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NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗
NASA NTRS1997

Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Kontinos, Dean A.↗
NASA NTRS1997

Local Interstellar Medium Properties and Deuterium Abundances for the Lines of Sight Toward HR 1099, 31 Comae, beta Ceti, and beta Cassiopeiae

We analyze Goddard High-Resolution Spectrograph data to infer the properties of local interstellar gas and the Deuterium/Hydrogen (D/H) ratio for lines of sight toward four nearby late-type stars-HR 1099, 31 Comae, beta Ceti, and beta Cassiopeiae. The data consist of spectra of the hydrogen and deuterium Lyman-(alpha) lines, and echelle spectra of the Mg IIh and k lines toward all stars except beta Cas. Spectra of the RS CVn-type spectroscopic binary system HR 1099 were obtained near opposite quadratures to determine the intrinsic stellar emission line profile and the interstellar absorption separately. Multiple-velocity components were found toward HR 1099 and beta Cet. The spectra of 31 Com and beta Cet are particularly interesting because they sample lines of sight toward the north and south Galactic poles, respectively, for which H I and D I column densities were not previously available. The north Galactic pole appears to be a region of low hydrogen density like the 'interstellar tunnel' toward epsilon CMa. The temperature and turbulent velocities of the Local InterStellar Medium (LISM) that we measure for the lines of sight toward HR 1099, 31 Com, beta Cet, and beta Cas are similar to previously measured values (T approx.7000 K and xi = 1.0-1.6 km/s). The deuterium/hydrogen ratios found for these lines of sight are also consistent with previous measurements of other short lines of sight, which suggest D/H approx. 1.6 x 10(sup -5). In contrast, the Mg abundance measured for the beta Cet line of sight (implying a logarithmic depletion of D(Mg) = +0.30 +/- 0.15) is about 5 times larger than the Mg abundance previously observed toward alpha Cen, and about 20 times larger than all other previous measurements for the LISM. These results demonstrate that metal abundances in the LISM vary greatly over distances of only a few parsecs.

Piskunov, Nikolai↗
NASA NTRS1997

Continued Development of the Discontinuous Galerkin Method for Computational Aeroacoustic Applications

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modifications. This feature leads to a simple and accurate treatment for wall boundary conditions and simple inflow and outflow boundary conditions. Curved walls are accurately treated with only minor changes to the implementation described in earlier work. The 'perfectly matched layer' approach to nonreflecting boundary conditions is easily applied to the discontinuous Galerkin. The compactness of the discontinuous Galerkin method makes it better suited for buffer-zone-type methods than high-order finite-difference methods. Results are presented for wall, characteristic inflow and outflow, and nonreflecting boundary conditions.

Atkins, H. L.↗
NASA NTRS1997

Application of the Discontinuous Galerkin Method to Acoustic Scatter Problems

The application of the quadrature-free form of the discontinuous Galerkin method to two problems from Category 1 of the Second Computational Aeroacoustics Workshop on Benchmark problems is presented. The method and boundary conditions relevant to this work are described followed by two test problems, both of which involve the scattering of an acoustic wave off a cylinder. The numerical test performed to evaluate mesh-resolution requirements and boundary-condition effectiveness are also described.

Atkins, H. L.↗
NASA NTRS1997

Concatenated Coding Using Trellis-Coded Modulation

In the late seventies and early eighties a technique known as Trellis Coded Modulation (TCM) was developed for providing spectrally efficient error correction coding. Instead of adding redundant information in the form of parity bits, redundancy is added at the modulation stage thereby increasing bandwidth efficiency. A digital communications system can be designed to use bandwidth-efficient multilevel/phase modulation such as Amplitude Shift Keying (ASK), Phase Shift Keying (PSK), Differential Phase Shift Keying (DPSK) or Quadrature Amplitude Modulation (QAM). Performance gain can be achieved by increasing the number of signals over the corresponding uncoded system to compensate for the redundancy introduced by the code. A considerable amount of research and development has been devoted toward developing good TCM codes for severely bandlimited applications. More recently, the use of TCM for satellite and deep space communications applications has received increased attention. This report describes the general approach of using a concatenated coding scheme that features TCM and RS coding. Results have indicated that substantial (6-10 dB) performance gains can be achieved with this approach with comparatively little bandwidth expansion. Since all of the bandwidth expansion is due to the RS code we see that TCM based concatenated coding results in roughly 10-50% bandwidth expansion compared to 70-150% expansion for similar concatenated scheme which use convolution code. We stress that combined coding and modulation optimization is important for achieving performance gains while maintaining spectral efficiency.

