The problem of detecting moving and stationary people in a room with a specialized radar system sensing through the wall is considered in the paper. The high-range resolution of the system is achieved by effective processing of reflected ultra-wideband stepped-frequency continuous-wave signals (SFCW). The paper presents a new method which is based on normalization of complex-valued samples of the received SFCW signals and extends traditional processing steps including quadrature-phase demodulation, sampling and inverse discrete Fourier transform. The proposed method is aimed at improving the performance of the interperiodic difference and variance of sample algorithms which are briefly described in relation to the SFCW radar system. The computer modeling showed that the introduced normalization mitigates the background noise and merely decreases the artifacts commonly appearing in radar images due to the non-uniform amplitude-frequency characteristics of the radar circuits. The described algorithms were implemented in a software part of the real-time working prototype of the radar system designed and assembled at the University research center. The results of field experiments confirmed the advantage of the proposed method in typical scenarios and showed the increase of the signal-to-noise ratio to 5 dB compared to traditional radar algorithm-processing SFCW signals.