Nonlinear effects limit analog circuit performance, causing both in-band and out-of-band distortion. The classical Volterra series provides an accurate model of many nonlinear systems, but the number of parameters grows extremely quickly as the memory depth and polynomial order are increased. Recently, concepts from compressed sensing have been applied to nonlinear system modeling in order to address this issue. This work investigates the theory and practice of applying compressed sensing techniques to nonlinear system identification under the constraints of typical radio frequency (RF) laboratories. The main theoretical result shows that these techniques are capable of identifying sparse Memory Polynomials using only single-tone training signals rather than pseudorandom noise. Empirical results using laboratory measurements of an RF receiver show that sparse Generalized Memory Polynomials can also be recovered from two-tone signals.