Digital Beamforming and Non-Uniform Displaced Phase Centre Sampling in Bi- and Multistatic SAR Gerhard Krieger, Nicolas Gebert, Alberto Moreira Microwaves and Radar Institute, German Aerospace Centre (DLR), Oberpfaffenhofen, Germany Abstract The displaced phase centre (DPC) technique will enable a wide swath SAR with high azimuth resolution. In a classic DPC system, the PRF has to be chosen such that the SAR carrier moves just one half of its antenna length between subsequent radar pulses. Any deviation from this PRF will result in a non-uniform sampling of the syn- thetic aperture. This paper shows that an unambiguous reconstruction of the SAR signal is also possible in case of such a non-optimum PRF. For this, an innovative reconstruction algorithm is derived, which enables a recov- ery of the unambiguous Doppler spectrum also in case of a non-uniform sampling of the synthetic aperture. This algorithm will also have a great potential for multistatic satellite constellations as well as the dual receive an- tenna mode in Radarsat 2 and TerraSAR-X. 1 Introduction Wide swath imaging and high azimuth resolution pose contradicting requirements on SAR system design. To overcome this fundamental limitation, several innova- tive techniques have been suggested which use multi- ple receiver apertures to acquire additional samples along the synthetic aperture. The apertures may be either on a single platform like in the classical Dis- placed Phase Centre (DPC) technique [1]-[6] or on different platforms [7]-[9] leading to a multistatic SAR where the size of each individual receiver is re- duced. Fig. 1 shows one example for each scneario, where a single transmitter illuminates a wide swath and n sub-apertures record simultaneously the scat- tered signal from the illuminated footprint. Under ideal conditions, this will allow for a reduction of the PRF by a factor of n without rising azimuth ambigui- ties. This reduction of the azimuth sampling rate be- comes possible by a coherent combination of the in- dividual receiver signals where the ambiguous parts of the Doppler spectra cancel each other. Note that such an ambiguity suppression can also be regarded as digital beamforming on receive where nulls in the joint antenna pattern are steered to the ambiguous zones. For optimum performance, the along-track dis- placement of the sub-apertures i={2,...,n} relative to the first receiver (i=1) should be chosen as Z k k n 1 i PRF v 2 x x i i 1 i ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − ≈ − (1) which will result in a uniform sampling of the re- ceived SAR signal. In this equation, PRF is the pulse repetition frequency of the transmitter and v is the ve- locity of the SAR carrier. Note that for a multistatic constellation the k i may be different for each receiver, which enables a great flexibility in choosing the along-track distance between the satellites. In a single platform system, all k i will be zero. Since the sub- aperture distance and the platform velocity are fixed in this case, a specific PRF will be required: x n v PRF ∆ ⋅ ⋅ = 2 (2) where we assume an antenna with n sub-aperture ele- ments separated by ∆x=x i+1 -x i . The PRF in a single- platform DPC system has thus to be chosen such that the SAR platform moves just one half of the total an- tenna length between subsequent radar pulses. How- ever, such a rigid selection of the PRF may be in con- flict with the timing diagram for some incident angles. It will furthermore exclude the opportunity to use an increased PRF for improved azimuth ambiguity sup- pression. v Rx 2 Rx 3 Rx 4 Rx 5 Rx 1 Tx v 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 Rx 1 Rx 2 Rx 3 Tx Fig. 1: Multiple aperture sampling for a single platform system (top) and a distributed satellite array (bottom). The effective phase centres are shown as squares. Solid squares correspond to samples of the synthetic aperture for the illustrated Transmitter (Tx) and receiver (Rx) positions. The dotted squares are for previous and sub- sequent samples assuming an appropriately chosen PRF.