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NASA NTRS2009

Metal Decorated Multi-Walled Carbon Nanotube/Polyimide Composites with High Dielectric Constants and Low Loss Factors

The measurement of observable electromagnetic phenomena in materials and their derived intrinsic electrical material properties are of prime importance in the discovery and development of material systems for electronic and aerospace applications. Nanocomposite materials comprised of metal decorated multi-walled carbon nanotubes (MWCNTs) were prepared by a facile method and characterized. Metal particles such as silver(Ag), platinum(Pt) and palladium(Pd) with diameters ranging from less than 5 to over 50 nanometers were distributed randomly on the MWCNTs. The present study is focused on silver decorated MWCNTs dispersed in a polyimide matrix. The Ag-containing MWCNTs were melt mixed into Ultem(TradeMark) and the mixture extruded as ribbons. The extruded ribbons exhibited a moderate to high degree of MWCNT alignment as determined by HRSEM. These ribbons were then fabricated into test specimens while maintaining MWCNT alignment and subsequently characterized for electrical and electromagnetic properties at 8-12 GHz. The results of the electromagnetic characterization showed that certain sample configurations exhibited a decoupling of the permittivity (epsilon ) and loss factor (epsilon") indicating that these properties could be tailored within certain limits. The decoupling and independent control of these fundamental electrical material parameters offers a new class of materials with potential applications in electronics, microwave engineering and optics.

Elliott, Holly A.↗

NASA NTRS2010

Conditions of Core Formation in the Early Earth: Single Stage or Heterogeneous Accretion?

Since approx.1990 high pressure and temperature (PT) experiments on metal-silicate systems have showed that partition coefficients [D(met/sil)] for siderophile (iron-loving) elements are much different than those measured at low PT conditions [1,2]. The high PT data have been used to argue for a magma ocean during growth of the early Earth [3,4]. In the ensuing decades there have been hundreds of new experiments carried out and published on a wide range of siderophile elements (> 80 experiments published for Ni, Co, Mo, W, P, Mn, V, Cr, Ga, Cu and Pd). At the same time several different models have been advanced to explain the siderophile elements in Earth's mantle: a) shallow depth magma ocean 25-30 GPa [3,5]; b) deep magma ocean; up to 50 GPa [6,7], and c) early reduced and later oxidized magma ocean [8,9]. Some studies have drawn conclusions based on a small subset of siderophile elements, or a set of elements that provides little leverage on the big picture (like slightly siderophile elements), and no single study has attempted to quantitatively explain more than 5 elements at a time. The purpose of this abstract is to identify issues that have lead to a difference in interpretation, and to present updated predictive expressions based on new experimental data. The resulting expressions will be applied to the siderophile element depletions in Earth's upper mantle.

Righter, Kevin↗

NASA NTRS2006

Catalytic-Metal/PdO(sub x)/SiC Schottky-Diode Gas Sensors

Miniaturized hydrogen- and hydrocarbon-gas sensors, heretofore often consisting of Schottky diodes based on catalytic metal in contact with SiC, can be improved by incorporating palladium oxide (PdOx, where 0 less than or equal to x less than or equal to 1) between the catalytic metal and the SiC. In prior such sensors in which the catalytic metal was the alloy PdCr, diffusion and the consequent formation of oxides and silicides of Pd and Cr during operation at high temperature were observed to cause loss of sensitivity. However, it was also observed that any PdOx layers that formed and remained at PdCr/SiC interfaces acted as barriers to diffusion, preventing further deterioration by preventing the subsequent formation of metal silicides. In the present improvement, the lesson learned from these observations is applied by placing PdOx at the catalytic metal/SiC interfaces in a controlled and uniform manner to form stable diffusion barriers that prevent formation of metal silicides. A major advantage of PdOx over other candidate diffusion-barrier materials is that PdOx is a highly stable oxide that can be incorporated into gas sensor structures by use of deposition techniques that are standard in the semiconductor industry. The PdOx layer can be used in a gas sensor structure for improved sensor stability, while maintaining sensitivity. For example, in proof-of-concept experiments, Pt/PdOx/SiC Schottky-diode gas sensors were fabricated and tested. The fabrication process included controlled sputter deposition of PdOx to a thickness of 50 Angstroms on a 400-m-thick SiC substrate, followed by deposition of Pt to a thickness of 450 Angstroms on the PdOx. The SiC substrate (400 microns in thickness) was patterned with photoresist and a Schottky-diode photomask. A lift-off process completed the definition of the Schottky-diode pattern. The sensors were tested by measuring changes in forward currents at a bias potential of 1 V during exposure to H2 in N2 at temperatures ranging from 450 to 600 C for more than 750 hours. The sensors were found to be stable after a break-in time of nearly 200 hours. The sensors exhibited high sensitivity: sensor currents changed by factors ranging from 300 to 800 when the gas was changed from pure N2 to 0.5 percent H2 in N2.

