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Two-tier femtocell networks- comprising a conventional cellular network plus embedded femtocell hotspots- offer an economically viable solution to achieving high cellular user capacity and improved coverage. With universal frequency reuse and DS-CDMA transmission however, the ensuing cross-tier interference causes unacceptable outage probability. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network. We evaluate a network-wide area spectral efficiency metric called the operating contour (OC) defined as the feasible combinations of the average number of active macrocell users and femtocell base stations (BS) per cell-site that satisfy a target outage constraint. The capacity analysis provides an accurate characterization of the uplink outage probability, accounting for power control, path loss and shadowing effects. Considering worst case interference at a corner femtocell, results reveal that interference avoidance through a time-hopped CDMA physical layer and sectorized antennas allows about a 7x higher femtocell density, relative to a split spectrum two-tier network with omnidirectional femtocell antennas. A femtocell exclusion region and a tier selection based handoff policy offers modest improvements in the OCs. These results provide guidelines for the design of robust shared spectrum two-tier networks.