Error probability study of hardware impaired (HWI) systems highly depends on the adopted model. Considering the distinct improper Gaussian features of HWI systems, captured by recent models, HWI-aware receivers are designed. An optimal maximum likelihood (ML) receiver serves as a performance benchmark, and a sub-optimal linear minimum mean square error (LMMSE) introduces a reduced-complexity implementation. Whereas, the conventional HWI-unaware minimum Euclidean distance (MED) receiver, based on the proper noise assumption, exhibits substandard performance. Next, the average error probability of the proposed optimal ML-receiver is analyzed, where several tight bounds and approximations are derived for various HWI systems. Motivated by the benefit of improper Gaussian signaling in mitigating HWI, which is proven in recent studies, asymmetric modulation is adopted and optimized for transmission. The numerical results demonstrate a bit error rate (BER) reduction up to 70% of the proposed HWI-aware receivers over HWI-unaware receivers. Moreover, the asymmetric modulation is shown to reduce the BER by 93%. These results signify the importance of incorporating accurate HWI models, designing appropriate receivers and optimizing signal transmission for BER performance compensation.