With the development of the fifth generation (5G) technologies and beyond, the requirements for future wireless communication systems become more stringent, which demand novel antenna design at millimetre waves. The most commonly proposed array topology for 5G usage is square 8x8 or 16x16 microstrip patches with the full digital beam-forming method. Such designs result in massive complexity, high power consumption, and heat generation, especially with the full digital beam-forming method. To reduce design complexity and power consumption, the hybrid beam-forming is proposed, in which the linear subarrays are used with a fixed beam pattern in elevation, and combined in an array with digital beam-forming to realize the beam scanning in azimuth. Recent studies in the MS3 group at TU Delft have demonstrated that the series-fed subarray can be used in hybrid beam-forming and can realize any desired pattern by independent control of amplitude and phase on each unit cell. However, the main drawbacks of the series-fed arrays are the radiation beam squint and pattern distortion under different frequencies, which can limit the radiation bandwidth. Therefore, it is necessary to investigate the design of the series-fed antenna arrays to reduce the beam squint and pattern distortion. In this thesis, the performance of series-fed antenna arrays radiating the csc2-shaped beam pattern is investigated in terms of beam squint and pattern distortion. The RMS value is used in this thesis to quantify the pattern distortion in series-fed arrays and is used as a performance metric. Firstly, seven types of edge-fed series-fed subarrays are designed and optimized in CST. Their performance in terms of beam squint and pattern distortion is evaluated with and without considering the mutual coupling effect. Then, the subarray with the most stable radiation pattern over the evaluated frequency band (25 GHz - 27 GHz) is selected. Following this, the center-fed series-fed proximity-coupled subarray is designed aiming to reduce the amount of beam squint while having a stable radiation pattern. The performance of the center-fed subarray is compared with the edge-fed configuration in terms of the beam squint and pattern distortion. The simulation results show that the center-fed configuration can significantly reduce the beam squint but can increase the pattern distortion. Finally, the array of center-fed series-fed proximity-coupled subarrays is designed and simulated in CST. The results show that the array is able to reduce the beam squint (within 1°) while having a reasonable pattern distortion (around 20% difference compared to the synthesized pattern) within the frequency range from 25.8 GHz to 26.5 GHz.