In this paper, we accurately model the impact of aggregate hardware impairments (HWIs) in communication systems as improper Gaussian signals (IGS), which can describe the asymmetric characteristics of different HWI sources. The proposed model encourages us to adopt the IGS scheme for transmission that represents a general signaling scheme compared with the conventional scheme, proper Gaussian signaling (PGS). First, we express the achievable rate of multiple-input and multiple-output system suffering from various HWIs employing PGS and IGS schemes, when the aggregate effect of HWI is modeled as IGS. Moreover, we tune the transmit IGS statistical characteristics to maximize the achievable rate for the HWI single-input and multiple-output system with two receiver combining schemes. Then, we propose an adaptive scheme to switch between maximal IGS and PGS schemes under certain conditions to improve the system performance with least computational/optimization overhead. Finally, we validate the analytic expressions through numerical and simulation results and quantify the gain reaped from adopting the IGS scheme compared with the PGS scheme.