Thompson, Michael W.↗
NASA NTRS1998

Optical Channelizer Evaluation Using Empirical Data and Simulation

Westinghouse Electric Corporation Division under NASA contract NAS3-25865 developed a proof-of-concept (POC) multichannel demultiplexer implemented as an acousto-optic radiofrequency (RF) with a spectrum analyzer. A detailed analysis of the experimental results indicate that the expected degradation caused by the acousto-optical channelizer is approximately 2.0 dB degradation at 10(exp -5) bit-error rate (BER) and 3.0 dB degradation at 10(exp -8) BER. This degradation may be quite acceptable when considering the excellent volume, mass, and power characteristics of acousto-optical channelizing relative to other technologies. In addition, system performance can be greatly improved by using digital pulse shaping in the modem and increasing the channel spacing from 40 to 45 kHz for 64 kbps quadrature phase-shift keying (QPSK) modulation.

Ivancic,William D.↗
NASA NTRS1997

High Performance Circularly Polarized Microstrip Antenna

A microstrip antenna for radiating circularly polarized electromagnetic waves comprising a cluster array of at least four microstrip radiator elements, each of which is provided with dual orthogonal coplanar feeds in phase quadrature relation achieved by connection to an asymmetric T-junction power divider impedance notched at resonance. The dual fed circularly polarized reference element is positioned with its axis at a 45 deg angle with respect to the unit cell axis. The other three dual fed elements in the unit cell are positioned and fed with a coplanar feed structure with sequential rotation and phasing to enhance the axial ratio and impedance matching performance over a wide bandwidth. The centers of the radiator elements are disposed at the corners of a square with each side of a length d in the range of 0.7 to 0.9 times the free space wavelength of the antenna radiation and the radiator elements reside in a square unit cell area of sides equal to 2d and thereby permit the array to be used as a phased array antenna for electronic scanning and is realizable in a high temperature superconducting thin film material for high efficiency.

Bondyopadhyay, Probir K.↗
NASA NTRS1998

The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96

The NASA Goddard Space Flight Center (GSFC), the National Imagery and Mapping Agency (NIMA), and The Ohio State University (OSU) have collaborated to develop an improved spherical harmonic model of the Earth's gravitational potential to degree 360. The new model, Earth Gravitational Model 1996 (EGM96), incorporates improved surface gravity data, altimeter-derived gravity anomalies from ERS-1 and from the GEOSAT Geodetic Mission (GM), extensive satellite tracking data-including new data from Satellite Laser Ranging (SLR), the Global Postioning System (GPS), NASA's Tracking and Data Relay Satellite System (TDRSS), the French DORIS system, and the US Navy TRANET Doppler tracking system-as well as direct altimeter ranges from TOPEX/POSEIDON (T/P), ERS-1, and GEOSAT. The final solution blends a low-degree combination model to degree 70, a block-diagonal solution from degree 71 to 359, and a quadrature solution at degree 360. The model was used to compute geoid undulations accurate to better than one meter (with the exception of areas void of dense and accurate surface gravity data) and realize WGS84 as a true three-dimensional reference system. Additional results from the EGM96 solution include models of the dynamic ocean topography to degree 20 from T/P and ERS-1 together, and GEOSAT separately, and improved orbit determination for Earth-orbiting satellites.

