For high-capacity and short-reach applications, carrier-assisted differential detection (CADD) has been proposed, in which the optical field of a complex-valued double sideband (DSB) signal is reconstructed without using a sharp-edge optical bandpass filter or local oscillator laser. The CADD receiver features a transfer function with periodical nulls in the frequency domain, while the signal-signal beat interference (SSBI) is severely amplified around the frequency nulls of the transfer function. Since the null magnitude at the zero frequency is inevitable, a guard band is required between the carrier and the signal, leading to a higher receiver bandwidth and implementation cost. To reduce the needed guard band, we propose a parallel dual delay-based CADD (PDD-CADD), in which an additional delay is placed parallel to the original delay in the conventional CADD. By this means, the modified transfer function has a sharper roll-off edge around the zero frequency. Consequently, the requirement on the guard band can be relaxed, which maximizes the bandwidth utilization of the system. The parallel delay is first optimized through numerical simulation. We then perform a proof-of-concept experiment to transmit a 100-Gb/s orthogonal frequency division multiplexing (OFDM) 16-ary quadrature amplitude modulation (16-QAM) signal over an 80-km single-mode fiber (SMF). After the fiber transmission, the proposed PDD-CADD can reduce the required guard band from 3 to about 1.2 GHz compared with the single delay-based conventional CADD. To our best knowledge, for the direct detection of a single polarization complex-valued DSB signal without using a sharp-roll-off optical filter, we achieve a record electrical spectral efficiency of 5.9 b/s/Hz.