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NASA NTRS2004

Multipulse PPM on memoryless channels

memoryless channels. First, we derive the maximum likelihood decision rule and an exact expression for the symbol error rate for n (greater-than or equal) 1, avoiding a numerically unstable aspect of = 1 formula of [GK76] and generalizing the n = 2 result of [SV03]. Next, we compare the capacity of multipulse PPM to that of conventional single-pulse PPM when averaged power, peak, and bandwidth constraints are simultaneously imposed. On the basis, we demonstrate that multipulse PPM does not produce appreciable gains over conventional PPM except at high average power.

optical communications↗

NASA NTRS2005

Coherent Optical Receiver for PPM Signals under Atmospheric Turbulence

Adaptive combining of experimentally obtained heterodyned pulse position modulated (PPM) signals with pulse-to-pulse coherence in the presence of simulated spatial distortions resembling atmospheric turbulence is demonstrated. The adaptively combined PPM signals are phased up via an LMS algorithm suitably optimized to operate with PPM in the presence of additive shot-noise. A convergence analysis of the algorithm is presented, and results with both, computer simulated and experimentally obtained PPM signals are analyzed.

coherent detection↗

DOE OSTI2026

Four ppm measurement of the antihydrogen ground-state hyperfine splitting

The hydrogen atom is a touchstone for the foundations, evolution and frontiers of quantum theory. Key spectral lines of this atom have been determined to remarkable precision. Our research focuses on the study of antihydrogen, the antimatter counterpart of hydrogen. We test fundamental symmetries of nature (such as simultaneous charge conjugation, parity inversion, and time reversal or CPT symmetry) through precision comparisons of these atomic systems. Recent 1S–2S spectroscopic measurements on trapped antihydrogen have achieved relative precisions of parts per trillion. However, the ground-state hyperfine splitting, which is sensitive to the internal structure of the antiproton, has only been measured to 400 parts per million (ppm). Here we report a 4 ppm measurement of the antihydrogen ground-state hyperfine splitting energy a 1S , advancing the state-of-the-art precision by two orders of magnitude. From microwave spectroscopy experiments with roughly 24,000 anti-atoms, we determine ${a}_{1{\rm{S}}}/h=\mathrm{1,420,404.8}\pm 1.1(\mathrm{stat.})\pm 5.6\,(\mathrm{sys.})\,\text{kHz}$ in a 1-T magnetic field, consistent with expectations for hydrogen. At this level, our measurement is sensitive to the internal structure of the antiproton, which contributes at about 40 ppm and is approaching the limit of existing theoretical analyses. The gains we report are the product of marked advances in magnetic trap field control, stabilization and characterization; anti-atom spin-state manipulation; and improved antihydrogen accumulation rate.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Detailed report on the measurement of the positive muon anomalous magnetic moment to 0.20 ppm

We present details on a new measurement of the muon magnetic anomaly, a μ =(g μ −2)/2. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses 3.1 GeV/c polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of a μ is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure a μ =116592057(25)×10 −11 (0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield a μ (FNAL)=116592055(24)×10 −11 (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is a μ (exp)=116592059(22)×10 −11 (0.19 ppm).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1982

Analysis of DSN PPM support during Voyager 2 Saturn encounter

The precision power monitor (PPM) is a precision radiometric instrument used to improve the efficiency of signal reception by the Deep Space Network. Real time estimates of the system operating temperature, the present (signal + noise)-to-noise ratio, and the signal power are utilized to increase the accuracy and resolution of the received spacecraft signal. Due to the critical nature of radio science data returning from Voyager 2 at Saturn Encounter, PPM support was required. The task was undertaken to validate the performance of equipment technically under research and development in time to meet the encounter deadline. Initial studies revealed PPM performance to be out of tolerance. Action was immediately taken to identify the system problems. Using data analysis as feedback, the system failures were identified and corrected in time to contribute to the encounter support efforts. As a result, the radio science data were collected successfully.

Bartok, C. D.↗

NASA NTRS1991

Bandwidth requirements for direct detection optical communication receivers with PPM signaling

The performance of a direct detection optical communication receiver for pulse position modulation (PPM) signal formats which contains an avalanche photodiode photodetector is calculated as a function of the parameters which characterize a raised cosine filter used in the receiver. It is shown that the performance penalty of this receiver relative to that of an optimal receiver which contains an integrator and assumes a perfectly rectangular PPM pulse shape is less than 1 dB at a receiver bit error rate of 10 exp -6. The advantage of the raised cosine filter is that the electrical bandwidth required is no more than one-half that of the integrator, that is, 1/tau as opposed to 2/tau where tau is the PPM time slot duration.

