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There is a need in mobile telephony to accurately locate the position of mobile handsets either for legislative requirements or as a means to apply variable charging on accounts based on handset location. This would allow a mobile 'phone to replace a conventional landline at no extra cost! This paper reports on the continuing development of a new design for a dual band handset antenna suitable for use as a mobile handset antenna working at 1.8 GHz and as a antenna suitable for use with a Global Positioning System (GPS). The antenna is based on a dielectric rod antenna fed from a waveguide utilising either a linearly or circularly polarised (CP) feed. A frequency selective surface (FSS) is wrapped around the rod's circumference, either fully or partially. The FSS is used to control the antenna pattern by a leaky wave action away from the FSS resonance. The effect of an endcap, either a flat or coned design, has been investigated to further shape the antenna radiation pattern. Modelled results using TLM are presented for the antenna described above. The modelled results are assumed to be correct based on previously reported work that has been verified with measurements. The modelling approach allows us to have an accurate design before costly hardware production is undertaken.