Numerous experiments have been designed to investigate the Cosmic Dawn (CD) and Epoch of Reionization (EoR) by examining redshifted 21 cm emissions from neutral hydrogen. Detecting the global spectrum of redshifted 21 cm signals is typically achieved through single-antenna experiments. However, this global 21 cm signal is deeply embedded in foreground emissions, which are about four orders of magnitude stronger. Extracting this faint signal is a significant challenge, requiring highly precise instrumental calibration. Additionally, accurately modelling receiver noise in single-antenna experiments is inherently complex. An alternative approach using a short-spacing interferometer is expected to alleviate these difficulties because the noise in different receivers is uncorrelated and averages to zero upon cross-correlation. The Short-spacing Interferometer Array for Global 21 cm Signal Detection (SIGMA) is an upcoming experiment aimed at detecting the global CD/EoR signal using this approach. We describe the SIGMA system with a focus on optimal antenna design and layout, and propose a framework to address cross-talk between antennas in future calibrations. The SIGMA system is intended to serve as a prototype to gain a better understanding of the system's instrumental effects and to optimize its performance further.