H-reversal trajectory: A new mission application for high-performance solar sails

The aim of this paper is to quantify the performance of a flat solar sail to perform a double angular momentum reversal maneuver and produce a new class of two-dimensional, non-Keplerian orbits in the ecliptic plane. For a given pair of orbital parameters, the orbital period and the perihelion distance, it is possible to find the minimum solar sail characteristic acceleration required to fulfil a double angular momentum reversal trajectory. This problem is addressed using an optimal formulation and is solved through an indirect approach. The new trajectories are symmetrical with respect to the sun-perihelion line and exhibit a bean-like shape. Two main difficulties must be properly taken into account. On one side the sail is required to perform a rapid reorientation maneuver when it approaches the perihelion. Suitable simulations have shown that such a maneuver is feasible. In the second place the new trajectories require the use of high performance solar sails. For example, assuming an orbital period equal to 5 years, the required solar sail characteristic acceleration is greater than 3.4 mm/s². Such a value, although beyond the currently available sail performance, is comparable to what is required by the original concept of H-reversal maneuvers introduced by Vulpetti in 1996.     

Optimal solar sail trajectory approximation with finite Fourier series

The heliocentric transfer of a solar sail-based spacecraft is usually studied from an optimal perspective, by looking for the control law that minimizes the total flight time. The optimal control problem can be solved either with an indirect approach, whose solution is difficult to obtain due to its sensitivity to an initial guess of the costates, or with a direct method, which requires a good estimate of a feasible (guess) trajectory. This work presents a procedure to generate an approximate optimal trajectory through a finite Fourier series. The minimum time problem is solved using a nonlinear programming solver, in which the optimization parameters are the coefficients of the Fourier series and the positions of the spacecraft along the initial and target orbits. Suitable constraints are enforced on the direction and magnitude of the sail propulsive acceleration vector in order to obtain feasible solutions. A comparison with the numerical results from an indirect approach shows that the proposed method provides a good approximation of the optimal trajectory with a small computational effort.     

Optimum and Suboptimum Synchronizer for Binary FSK Communication Systems

This paper considers a binary frequency-shift-keying (FSK) communication system with an adaptive receiver. Partially coherent detection is accomplished exploiting phase and bit synchronization directly extracted from the information-bearing waveform. The optimum (maximum a posteriori probability criterion) estimators of the relevant channel parameters are found along with some suboptimum realizations. It turns out that these schemes are decision-directed tracking systems that may be implemented using standard circuitry.     

Noise Performance of a Gated Phase-Locked Loop

The objectives of this paper are two. The first is to show that a gated phase-locked loop (GPLL) is a tracking device whose operation approximates that of a maximum likelihood estimator of the phase of a pulsed sinusoid imbedded in noise. The second is to determine the behavior of theb loop in the presence of noise. It is found that the loop performance is equivalent to that of a continuous phase-locked loop driven by the same noise, plus a continuous sinusoid which has the same power as the pulsed sinusoid at the input of the GPLL.     

A Self Bit Synchronizer Matched to the Signal Shape

A suboptimum self bit synchronizer is considered that matches the signal shape, i. e., operates making a clever use of the knowledge of the signaling waveform. The noise performance of this system is analyzed for high signal-to-noise ratios, and an expression is obtained for the variance of the timing errors. This variance is compared with that of systems proposed by other authors on the basis of equal closed-loop noise bandwidth and equal signal shape. It is found that the use of this matched synchronizer enables appreciable timing jitter reductions.     

Optimal interplanetary rendezvous combining electric sail and high thrust propulsion system

The aim of this paper is to study, from a mission analysis point of view, the performance of a hybrid propulsion concept for a two-dimensional transfer towards a planet of the Solar System. The propulsion system is obtained by combining a chemical thruster, used for the phases of Earth escape and/or target planet capture, with an electric sail, which provides a continuous thrust during the heliocentric transfer. Two possible mission scenarios are investigated: in the first case the sailcraft reaches the target planet with zero hyperbolic excess velocity, thus performing a classical rendezvous mission in a heliocentric framework. In the second mission scenario, a given final hyperbolic excess velocity relative to the planet is tolerated in order to decrease the mission flight time. The amount of final hyperbolic excess velocity is used as a simulation parameter for a tradeoff study in which the minimum flight time is related to the total velocity variation required by the chemical thruster to accomplish the mission, that is, for Earth escape and planetary capture.     

Limiting the Impulsive Noise in a PLL

This paper analyzes the operation of a phase-locked loop (PLL) preceded by a bandpass limiter (BPL) in the presence of impulsive noise. It is shown that the effect of the limiter consists essentially in a change of the statistics of the pulse strengths of the noise, so that the behavior of a BPL + PLL can be deduced from that of a simple PLL by suitable adjustment of the noise model. It is found that the limiter greatly enhances the PLL performance by reducing both the phase-error variance in the loop and the probability of cycle slippage. Finally, the design of the filter of the BPL is discussed, resulting in the conclusion that the best results are obtained by using a singletuned RLC circuit.     

Probability Density of the Click Duration in an Ideal FM Discriminator

The expression of the probability density function PClick(T) of the duration r of the clicks is determined as a function of 1) the expected number of clicks per second, Felick 2) the expected number of times per second that the noise component x(t) in phase with the carrier has instantaneous amplitude larger than that of the carrier itself 3) the probability density function peross(T) of the duration of the time intervals in which x(t) < -A 4) the probability that the values of the noise component in quadrature with the carrier will be of opposite sign at the extremes of time intervals of duration v. Using for Pcross(T) an approximate formula that holds fairly well in the range of the values of the signal-to-noise power ratio ? usually encountered, PIick(T) has been calculated for several values of a and for two shapes of the noise spectrum, Gaussian and rectangular. Finally, an expression is given for the mean value of T.     

An Extension of Viterbi's Analysis of the Cycle Slipping in a First-Order Phase-Locked Loop

The phenomenon of cycle slipping in a first-order phase-locked loop is reconsidered and a simple expression for the expected number ? of cycles slipped per second is given in the form of a rapidly converging series. In this way the computation of ? becomes much easier than with previously known formulas. A formula allowing the computation of the expected number of cycles gained or lost per second is also given. These results are obtained by extending a technique used by Viterbi. The outcome of experimental verifications of the theory is also reported.     

Synchronization of QAM Signals in the Presence of ISI

A data-aided carrier reconstruction method is described for quadrature amplitude modulation (QAM) data communications over narrow-band transmission channels. Previous analyses of this problem have assumed an "infinite" bandwidth of the communication link, so that negligible intersymbol interference (ISI) resulted. On the contrary, when ISI takes place, a different structure must be used which operates on sampled data. The performance of this structure is expressed analytically as a function of 1) the statistics of the message symbols, 2) the characteristics of the channel, and 3) the parameters of the tracking system. Excellent agreement has been found between the theory and the results of a computer simulation.