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 $2^b$ levels ($b\in\mathbb N$) of the obtained constellation can be represented by a basic level and $b+2$ 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.