Practical wireless devices are considered too small to support multi-antenna communications. Several studies have proposed optimal MIMO transceiver design in the presence of mutual coupling by use of matching networks. However, most studies assume a narrowband model. For broadband systems, Fano's matching theory reveals gain-bandwidth trade-offs for physically realizable networks. In this paper, we formulate matching network design for broadband coupled multi-antenna transceivers with circular arrays and investigate the role coupling plays in determining the RF bandwidth of the system. It will be shown that in the presence of coupling, the spatial modes of an antenna array have different bandwidths and that for 2-element arrays with practical bandwidths, a quarter-wavelength spacing is good enough.