Digital Beamforming for HRWS-SAR Imaging System Design, Performance and Optimization Strategies Nicolas Gebert, Gerhard Krieger, Alberto Moreira Microwaves and Radar Institute, DLR (German Aerospace Center), Oberpfaffenhofen, Germany Email: nico.gebert@dlr.de Abstract - Multi-aperture synthetic aperture radar (SAR) systems in combination with an appropriate coherent processing of the individual aperture signals enable high resolution wide swath (HRWS) SAR imaging [1]-[8]. An innovative reconstruction algo- rithm for such a digital beamforming on receive was presented in [9]-[12] that allows for HRWS even in case of a non-uniformly sampled data array in azimuth. This paper will compare this al- gorithm to different azimuth processing strategies regarding their performance in dependency of the overall sampling. Further, op- timization strategies are discussed to maximize the system’s per- formance by pattern tapering on transmit and “Pre-Beamshaping on Receive” networks that allow for pattern tapering on receive and adaptively adjust the virtual sample positions. 1 Introduction 1.1 Multi-Aperture Sampling Several innovative techniques using multiple receive apertures (‘Rx’) have been suggested to overcome the inherent limita- tions of conventional SAR to perform HRWS imaging [1]-[8]. For optimum performance the relation between sensor velocity v and the along-track offsets Δx of the N sub-apertures has to result in equally spaced effective phase centers thus leading to a uniform sampling of the received signal (cf. Fig. 1, left). This requires the following relation: x N v PRF opt Δ ⋅ ⋅ = 2 (1) If a non-optimum PRF is chosen, the gathered samples are spaced non-uniformly. This requires a further processing step after down-conversion and quantization of the multi-aperture azimuth signal before conventional monostatic focusing algo- rithms can be applied. For this, the individual aperture signals are regarded as independent Rx channels (cf. Fig. 1, right). The purpose of the azimuth processing is to combine the N chan- nels, each of bandwidth N·PRF but sub-sampled with PRF, to obtain a signal effectively sampled with N·PRF=PRF eff . Thus the Nyquist criterion is fulfilled in average after the processing, which yields - ideally - an output signal that is free of aliasing. 2 Azimuth Processing 2.1 Algorithms In the following, three more methods to process the azimuth signal of a multi-aperture signal are presented and compared to the „reconstruction algorithm“. 1) Displaced Phase Center Antenna (DPCA): This technique proposes to recover the azimuth signal by interleaving the sam- ples of the different Rx channels without any further process- ing [1]. Consequently, the stringent timing requirement of Eq. (1) has to be fulfilled to obtain a signal that is equivalent to a monostatic signal of N times the PRF. In any other case the sample positions deviate from the ideal positions, but they are treated as if the signal was sampled uniformly. 2) Phase Correction: This method takes the properties of the SAR signal into account. It is based on an analysis of the multi-aperture signal’s phase compared to the phase of a monostatic and uniformly sampled signal. This yields a phase difference depending on Doppler frequency. By applying an appropriate phase correction to the multi-aperture data, its phase is adjusted in a way such that the resulting phase corre- sponds to the monostatic and uniformly sampled signal. [3] 3) The Reconstruction Algorithm is based on solving a sys- tem of linear equations to unambiguously recover the formerly aliased azimuth spectrum. A detailed derivation and investiga- tion can be found in [9]-[12]. As already indicated in [9], this method comprises the approach in 4) and leads to nearly iden- tical results in a single platform system. 4) Null-Steering: This space-time approach is based on adap- tively adjusting the weighting coefficients of the azimuth chan- Rx 1 Rx 3 Rx 4 Rx 5 Tx Rx 2 1 2 3 4 5 x 1 2 4 5 t i-1 t i t i+1 2 Δx Δx Rx 1 Rx 3 Rx 4 Rx 5 Tx Rx 2 1 2 3 4 5 x 1 2 4 5 t i-1 t i t i+1 2 Δx Δx Rx 1 Rx 3 Rx 4 Rx 5 Tx Rx 2 1 2 3 4 5 x 1 2 4 5 t i-1 t i t i+1 2 Δx Δx N·PRF (aliasing-free) Mixing A/D Conversion Digital Signal Processing Focusing & Higher-Level Processing A D A D Monostatic SAR Processing Azimuth Processing . . . N channels SAR Image PRF (sub-sampled) N·PRF (aliasing-free) Mixing A/D Conversion Digital Signal Processing Focusing & Higher-Level Processing A D A D Monostatic SAR Processing Azimuth Processing . . . N channels SAR Image PRF (sub-sampled) Fig. 1: Left: Multi-Aperture System consisting of 5 Rx apertures and a separate Tx antenna and corresponding virtual sample positions for subsequent pulses t i-1 , t i , t i+1 . Right: Block diagram of the processing. After down-converting and digitizing every aperture’s signal, the azimuth processing combines N aliased channels to one output signal with N times the original sampling ratio.