IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 4, APRIL 2007 1549 Pulse-Shaping Numerical Procedures for Ultrawide Bandwidth Systems C. Buccella, M. Feliziani, and G. Manzi Department of Electrical and Computer Engineering, University of L’Aquila, L’Aquila, Italy This paper deals with the radiation produced by ultrawide-band (UWB) impulse radio transmitters. A numerical procedure is first proposed in order to define the ideal UWB pulse able to be compliant with the FCC emission mask, taking into account the effect of the UWB radiating antenna. The obtained ideal UWB pulse is then decomposed in a linear combination of Gaussian pulses. A numerical procedure for electromagnetic field calculation is finally applied to verify the compliance of the generated pulse with the FCC emission standards. Index Terms—Antenna radiation, cognitive radio, electromagnetic compatibility (EMC), numerical computation, pulse shaping, ul- trawide-band (UWB) radio communication. I. INTRODUCTION U LTRAWIDE-BAND (UWB) impulse radio (IR) is a re- cent communication technique which operates in the unli- censed frequency bands [1], [2]. In these bands, even if any user can transmit without any authorization, the amount of interfer- ence introduced by the UWB transmission must be limited in order to avoid interference to other users’ communications. In few words, the UWB radio signals must coexist with other radio signals [3], [4]. Possible interference from and onto other com- munication systems must be contained within regulated values that indicate the maximum tolerable power to be present in the air interface at any given frequency, as set by the Federal Com- munications Commission (FCC) emission mask for indoor and outdoor UWB devices. In this work, the problem under study consists of the numer- ical computation of the electromagnetic field produced by an UWB radio communication system which must be compliant with the FCC emission mask given in maximum equivalent isotropic radiated power (EIRP) in the frequency domain [1]. By respecting this constraint, the problem is the definition of the wave shape of the UWB pulses [5] that must be generated by the UWB pulse generator, which also has some other tech- nological constraints. These last constraints are mainly due to the needs of the electronic circuitry for UWB pulse generation and to the FCC regulations for UWB systems [2]. The problem is quite complex, involving many EM field and communication aspects, and is also considered a very hot topic in view of the incoming cognitive radio. The description of the proposed method is reported in the following sections. II. MATHEMATICAL MODEL The problem under study consists of the numerical compu- tation of the electromagnetic field produced by an UWB radio Digital Object Identifier 10.1109/TMAG.2007.892465 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. communication system, which must be compliant with the FCC emission mask for indoor UWB devices. Our study can be di- vided in several steps as described in the following: a) numerical characterization of the UWB antenna; b) evaluation of the maximum radiated power generated by an UWB antenna in order to be compliant with the FCC mask for indoor UWB devices; c) definition of the equivalent circuit of the UWB transmitter and evaluation of the UWB ideal voltage source in the frequency domain and transformation in the time domain; d) evaluation of the real pulse voltage source in the time domain by decomposition of the transient ideal voltage source in a linear combination of simple pulses with a fixed number of series terms and with fixed time delays; e) numerical calculation of the electromagnetic field gener- ated by the UWB radio system in the environment. A. Characterization of the UWB Antenna The UWB antenna must be a broadband antenna with good performances in the frequency range of UWB radio communi- cations, i.e., 3–10 GHz. The characterization of the UWB an- tenna must be carried out for all the frequencies of interest. The UWB antenna shape and type can be complex, and its charac- terization cannot be simple. The more complicated UWB an- tennas are often characterized by measured parameters such as directivity and gain, radiation pattern, effective aperture, and/or antenna factor. Moreover, sophisticated software tools for elec- tromagnetic field numerical solutions can also be able to deter- mine the radiated power and the shapes of the radiated emission patterns. For our work, it is mandatory to know the radiated power , the antenna input impedance , and the gain for the considered UWB antenna in the frequency range of interest. B. Evaluation of the Maximum Radiated Power The purpose of this subsection is to evaluate the maximum ra- diated power admissible for UWB indoor radio communi- cations in order to meet the FCC regulations. The FCC mask for indoor UWB devices is defined in terms of EIRP in frequency 0018-9464/$25.00 © 2007 IEEE