Dual-Branch Pre-Distorted Enhanced ADO-OFDM for Full-Duplex Underwater Optical Wireless Communication System

In this paper, dual-branch pre-distorted enhanced asymmetrically clipped direct current (DC) biased optical orthogonal frequency division multiplexing (PEADO-OFDM) for underwater optical wireless communication (UOWC) is firstly proposed and simulated. The performances of PEADO-OFDM on the underwater optical channel model (UOCM) are analyzed and further compared with the typical ADO-OFDM. Using the Monte Carlo method for the modeling of UOCM, we adopt a double-gamma function to represent three different water qualities including clear, coastal and harbor waters. The full-duplex architecture enables the removal of Hermitian symmetry (HS) from conventional optical OFDM and can increase the spectral efficiency at the cost of hardware complexity. A new PEADO-OFDM transmitter is also proposed to reduce the complexity of the transmitter. The simulation results exhibit that our proposed dual-branch PEADO-OFDM scheme outperforms the typical ADO-OFDM scheme in spectral efficiency, bit error rate (BER) and stability over the underwater channels of three different water qualities.

A Quantized Riemann–Hilbert Problem in Donaldson–Thomas Theory

We introduce Riemann–Hilbert problems determined by the refined Donaldson–Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution.

ASYMPTOTICS OF SPACING DISTRIBUTIONS AT THE HARD EDGE FOR β-ENSEMBLES

In a previous work [J. Math. Phys.35 (1994) 2539–2551], generalized hypergeometric functions have been used to a give a rigorous derivation of the large s asymptotic form of the general β > 0 gap probability [Formula: see text], provided both βa/2 ∈ ℤ≥0 and 2/β ∈ ℤ+. It is shown how the details of this method can be extended to remove the requirement that 2/β ∈ ℤ+. Furthermore, a large deviation formula for the gap probability Eβ(n; (0, x); ME β, N(λaβ/2e-2βNλ)) is deduced by writing it in terms of the characteristic function of a certain linear statistic. By scaling x = s/(4N)2 and taking N → ∞, this is shown to reproduce a recent conjectured formula for [Formula: see text], βa/2 ∈ ℤ≥0, and moreover to give a prediction without the latter restriction. This extended formula, which for the constant term involves the Barnes double gamma function, is shown to satisfy an asymptotic functional equation relating the gap probability with parameters (β, n, a), to a gap probability with parameters (4/β, n′, a′), where n′ = β(n + 1)/2 - 1, a′ = β(a - 2)/2 + 2.