  Multi user orthogonal chirp spread spectrum (OCSS) can improve the spectral
inefficiency of chirp spread spectrum (CSS) but is only feasible with perfect
synchronism and without any channel dispersion. Asynchronism, channel
dispersion, or unexpectedly large Doppler shifts can cause multiple access
interference (MAI), which degrades performance. Conditions with small timing
offsets we term quasi-synchronous (QS). In this paper, we propose two new sets
of nonlinear chirps to improve CSS system performance in QS conditions. We
analytically and numerically evaluate cross-correlation distributions. We also
derive the bit error probability for Binary CSS analytically and validate our
theoretical result with both numerical and simulation results; our error
probability expression is applicable to any binary time-frequency (TF) chirp
waveform. Finally, we show that in QS conditions our two new nonlinear chirp
designs outperform the classical linear chirp and all existing nonlinear chirps
from the literature. To complete our analysis, we demonstrate that our
nonlinear CSS designs outperform existing chirps in two realistic (empirically
modeled) dispersive air to ground channels.