Hunter, Gary W.↗

NASA NTRS2010

Toward Right-Fidelity Rotorcraft Conceptual Design

The aviation Advanced Design Office (ADO) of the US Army Aeroflightdynamics Directorate (AMRDEC) performs conceptual design of advanced Vertical Takeoff and Landing (VTOL) concepts in support of the Army's development and acquisition of new aviation systems. In particular, ADO engages in system synthesis to assess the impact of new technologies and their application to satisfy emerging warfighter needs and requirements. Fundamental to ADO being successful in accomplishing its role; is the ability to evaluate a wide array of proposed air vehicle concepts, and independently synthesize new concepts to inform Army and DoD decision makers about the tradespace in which decisions will be made (Figure 1). ADO utilizes a conceptual design (CD) process in the execution of its role. Benefiting from colocation with NASA rotorcraft researchers at the Ames Research Center, ADO and NASA have engaged in a survey of the current rotorcraft PD practices and begun the process of improving those capabilities to enable effective design and development of the next generation of VTOL systems. A unique aspect of CD in ADO is the fact that actual designs developed in-house are not intended to move forward in the development process. Rather, they are used as reference points in discussions about requirements development and technology impact. The ultimate products of ADO CD efforts are technology impact assessments and specifications which guide industry design activity. The fact that both the requirement and design are variables in the tradespace adds to the complexity of the CD process. A frequent need is ability to assess the relative "cost" of variations in requirement for a diverse set of VTOL configurations. Each of these configurations may have fundamentally different response characteristics to this requirement variation, and such insight into how different requirements drive different designs is a critical insight ADO attempts to provide decision makers. The processes and tools utilized are driven by the timeline in which questions must be answered. This can range from quick "back-of-the-envelope" assessments of a configuration made in an afternoon, to more detailed tradespace explorations that can take upwards of a year to complete. A variety of spreadsheet based tools and conceptual design codes are currently in use. The in-house developed conceptual sizing code RC (Rotorcraft) has been the preferred tool of choice for CD activity for a number of years. Figure 2 illustrates the long standing coupling between RC and solid modeling tools for layout, as well as a number of ad-hoc interfaces with external analyses. RC contains a sizing routine that is built around the use of momentum theory for rotors, classic finite wing theory, a referred parameter engine model, and semi-emperical weight estimation techniques. These methods lend themselves to rapid solutions, measured in seconds and minutes. The successful use of RC, however requires careful consideration of model input parameters and judicious comparison with existing aircraft to avoid unjustified extrapolation of results. RC is in fact a legacy of a series of codes whose development started in the early 1970s, and is best suited to the study of conventional helicopters and XV-15 style tiltrotors. Other concepts have been analyzed with RC, but typically it became necessary to modify the source code and methods for each unique configuration. Recent activity has lead to the development of a new code, NASA Design and Analysis of Rotorcraft (NDARC). NDARC uses a similar level of analytical fidelity as RC, but is built on a new framework intended to improve modularity and ability to rapidly model a wider array of concepts. Critical to achieving this capability is the decomposition of the aircraft system into a series of fundamental components which can then be assembled to form a wide-array of configurations. The paper will provide an overview of NDARC and its capabilities.

