FFT based algorithm to demodulate high frequency chirp signals

This study presents an innovative algorithm to extract binary data from a high frequency linear chirp signal contained in wideband radar pulse signal. The algorithm is designed for chirp signals (bandwidth of 125 - 1375 MHz) with a maximum chirp rate of 750 MHz per 100 ns and a maximum chirp range equivalent to the signal bandwidth. Additionally a maximum bit length of 64 bits and a SNR range of -20dB - 20dB is used. These parameters are randomized and used to generate the chirp signal containing the data stream with white Gaussian noise. A three-step process is adopted to demodulate the signal and extract the data stream. The first step is to subject the input chirp signal with Gaussian noise to the Short-Time Fourier Transform (STFT). An analysis window of size 32 samples is used for the Fast Fourier Transform (FFT) operation which is used to extract the current frequency value of the window. The window is then advanced by a single sample and the process is repeated until the entire signal has been traversed. The STFT operations results in an output signal of frequency in time. The second step makes use of the overlap-add method to filter out any variation in the STFT signal that exists due to noise. Similar to the STFT operation, a 32 sample window is used along with an FIR filter of equal length. The result of this filtering operation is a smooth representation of the change in frequency over time of the input linear chirp signal. The final step is to translate the slopes of the Filtered STFT signal to binary values. Once again a 32 sample window is used to calculate the difference in frequency of the first and last element of the window. Based on the sign of the result the output value is “one” for a positive result and “zero” for a negative result. This window is then advanced through the entire signal resulting in a pure binary signal. An assumption is made, that the number of bits in the signal is known and is used to calculate the number of samples per bit. The bit sample size is then used to measure the mode of values present in each sample segment. Extensive simulations were performed to ascertain the performance of the algorithm. Simulation with the number of bits and SNR limited from 1 - 32 bits and 0 - 20 dB respectively had an overall demodulation success of 72% with a BER of 4.6%, while simulation with the number of bits and SNR limited from 1 - 64 bits and -20 - 20 dB respectively had an overall result of 41% with a BER of 3.1%. The simulation results serve as a means of identifying the limitation imposed by SNR and the number of bits on chirp signal demodulation operation.