Spread spectrum communications

Fourier telescopy imaging is a recently-developed imaging method that relies on active
structured-light illumination of the object. Reflected/scattered light is measured by a large
“light bucket” detector; processing of the detected signal yields the magnitude and phase
of spatial frequency components of the object reflectance or transmittance function. An
inverse Fourier transform results in the image.
In 2012 a novel method, known as time-average Fourier telescopy (TAFT), was
introduced by William T. Rhodes as a means for diffraction-limited imaging through
ground-level atmospheric turbulence. This method, which can be applied to long
horizontal-path terrestrial imaging, addresses a need that is not solved by the adaptive
optics methods being used in astronomical imaging.
Field-experiment verification of the TAFT concept requires instrumentation that is not
available at Florida Atlantic University. The objective of this doctoral research program is thus to demonstrate, in the absence of full-scale experimentation, the feasibility of
time-average Fourier telescopy through (a) the design, construction, and testing of smallscale
laboratory instrumentation capable of exploring basic Fourier telescopy datagathering
operations, and (b) the development of MATLAB-based software capable of
demonstrating the effect of kilometer-scale passage of laser beams through ground-level
turbulence in a numerical simulation of TAFT.

Time Average Fourier Telescopy (TAFT) has been proposed as a means for obtaining high-resolution, diffraction-limited images over large distances through ground-level horizontal-path atmospheric turbulence. Image data is collected in the spatial-frequency, or Fourier, domain by means of Fourier Telescopy; an inverse two dimensional Fourier transform yields the actual image. TAFT requires active illumination of the distant object by moving interference fringe patterns. Light reflected from the object is collected by a “light-bucket” detector, and the resulting electrical signal is digitized and subjected to a series of signal processing operations, including an all-critical averaging of the amplitude and phase of a number of narrow-band signals.

In this thesis, we study the effect of Rice fading on the performance of Global Positioning System (GPS) receivers. The field-theoretic foundation of pseudo-random-noise (PRN) codes, their implementation, and their use in generating unique navigation messages in the GPS receiver is reviewed. The processing of the spread-spectrum signals within the digital delay locked loop (DDLL) in the receiver is also considered. In particular, we derive numerical expressions that can be easily evaluated for the probability error and the mean-time to lose-lock, for a DDL operating in an additive white gaussian noise (AWGN) channel in the presence of Rice fading. The results obtained generalize results in the literature for the Rayleigh fading environment.