Lemoine, F. G.↗
NASA NTRS1999

A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2

Goddard Ocean Tide model GOT99.2 is a new solution for the amplitudes and phases of the global oceanic tides, based on over six years of sea-surface height measurements by the TOPEX/POSEIDON satellite altimeter. Comparison with deep-ocean tide-gauge measurements show that this new tidal solution is an improvement over previous global models, with accuracies for the main semidiurnal lunar constituent M2 now below 1.5 cm (deep water only). The new solution benefits from use of prior hydrodynamic models, several in shallow and inland seas as well as the global finite-element model FES94.1. This report describes some of the data processing details involved in handling the altimetry, and it provides a comprehensive set of global cotidal charts of the resulting solutions. Various derived tidal charts are also provided, including tidal loading deformation charts, tidal gravimetric charts, and tidal current velocity (or transport) charts. Finally, low-degree spherical harmonic coefficients are computed by numerical quadrature and are tabulated for the major short-period tides; these are useful for a variety of geodetic and geophysical purposes, especially in combination with similar estimates from satellite laser ranging.

Ray, Richard D.↗
NASA NTRS1999

Mantle Q at Period 12.4 Hours: New Estimates from Satellite Tracking and Altimetry

The most convincing estimates of mantle Q at periods of many hours have historically come from extrapolating seismic and free-oscillation estimates via some assumed frequency dependence, sometimes contrained by estimates from the Chandler Wobble. At the semidiurnal tidal period, direct estimates of Q have been difficult to obtain because of the dominating signals of the ocean tides, which account for more than 95!k of the tidal energy dissipation. But knowledge of the ocean tides has been rapidly improving, primarily owing to satellite altimetry, and in 1996 we reported (NATURE, 381, 595-7) an estimate of solid-earth tidal energy dissipation and mantle Q based on combining satellite altimeter measurements with tracking observations of tidally induced satellite orbit perturbations. Tidal estimates from both reveal a small systematic difference in the quadrature component of the degree-2, order-2 spherical harmonic coefficients, which we attribute to a small lag in the earth's body tide. The formalism accounts for this lag in both the altimeter and tracking solutions and also accounts for a very small contribution from the lunar atmospheric tide. Since this original report, both altimeter and tracking estimates have improved. Recent solutions for the body-tide lag at the M2 period are 0.20 +/- 0.09 degrees, implying an energy dissipation of 100 +/- 50 gigawatts and a solid-earth Q of 300. Further new solutions will be discussed, as will the prospects for significantly reducing error bars and for obtaining estimates from other tides in the diurnal band.

Ray, Richard D.↗
NASA NTRS1999

The Biolink Implantable Telemetry System

Most biotelemetry applications deal with the moderated data rates of biological signals. Few people have studied the problem of transcutaneous data transmission at the rates required by NASA's Life Sciences-Advanced BioTelemetry System (LS-ABTS). Implanted telemetry eliminate the problems associated with wire breaking the skin, and permits experiments with awake and unrestrained subjects. Our goal is to build a low-power 174-216MHz Radio Frequency (RF) transmitter suitable for short range biosensor and implantable use. The BioLink Implantable Telemetry System (BITS) is composed of three major units: an Analog Data Module (ADM), a Telemetry Transmitter Module (TTM), and a Command Receiver Module (CRM). BioLink incorporates novel low-power techniques to implement a monolithic digital RF transmitter operating at 100kbps, using quadrature phase shift keying (QPSK) modulation in the 174-216MHz ISM band. As the ADM will be specific for each application, we focused on solving the problems associated with a monolithic implementation of the TTM and CRM, and this is the emphasis of this report. A system architecture based on a Frequency-Locked Loop (FLL) Frequency Synthesizer is presented, and a novel differential frequency that eliminates the need for a frequency divider is also shown. A self sizing phase modulation scheme suitable for low power implementation was also developed. A full system-level simulation of the FLL was performed and loop filter parameters were determined. The implantable antenna has been designed, simulated and constructed. An implant package compatible with the ABTS requirements is also being proposed. Extensive work performed at 200MHz in 0.5um complementary metal oxide semiconductors (CMOS) showed the feasibility of integrating the RF transmitter circuits in a single chip. The Hajimiri phase noise model was used to optimize the Voltage Controlled Oscillator (VCO) for minimum power consumption. Two test chips were fabricated in a 0.5pm, 3V CMOS process. Measured phase noise for a 1.5mW, 200MHz ring oscillator VCO is -80dBc/Hz at 100KHZ offset, showing good agreement with the theory. We also propose a novel superregenerative receiver architecture for implementing the command receiver. The superregenerative receiver's simplicity, low cost, and low power consumption has made it the receiver of choice for short-distance data communications, remote control and home automation. We present the design of a superregenerative AM receiver implemented in a 0.5um CMOS technology that operates at 433.92MHz and dissipates only 300uW. Further work entails detailed transistor-level design of the FLL and superregenerative receiver and a monolithic implementation of an implantable transceiver in 0.5um CMOS technology.

