It is well-known that ultra-wideband (UWB) radar suffers substantial disturbances due to spectral overlap with common radio frequency interferers (RFI), such as commercial radio/TV broadcasts, cell phones, and ISM equipment. We can expect RFI to become more prevalent as the cost of the technology decreases and devices become more widely commercialized. Fortunately, the energy of typical RFI is concentrated in narrow frequency bands – i.e. sparse in the frequency domain – which lends the RFI removal task to a sparsity-driven estimation approach. Moreover, the radar echoes tend to be sparse in the time domain. The recent SParse Iterative Covariance-based Estimation (SPICE) algorithm is employed to exploit these properties for effective RFI mitigation. We compare the performance of SPICE with that of the robust principal component analysis (RPCA) in a simulated interference environment consisting of an actual ambient RFI recording scaled and added to an unadulterated radar signal. SPICE is a user-parameter free algorithm, making it easy to use in practical applications such as RFI mitigation; while, in contrast, RPCA requires a tuning parameter, whose optimal value was found to depend on the signal-to-interference ratio of the contaminated data. Moreover, SPICE is computationally more efficient than RPCA.