Davidson, Frederic M.↗

NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗

DOE OSTI2025

Measurement of the muon magnetic anomaly to 0.20 ppm by the Muon g-2 experiment at Fermilab

The Muon $g-2$ experiment at Fermilab aims to measure the muon magnetic moment anomaly, $a_{\mu}=(g-2)/2$, with a final accuracy of 0.14 parts per million (ppm). The experiment’s first result was published in 2021, based on data collected in 2018, and in 2023 a new result was published based on two more years of data taking, 2019 and 2020. The combination of the two results from Fermilab and the previous one from Brookhaven National Laboratory brought the uncertainty on the experimental measurement of $a_{\mu}$ to the unprecedented value of 0.19 ppm. This paper will present details about the improvements of statistical and systematic uncertainties on $a_{\mu}$ since the 2021 result.

Cotrozzi, Lorenzo [Liverpool U.; INFN, Pisa]↗

NASA NTRS1972

Synchronization using pulsed edge tracking in optical PPM communication system

A pulse position modulated (PPM) optical communication system using narrow pulses of light for data transmission requires accurate time synchronization between transmitter and receiver. The presence of signal energy in the form of optical pulses suggests the use of a pulse edge tracking method of maintaining the necessary timing. The edge tracking operation in a binary PPM system is examined, taking into account the quantum nature of the optical transmissions. Consideration is given first to pure synchronization using a periodic pulsed intensity, then extended to the case where position modulation is present and auxiliary bit decisioning is needed to aid the tracking operation. Performance analysis is made in terms of timing error and its associated statistics. Timing error variances are shown as a function of system signal to noise ratio.

Gagliardi, R.↗

NASA NTRS1982

PPM demodulation for Reed-Solomon decoding for the optical space channel

The use of Reed-Solomon (RS) block codes over the pulse position modulated (PPM) frames to obtain the largest degree of error correction is considered. Since RS codes can correct both symbol errors and symbol erasures, a question arises as to the best way to demodulate the PPM laser fields in order to generate the input symbols for the RS decoder. The method selected for demodulating (converting the received laser field to digital symbols) defines the erasure and transmitted symbols of the laser link, and therefore determines the work error probabilities of the system. Several demodulating schemes are considered, and the effect of each on RS decoding performance computed. This computation was carried out for various optical receiver models. It is shown that simple threshold decisioning of pulse slots produces performance that degrades as the background noise increases. This is caused by the generation of too many erasures for the RS decoder to handle. A decision scheme, delta-max demodulation which offers improvement over threshold decisioning by redefining the generation of an erasure is proposed.

Divsalar, D.↗

NASA NTRS1982

Electron microprobe analysis of trace elements in minerals at 10 PPM concentrations

An improved technique is developed for measuring backgrounds during trace element analysis of crystals and glass using electron microprobes. This technique overcomes major difficulties encountered with conventional techniques, such as the problem of obtaining the net X-ray intensity of the characteristic emission line of interest with sufficient precision and accuracy, as well as the error due to the inability to directly measure the intensity at the wavelength of the characteristic line on the sample being analyzed. It is shown that this technique can yield reproducible results to within 4 ppm in olivine, and has a minimum uncertainty and detection limit of 10 ppm Nd in olivine.

Mckay, G. A.↗

NASA NTRS1984

An Easy-to-implement Coding Scheme for Multifrequency PPM

In implementing multifrequency PPM, a naturally arising question is: Let P be a fixed number; among all integer valued processes X1, X2, X3, with E ( X(n+1)-X(n) squared) less than or = P, which has the largest entropy? Earlier work by McEliece and Rodemich answered this question, but there is no obvious way to use this process to implement a code for multifrequency PPM. The present article describes an easy-to-implement process X1, X2, with E ( X(n+1)-X(n) squared) less than or = P, whose entropy is nearly as great as that of the McEliece-Rodemich process.

Mceliece, R. J.↗

NASA NTRS1985

Synchronization for Optical PPM Signals

Method based on statistical properties of weak pulse-positionmodulated (PPM) signal enables synchronization of receiver clock with received-signal time base. Method applies to weak optical M-ary PPM signals, for which there is only one pulse of length Tp transmitted during one of timeslots of length T in each successive interval of M timeslots. Method requires small dead time, Td, at beginning and end of each timeslot, during which pulse amplitude is zero.

