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Multichannel synthetic aperture radar (SAR) in azimuth can resolve the contradiction between high resolution and wide swath faced with traditional SAR imaging. However, channel errors will degrade the performance of imaging. This paper compares the performances of four channel error estimation algorithms under different clutter distributions and SNR conditions. Further, explanations are given for performance differences of the four algorithms, which provide evidence for method selection in engineering applications.

Conventional SAR system suffers from the limitation of achieving high resolution and wide swath (HRWS) simultaneously [

This paper mainly deals with the problem of channel errors in multi-channel HRWS SAR systems. In recent years many algorithms have been put forward to estimate the channel errors. The four main methods are time- domain correlation method (TDCM) [

The geometric model of an actual multi-channel SAR system is shown in

Taking the channel errors caused by several factors into account [

where

Since channel magnitude errors can be estimated and compensated by simple channel balancing [

The TDCM is presented in [

where

From the principle of the average cross correlation method in the baseband Doppler centroid estimation, there is

where

Assume that the first channel is the reference channel, phase error of the mth channel is

The OSM is presented in [

Channel phase errors are estimated by minimize the cost function:

where _{n} corresponds to the noise subspace, whose column vectors are noise eigenvectors.

Let the first channel be the reference channel, and denote

where.

The SSCM is expressed in [

Let

According to the uniqueness of orthogonal projection operator, we can get

Let

The APM is expressed in [

Let

Then the relative phase error of the mth channel can be expressed by

In this section, experiment is done to compare the performance of the above mentioned four algorithms. The parameters are listed in _{M} is the pulse repetition frequency, and

To compare the four methods discussed above, we use two indexes: estimation deviation and the maximum azimuth ambiguity-to-signal ratio (AASR_{MAX}). Estimation deviation means the bias between the real phase error and the estimated phase error. AASR_{K} is the ratio of power of kth (k = 1 - 8) ambiguity component to power of the ambiguity free signal after phase error estimation and compensation [

Besides, AASR_{MAX} is the maximum of AASR_{K} (k = 1 - 8).

In this section, clutters are assumed to be Gaussian distribution, and SNR varies from 0 dB to 20 dB. The estimation deviations of eight channels are illustrated in _{MAX} are listed in

In engineering application, clutter scenario does not obeyideal Gaussian distribution. Log-normal distribution, Weibull distribution and K-distribution are mainly considered as sea clutter model when HRWS SAR detects the seasurface.

This section mainly compares the performance of the four algorithms when clutter obeys Log-normal distribution, Weibull distribution and K-distribution, respectively. The estimation deviations of eight channels under SNR = 0 dB are illustrated in _{MAX} for different clutter distributions and different SNR are listed in

Without eigenvalue decomposition and matrix inversion, the computational load of TDCM is the lowest. However, TDCM works worse than the other three algorithms under all simulated clutter distributions and SNR, for the deviation is cumulative when the phase error accumulates.

APM also does not need eigenvalue decomposition and matrix inversion, which is characterized by light computational load. But this method only applies to uniform distribution scenes. When the clutter obeys Weibull distribution and K-distribution, it works worse than OSM and SSCM under low SNR conditions (0 - 10 dB). While under high SNR conditions (>10 dB), the differences of APM, OSM, and SSCM are very small. The frequency spectrums of Weibull distribution and K-distribution are not quite homogeneous, so the performance of APM deteriorates when the noise is relatively large. For Gaussian distribution and Log-normal distribution clutters, the scenarios are homogeneous, so APM works as well as OSM and SSCM.

