Assuming that bandwidth is dear, a reasonable design objective for wireless personal communications systems is to maximize the total throughput (number of users times data rate), subject to constraints on complexity and quality of service. In a conventional time division multiple access system (TDMA), users are assigned time slots which they keep from frame to frame, with the interfering mobiles assigned slots in the same way. As interference levels vary widely between slots due to such factors as shadowing and geographic proximity, some users suffer from persistently poor signal to interference ratios (SIR), and thus low quality of service. To overcome this, the use of frequencies is restricted so that some minimum geographic separation between users sharing a channel is guaranteed. Because systems are designed to tolerate 90 percent or 99 percent worst case conditions, large frequency reuse distances are often required, reducing the bandwidth available in each cell. In this article, we outline some of the many techniques that have been proposed in recent years to deal with the uneven SIR distribution while achieving a higher throughput than conventional TDMA. These may be broadly categorized as either interference averaging or interference avoidance. For example, direct sequence code division multiple access (DS-CDMA) systems with large spreading factors not only yield protection against multipath fading, but average over the interferers. The average interference is exchanged for the worst case, resulting in significantly improved capacity. Dynamic channel and power allocation algorithms on the other hand select either time slots or frequency hopping patterns which avoid strong interferers. As will be seen, this leads to a higher capacity than even synchronous DS-CDMA systems, assuming the interference can be tracked. Interference suppression using antenna arrays, and multiple receiver sites can then be used to improve the performance of either basic system. It is not our purpose to present an exhaustive survey of all possible system design choices, but rather to acquaint the reader with some of the basic trade-offs available for dedicated and multiple access radio systems. In particular, our focus is on the application of digital signal processing techniques to improve the capacity of wireless communications systems, with an emphasis on the physical layer. Moreover, while we will compare many types of systems with respect to a common propagation environment by means of simulation, the reader is cautioned that the model chosen is quite simple; such comparisons serve chiefly to motivate more detailed engineering investigation of what is actually required to achieve higher capacity. The remainder of the article is organized as follows. In the following section we outline techniques fur dealing with variable propagation conditions for single user channels. In the third section we perform comparisons of interference averaging and avoidance multiple access strategies for cellular systems, with capacity as a function of minimum acceptable SIR. In the fourth section we discuss some interference suppression methods. The fifth section presents the use of multiple base stations as a means of further increasing capacity. Throughout all of the above, our discussion is centered on connection-oriented traffic such as voice and video, with communication mediated by a network of base stations. In the sixth section we discuss three different personal communication systems being developed at UCLA, illustrating some of the design trade-offs available in achieving low power consumption, high spectral efficiency, and flexible network topology. We conclude with a summary of our perception of the system design choices available at the physical layer.