Understanding wireless channels is crucial for the design of wireless systems. For mobile communication, sounders and antenna arrays with short measurement times are required to simultaneously capture the dynamic and spatial channel characteristics. Switched antenna arrays are an attractive option that can overcome the high cost of real arrays and the long measurement times of virtual arrays. Optimization of the switching sequences is then essential to avoid aliasing and increase the accuracy of channel parameter estimates. This paper provides a novel and comprehensive analysis of the design of switching sequences. We first review the conventional spatio-temporal ambiguity function, extend it to dual-polarized antenna arrays, and analyze its prohibitive complexity when designing for ultra-massive antenna arrays. We thus propose a new method that uses the Fisher information matrix to tackle the estimation accuracy. We also propose to minimize the ambiguity by choosing a switching sequence that minimizes side lobes in its Fourier spectrum. In this sense, we divide the sequence design problem into Fourier-based ambiguity reduction and Fisher-based accuracy improvement, and coin the resulting design approach as Fourier-Fisher. Simulations and measurements show that the Fourier-Fisher approach achieves identical performance and significantly lower computational complexity than that of the conventional ambiguity-based approach.