Sinsay, Jeffrey D.↗

NASA NTRS2010

Catalyst for Carbon Monoxide Oxidation

In many applications, it is highly desirable to operate a CO2 laser in a sealed condition, for in an open system the laser requires a continuous flow of laser gas to remove the dissociation products that occur in the discharge zone of the laser, in order to maintain a stable power output. This adds to the operating cost of the laser, and in airborne or space applications, it also adds to the weight penalty of the laser. In a sealed CO2 laser, a small amount of CO2 gas is decomposed in the electrical discharge zone into corresponding quantities of CO and O2. As the laser continues to operate, the concentration of CO2 decreases, while the concentrations of CO and O2 correspondingly increase. The increasing concentration of O2 reduces laser power, because O2 scavenges electrons in the electrical discharge, thereby causing arcing in the electric discharge and a loss of the energetic electrons required to boost CO2 molecules to lasing energy levels. As a result, laser power decreases rapidly. The primary object of this invention is to provide a catalyst that, by composition of matter alone, contains chemisorbed water within and upon its structure. Such bound moisture renders the catalyst highly active and very long-lived, such that only a small quantity of it needs to be used with a CO2 laser under ambient operating conditions. This object is achieved by a catalyst that consists essentially of about 1 to 40 percent by weight of one or more platinum group metals (Pt, Pd, Rh, Ir, Ru, Os, Pt being preferred); about 1 to 90 percent by weight of one or more oxides of reducible metals having multiple valence states (such as Sn, Ti, Mn, Cu, and Ce, with SnO2 being preferred); and about 1 to 90 percent by weight of a compound that can bind water to its structure (such as silica gel, calcium chloride, magnesium sulfate, hydrated alumina, and magnesium perchlorate, with silica gel being preferred). Especially beneficial results are obtained when platinum is present in the catalyst composition in an amount of about 5 to 25 (especially 7) percent by weight, SnO2 is present in an amount of about 30 to 40 (especially 40) percent by weight, and silica gel is present in an amount of 45 to 55 (especially 50) percent by weight. The composition of this catalyst was suggested by preliminary experiments in which a Pt/SnO2 catalyst was needed for bound water to enhance its activity. These experimental results suggested that if the water were bound to the surface, this water would enhance and prolong catalyst activity for long time periods. Because the catalyst is to be exposed to a laser gas mixture, and because a CO2 laser can tolerate only a very small amount of moisture, a hygroscopic support for the catalyst would provide the needed H2O into the gas. Silica gel is considered to be superior because of its property to chemisorb water on its surface over a wide range of moisture content.

Davis, Patricia↗

NASA NTRS2001

Highly Siderophile Element Abundances in Martian Meteorites

Critical evaluation of new and literature data for highly siderophile elements (HSE) in Martian (SNC) meteorites allows several first order conclusions to be drawn. (i) Re concentrations in SNC meteorites are nearly constant (within a factor of two) and do not correlate with rock type. Exceptions to this rule are Chassigny and Dar al Gani (DaG) 476, both of which are inferred to have experienced terrestrial Re contamination. (ii) Fractionations between Rh and Pd are small. Excluding Shergotty, the Rh/Pd ratio of the SNC suite is 0.22\pm0.05. (iii) Os and Ir contents vary by about four orders of magnitude; and positive correlations with MgO, Cr, and Ni suggest that these variations are not controlled by sulfide fractionation. A possible exception is the orthopyroxenite ALH84001, whose HSE's (including Ni, which is compatible in opx) are very low. (iv) Zagami, Shergotty, and Nakhla have nearly identical HSE signatures. Shergotty and Zagami have experienced assimilation-fractional crystallization (AFC) and have "crustal" Sr and Nd isotopic signatures. Conversely, the Nakhla parent was a small degree partial melt of a depleted mantle that interacted little with the Martian crust. These observations suggest that "evolved" HSE signatures can be produced by either fractional crystallization or small degrees of partial melting. (v) Chassigny and other mafic SNC's have HSE signatures that are very distinct from those of Nakhla-Zagami-Shergotty. The HSE elemental ratios of mafic SNC's approach chondritic, implying that the Martian mantle has nearly chondritic relative abundances of the HSE's. (vi) This chondritic HSE signature is observed in SNC's of various ages, suggesting that this is an ancient feature that has not evolved over time. (vii) No correlation is observed between HSE's and signatures of crustal contamination (e.g., Sr isotopes), indicating that the HSE signatures of the SNC suite are not derived from the crust. (vii) The Ru/Pd for the SNC suite ratio is about 0.5 chondritic. We attribute this depletion of Ru to the presence of spinel in the SNC source regions. (viii) Assignment of this depletion of Ru to spinel seems to also imply that spinel is not the cause of Os and Ir fractionations, requiring some other mafic phase to account for the observed variations. -----.

