Ultra-wide bandwidth communication systems are known to suffer from non-Gaussian interference. In general, wireless ad-hoc networks, due to the lack of perfect power control and the random placement of nodes, are very likely to experience non-Gaussian multiple access interference. In systems with additive non-Gaussian noise, non-Gaussian signal detection and nonlinear signal processing can play important roles, especially in suppressing the multiple access interference. Practical ultra-wide bandwidth receiver designs based on the α-stable non-Gaussian additive impairment model are proposed and evaluated. It is demonstrated that the α-stable model together with a fractile based parameter estimation technique constitute a robust technique for adaptive receiver designs. The proposed receivers based on the α-stable model suppress multiple access interference, adapt to the noise and the interference in the environment, and are robust to estimation errors in the receiver parameters. The proposed receivers provide much better bit error rates than linear detectors and previously known nonlinear detectors.