# A trade-off analysis of Fully Focused SAR processing algorithms for high PRF altimeters

**CoAuthors**

**Event: **2018 Ocean Surface Topography Science Team Meeting

**Session: **Instrument Processing: Measurement and Retracking

**Presentation type: **Type Poster

The Fully Focused (FF) processing of high PRF radar altimeter science data is a new concept recently proposed in [1] as a way to focus nadir-looking altimeter echoes for an illumination time longer than the extent of a burst.

Under the assumption that the altimeter preserves the coherency of the transmitted pulses during, at least, a target illumination time, it is possible to focus in the along-track and perform an interburst coherent integration potentially during the entire illumination time of a scatterer on the surface. This way, the following advantages are achieved: (i) the along-track resolution can be increased to its theoretical limit, that is half the physical antenna length, (ii) the highest number of looks per time unit is reached and so a higher speckle reduction can be obtained by reduction of resolution.

The FF algorithm proposed in [1] is based on the time-domain Back-Projection (BP), that aims at the progressive compensation of the different phase terms in the impulse response function. BP is a robust algorithm to focus altimeter data; however, the processing is quite cumbersome because each ground sample requires ad-hoc computation and correction of the phase terms that are function of the relative sensor-target distance and so of the local geometry.

The purpose of this abstract is to present a trade-off analysis among time-domain Back-Projection and different frequency-domain focusing algorithms, that are able to reduce the computational complexity with

respect to the BP and without sensibly reducing the quality of the focused data. The trade-off analysis was performed by analysis of simulated data for closed and open burst configurations as well as of in-orbit CryoSat acquisitions. The results of this analysis allowed to verify that using frequency-domain focusing algorithms it is possible to reduce the number of complex multiplications by three order of magnitude with respect BP while preserving the expected shape of the 2D focused Impulse Response Function (see the attached figure that refers to simulated data).

[1] A. Egido and W. H. F. Smith, “Fully focused sar altimetry: Theory and applications,” IEEE Trans. Geosci. Remote Sens., vol. 55, no. 1, pp. 392–406, Jan 2017.

Under the assumption that the altimeter preserves the coherency of the transmitted pulses during, at least, a target illumination time, it is possible to focus in the along-track and perform an interburst coherent integration potentially during the entire illumination time of a scatterer on the surface. This way, the following advantages are achieved: (i) the along-track resolution can be increased to its theoretical limit, that is half the physical antenna length, (ii) the highest number of looks per time unit is reached and so a higher speckle reduction can be obtained by reduction of resolution.

The FF algorithm proposed in [1] is based on the time-domain Back-Projection (BP), that aims at the progressive compensation of the different phase terms in the impulse response function. BP is a robust algorithm to focus altimeter data; however, the processing is quite cumbersome because each ground sample requires ad-hoc computation and correction of the phase terms that are function of the relative sensor-target distance and so of the local geometry.

The purpose of this abstract is to present a trade-off analysis among time-domain Back-Projection and different frequency-domain focusing algorithms, that are able to reduce the computational complexity with

respect to the BP and without sensibly reducing the quality of the focused data. The trade-off analysis was performed by analysis of simulated data for closed and open burst configurations as well as of in-orbit CryoSat acquisitions. The results of this analysis allowed to verify that using frequency-domain focusing algorithms it is possible to reduce the number of complex multiplications by three order of magnitude with respect BP while preserving the expected shape of the 2D focused Impulse Response Function (see the attached figure that refers to simulated data).

[1] A. Egido and W. H. F. Smith, “Fully focused sar altimetry: Theory and applications,” IEEE Trans. Geosci. Remote Sens., vol. 55, no. 1, pp. 392–406, Jan 2017.