This paper studies the impact of asymmetric hardware distortion (HWD) on the performance of receive diversity systems using linear and switched combining receivers. The asymmetric attribute of the proposed model motivates the employment of improper Gaussian signaling (IGS) scheme rather than the traditional proper Gaussian signaling (PGS) scheme. The achievable rate performance is analyzed for the ideal and non-ideal hardware scenarios using PGS and IGS transmission schemes for different combining receivers. In addition, the IGS statistical characteristics are optimized to maximize the achievable rate performance. Moreover, the outage probability performance of the receive diversity systems is analyzed yielding closed form expressions for both PGS and IGS based transmission schemes. HWD systems that employ IGS is proven to efficiently combat the self interference caused by the HWD. Furthermore, the obtained analytic expressions are validated through Monte-Carlo simulations. Eventually, non-ideal hardware transceivers degradation and IGS scheme acquired compensation are quantified through suitable numerical results.