## 1 Introduction
Massive MIMO is an attractive technology to support the desired 1000-fold system throughput improvements for 5G cellular communication systems [18]. In recent years, with the growing demand for higher data rates in post-5G mobile communications, mm-wave bands have received considerable research interest [19; 20; 21]. Recently, the mm-wave bandpass filters (BPFs) have attracted significant attention with the development of 5G systems [22]. Also, waveguide directional couplers are widely used in microwave andmm-wave systems [23]. Integrating a MIMO antenna and a substrate-integrated waveguide BPF in a single quarter/quintuple mode cavity can significantly reduce the overall loss, cost, and complexity of front-end systems and have potential applications in contemporary wireless communication devices [24; 25]. The diversity performance of the MIMO antenna is evaluated by the low envelope correlation coefficient (ECC) and high isolation between/among ports. These two factors are greatly affected by the distance between the antenna elements (AEs) [3]. The main problem with UWB MIMO antennas (UMAs) is the high mutual coupling between closely spaced AEs. The energy consumed by neighboring AEs when one AE is working depicts the mutual coupling. In general, the modification in impedance matching, reflection coefficients, and far-field radiation patterns of the AEs are consequences of the high mutual coupling. Practically, the mutual coupling relies upon the MIMO design and on the excitations of other nearby AEs. The systems of mutual coupling rely on the transmitting/receiving mode [26]. To explain this, two AEs \(m\) and \(n\) in the MIMO antenna are presented in Figure 1a,b in both transmitting and receiving modes, respectively. In the transmitting mode, AE \(n\) is energized as \(W1\). This energy radiates into space as \(W2\), and toward the AE \(m\) as \(W3\). The AE \(m\) rescatters part of the energy into space as \(W4\), and the remaining goes toward the port as \(W5\). The AE \(n\) obtains a small part of the rescattered energy \(W4\) as \(W6\). This cycle of mutual coupling will go on endlessly. However, because of the significant decrease in rescattered energy at each iteration, it is desirable to consider the first few iterations. Therefore, total far-field radiation is a vector sum of the rescattered and radiated far-fields. This shows that the antenna radiation pattern is modified due to high mutual coupling. The wave \(W5\) connects vectorially to the reflected and incident waves of the AE \(m\). This enhances the standing plane wave, which in turn alters the impedance matching of the AE \(m\). The mutual coupling modifies the mutual input impedance as well as antenna self-impedance. In the transmitting mode, various ports of a MIMO antenna may have arbitrary phase excitations. This will affect both the mutual coupling and the impedance matching of AEs. If a wave \(W1\) encroaches onto the MIMO antenna in receiving mode, reaching first at the \(m\)th AE, it first instigates a current in the AE \(m\). Some portion of the incident plane wave goes into the AE \(m\) as \(W2\), while its portion is re-scattered into space as \(W3\). A portion of the re-scattered plane wave is coordinated toward the AE \(n\) as \(W4\), where it combines vectorially with the incident plane wave \(W1\). Henceforth, the plane wave received by an AE is the vector addition of the coupled waves and the direct waves from other neighboring AEs. To limit the re-scattered energy or boost the received energy, the terminating load impedance of the AE \(m\) ought to be picked so that the reflected wave \(W5\) cancels the  
Figure 1: Mutual coupling in (**a**) transmitting mode and (**b**) receiving mode. {Note: \(W=\) Wave}. re-scattered wave \(W3\). The AE performance is determined by the excitation of one AE and the termination of other AE/s with 50 \(\Omega\) load/s in the receiving mode. There are a number of challenges faced by the researchers to improve isolation between closely spaced AEs.