large signal-to-noise ratio is less than 0.5° as the judging criterion, and each variable point is simulated 200 times.

Figure 2 Circle

(a) signal-to-noise ratio-correct rate curve

(b) Fast shot number-correct rate curve

(c) Signal-to-noise ratio difference-correct rate curve

Fig. 3 The correct rate curve of the solution-phase-parameter (dry) algorithm

As can be seen from Fig. 3 (a), (b), (c), the music algorithm with the solution-to-phase (dry) processing can reach a higher correct rate when the condition is satisfied, and the accuracy rate of the virtual translation algorithm is relatively high.

Simulation of coherent capability of 2-two dimensional array

For the pattern shown in Figure 2, the center frequency of 18GHz, pulse width of 10US, FM slope 2M/10US Linear FM signal as the target signal, the sampling rate is 80MHz, the array of ultra-resolution direction-finding algorithm simulation.

1° non-coherent (dry) signal direction-finding performance

Using signal-to-noise ratio of 10dB, the center frequency of 5MHz, the difference between the power of 1dB three non-phase signal as an incident signal, the incident direction is ( -20,10) °, (-18.5, 12.5) °, (25,16) °, with 0.25° as the scanning step, simulation, 4.

Fig. 4 spatial spectra of 3 non-coherent signals

In Figure 4, it can be found that the spatial spectrum of the non-correlated signal in the array has a sharp spectral peak, accurate estimation of the direction of the wave, and less pseudo-peak value, pseudo-peak and real peak difference, can distinguish the adjacent two signals.

The direction-finding performance of 2° phase-parameter signal

Using the maximum Snr 20dB, the center frequency Difference 2kHz, the signal power difference 3dB three phase signal as the incident signal, the incident direction is ( -20,10) °, (-17.5, 12.5) °, (25,16) °, with 0.25° as the scanning step, simulation, 5, 6.

Fig. 5 spatial spectra of the coherent signals

In Figure 5, it can be seen that the direct application of music algorithm to the direction estimation, the peak is not sharp enough, and there is error Spectrum peak, the maximum power signal direction of the results of large difference.

This is because the basic algorithm of music is based on subspace decomposition, and the correlation matrix of coherent signal pairs is no longer diagonal and the matrix rank decreases, and the direct subspace algorithm is no longer valid.

Fig. 6 spatial spectra of coherent signal smoothing

Figure 6 in the smooth after a better resolution of the direction of the signal, the spectral peak sharp, compared to non-phase parameter signal, spectral peak graph slightly fluctuation, but does not affect the direction of the results, to the high accuracy of the wave.

Common solution-phase parameter (dry) algorithm for spatial spectra