In this study, we propose the design of an antenna array applicable to fifth-generation (5G) smartphones. The proposed antenna structure consists of a 2 x 2 patch antenna. The proposed antenna has a small size of 106.07 x 106.07 mm2 and is printed on an FR-4 substrate. It has good radiation efficiency in the 3.6 GHz band and a high gain of 10.6 dB. The bandwidth of the proposed antenna, which is useful for 5G applications, is approximately 0.38 GHz (3.877 - 3.295 GHz) and includes the allocated band from (3400 MHz to 3600 MHz) for 5G cellular communication systems. The objective of this work is to characterise a new antenna using the wave concept iterative procedure (WCIP), a fast numerical method, and validation is carried out by comparison using finite integration techniques (FIT). The results obtained from the two methods are in close agreement, validating the design concept. Thanks to its simple structure, compact size, good radiation performance and ease of manufacture and integration with application-specific printed circuit boards, this antenna is suitable for 5G applications. The structure was created and examined using a Keysight PNA network analyser to demonstrate its effectiveness and compliance. The prototype antenna shown is tested and the measured results are in good agreement with the WCIP method.