Phase measurement accuracy in noise waveform synthetic aperture radar

Detection of small changes in natural formations and human-made constructions is a promising application of synthetic aperture radar (SAR). This paper deals with a specific radar, which is a ground-based SAR using noise waveform. Being fully coherent, SAR provides both phase and amplitude information for every pixel in the mapped area. This gives rise to the possibility of comparing phases between the images taken from the same position at different times in order to extract information about the changes that have occurred between subsequent radar measurements. Such a technique, called coherent change detection (CCD), allows changes of a subwavelength size to be detected. The use of a noise waveform for sounding ensures high electromagnetic compatibility and interference immunity. Moreover, it enables long integration time in the detection stage. However, the random nature of probing signals used in noise radars leads to randomness of the output signals and the preservation of residual fluctuation in the images generated. This random residual, along with external noise, influences the overall accuracy of the phase measurement in noise radar. In this paper, the theoretical and experimental investigation of this specific influence of noise on the precision of phase measurements is presented. The theoretical part of the paper is focused on the estimation of the Cramer-Rao lower bound for the phase measurements using both statistical theory and geometrical interpretation of complex signals. In the experimental part, these findings are verified with dedicated measurements of a metallic sphere displacement, carried out with the help of a ground-based noise waveform SAR.