Time-Hopping Patterns derived from Permutation Sequences for Ultra-Wide-Band Impulse-Radio Applications TOMASO ERSEGHE Dipartimento di Elettronica ed Informatica Universit` a di Padova Via Gradenigo 6/A, 35131 Padova ITALY Abstract: - Time-hopping (TH) communication techniques have gathered increasing attention since the intro- duction of ultra-wide-band impulse-radio, by Scholtz, in 1993. In these systems, the design of TH sequences is a critical point, since they constitute the only source of diversity that protects the transmitted signal from the interference caused by multipath and by the presence of other users. Moreover, they represent a reliable source for synchronization and channel estimation. In this paper the author addresses the issue of build- ing TH patterns with very good correlation properties by use of a construction based upon the theory of permutation-sequences (PSs) that was recently proposed in the context of frequency-hopping by Moreno. The paper devotes much care in the analytical evaluation of correlation properties (correcting some mistakes of the literature) and in the identification of the widest possible class of TH patterns based upon PSs. Key-Words: - Impulse radio, ultra wide band, time hopping, frequency hopping, permutation sequences. 1 Introduction Time-hopping (TH) multi-user-diversity techniques have gathered increasing attention since the intro- duction, in 1993, of ultra-wide-band impulse-radio (UWB-IR) [1]. UWB-IR is a multi-user modulation technique that employs ultra narrow pulses of temporal extension of less than a nanosecond (hence of ultra-wide-bandwidth in excess of a few GHz). The way to encode information is an hybrid mod- ulation that uses TH code division multiple access and binary PPM modulation. The signal associated to user is thus [3], [4] (1) where is the frame duration, and we have one pulse per user per frame, is the TH sequence associated with user , and is a binary encoded sequence carrying the information to be transmitted 1 . 1 In the standard UWB-IR format, the encoded sequence is derived from a source binary sequence by a sim- ple bit-repetition approach [1], [4]. Equation (1) takes into ac- Figure 1: Exemplification of the TH signal asso- ciated to the TH sequence with . The design of TH sequences is a critical point for any communication technique employing TH, and so for UWB-IR, since they constitute the main source of diversity for the system. By inspection of (1), we see that the TH sequence , with elements belonging to the alphabet , is in practice de- termining the sub-frame of duration in which data- transmission occurs (and we assume that ). Thus, the situation is that depicted in Fig. 1, where it count that more efficient methods could be used to encode the source-sequence.