Vilnrotter, V. A.↗

NASA NTRS1985

Phase locked loop synchronization for direct detection optical PPM communication systems

Receiver timing synchronization of an optical pulse position modulation (PPM) communication system can be achieved using a phase locked loop (PLL) if the photodetector output is properly processed. The synchronization performance is shown to improve with increasing signal power and decreasing loop bandwidth. Bit error rate (BER) of the PLL synchronized PPM system is analyzed and compared to that for the perfectly synchronized system. It is shown that the increase in signal power needed to compensate for the imperfect synchronization is small (less than 0.1 dB) for loop bandwidths less than 0.1% of the slot frequency.

Chen, C. C.↗

NASA NTRS1987

Phase error statistics of a phase-locked loop synchronized direct detection optical PPM communication system

Receiver timing synchronization of an optical Pulse-Position Modulation (PPM) communication system can be achieved using a phased-locked loop (PLL), provided the photodetector output is suitably processed. The magnitude of the PLL phase error is a good indicator of the timing error at the receiver decoder. The statistics of the phase error are investigated while varying several key system parameters such as PPM order, signal and background strengths, and PPL bandwidth. A practical optical communication system utilizing a laser diode transmitter and an avalanche photodiode in the receiver is described, and the sampled phase error data are presented. A linear regression analysis is applied to the data to obtain estimates of the relational constants involving the phase error variance and incident signal power.

Natarajan, Suresh↗

NASA NTRS1986

Performance of PLL synchronized optical PPM communication systems

Receiver timing synchronization of an optical PPM communication system can be achieved using a phase-locked loop (PLL) if the photodetector output is properly processed. The synchronization performance is shown to improve with increasing signal power and decreasing loop bandwidth. The bit error rate performance of the PLL synchronized PPM system is analyzed and compared to that of the perfectly synchronized system. It is shown that the increase in signal power needed to compensate for the imperfect sychronization is small (less than 0.1 dB) for loop bandwidths less than 0.1 percent of the slot frequency.

Chen, C.-C.↗

NASA NTRS1989

Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors

Slot timing recovery in a direct-detection optical PPM communication system can be achieved by processing the photodetector output waveform with a nonlinear device whose output forms the input to a phase-locked loop. The choice of a simple transition detector as the nonlinearity is shown to give satisfactory synchronization performance. The rms phase error of the recovered slot clock and the effect of slot timing jitter on the bit error probability were directly measured. The experimental system consisted of an AlGaAs laser diode (wavelength = 834 nm) and a silicon avalanche photodiode photodetector. The system used Q = 4 PPM signaling and operated at a source data rate of 25 Mbits/s. The mathematical model developed to compute the rms phase error of the recovered clock is shown to be in good agreement with results of actual measurements of phase errors. The use of the recovered slot clock in the receiver resulted in no significant degradation in receiver sensitivity compared to a system with perfect slot timing. The system achieved a bit error probability of 10 to the -6th at a received optical signal energy of 55 detected photons per information bit.

Davidson, Frederic M.↗

NASA NTRS1994

X-ray clusters from a high-resolution hydrodynamic PPM simulation of the cold dark matter universe

A new three-dimensional hydrodynamic code based on the piecewise parabolic method (PPM) is utilized to compute the distribution of hot gas in the standard Cosmic Background Explorer (COBE)-normalized cold dark matter (CDM) universe. Utilizing periodic boundary conditions, a box with size 85 h(exp-1) Mpc, having cell size 0.31 h(exp-1) Mpc, is followed in a simulation with 270(exp 3)=10(exp 7.3) cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, Sigma(sub 8)=1.05, Omega(sub b)=0.06, we find the X-ray-emitting clusters, compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. The results, which are compared with those obtained in the preceding paper (Kang et al. 1994a), may be used in conjuction with ROSAT and other observational data sets. Overall, the results of the two computations are qualitatively very similar with regard to the trends of cluster properties, i.e., how the number density, radius, and temeprature depend on luminosity and redshift. The total luminosity from clusters is approximately a factor of 2 higher using the PPM code (as compared to the 'total variation diminishing' (TVD) code used in the previous paper) with the number of bright clusters higher by a similar factor. The primary conclusions of the prior paper, with regard to the power spectrum of the primeval density perturbations, are strengthened: the standard CDM model, normalized to the COBE microwave detection, predicts too many bright X-ray emitting clusters, by a factor probably in excess of 5. The comparison between observations and theoretical predictions for the evolution of cluster properties, luminosity functions, and size and temperature distributions should provide an important discriminator among competing scenarios for the development of structure in the universe.

Bryan, Greg L.↗