99 research outputs found
Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics
The mutual information between a complex-valued channel input and its
complex-valued output is decomposed into four parts based on polar coordinates:
an amplitude term, a phase term, and two mixed terms. Numerical results for the
additive white Gaussian noise (AWGN) channel with various inputs show that, at
high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the
mixed terms. For the AWGN channel with a Gaussian input, analytical expressions
are derived for high SNR. The decomposition method is applied to partially
coherent channels and a property of such channels called "spectral loss" is
developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be
one effect that needs to be taken into account to explain the behavior of the
capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on
Information Theor
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
A Two-Dimensional Signal Space for Intensity-Modulated Channels
A two-dimensional signal space for intensity- modulated channels is
presented. Modulation formats using this signal space are designed to maximize
the minimum distance between signal points while satisfying average and peak
power constraints. The uncoded, high-signal-to-noise ratio, power and spectral
efficiencies are compared to those of the best known formats. The new formats
are simpler than existing subcarrier formats, and are superior if the bandwidth
is measured as 90% in-band power. Existing subcarrier formats are better if the
bandwidth is measured as 99% in-band power.Comment: Submitted to IEEE Communications Letters, Feb. 201
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
Design guidelines for spatial modulation
A new class of low-complexity, yet energyefficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO) has emerged. These systems are capable of exploiting the spatial dimensions (i.e. the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication whilst relying on a single-Radio Frequency (RF) chain. Moreover, SM may also be viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/ cooperative protocol design issues, and on their meritorious variants
Conditions for a Monotonic Channel Capacity
Motivated by results in optical communications, where the performance can
degrade dramatically if the transmit power is sufficiently increased, the
channel capacity is characterized for various kinds of memoryless vector
channels. It is proved that for all static point-to-point channels, the channel
capacity is a nondecreasing function of power. As a consequence, maximizing the
mutual information over all input distributions with a certain power is for
such channels equivalent to maximizing it over the larger set of input
distributions with upperbounded power. For interference channels such as
optical wavelength-division multiplexing systems, the primary channel capacity
is always nondecreasing with power if all interferers transmit with identical
distributions as the primary user. Also, if all input distributions in an
interference channel are optimized jointly, then the achievable sum-rate
capacity is again nondecreasing. The results generalizes to the channel
capacity as a function of a wide class of costs, not only power.Comment: This is an updated and expanded version of arXiv:1108.039
Signaling for Optical Intensity Channels
With the growing popularity of social media services, e-commerce, and many other internet-based services, we are witnessing a rapid growth in the deployment of data centers and cloud computing platforms. As a result, the telecommunications industry has to continue providing additional network capacity to meet the increasing demand for bandwidth. The use of fiber-optic communications plays a key role in meeting this demand. Coherent optical transceivers improve spectral efficiency by allowing the use of multilevel in-phase and quadrature (I/Q) modulation formats, which encode information onto the optical carrier’s amplitude and phase. However, for short-haul optical links, using noncoherent optical transceivers, also known as intensity-modulated direct-detection (IM/DD) systems, is a more attractive low-cost approach. Since only the intensity of light can carry information, designing power- and spectrally-efficient modulation formats becomes challenging. Subcarrier modulation, a concept studied in wireless infrared communications, allows the use of I/Q modulation formats with IM/DD systems at the expense of power and spectral efficiency.
This thesis addresses the problem of optimizing single-subcarrier modulation formats for noncoherent fiber and wireless optical communication systems in order to achieve a good trade-off between spectral efficiency, power efficiency, and cost/complexity. For the single-subcarrier three-dimensional signal space, denoted as raised-QAM in the literature, we propose a set of 4-, 8-, and 16-level modulation formats which are numerically optimized for average electrical, average optical, and peak power. In the absence of error-correcting codes, the optimized formats offer gains ranging from 0.6 to 3 dB compared to the best known formats. However, when error-correcting codes with performance near capacity are present, the obtained modulation formats offer gains ranging from 0.3 to 1 dB compared to previously known formats. In addition, laboratory experiments using the obtained 4- and 8-ary modulation formats were carried out. The performance improvement over the previously known formats conforms with the theoretical results.
To address transceiver complexity, a two-dimensional signal space for optical IM/DD systems is proposed. The resulting modulation formats have simpler modulator and demodulator structures than the three-dimensional formats. Their spectra have in general narrower main lobes but slower roll-off, which make them a good choice for single-wavelength optical systems. The three-dimensional formats are more suitable for wavelength-division multiplexing systems, where crosstalk between adjacent channels is important
Constellation Optimization in the Presence of Strong Phase Noise
In this paper, we address the problem of optimizing signal constellations for
strong phase noise. The problem is investigated by considering three
optimization formulations, which provide an analytical framework for
constellation design. In the first formulation, we seek to design
constellations that minimize the symbol error probability (SEP) for an
approximate ML detector in the presence of phase noise. In the second
formulation, we optimize constellations in terms of mutual information (MI) for
the effective discrete channel consisting of phase noise, additive white
Gaussian noise, and the approximate ML detector. To this end, we derive the MI
of this discrete channel. Finally, we optimize constellations in terms of the
MI for the phase noise channel. We give two analytical characterizations of the
MI of this channel, which are shown to be accurate for a wide range of
signal-to-noise ratios and phase noise variances. For each formulation, we
present a detailed analysis of the optimal constellations and their performance
in the presence of strong phase noise. We show that the optimal constellations
significantly outperform conventional constellations and those proposed in the
literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu
When to Use Optical Amplification in Noncoherent Transmission: An Information-Theoretic Approach
The standard solution for short-haul fiber-optic communications is to deploy noncoherent systems, i.e., to modulate and detect only the light intensity. In such systems, the signal is corrupted with optical noise from amplifiers and with thermal (electrical) noise. The capacity of noncoherent optical links has been studied extensively in the presence of either optical noise or thermal noise. In this paper, for the first time, we characterize the capacity under an average power constraint with both noise sources by establishing upper and lower bounds. In the two extreme cases of zero optical noise or zero thermal noise, we assess our bounds against some well-known results in the literature; improvements in both cases are observed. Next, for amplified fiber-optic systems, we study the trade-off between boosting signal energy (mitigating the effects of thermal noise) and adding optical noise. For a wide spectrum of system parameters and received power levels, we determine the optimal amplification gain. While mostly either no amplification or high-gain amplification is optimal, the best performance is for some parameter intervals achieved at finite gains
Subset-Optimized Polarization-Multiplexed PSK for Fiber-Optic Communications
A more power-efficient modulation format than polarization-multiplexed quadrature phase-shift keying (PM-QPSK) can be obtained by optimizing the amplitude ratio between symbols with odd and even parity in the PM-QPSK constellation. The optimal amplitude ratio approaches the golden ratio at high signal-to-noise ratio (SNR), yielding a 0.44 dB increase in asymptotic power efficiency compared to PM-QPSK. Union bound expressions are derived for the bit and symbol error rate of the new format, which together with Monte Carlo simulations give the power efficiency at both low and high SNR. A similar optimization performed on PM-8PSK gains 1.25 dB
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