Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems

Abstract

We optimize modulation formats for the additive white Gaussian noise channel with nonnegative input, also known as the intensity-modulated direct-detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical, average optical, and peak power. The nonnegative constraint on the input to the channel is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1.5 bit/s/Hz, the modulation format optimized for average electrical power has a 2.55 dB average electrical power gain over the best known format to achieve a symbol error rate of 10 −6 . The corresponding gains for formats optimized for average and peak optical power are 1.35 and 1.72 dB, respectively. Using modulation formats optimized for peak power in average-power limited systems results in a smaller power penalty than when using formats optimized for average power in peak-power limited systems. We also evaluate the modulation formats in terms of their mutual information to predict their performance in the presence of capacity-achieving errorcorrecting codes, and finally show numerically and analytically that the optimal modulation formats for reliable transmission in the wideband regime have only one nonzero point.

Fundamental Limits of Parallel Optical Wireless Channels: Capacity Results and Outage Formulation

“…Next, we study the behavior of the optimal solution at high, low, and moderate SNR. 5 We formally define c N +1 = 0. 6 For brevity, occasionally we will use '+' and '−' to denote E This article has been accepted for publication in a future issue of this journal, but has not been fully edited.…”

“…Of particular interest are systems employing intensitymodulation and direct-detection (IM-DD) due to their practical simplicity. For instance, [5], [6] studied constellation design and [7]- [9] studied OFDM for IM-DD systems. Informationtheoretic achievable rates in IM-DD channels have been studied in [10] which focused on on-off keying, and in [11] which considered higher order modulation.…”

Low-SNR Asymptotic Capacity of MIMO Optical Intensity Channels with Peak and Average Constraints

“…To prove its asymptotic tightness at low SNR, we inspire from earlier works asserting the optimality of binary inputs at low SNR, such as [4], [32], [33]. We show that the asymptotically low-SNR optimal input in the MIMO IM-DD context is a maximally correlated vector-binary distributed input.…”

Bandlimited Optical Intensity Modulation Under Average and Peak Power Constraints

“…The optimization of a set of M -ary (e.g. M = 4, 8, 16) single-subcarrier modulation formats for IM/DD systems with and without confining them to a lattice structure was studied in [29] and a wider class of pulse sets were considered. The gain of the optimized formats over previously known formats range from 0.3 dB to 1 dB.…”

“…The gain of the optimized formats over previously known formats range from 0.3 dB to 1 dB. A simplified two-dimensional signal space with reduced complexity compared to the three-dimensional formats studied in [29] was presented in [30]. It was shown that the two-dimensional formats wee good for single-wavelength optical systems since the formats have superior performance if the bandwidth is measured as 90% in-band power.…”