DSP

This is a micro repository that will contain common digital signal processing techniques often found in GNSS signal processing. Code will be in C and C++. This includes Gold Code assignments for Pseudo-random number generation, cross correlation, and invoking use of Fast Fourier Transform. Although there is a quick example FFT.c which uses the famous fftw3 library, I've preferred to use LiquidDSP, which is a compact end-to-end DSP & wireless communications toolbox in pure C, and my personal favorite. liquiddsp also has its own wrapper for fftw3.

The gps.c example, is a complete example that simulates a transmitted GPS signal, that is received by an ADC that samples at 20 MSps, with attention paid to the Coarse Acquisition code (C/A) code only, Therefore, the digital input data (C/A code) has a frequency of 1.023 MHz, for simplicity, the carrier frequency is taken to be 2 MHz, and the CA code is made to be repeated (stretched) at 8 * 1.023e6 MSps These parameters are obtained theoretically from the relation:

$f_o = f_i - n(f_s / 2) ~= f_s / 4$ This has to do with undersampling vs oversampling, which isn't crucial, since at the end carrier wipeoff and despreading will only leave the nav data. Please see https://github.com/psas/gps/blob/master/docs/_01_Gold_Codes.ipynb for a better discussion on CA code. The output is the plot PSD.pdf which is the power spectrum of a carrier wave of an GPS L1 signal BPSK modulated with the PRN code along with the 50 Hz nav data for a given a satellite, and PSD_AWGN.pdf is the recreated PSD with Complex Additive White Gaussian Noise typically introduced in wireless channel modeling.

For properly compiling gps.c, simply invoke gcc gpc.c -o main -lm -lliquid

To install liquiddsp, check out the main repository of the author: https://github.com/jgaeddert/liquid-dsp. The C++ version does not require any external library, and in my opinion is indeed easier to build off from.

To do list:

• Simulate power spectrum of GPS L1 signal
• Add nav data to GPS Signal
• Add complex Additive White Gaussian Noise
• Simulate Phase Locked Loop for carrier tracking later
• Model BPSK constellation
• Carry out despreading, correlation, and tracking