Betancourt-Zamora, Rafael J.↗
NASA NTRS2000

Higher Order Modeling In the BEM/FEM Hybrid Formulation

Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.

Fink, Patrick W.↗
NASA NTRS2000

Flight Dynamics Analysis for Leonardo-BRDF

Leonardo-BRDF (Bidirectional Reflectance Distribution Function) is a new NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the flight dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal Lambert initialization scheme is presented with the required Delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated Delta-V's are calculated to maintain the formation in the presence of perturbations.

Hughes, Steven P.↗
NASA NTRS2001

Preliminary Results from Coordinated UVCS-CDS-Ulysses Observations

The June 2000 quadrature between the Sun, Earth, and Ulysses took place with Ulysses at a distance of 3.35 AU from the Sun and at heliocentric latitude 58.2 deg south, in the southeast quadrant. This provided an opportunity to observe the corona close to the Sun with Coronal Diagnostic Spectrometer (CDS) and Ultraviolet Coronograph Spectrometer (UVCS) and, subsequently, to sample the same plasma when it reached Ulysses. Here we focus on simultaneous observations of UVCS and CDS made on June 12, 13, 16 and 17. The UVCS data were acquired at heliocentric altitudes ranging from 1.6 to 2.2 solar radii, using different grating positions, in order to get a wide wavelength range. CDS data consisted of Normal Incidence Spectrometer (NIS) full wavelength rasters of 120" x 150" centered at altitudes up to 1.18 solar radii, together with Grazing Incidence Spectrometer (GIS) 4" x 4" rasters within the same field of view, out to 1.2 solar radii. The radial direction to Ulysses passed through a high latitude streamer, throughout the 4 days of observations, Analysis of the spectra taken by UVCS shows a variation of the element abundances in the streamer over our observing interval: however, because the observations were in slightly different parts of the streamer on different days, the variation could be ascribed either to a temporal or spatial effect. The oxygen abundance, however, seems to increase at the edge of the streamer, as indicated by previous analyses. This suggests the variation may be a function of position within the streamer, rather than a temporal effect. Oxygen abundances measured by SWICS on Ulysses are compared with the CDS and UVCS results to see whether changes measured in situ follow the same pattern.

Parenti, S.↗
NASA NTRS2001

A Preliminary Formation Flying Orbit Dynamics Analysis for Leonardo-BRDF

Leonardo-BRDF is a NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the orbit dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal two-burn initialization scheme is presented with the required delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated delta-V's are calculated to maintain the formation in the presence of perturbations.

Hughes, Steven P.↗
NASA NTRS2001

Forced and Free Intra-Seasonal Variability Over the South Asian Monsoon Region Simulated by 10 AGCMs