Jones, J. H.↗

NASA NTRS2010

Experimental Methodology for Determining Turbomachinery Blade Damping Using Magnetic Bearing Excitation and Non-Contacting Optical Measurements

Experiments to determine the effects of turbomachinery fan blade damping concepts such as passively shunted piezoelectric materials on blade response are ongoing at the NASA Glenn Research Center. A vertical rotor is suspended and excited with active magnetic bearings (AMBs) usually in a vacuum chamber to eliminate aerodynamic forces. Electromagnetic rotor excitation is superimposed onto rotor PD-controlled support and can be fixed to either a stationary or rotating frame of reference. The rotor speed is controlled with an air turbine system. Blade vibrations are measured using optical probes as part of a Non-Contacting Stress Measurement System (NSMS). Damping is calculated from these measurements. It can be difficult to get accurate damping measurements using this experimental setup and some of the details of how to obtain quality results are seemingly nontrivial. The intent of this paper is to present those details.

Provenza, Andrew J.↗

NASA NTRS2010

Chemical sensors using coated or doped carbon nanotube networks

Methods for using modified single wall carbon nanotubes ("SWCNTs") to detect presence and/or concentration of a gas component, such as a halogen (e.g., Cl.sub.2), hydrogen halides (e.g., HCl), a hydrocarbon (e.g., C.sub.nH.sub.2n+2), an alcohol, an aldehyde or a ketone, to which an unmodified SWCNT is substantially non-reactive. In a first embodiment, a connected network of SWCNTs is coated with a selected polymer, such as chlorosulfonated polyethylene, hydroxypropyl cellulose, polystyrene and/or polyvinylalcohol, and change in an electrical parameter or response value (e.g., conductance, current, voltage difference or resistance) of the coated versus uncoated SWCNT networks is analyzed. In a second embodiment, the network is doped with a transition element, such as Pd, Pt, Rh, Ir, Ru, Os and/or Au, and change in an electrical parameter value is again analyzed. The parameter change value depends monotonically, not necessarily linearly, upon concentration of the gas component. Two general algorithms are presented for estimating concentration value(s), or upper or lower concentration bounds on such values, from measured differences of response values.

Li, Jing↗

NASA NTRS2010

Process for Making a Noble Metal on Tin Oxide Catalyst

To produce a noble metal-on-metal oxide catalyst on an inert, high-surface-area support material (that functions as a catalyst at approximately room temperature using chloride-free reagents), for use in a carbon dioxide laser, requires two steps: First, a commercially available, inert, high-surface-area support material (silica spheres) is coated with a thin layer of metal oxide, a monolayer equivalent. Very beneficial results have been obtained using nitric acid as an oxidizing agent because it leaves no residue. It is also helpful if the spheres are first deaerated by boiling in water to allow the entire surface to be coated. A metal, such as tin, is then dissolved in the oxidizing agent/support material mixture to yield, in the case of tin, metastannic acid. Although tin has proven especially beneficial for use in a closed-cycle CO2 laser, in general any metal with two valence states, such as most transition metals and antimony, may be used. The metastannic acid will be adsorbed onto the high-surface-area spheres, coating them. Any excess oxidizing agent is then evaporated, and the resulting metastannic acid-coated spheres are dried and calcined, whereby the metastannic acid becomes tin(IV) oxide. The second step is accomplished by preparing an aqueous mixture of the tin(IV) oxide-coated spheres, and a soluble, chloride-free salt of at least one catalyst metal. The catalyst metal may be selected from the group consisting of platinum, palladium, ruthenium, gold, and rhodium, or other platinum group metals. Extremely beneficial results have been obtained using chloride-free salts of platinum, palladium, or a combination thereof, such as tetraammineplatinum (II) hydroxide ([Pt(NH3)4] (OH)2), or tetraammine palladium nitrate ([Pd(NH3)4](NO3)2).

