  In optical communication systems, orthogonal frequency division multiplexing
(OFDM) is widely used to combat inter-symbol interference (ISI) caused by
multipath propagation. Optical systems which use intensity modulation and
direct detection (IM/DD) can only transmit real valued symbols, but the inverse
discrete Fourier transform (IDFT) or its computationally efficient form
inverse-fast Fourier transform (IFFT) required for the OFDM waveform
construction produces complex values. Hermitian symmetry is often used to
obtain real valued symbols. For this purpose, some trigonometric
transformations such as discrete cosine transform (DCT) are also used, however
these transformations can eliminate the ISI only under certain conditions. In
this paper, we propose a completely different method for the construction of
OFDM waveform with IFFT to obtain real valued symbols by combining the real and
imaginary parts (CRIP) of IFFT output electrically (E-CRIP) or optically
(O-CRIP). Analytical analysis and simulation works are presented to show that
compared to the Hermitian symmetric system, the proposed method slightly
increases the spectral efficiency, eliminates ISI, significantly reduces the
amount of needed calculation and does not effect the error performance. In
addition, the O-CRIP method is less affected by clipping noise that may occur
due to the imperfections of the transmitter front-ends.
