20. Spectral Properties and Error Rate Performance of Digital Chirp Communication System

In the first part, new and easy-to-compute closed-form expressions for average symbol error probability of digital M-ary chirp communication system impaired by additive white Gaussian noise and fading are derived. Three fading environments, Rayleigh, Nakagami-m, and generalized-K, that represent most practical wireless channels are considered. The closed-form expressions derived are then used to illustrate the performances of 2-, 4-, and 8-ary chirp systems as a function of average received signal-to-noise ratio (SNR), modulation and fading environment parameters. The proposed mathematical analysis can be easily used to design an efficient and reliable M-ary chirp communication system for application over fading channels. In addition, A general method is introduced for the calculation of power spectra of M-ary chirp signals. This method can handle arbitrary M-ary data and works for an arbitrary set (h, w) of modulation parameters; h is the modulation index and w is the sweep width parameter. Numerical results for the power spectrum of the M-ary chirp signals are presented and are illustrated as a function of set of modulation parameters. It is shown that the M-ary chirp system offers advantages over other conventional modulation techniques, making it an attractive wide-band modulation technique from the point of view of the power and the bandwidth trade-off.