  The optical wireless communication (OWC) with the intensity modulation (IM),
requires the modulated radio frequency (RF) signal to be real and non-negative.
To satisfy the requirements, this paper proposes two types of mixed orthogonal
frequency division multiplexing (X-OFDM) waveform. The Hermitian symmetry (HS)
character of the sub-carriers in the frequency domain, guarantees the signal in
the time domain to be real, which reduces the spectral efficiency to $1/2$. For
the odd sub-carriers in the frequency domain, the signal in the time domain
after the inverse fast fourier transform (IFFT) is antisymmetric. For the even
sub-carriers in the frequency domain, the signal in the time domain after the
IFFT is symmetric. Based on the antisymmetric and symmetric characters, the two
types of X-OFDM waveform are designed to guarantee the signal in the time
domain to be non-negative, where the direct current (DC) bias is not needed.
With $N$ sub-carriers in the frequency domain, the generated signal in the time
domain has $3N/2$ points, which further reduces the spectral efficiency to $1/3
= 1/2 \times 2/3$. The numerical simulations show that, the two types of X-OFDM
waveform greatly enhance the power efficiency considering the OWC channel with
the signal-dependent noise and/or the signal-independent noise.

Signal Processing;Systems and Control;Systems and Control