A new theoretical approach for designing a low-noise amplifier (LNA) for the ultra-wideband (UWB) radio is presented. Unlike narrowband systems, the use of the noise figure (NF) performance metric becomes problematic in UWB systems because of the difficulty in defining the signal-to-noise ratio (SNR). By defining the SNR as the matched filter bound (MFB), the NF measures the degree of degradation caused by the LNA in the achievable receiver performance after the digital decoding process. The optimum matching network that minimizes the NF as defined above has been solved. Since realizing the optimum matching network is in general difficult, an approach for designing a practical but suboptimum matching network is also presented. The NF performance of both the optimum and the suboptimum matching networks is studied as a function of the LNA gain.