M | PRF_{M} (Hz) | |||
---|---|---|---|---|

8 | 12.16 | 0.054 | 1.054 × 10^{4 } | 7.587 × 10^{3} |

Performance indicator | SNR (dB) | TDCM | OSM | SSCM | APM |
---|---|---|---|---|---|

Maximum estimation deviations (degree) | 0 | −4.5426 | 1.3959 | 1.3959 | −2.0650 |

5 | −4.2495 | 0.8181 | 0.8181 | −0.9042 | |

10 | −4.0334 | 0.4654 | 0.4654 | 0.4852 | |

20 | −3.2007 | −0.2280 | −0.2280 | −0.2215 | |

AASRMAX (dB) | 0 | −38.0153 | −42.6855 | −42.6855 | −39.9564 |

5 | −37.3947 | −45.9853 | −46.3163 | −44.2362 | |

10 | −38.2960 | −49.5419 | −49.5419 | −50.0598 | |

20 | −39.4288 | −51.4076 | −51.4076 | −51.3883 |

Clutter Distribution | SNR(dB) | TDCM | OSM | SSCM | APM |
---|---|---|---|---|---|

Log-normal distribution | 0 | −1.8387 | −1.7378 | −1.7378 | −1.7966 |

10 | −1.1058 | −0.5793 | −0.5793 | −0.5430 | |

20 | −0.8439 | −0.2104 | −0.2104 | −0.1943 | |

Weibull distribution | 0 | −2.2719 | 2.9642 | 2.9642 | 4.3430 |

10 | 3.3355 | 0.8791 | 0.8791 | 1.0050 | |

20 | 4.2251 | 0.2599 | 0.2599 | 0.2721 | |

K-distribution | 0 | 5.6282 | −2.1395 | −2.1395 | −3.5778 |

10 | 4.7262 | −0.7711 | −0.7711 | −0.8575 | |

20 | 3.9462 | −0.2767 | −0.2767 | −0.2820 |

Clutter Distribution | Before error compensation | SNR (dB) | TDCM | OSM | SSCM | APM |
---|---|---|---|---|---|---|

Log-normal distribution | −25.1927 | 0 | −43.2373 | −46.0874 | −46.0874 | −42.6242 |

10 | −45.7383 | −50.1350 | −50.1350 | −50.4650 | ||

20 | −46.9298 | −51.5807 | −51.5807 | −51.4993 | ||

Weibull distribution | −25.1927 | 0 | −35.1346 | −38.9284 | −38.9284 | −33.5966 |

10 | −39.1445 | −47.2660 | −47.1231 | −46.1919 | ||

20 | −40.1673 | −51.5414 | −51.5371 | −51.7242 | ||

K-distribution | −25.1927 | 0 | −36.2404 | −39.2750 | −40.0067 | −34.1553 |

10 | −40.6513 | −46.1806 | −46.6014 | −42.3101 | ||

20 | −40.3331 | −50.9115 | −50.5628 | −49.9990 |

The OSM and SSCM use the signal subspace and noise subspaces after eigenvalue decomposition of the correlation matrix, respectively. Assuming L Doppler bins are used to estimate the phase errors, the computational load of OSM and SSCM are 2 LM^{3} and LM^{3} + M^{3}, respectively. Their performances are best under all simulated clutter distribution and SNR conditions.

In application, when the scenes are homogeneous, such as agricultural and natural areas, APM can be chosen to estimate the channel phase errors for its accuracy and light computational load. In contrast, for heterogeneous scenes such as urban or sea surfaces, OSM and SSCM are suitable for phase error estimation.

In this paper, four channel error estimation methods for multichannel HRWS SAR system are compared under different SNR conditions and clutter distributions. From the simulation results, we can conclude that the estimation deviations are not relevant to real phase error distribution, and only relate to SNR and the clutter distribution. In addition, the performance of time-domain correlation method is poorer than the other three methods. For Doppler-domain methods, the APM works as well as the OSM and SSCM for homogeneous clutter scenes, but worse than OSM and SSCM for heterogeneous surfaces. OSM and SSCM work best for all clutter scenes.

Tingting Jin,Xiaolan Qiu,Donghui Hu,Chibiao Ding, (2016) Channel Error Estimation Methods Comparison under Different Conditions for Multichannel HRWS SAR Systems. Journal of Computer and Communications,04,88-94. doi: 10.4236/jcc.2016.43014