Davis, Patricia↗

NASA NTRS2006

Challenges and Progress in the Development of High-Temperature Shape Memory Alloys Based on NiTiX Compositions for High-Force Actuator Applications

Interest in high-temperature shape memory alloys (HTSMA) has been growing in the aerospace, automotive, process control, and energy industries. However, actual materials development has seriously lagged component design, with current commercial NiTi alloys severely limited in their temperature capability. Additions of Pd, Pt, Au, Hf, and Zr at levels greater than 10 at.% have been shown to increase the transformation temperature of NiTi alloys, but with few exceptions, the shape memory behavior (strain recovery) of these NiTiX systems has been determined only under stress free conditions. Given the limited amount of basic mechanical test data and general lack of information regarding the work attributes of these materials, a program to investigate the mechanical behavior of potential HTSMAs, with transformation temperatures between 100 and 500 C, was initiated. This paper summarizes the results of studies, focusing on both the practical temperature limitations for ternary TiNiPd and TiNiPt systems based on the work output of these alloys and the ability of these alloys to undergo repeated thermal cycling under load without significant permanent deformation or "walking". These issues are ultimately controlled by the detwinning stress of the martensite and resistance to dislocation slip of the individual martensite and austenite phases. Finally, general rules that govern the development of useful, high work output, next-generation HTSMA materials, based on the lessons learned in this work, will be provided

Padula, Santo, II↗

NASA NTRS2011

High Pressure and Temperature Core Formation as an Alternative to the "Late Veneer" Hypothesis

The highly siderophile elements (HSE; Re, Au and the Platinum Group Elements - Pd Pt, Rh, Ru, Ir, Os) are commonly utilized to constrain accretion processes in terrestrial differentiated bodies due to their affinity for FeNi metal [1]. These eight elements exhibit highly siderophile behavior, but nonetheless have highly diverse metal-silicate partition coefficients [2]. Therefore the near chondritic relative concentrations of HSEs in the terrestrial and lunar mantles, as well as some other bodies, are attributed to late accretion rather than core formation [1]. Evaluation of competing theories, such as high pressure metal-silicate partitioning or magma ocean hypotheses has been hindered by a lack of relevant partitioning data for this group of eight elements. In particular, systematic studies isolating the effect of one variable (e.g. temperature or melt compositions) are lacking. Here we undertake new experiments on all eight elements, using Fe metal and FeO-bearing silicate melts at fixed pressure, but variable temperatures. These experiments, as well as some additional planned experiments should allow partition coefficients to be more accurately calculated or estimated at the PT conditions and compositions at which core formation is thought to have occurred.

Righter, Kevin↗

NASA NTRS2005

Adaptive Thresholding and Parameter Estimation for PPM

A method of adaptive setting of a threshold level for the detection of pulses in a pulse-position modulation (PPM) free-space optical communication system has been developed. In simplified terms, it is desirable to set a threshold value high enough to greatly reduce the probability (PFA as defined below) of erroneously detecting noise as signal pulses but not so high as to greatly reduce the probability (PD as defined below) of detecting any signal pulses that may be present along with noise. In the present method, the threshold level is varied with time, in response to changing conditions in the optical-communication channel, in an effort to maintain a balance between the aforesaid competing requirements. An integral part of this adaptation scheme is a scheme for estimating key parameters of the optical-communication channel in particular, parameters that describe the fading and total attenuation in the channel, and parameters that characterize spreading of pulses by atmospheric and other effects. The method can be implemented by software processing of digitized optoelectronic-detector output, and has been tested by computational simulation. In the first stage of processing by this method, the digitized values of the detector output during noise-only time slots of received PPM symbols are averaged to obtain a background level. This background level is subtracted from the detector output in the hope of reducing or eliminating the noise component in the remaining signal. (This background level should not be confused with the detection threshold, which is computed in the last stage of processing.) Next, the remaining signal - in effect, a vector of pulse samples - is normalized by dividing it by its L1 norm (in general, the L1 norm of a vector is defined as the sum of absolute magnitudes of its orthogonal components).

