## Algorithm of Synthesizing Radar Scene Images in Passive SAR being the Part of Airborne Bi-static Radar System of General Configuration |

Alekseev S.B., Lepekhina T.A., Likhansky S.G., Nikolaev V.I. (Joint Stock Company “Radio Engineering Corporation “Vega”) |

Abstract - The paper is devoted to the problem of radar images synthesis in airborne bi-static look of improved generality – the carriers (planes) of bi-static pair have the constant (different) velocity vectors and fly on constant (different) heights with arbitrary angle relatively each other. (Partial case of this situation – one of carriers has zero velocity and is being Earth-based radar station.)
The bi-static analog of Spotlight Mode considered in the paper. The active SAR (SAR-1) en-lights the unchangeable piece of Earth surface (scene), the ray of passive SAR (SAR-2) is being directed into Earth projection point of active SAR-1 ray, i.e., into scene center. The both SAR’s are being supposed to have the possibility of electronic ray steering and fast flexible formation of emitting direction diagram (being, for example, the Active Phased Aerial Arrays).
The formation of digital radio-hologram process flows in passive SAR-2.
The hologram is being supposed to be compressed by range (initially, before synthesis).
The following two themes are considered in detail in this paper:
1) The a-prior formation of secondary data arrays, being necessary for image synthesis, based on primary navigation data and on input information about demanded geometric resolution of image.
2) The image synthesizing algorithm, for which are being considered both the general structure with appropriate theoretic explanations and the detailed step-by-step illustration.
In frames of the first theme (a-prior processing) are being solved the following problems:
a) Exploration of dependence of bi-static pair resolution abilities from on-Earth target position relatively current position of carriers with account of their movement.
b) Calculation the time interval of synthesizing, providing the demanded resolution of image.
c) The bi-static look mathematical reduction to side mono-static look using the analysis of summary slant range migration law {SAR-1 – target – SAR-2} and it’s variations (provided by target shifts) and also using the compensation of linear part of migration law (for scene center).
d) Construction of inverse geo-coding law, mapping horizontal scene coordinates into trajectory connected coordinates (range and way) and taking place in formula of synthesizing integral operator, which transforms the hologram into the image.
e) Calculation (in form of Taylor series by radial velocity) of Legendre Transform of migration law and of it’s variations up to second degree (provided by target shifts within scene).
By usage of received results are being calculated the coefficient arrays defining (by scene coordinates up to second degree) the set of spectral-domain reference functions (references) for synthesizing image array being written in scene coordinates (not along-way ones). Using the obtained formulae, the integral operator of synthesizing can be reduced to the form, adapted to fast algorithmic realization.
In frames of the second theme (synthesizing algorithm) are being solved the following problems:
a) Obtained and explored the formulae of non-linear transform of spectral variables reducing (approximately, «by modulo» second-degree variations of reference phases by scene coordinates) the synthesizing integral operator to simple form (allowing fast algorithmic realization) – the form of Inverse Fourier Transform (two-dimensional).
b) The exact and simple algorithmic realization of above-mentioned spectral domain transform is found (Stolt Transform generalization). This transform allows step-by-step representation by limited number sequence of one-dimensional operators of scaling and shift. (Only one scaling is non-linear – the others are linear ones and each of them allow simple realization by means of Fourier analysis.)
c) The problem of account second variations (by scene coordinates) of reference phases is solved by means of term-by-term Inverse Fourier transformation of appropriate fast-convergent binary series.
The step-by-step imitational computer modeling of the all above-mentioned algorithms have been fulfilled for different bi-static look configurations, wave bands and demanded resolutions. The correctness of all described in the paper mathematical models was proved by means of this modeling.
The high-quality and high-resolution (up to sub-meter and decimeter) images have been received as a result of this modeling. |

Keywords - Fourier transform, Legendre transform, Taylor series, direct convolution, binary series, bistatic look, synthetic aperture radar. |

## Алгоритм синтеза радиолокационного изображения наземной обстановки в пассивном РСА при самолетном бистатическом обзоре общего вида |

Алексеев С.Б., Лепёхина Т.А., Лиханский С.Г., Николаев В.И. (АО "Концерн радиостроения "Вега", г. Москва) |

Аннотация - Предложен алгоритм синтеза изображения наземной обстановки в пассивном радиолокаторе при самолетном бистатическом обзоре общей конфигурации – носители летят с произвольными скоростями под произвольным углом друг к другу. При этом рассмотрен аналог прожекторного режима применительно к бистатической паре. Дано изложение как предварительных вычислений массивов вторичной информации для синтеза по первичной навигационной информации, так и всех этапов алгоритма. |

Ключевые слова - преобразование Фурье, преобразование Лежандра, прямая свертка, бинарный ряд, бистатический обзор, радиолокатор с синтезированной апертурой. |