This study examines intra-seasonal (20-70 day) variability in the South Asian monsoon region during 1997/98 in ensembles of 10 simulations with 10 different atmospheric general circulation models. The 10 ensemble members for each model are forced with the same observed weekly sea surface temperature (SST) but differ from each other in that they are started from different initial atmospheric conditions. The results show considerable differences between the models in the simulated 20-70 day variability, ranging from much weaker to much stronger than the observed. A key result is that the models do produce, to varying degrees, a response to the imposed weekly SST. The forced variability tends to be largest in the Indian and western Pacific Oceans where, for some models, it accounts for more than 1/4 of the 20-70 day intra-seasonal variability in the upper level velocity potential during these two years. A case study of a strong observed MJO (intraseasonal oscillation) event shows that the models produce an ensemble mean eastward propagating signal in the tropical precipitation field over the Indian Ocean and western Pacific, similar to that found in the observations. The associated forced 200 mb velocity potential anomalies are strongly phase locked with the precipitation anomalies, propagating slowly to the east (about 5 m/s) with a local zonal wave number two pattern that is generally consistent with the developing observed MJO. The simulated and observed events are, however, approximately in quadrature, with the simulated response 2 leading by 5-10 days. The phase lag occurs because, in the observations, the positive SST anomalies develop upstream of the main convective center in the subsidence region of the MJO, while in the simulations, the forced component is in phase with the SST. For all the models examined here, the intraseasonal variability is dominated by the free (intra-ensemble) component. The results of our case study show that the free variability has a predominately zonal wave number one pattern, and has propagation speeds (10 - 15 m/s) that are more typical of observed MJO behavior away from the convectively active regions. The free variability appears to be synchronized with the forced response, at least, during the strong event examined here. The results of this study support the idea that coupling with SSTs plays an important, though probably not dominant, role in the MJO. The magnitude of the atmospheric response to the SST appears to be in the range of 15% - 30% of the 20-70 day variability over much of the tropical eastern Indian and western Pacific Oceans. The results also highlight the need to use caution when interpreting atmospheric model simulations in which the prescribed SST resolve MJO time scales.

Wu, Man Li C.↗
NASA NTRS2001

EFQPSK Versus CERN: A Comparative Study

This report presents a comparative study on Enhanced Feher's Quadrature Phase Shift Keying (EFQPSK) and Constrained Envelope Root Nyquist (CERN) techniques. These two techniques have been developed in recent times to provide high spectral and power efficiencies under nonlinear amplifier environment. The purpose of this study is to gain insights into these techniques and to help system planners and designers with an appropriate set of guidelines for using these techniques. The comparative study presented in this report relies on effective simulation models and procedures. Therefore, a significant part of this report is devoted to understanding the mathematical and simulation models of the techniques and their set-up procedures. In particular, mathematical models of EFQPSK and CERN, effects of the sampling rate in discrete time signal representation, and modeling of nonlinear amplifiers and predistorters have been considered in detail. The results of this study show that both EFQPSK and CERN signals provide spectrally efficient communications compared to filtered conventional linear modulation techniques when a nonlinear power amplifier is used. However, there are important differences. The spectral efficiency of CERN signals, with a small amount of input backoff, is significantly better than that of EFQPSK signals if the nonlinear amplifier is an ideal clipper. However, to achieve such spectral efficiencies with a practical nonlinear amplifier, CERN processing requires a predistorter which effectively translates the amplifier's characteristics close to those of an ideal clipper. Thus, the spectral performance of CERN signals strongly depends on the predistorter. EFQPSK signals, on the other hand, do not need such predistorters since their spectra are almost unaffected by the nonlinear amplifier, Ibis report discusses several receiver structures for EFQPSK signals. It is observed that optimal receiver structures can be realized for both coded and uncoded EFQPSK signals with not too much increase in computational complexity. When a nonlinear amplifier is used, the bit error rate (BER) performance of the CERN signals with a matched filter receiver is found to be more than one decibel (dB) worse compared to the bit error performance of EFQPSK signals. Although channel coding is found to provide BER performance improvement for both EFQPSK and CERN signals, the performance of EFQPSK signals remains better than that of CERN. Optimal receiver structures for CERN signals with nonlinear equalization is left as a possible future work. Based on the numerical results, it is concluded that, in nonlinear channels, CERN processing leads towards better bandwidth efficiency with a compromise in power efficiency. Hence for bandwidth efficient communications needs, CERN is a good solution provided effective adaptive predistorters can be realized. On the other hand, EFQPSK signals provide a good power efficient solution with a compromise in band width efficiency.

Borah, Deva K.↗