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.
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