for robust solutions when optimizing for phase and amplitude of conventional phased array, has been investigated in [@deGreef2010a] considering perfusion uncertainties, and in [@deGreef2011a] considering dielectric uncertainties. The authors emphasize on the role of uncertainty in such designs (hyperthermia planning) since it influences the calculation of power distribution, and correspondingly temperature distribution.

The paper is organized as follows: In Section \[sec:system model\], we describe the system model and the relevant variables. In Section \[sec:problem formulation\], the signal design problem is presented. First, we consider the state-of-the-art method based on ‘waveform diversity’ [@08:Guo; @Stoica2007a; @JLi2009a], then we generalize the design problem by introducing a deterministic and bounded set of possible model errors which results in an infinite number of constraints. Importantly we show that this seemingly intractable problem can be equivalently formulated as a tractable convex optimization problem. In Section \[sec:numerical\_results\], we evaluate the design scheme. We evaluate the performance of our proposed robust power distribution scheme specifically for local hyperthermia breast cancer treatment. This example application is motivated by the alarming statistics pointing to breast cancer as one of the leading causes of death among women worldwide [@CancerReport2014UK; @CancerReport2014US; @CancerReport2013French][^1]. The case of no model mismatch is investigated first, and 