In this paper, we investigate the effects of RF transceiver's imperfections on the multi-antenna interference rejection combing (IRC) based black-space cognitive radio (BS-CR) operation. In particular, we explore the effects of power amplifier (PA) nonlinearities and carrier frequency offset (CFO) on the blind IRC technique. The BS-CR operation mode supports effective reuse of the primary user (PU) spectrum, especially for relatively short-distance CR communication. We assume that both the PU system and the BS-CR use orthogonal frequency division multiplexing (OFDM) waveforms with common numerology. In this case the PU interference on the BS-CR signal is strictly flat-fading at subcarrier level, and it can be suppressed using subcarrier-wise IRC processing. Spatial sample covariance matrix-based IRC adaptation is applied during silent gaps in CR operation. We propose an analytical framework for modeling CFO effects, together with experimental study of CFO and PA nonlinearity effects. The performance of the IRC scheme is tested considering terrestrial digital TV broadcasting (DVB-T) as the primary service. The validity of the offered expressions for CFO effects are justified through comparisons with respective results from computer simulations. The effect of CFO between the primary and secondary systems is found to be critical for BS-CR operation, while the effect of CR transmitter's nonlinearity is no worse than in basic OFDM schemes, and the PU transmitter's nonlinearity has minor effect on BS-CR operation.