2,142 research outputs found
Designing Power-Efficient Modulation Formats for Noncoherent Optical Systems
We optimize modulation formats for the additive white Gaussian noise channel
with a nonnegative input constraint, 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 and optical
power. The nonnegativity input signal constraint is translated into a conical
constraint in signal space, and modulation formats are designed by sphere
packing inside this cone. Some remarkably dense packings are found, which yield
more power-efficient modulation formats than previously known. For example, at
a spectral efficiency of 1 bit/s/Hz, the obtained modulation format offers a
0.86 dB average electrical power gain and 0.43 dB average optical power gain
over the previously best known modulation formats to achieve a symbol error
rate of 10^-6. This modulation turns out to have a lattice-based structure. At
a spectral efficiency of 3/2 bits/s/Hz and to achieve a symbol error rate of
10^-6, the modulation format obtained for optimizing the average electrical
power offers a 0.58 dB average electrical power gain over the best
lattice-based modulation and 2.55 dB gain over the best previously known
format. However, the modulation format optimized for average optical power
offers a 0.46 dB average optical power gain over the best lattice-based
modulation and 1.35 dB gain over the best previously known format.Comment: Submitted to Globecom 201
Seven Staggering Sequences
When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison
gave it an enthusiastic review in the Scientific American and Martin Gardner
was kind enough to say in his Mathematical Games column that "every
recreational mathematician should buy a copy forthwith." That book contained
2372 sequences. Today the "On-Line Encyclopedia of Integer Sequences" contains
117000 sequences. This paper will describe seven that I find especially
interesting. These are the EKG sequence, Gijswijt's sequence, a numerical
analog of Aronson's sequence, approximate squaring, the integrality of n-th
roots of generating functions, dissections, and the kissing number problem.
(Paper for conference in honor of Martin Gardner's 91st birthday.)Comment: 12 pages. A somewhat different version appeared in "Homage to a Pied
Puzzler", E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters,
Wellesley, MA, 2009, pp. 93-11
Which is the most power-efficient modulation format in optical links?
By exploiting the electromagnetic wave's four-dimensional signal space, we find that for the additive white Gaussian noise channel, the modulation format with best sensitivity to be an 8-level format with 1.76 dB asymptotic gain over BPSK, for uncoded optical transmission with coherent detection. Low-complexity modulators are presented for the format, as well as an interpretation in terms of quantum-limited sensitivity
Power-efficient modulation formats in coherent transmission systems
Coherent optical transmission systems have a four-dimensional (4-D) signal space (two quadratures in two polarizations). These four dimensions can be used to create modulation formats that have a better power efficiency (higher sensitivity) than the conventional binary phase shift keying/quadrature phase shift keying (BPSK/QPSK) signals. Several examples are given, with some emphasis on a 24-level format and an 8-level format, including descriptions of how they can be realized and expressions for their symbol and bit error probabilities. These formats are, respectively, an extension and a subset of the commonly used 16-level dual-polarization QPSK format. Sphere packing simulations in 2, 3, and 4 dimensions, up to 32 levels, are used to verify their optimality. The numerical results, as the number of levels increases, are shown to agree with lattice-theoretical results. Finally, we point out that the use of these constellations will lead to improved fundamental sensitivity limits for optical communication systems, and they may also be relevant as a way of reducing power demands and/or nonlinear influence. \ua9 2009, IEEE. All rights reserved
Multidimensional Optimized Optical Modulation Formats
This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation
Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems
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 error-
correcting codes, and finally show numerically and analytically that the
optimal modulation formats for reliable transmission in the wideband regime
have only one nonzero point.Comment: submitted to IEEE Transactions on Information Theory, June 201
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