A unified spectral analysis of generalized time-hopping spread-spectrum signals in the presence of timing jitter

This paper characterizes the power spectral density (PSD) of various time-hopping spread-spectrum (TH-SS) signaling schemes in the presence of random timing jitter, which is characterized typically by a discrete-time stationary random process (independent of the TH sequences and data sequence) with known statistical properties. A flexible model for a general TH-SS signal is proposed and a unified spectral analysis of this generalized TH-SS signal is carried out using a systematic and tractable technique. The key idea is to express the basic baseband pulse in terms of its Fourier transform which allows flexibility in specifying different TH formats throughout the general derivation. The power spectrum of various TH-SS signaling schemes can then be obtained as a special case of the generalized PSD results. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific results are then given for the cases of practical interest, namely, uniform and Gaussian distributed jitter. Applications of this unified spectral analysis includes: (1) clocked TH by a random sequence; (2) framed TH by a random sequence; and (3) framed TH by a pseudorandom periodic sequence. Detailed descriptions of these different TH techniques are given where the first two techniques employ a random sequence (stochastic model) and the third technique employs a pseudorandom sequence (deterministic model).