Computation of Signal Gain and Noise Gain of a SAR Processor

Kurzfassung

For the applicability of a SAR system as a radiometric measurement system, the knowledge of its end to end gain, from the raw data acquisition to the ready-made SAR image, is a prerequisite. In the process, the computation and desirably the normalization of the SAR processor gain is a task which should not be underestimated, as several processing steps and a multitude of influencing variables has to be considered. In order to satisfactorily solve this task in the framework of SAR processor development, each processing step has to be analyzed thoroughly whether and by which factor it changes the signal power. Another important characteristic with respect to radiometry is the noise figure in the focused SAR image. Here too, the computation of the processor gain is a major issue. However, echo signal and the receiver noise, the latter might be evaluated on base of so-called noise pulse recorded before and after the actual datatake, differ in their spectral shape. Therefore the effect of a signal processing step on both, signal and noise, is in general different and has to be analyzed separately. As the computation of signal and noise gain coincide in their methodology, both aspects shall be jointly discussed in the presentation. Using the example of the Extended Chirp Scaling algorithm which is the basis for the TerraSAR-X Multimode SAR Processor (TMSP), the attention shall be turned to which kinds of processing steps might affect signal and noise gain and how to quantify the effect. A fundamental design decision is whether a SAR processor shall be power or energy normalized. The former has the advantage that brightness and saturation degree of the SAR image do not depend on the pixel spacing in azimuth and range. The squared amplitude of a pixel corresponds to the radar backscatter coefficient. The distinction between power and energy normalization gains relevance for processing steps like spectral zero padding which originally keeps the signal energy but not the power. Here, power normalization necessitates an adequate amplification of the signal. During the range pre-compression step the recorded echo signal is correlated by the complex conjugate signal of a chirp pulse replica. Therefore, the squared chirp pulse energy occurs in the filtered signal because the energy originates once from the transmitted radar pulse and once from the used replica. Accordingly, the signal amplitude has to be attenuated by the integral of the squared amplitude of the chirp (i.e. the chirp energy). Band-pass filters are one potential source for differences between signal and noise gain provided that the bandwidth of the echo signal and of the noise pulses that estimate the receiver noise are different. In this case the band-pass filter removes different portions of power from signal and noise. Another processing step which influences the spectral shape of signal and noise is the azimuth antenna pattern removal which equalizes the SAR echoes along the aperture and intentionally leads to an almost rectangular spectrum of the band limited echo signal. In contrast, no antenna pattern originally occurred in the noise signal so that exactly this processing step impresses the reciprocal antenna pattern to the noise spectrum, amplifying the edges of the spectrum. Once a colored noise spectrum resulted, its spectral shape has to be considered in the processing gain analysis of all subsequent processing steps. In particular, this refers to spectral weighting (e.g. by a Hamming window). A normalization of the applied window function w.r.t. a rectangular spectrum is adequate for the SAR signal. In contrast, the noise gain results as weighted average of the window function, where the weighting function is the spectrum of the colored noise. Due to the importance of the SAR processor for the overall SAR system calibration, a correct normalization is indispensable. It is required from the first days of the mission.