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Humankind has made remarkable progress in the area of space exploration and a cost-effective method for exploring our space frontiers involves radar imaging.  As our deep space frontiers continue to expand, additional demands are made of these systems.

Traditional imaging systems involve gigantic reflector (“dish”) antennae which can be steered to focus on a particular area of interest.  A classic example, NASA’s Deep Space Network employs reflectors as big as 70m with effective isotropic radiated power (EIRP) levels of 146 dBm (~ 0.4 TW) at X-band (7.2 GHz).  These levels are close to the maximum operational values – larger antennae can not be easily steered and higher power levels would result in tremendous losses.  However, it is estimated that that EIRP requirements for the year 2030 would be of the order of 159 dBm (~ 0.8 TW) at X-band.  The only feasible solution toward obtaining such up-link powers lies in using an array of moderately sized antennas which would provide substantial cost savings, reliability and extendibility.  Using a widely dispersed array has the effect of simulating an enormous “synthetic” aperture which in turn leads to a better resolution.

As with any antenna array, to maximize gain, the phase centers of the various elements with respect to each other needs to be known to a fraction of a wavelength.  Due to the wide area over which antennas could be spread, and the high frequency, the only feasible technique to calculate these relative phases is to have the array focus on a point target in the far field and form what is known as an interferogram.  The point target should “look” the same to every element and the system can thus be phase-calibrated.

Unfortunately, for such a large array, the far field is very far (>60,000 Km) and putting a small visible target there is very tough.  One option is to use a satellite in the near-field and then perform mathematical manipulations to calibrate it for the far-field but this method fails due to the uncertainty of the exact position of such satellites.  The other method, proposed in [1], involves using a natural satellite – the Moon – as a calibration target.  However, the Moon is very large to be treated as a point target (the Moon would look different from different antennas spaced apart) and the problem is complicated into focusing on a small portion of the Moon – small enough to be treated as a point target.  This is achieved by having several moderately sized transmitter antennas (<10m diameter each) which have over-lapping large illuminating footprints which cover nearly the entire lunar surface, and one large receiver (~34m) which limits the footprint “seen”.  Even this reduced footprint is too large to be treated as a point target and it needs to be pixilated such that each pixel can be treated as a point target. As shown in the figure, for antennas 1 and 2, the difference in look-angles for a particular pixel is negligibly small.

The small receiver footprint is resolved into pixels in the range direction by time-delays of the echoes.  This can be understood by dividing the Moon into concentric rings – each of these rings provide the same time-delay (assuming the moon to be a perfect sphere).    In the cross-range direction, the relative motion between the earth and the moon is exploited to resolve the image.  The moon is divided into semi-annuli and points on any particular annulus provide the same Doppler shift.  By filtering the received image for different frequency shifts, we can “slice” the moon up in the cross-range direction.  As shown in the image, an annulus of constant time delay and a semi-annulus of constant Doppler shift intersect in two points (A and B) and this ambiguity is avoided by ensuring that the receiver focuses on one hemisphere at a time.

A significant challenge lies in separating each transmitted signal from

(a)    Reflection from every other pixel, and,

(b)   Every other transmitted signal and its reflections.

This is achieved by coding the transmitted signals using codes commonly used in mobile phone communication (Code-Division Multiple Access  or CDMA) known as Pseudo-Noise (PN) sequences.  The receiver has multiple correlators (matched filters) – one for each transmitter – storing identical copies of the codes and the received signal is decoded.  These codes possess the properties of high autocorrelation and low cross-correlation.  There are several such codes and an investigation by the author [2] found that using circularly shifted maximal length sequences (m-sequences) – a class of PN sequences –provided superior performance.  Comparing the different received signals from a common pixel, the relative phases of the elements can be determined and the array thereby calibrated.  Once calibrated, the array can then be used to focus on more distant celestial bodies and provide us with spectacular images.

References:

[1] F. Wang, K. Jumani and K. Sarabandi, University of Michigan, Ann Arbor, “Uplink Calibration for Ground Array of Large Reflectors Using Lunar InSAR Imagery”, Technical Report by the University of Michigan, Ann Arbor, for NASA JPL, July 2006

[2] K. Jumani, K. Sarabandi, University of Michigan, Ann Arbor, “An Investigation of PN sequences for Multistatic SAR/InSAR Applications”, IEEE IGARSS 2007 Symposium, Barcelona, Spain