refer to this approach as robust waveform diversity.

problem formulation {#sec:problem formulation}
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The waveform-diversity-based technique [@04:Fuhrmann; @Stoica2007a; @Stoica2007b; @08:Guo; @08:Fuhrmann; @14:Shariati2014c] have been used for designing beampatterns subject to practical constraints. In general, we aim to control and shape the spatial power distribution at a set of target points while simultaneously minimizing power leakage in the remaining area. By exploiting a combination of different waveforms in , the degrees of freedom increase for optimizing the beampattern under constraints.

After reviewing the standard waveform diversity approach, we focus on the practical scenario where the assumed array steering vector model is subject to perturbations. In the subsequent section, the proposed robust technique is evaluated by numerical simulations, comparing the performance with and without robustified solution under perturbed steering vectors.

Waveform Diversity based Ultrasound System
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In the MIMO radar literature, sidelobe minimization is a beampattern design problem that has been addressed by using the waveform diversity methodology, cf., [@04:Fuhrmann; @Stoica2007a; @Stoica2007b; @08:Fuhrmann]. This design problem can be thought of as an optimization problem where the probing waveforms covariance matrix $\R$ is the optimization variable to be chosen under positive semi-definiteness assumption and with a constraint on the total power. The waveform-diversity-based 