Arabshahi, Payman↗

NASA NTRS2011

Coated or doped carbon nanotube network sensors as affected by environmental parameters

Li, Jing↗

NASA NTRS2004

Patterned Growth of Carbon Nanotubes or Nanofibers

A method and apparatus for the growth of carbon nanotubes or nanofibers in a desired pattern has been invented. The essence of the method is to grow the nanotubes or nanofibers by chemical vapor deposition (CVD) onto a patterned catalyst supported by a substrate. The figure schematically depicts salient aspects of the method and apparatus in a typical application. A substrate is placed in a chamber that contains both ion-beam sputtering and CVD equipment. The substrate can be made of any of a variety of materials that include several forms of silicon or carbon, and selected polymers, metals, ceramics, and even some natural minerals and similar materials. Optionally, the substrate is first coated with a noncatalytic metal layer (which could be a single layer or could comprise multiple different sublayers) by ion-beam sputtering. The choice of metal(s) and thickness(es) of the first layer (if any) and its sublayers (if any) depends on the chemical and electrical properties required for subsequent deposition of the catalyst and the subsequent CVD of the carbon nanotubes. A typical first-sublayer metal is Pt, Pd, Cr, Mo, Ti, W, or an alloy of two or more of these elements. A typical metal for the second sublayer or for an undivided first layer is Al at a thickness .1 nm or Ir at a thickness .5 nm. Proper choice of the metal for a second sublayer of a first layer makes it possible to use a catalyst that is chemically incompatible with the substrate. In the next step, a mask having holes in the desired pattern is placed over the coated substrate. The catalyst is then deposited on the coated substrate by ion-beam sputtering through the mask. Optionally, the catalyst could be deposited by a technique other than sputtering and/or patterned by use of photolithography, electron- beam lithography, or another suitable technique. The catalytic metal can be Fe, Co, Ni, or an alloy of two or more of these elements, deposited to a typical thickness in the range from 0.1 to 20 nm.

Delzeit, Lance D.↗

NASA NTRS2011

Carbon Dioxide Gas Sensors and Method of Manufacturing and Using Same

A gas sensor includes a substrate and a pair of interdigitated metal electrodes selected from the group consisting of Pt, Pd, Au, Ir, Ag, Ru, Rh, In, and Os. The electrodes each include an upper surface. A first solid electrolyte resides between the interdigitated electrodes and partially engages the upper surfaces of the electrodes. The first solid electrolyte is selected from the group consisting of NASICON, LISICON, KSICON, and .beta.''-Alumina (beta prime-prime alumina in which when prepared as an electrolyte is complexed with a mobile ion selected from the group consisting of Na.sup.+, K.sup.+, Li.sup.+, Ag.sup.+, H.sup.+, Pb.sup.2+, Sr.sup.2+ or Ba.sup.2+). A second electrolyte partially engages the upper surfaces of the electrodes and engages the first solid electrolyte in at least one point. The second electrolyte is selected from the group of compounds consisting of Na.sup.+, K.sup.+, Li.sup.+, Ag.sup.+, H.sup.+, Pb.sup.2+, Sr.sup.2+ or Ba.sup.2+ ions or combinations thereof.

Hunter, Gary W.↗

NASA NTRS2011

Predicting Regional Drought on Sub-Seasonal to Decadal Time Scales

Drought occurs on a wide range of time scales, and within a variety of different types of regional climates. It is driven foremost by an extended period of reduced precipitation, but it is the impacts on such quantities as soil moisture, streamflow and crop yields that are often most important from a users perspective. While recognizing that different users have different needs for drought information, it is nevertheless important to understand that progress in predicting drought and satisfying such user needs, largely hinges on our ability to improve predictions of precipitation. This talk reviews our current understanding of the physical mechanisms that drive precipitation variations on subseasonal to decadal time scales, and the implications for predictability and prediction skill. Examples are given highlighting the phenomena and mechanisms controlling precipitation on monthly (e.g., stationary Rossby waves, soil moisture), seasonal (ENSO) and decadal time scales (PD~ and AMO).

Schubert, Siegfried↗

NASA NTRS2012

Low TCR nanocomposite strain gages

A high temperature thin film strain gage sensor capable of functioning at temperatures above 1400.degree. C. The sensor contains a substrate, a nanocomposite film comprised of an indium tin oxide alloy, zinc oxide doped with alumina or other oxide semiconductor and a refractory metal selected from the group consisting of Pt, Pd, Rh, Ni, W, Ir, NiCrAlY and NiCoCrAlY deposited onto the substrate to form an active strain element. The strain element being responsive to an applied force.

Gregory, Otto J.↗

NASA NTRS2012

Methods and apparatuses for signaling with geometric constellations

Communication systems are described that use signal constellations, which have unequally spaced (i.e. geometrically shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes d.sub.min, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.

Barsoum, Maged F.↗