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Far-field shaping of small antennas is a challenge and the realizations ofnon-dipole radiation of small to intermediate sized antennas are difficult.Here we examine the antenna bandwidth cost associated with such constraints,and in certain cases we design antennas that approach the bounds. Far-fieldshaping is in particular interesting for Internet-of-things (IoT) and Wi-Fiapplications since e.g. spatial filtering can mitigate package loss through areduction of mutual interference, and hence increase the power efficiency ofthe devices. Even a rather careful far-field shaping of smaller antennas can beassociated with a steep reduction in the best available bandwidth. It is thusimportant to develop constraints that a small antenna can support. We describea power front-to-back ratio, and a related, beam-shaping constraint that can beused in optimization for the minimum Q-factor. We show that such a non-convexQ-factor optimization can be solved with the semi-definite relaxationtechnique. We furthermore show that certain of the above optimized non-standardradiation patterns can be realized with a multi-position feeding strategy witha moderate loss of Q-factor: $Q_\text{antenna}\leq 1.61Q_\text{optimal}$.

Antenna Current Optimization and Realizations for Far-Field Pattern Shaping