Non-Linear Chirp Spread Spectrum Communication Systems of Binary Orthogonal Keying Mode

Chirp spread spectrum (CSS) is a suitable choice of modulation signals for wireless communications, due to its inherited advantages such as low transmission power, simplicity of implementation, good interference rejection capability. Linear chirps are common choices in practical CSS systems of binary orthogonal keying (BOK) mode. However, linear chirps generally require the time-bandwidth product of each chirp signal to be 60 sHz or more in order to achieve desirable orthogonality requirements. Thus, a BOK CSS system based on linear chirps has to occupy very wide bandwidth, which is a very precious resource for wireless communication. Clearly, the requirement on broad frequency bandwidth is a major limiting factor for the widespread adoption of the BOK linear CSS system in practice. To overcome this drawback, it is worthwhile to explore other types of chirp signals outside the linear domain, which can potentially reduce the bandwidth requirement without jeopardizing the system performance. This is the main objective of the current research. In this dissertation, a pair of non-linear chirps has been discovered, which has the potential to replace linear chirps for BOK CSS systems. After exploring desirable properties of non-linear chirps, it is demonstrated that a significant performance advantage on orthogonality over linear chirps can be achieved by a pair of sine or cosine chirps. Subsequently, properties of sine and cosine chirps are analyzed mathematically. Derivations of spectral characteristics, autocorrelation and cross-correlation for both sine and cosine chirps are carried out respectively. Finally, comparison of sine chirps of four different time periods (i.e. half time period, full time period, triple time period, and quadruple time period) are made in terms of their cross-correlation and autocorrelation properties. It has been concluded that full period sine (FPS) chirps are the better choice for this particular application among the sine chirps. Performance of a BOK CSS system based on FPS chirps has been evaluated in three typical scenarios. Firstly, BER (bit error rate) performance of the BOK FPS CSS system in an additive white Gaussian noise (AWGN) channel is derivated. Furthermore, performance comparison in terms of BERs between linear chirps and FPS chirps is examined. Secondly, effects of Doppler shift on the BOK FPS CSS system are analyzed. The effect of Doppler shift between linear chirps and FPS chirps has been compared. Thirdly, BER performance of the BOK FPS CSS system in a fading environment (Rayleigh channel) has been analyzed. Moreover, BER performance comparisons between linear chirps and FPS chirps in the AWGN+Rayleigh channel with and without a Doppler shift have also been studied. Using analytic means and numerical simulations, this dissertation has conclusively demonstrated that a pair of orthogonal FPS chirps has the capability of replacing linear chirp in BOK CSS systems