Non-linear trigonometric and hyperbolic chirps in multiuser spread spectrum communication systems

Novel non-linear trigonometric and hyperbolic chirp waveforms are introduced in multiuser spread spectrum communication environment for binary data transmission. Three subclasses of non-linear trigonometric and hyperbolic chirp signals namely sinusoidal (sine-CSS), hyperbolic arc sinusoidal (asinh-CSS) and hyperbolic tangent (tanh-CSS) are described and their properties are given. Cross-correlations of these trigonometric and hyperbolic chirp signals are derived and presented as closed-form expressions. Moreover, the chirp rates in these signals are derived as a function of user in the multiuser environment using the orthogonal structure inherent in nonlinear chirp signals. A generic multiuser communication system model that employs non-linear chirp signals is presented and its bit error rate (BER) performance is analyzed in additive white Gaussian noise (AWGN) channel, and Rayleigh and Nakagami-m fading environments as a function of the number of users in the system, signal-to-noise ratio (SNR), and multiple access interference (MAI). Numerical results demonstrate that these proposed chirp signals with proper chirp rate assignment are very effective in reducing MAI.