To meet the increasing capacity demand on wireless networks, there have been intense efforts in the past decade on developing multi-user receiver structures which mitigate the interference between users in spread-spectrum and antenna array systems. While much of the research is performed at the physical layer, the capacity of networks with multi-user receivers and the associated resource allocation problems are less well-understood. In this paper, we show that under some conditions, the capacity of a single cell for several important receivers can be very simply characterized via a notion of effective bandwidth: the QoS requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The number of degrees of freedom is the processing gain in a spread-spectrum system and the number of antenna elements in an antenna array. The effective bandwidth of a user depends only on its own QoS requirement, expressed in terms of the desired signal-to-interference ratio. It is hoped that such an abstraction of resource requirement will help in bridging the resource allocation problems at the networking layer and multi-user techniques at the physical layer.