 Abstract-A very small coplanar waveguide (CPW)-fed rectangular slot antenna with dual band notched characteristics for super ultrawideband (UWB) applications is proposed. This antenna consists of a rectangular slot, a beveled rectangular patch, two S-shaped slits cut in the ground plane and an elliptical ring slot (ERS) etched in the patch. The corners of a simple rectangular patch are beveled to improve the impedance bandwidth, especially at the middle frequencies of the band. In addition, a pair of semi-circle slots are etched in the ground plane to enhance the bandwidth to more than 23 GHz. A pair of S-shaped slits connected to the rectangular slot, and an elliptical ring slot cut in the beveled rectangular patch, are employed to create band notched performances in WiMAX and WLAN spectrum, respectively. The proposed antenna has a very small size of 15×15 mm 2 , and therefore it is one of the smallest ultra wideband slot antennas which have been reported until now, and provides a very wide impedance bandwidth from 2.6 to more than 23 GHz for VSWR<2 with dual band notched properties. Index Terms-S-shaped and elliptical ring slots, beveled rectangular slot, dual band-notched properties, semi-circle slot.0018-926X (c)

I. ANALYTICAL DERIVATION OF 3-D TOA/2-D-AOA DISTRIBUTIONSA signal, transmitted from a mobile user in a landmobile radiowave wireless cellular communication system, arrives at the cellular base station through multiple propagation multipaths. Each multipath carries its own propagation history of electromagnetic reflections and diffractions and corruption by multiplicative noise-a history reflected in that multipath's amplitude, Doppler, arrival angle, and arrival time delay at the receiving antenna(s). The values of these amplitudes, Doppler frequency shifts, arrival angles, and arrival time delays depend on the electromagnetic properties of and the spatial geometry among the mobile transmitter, the scatterers, and the receiving antennas. Each receiving antenna's data measurement sums these individually unobservable multipaths.The time of arrival (TOA) 1 distribution function characterizes the channel's temporal delay spread and frequency incoher- ence, which in turn determines the obtainable temporal diversity and the extent of intersymbol interference. The two-dimensional (2-D) azimuth-elevation angle of arrival (AOA) determines the angular spread and spatial decorrelation across the spatial aperture of an receiving antenna. The multipaths' nonzero elevation AOAs are most common in urban areas or over hilly terrains or with low-lying receiving antennas, where the propagating wave reflects off vertical structures like buildings or hills. The nonzero elevation AOA is critical for the use of a vertical or planar receiving antenna array, a fact recognized by the European Union's COST Action 259 [19]."Geometric modeling" idealizes the aforementioned wireless propagation environment via a geometric abstraction of the spatial relationships among the transmitter, the scatterers, and the base station. Geometric models thus attempt to embed measurable fading metrics integrally into the propagation channel's idealized geometry, such that the geometric parameters would affect these various fading metrics in an interconnected manner to reveal conceptually the channel's underlying fading dynamics. This work will maximally embed all derived statistics intrinsically within the propagation channel's geometry and to avoid a priori ad hoc statistical assumptions of the received signal's measurable statistics. See [27] for additional discussion on the nature of geometric modeling of wireless propagation.Geometric modeling contrasts with site-specific/terrain-specific/building-specific empirical measurements or ray-shooting/ ray-tracing computer simulations, which are applicable only to the one particular propagation setting under investigation but cannot be easily generalized to wider scenarios. One geometric model can apply for a wide class of propagation settings, producing the received signal's measurable fading metrics (e.g., the uplink and downlink probability density functions of the multipaths' arrival delay and 2-D arrival angle as in this paper) applicable generally within that class of channels.Geometric modeling contras...

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