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The performance of a QPSK (quadrature phase-shift keying) lock detector is described, taking into account the degradation due to carrier phase jitter. Such an analysis is necessary for accurate performance prediction purposes in scenarios where both the loop SNR is low and the estimation period is short. The derived formulas are applicable to several QPSK loops and are verified using computer simulations.
A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.
A theoretical investigation of the velocity profiles for laminar mixing of a high-velocity stream with a region of fluid at rest has been made assuming that the Prandtl number is unity. A method which involves only quadratures is presented for calculating the velocity profile in the mixing layer for an arbitrary value of the free-stream Mach number. Detailed velocity profiles have been calculated for free-stream Mach numbers of 0, 1, 2, 3, and 5. For each Mach number, velocity profiles are presented for both a linear and a 0.76-power variation of viscosity with absolute temperature. The calculations for a linear variation are much simpler than those for a 0.76-power variation. It is shown that by selecting the constant of proportionality in the liner approximation such that it gives the correct value for the viscosity in the high-temperature part of the mixing layer, the resulting velocity profiles are in excellent agreement with those calculated by a 0.76-power variation.
Report presents theoretical analysis of relationships among: shapes and bandwidths of data pulses in pulse-amplitude modulation (PAM) and quadrature amplitude modulation (QAM); pulse-repetition rates (baud rates); and presence or absence of sinusoidal baud-frequency components in envelopes (magnitudes) of overall received signals.
The quantum theory of coherent radiation frequency doubling in crystals with quadratic and cubic optical nonlinearities is developed. The possibility of producing the quadrature-squeezed state of the second harmonic (SH) field is shown. The nonclassical SH states arise due to self-action effect.
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.
The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.
An airborne, forward-looking, pulse, Doppler radar has been developed in conjunction with the joint FAA/NASA Wind Shear Program. This radar represents a first in an emerging technology. The radar was developed to assess the applicability of an airborne radar to detect low altitude hazardous wind shears for civil aviation applications. Such a radar must be capable of looking down into the ground clutter environment and extracting wind estimates from relatively low reflectivity weather targets. These weather targets often have reflectivities several orders of magnitude lower than the surrounding ground clutter. The NASA radar design incorporates numerous technological and engineering achievements in order to accomplish this task. The basic R/T unit evolved from a standard Collins 708 weather radar, which supports specific pulse widths of 1-7 microns and Pulse Repetition Frequencies (PRF) of less than 1-10 kHz. It was modified to allow for the output of the first IF signal, which fed a NASA developed receiver/detector subsystem. The NASA receiver incorporated a distributed, high-speed digital attenuator, producing a range bin to range bin automatic gain control system with 65 dB of dynamic range. Using group speed information supplied by the aircraft's navigation system, the radar signal is frequency demodulated back to base band (zero Doppler relative to stationary ground). The In-phase & Quadrature-phase (I/Q) components of the measured voltage signal are then digitized by a 12-bit A-D converter (producing an additional 36 dB of dynamic range). The raw I/Q signal for each range bin is then recorded (along with the current radar & aircraft state parameters) by a high-speed Kodak tape recorder.
This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.
This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.
A system design for aeronautical audio broadcasting, with C-band uplink and L-band downlink, via Inmarsat space segments is presented. Near-transparent-quality compression of 5-kHz bandwidth audio at 20.5 kbit/s is achieved based on a hybrid technique employing linear predictive modeling and transform-domain residual quantization. Concatenated Reed-Solomon/convolutional codes with quadrature phase shift keying are selected for bandwidth and power efficiency. RF bandwidth at 25 kHz per channel, and a decoded bit error rate at 10(exp -6) with E(sub b)/N(sub o) at 3.75 dB are obtained. An interleaver, scrambler, modem synchronization, and frame format were designed, and frequency-division multiple access was selected over code-division multiple access. A link budget computation based on a worst-case scenario indicates sufficient system power margins. Transponder occupancy analysis for 72 audio channels demonstrates ample remaining capacity to accommodate emerging aeronautical services.
This paper describes some low cost approaches to coherent BPSK demodulation for mobile satellite receivers. The specific application is an Inmarsat-C Land Mobile Earth Station (LMES), but the techniques are applicable to any PSK demodulator. The techniques discussed include combined sampling and quadrature downconversion with a single A/D and novel DSP algorithms for carrier acquisition offering both superior performance and economy of DSP resources. The DSP algorithms run at 5.7 MIPS, and the entire DSP subsystem, built with commercially available parts, costs under $60 at quantity-10,000.
A time-and-space accurate and computationally efficient fully three dimensional unsteady temperature field analysis computer code has been developed for truly arbitrary configurations. It uses boundary element method (BEM) formulation based on an unsteady Green's function approach, multi-point Gaussian quadrature spatial integration on each panel, and a highly clustered time-step integration. The code accepts either temperatures or heat fluxes as boundary conditions that can vary in time on a point-by-point basis. Comparisons of the BEM numerical results and known analytical unsteady results for simple shapes demonstrate very high accuracy and reliability of the algorithm. An example of computed three dimensional temperature and heat flux fields in a realistically shaped internally cooled turbine blade is also discussed.
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
The real-time array feed compensation system is currently being evaluated at DSS 13. This system recovers signal-to-noise ratio (SNR) loss due to mechanical antenna deformations by using an array of seven Ka-band (33.7-GHz) horns to collect the defocused signal fields. The received signals are downconverted and digitized, in-phase and quadrature samples are generated, and combining weights are applied before the samples are recombined. It is shown that when optimum combining weights are employed, the SNR of the combined signal approaches the sum of the channel SNR's. The optimum combining weights are estimated directly from the signals in each channel by the Real-Time Block 2 (RTB2) correlator; since it was designed for very-long-baseline interferometer (VLBI) applications, it can process broadband signals as well as tones to extract the required weight estimates. The estimation algorithms for the optimum combining weights are described for tones and broadband sources. Data recorded in correlator output files can also be used off-line to estimate combiner performance by estimating the SNR in each channel, which was done for data taken during a Jupiter track at DSS 13.
The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.