Geometric Constellation Shaping for Wireless Optical Intensity Channels: An Information-Theoretic Approach

A simple geometric shaping method is proposed for optical wireless communication systems based on intensity modulation and direct detection (IM/DD) from an information-theoretic perspective. Constellations consisting of equiprobable levels with exponential-like distribution are obtained, which possesses asymptotic optimality in the sense that the high-SNR capacity of average-intensity constrained optical intensity channel can be approached by such constellations with increasing size. All <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{b}$ </tex-math></inline-formula> levels (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b\in \mathbb {N}$ </tex-math></inline-formula>) of the obtained constellation can be represented by a basic level and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b+2$ </tex-math></inline-formula> bits, thereby reducing the required resolution of the digital-to-analog converter (DAC) without affecting the asymptotic optimality. Achievable information rate evaluations verify the asymptotic optimality. As an example, error performance results of a simple 16-level LDPC coded modulation scheme show that a shaping gain of 0.65 dB can be obtained by applying the proposed constellation design. This method can also be applied to more specific IM/DD channel models, since it only requires a near-optimal continuous input distribution.