Wide Area, Fine Resolution Sar from Multi-aperture Radar Arrays

Wideband Multi-static radar provides scattering observations over frequency, time, and space, thus allowing for measurements in delay, Doppler, and angle-of–arrival (i.e., spatial frequency). Stationary targets ambiguous in delay and/or Doppler cannot be physically collocated, so that their spatial responses will not generally be ambiguous or even significantly correlated. As a result, a multi-static radar can be designed such that the sensor space-time-frequency ambiguity function produces no large (e.g., grating) lobes over a large illuminated area. The size of this “unambiguous” imaging area is dependent on the number of spatial apertures implemented in the wide band design, increasing in size as the number of spatial elements is increased. The constraint on this design is the value of the measurement clutter rank, as compared to the sensor measurement dimension. Essentially, the number of illuminated resolution cells cannot exceed the number of independent measured samples. Additional spatial elements (apertures) can increase the measurement dimension without affecting clutter rank. If a sufficient number of spatial elements are available, a SAR image can be formed for a distributed target of any clutter rank (i.e., resolution and image area). It can be shown that a necessary condition is that the total aperture area must exceed the minimum aperture area condition imposed on traditional (single aperture) SAR. However, in a multiaperture design, this total area does not determine, or limit, the extent of the illuminated area. The size of each individual element sets the illumination area, and thus adding spatial elements to a multi-static SAR design will generally improve sensor performance, without altering the illumination area or resolution size. For contiguous spatial arrays, we find that SAR images can be formed by simply extending traditional correlation processing over space and time. For sparse, random arrays, we find that SAR image formation requires a MMSE (i.e., Wiener) estimator. The computational cost of this linear estimator can be reduced by either implementing a reduced rank version, or by applying an iterative Wiener processor (i.e. a Kalman filter). For all these SAR processors, we find that image quality improves as the number of spatial elements is increased.