Low-cost, spectrally efficient self-coherent detection capable of optical field recovery is desired for inter-data center connections and metro networks. In this work, a simplified symmetric carrier assisted differential detection (S-CADD) receiver structure is proposed, which removes the single-ended photodiode branch and saves one ADC in standard asymmetric CADD (A-CADD) receivers. To compensate for the signal-signal beating (SSBI) impairment, a low-complexity iterative SSBI mitigation algorithm is put forward as well. The computational complexity is reduced by moving equalization, de-modulation and modulation out of each iteration. Based on single-carrier twin-single sideband (SSB) pulse- and quadrature-amplitude modulation (PAM and QAM) signals, the OSNR sensitivity with different carrier-to-signal power ratios (CSPRs) at back-to-back (BTB) scenario, the bit-error rates (BER) performance after 1000km fiber transmission, and the received optical power sensitivity at BTB are theoretically and numerically compared for both S-CADD and A-CADD receivers, respectively.