Ranging information is routinely used for orbit determination and spacecraft positioning. Currently, RF radio links are used to periodically measure radiometric observables from which range information is derived. With the advent of high-speed free space optical links, both in the near-Earth and deep space domains, techniques for deriving range information in bidirectional optical links and mixed RF-optical links are gaining relevance. This paper presents two methods for obtaining range information between a ground station and a spacecraft, which we term Synchronous Mode (SM) and Asynchronous Mode (AM). In the synchronous mode, the spacecraft ties the arrival of a Ranging Codeword (RCW) in the uplink with the departure of a RCW in the downlink. Phases of the uplink and downlink signals (and their associated time tags) are measured at the ground station and serve as observables for deriving the range information. The AM uses a similar principle, but one phase measurement (and time tag) is performed by the ground station uplink subsystem, while the second phase measurement is performed by the spacecraft and associated with a time tag generated by the station’s downlink subsystem. This method has the advantage of not requiring synchronicity between the uplink and downlink on board the spacecraft and, at the same time, avoids stringent clock requirements on the mission.
The Laser Communications Relay Demonstration (LCRD) will implement an optical communications link between
a pair of Earth terminals via an Earth-orbiting satellite relay. Optical turbulence over the communication
paths will cause random
uctuations, or fading, in the received signal irradiance. In this paper we characterize
losses due to fading caused by optical turbulence. We illustrate the performance of a representative relay link,
utilizing a channel interleaver and error-correction-code to mitigate fading, and provide a method to quickly
determine the link performance.
When a photon is detected by a Geiger-mode avalanche photo-diode (GMAPD), the detector is rendered inactive, or blocked, for a certain period of time. In this paper we derive the blocking probability for a GMAPD whose input is either an unmodulated, Bernoulli modulated or pulse-position-modulated (PPM) Poisson process. We demonstrate how the PPM and Bernoulli cases differ, illustrating that the PPM blocking probability is larger than the Bernoulli. The blocking rates may be decreased by focusing the incident light on an array of detectors. We show that the binomial output statistics of an array of GMAPDs may be modeled as Poisson and measure the error in this approximation via the relative entropies of the two distributions.
We present a decoding architecture for high-speed free-space laser communications. This system will be used by NASA's Mars Laser Communication Demonstration (MLCD) project, the first use of high-speed laser communication from deep space. The Error Correction Code (ECC) and modulation techniques for this project have been motivated by an analysis of capacity, and existing designs have been shown to operate within 0.9 dB of the Shannon limit on the nominal operating point. In this paper, we give the algorithmic description and FPGA implementation details that led to the development of a 50 Mbps hardware decoder.
We describe several properties of deep space optical channels that lead to an appropriate selection of modulation format, pulse position
modulation (PPM) order, error control code rate, and coding scheme. The selection process is motivated by capacity considerations. We compare the Shannon limit to the performance of Reed-Solomon codes and convolutional codes concatenated with PPM and show that, when iteratively decoded, concatenated convolutional codes operate
approximately 0.5 dB from capacity over a wide range of signal levels,
about 2.5 dB better than Reed-Solomon codes.
We investigate methods of coding for a channel subject to a large dead-time constraint, i.e., a constraint on the minimum spacing between transmitted pulses, with the deep-space optical channel as the motivating example. Several constrained codes designed to satisfy the dead-time constraint are considered and compared on the basis of throughput, complexity, and decoded error-rate. The performance of an iteratively decoded serial concatenation of a modulation code with an outer code is evaluated and shown to provide significant gains over Reed-Solomon concatenated with Pulse Position Modulation.
Two commercially available large area silicon avalanche photodiodes (APD) were characterized in the laboratory. The response of the APD's to a sequence of 8-bit pulse position modulated (256-PPM) laser pulses, with and without additive background noise, was recorded and stored for post analysis. Empirical probability density functions (pdf's) were constructed from the signal and noise slot data and compared to pdf's predicted by an analytical model based on Webb+Gaussian statistics. The pulse sequence was used to generate bit-error rate (BER) versus signal photons per pulse plots, albeit with large error bars due to the limited number of signal pulses stored. These BER measurements were also compared with analytical results obtained by using the Gaussian and Webb+Gaussian models for APD channel statistics. While the measurements qualitatively reflect features predicted by theory, significant quantitative deviations were displayed between the measurements and theory. The source of these discrepancies is not currently well understood, but it is surmised that inaccurate knowledge of detector parameters such as gain and noise equivalent temperature models may explain the discrepancies.
In this paper we derive the capacity of Pulse Position Modulation (PPM) on a general soft output, memoryless channel, and evaluate the capacity formula for a variety of optical channel models, including AWGN, Webb, and Webb plus Gaussian distributions. Unlike a typical RF link, the optical channel has correlated signal and noise, complicating the statistical model to the point that capacity and code performance cannot be summarized by a single SNR parameter. Nevertheless, we are able to define a small set of fundamental parameters (two for AWGN and three for Webb) which are sufficient to determine the capacity. Numerical results indicate that over a wide range of operating points, a single fundamental parameter dominates the capacity calculation. A second contribution of the paper is the description of the relationship between the fundamental parameters and a multitude of physical parameters that describe the laser, channel, and detector. Using this relationship and the gradient of capacity, the sensitivity of capacity with respect to each fundamental and physical parameter is derived. This enables engineers to focus laser and detector development efforts in areas that will result in the largest capacity increases.
The capacity is determined for an optical channel employing Pulse Position Modulation (PPM) and an Avalanche PhotoDiode (APD) detector. This channel is different from the usual optical channel in that the detector output is characterized by a Webb-plus-Gaussian distribution, not a Poison distribution. The capacity is expressed as a function of the PPM order, slot width, laser dead time, average number of incident signal and background photons received, and APD parameters. Based on a system using a laser and detector proposed for X2000 second delivery, numerical results provide upper bounds on the data rate and level of background noise that the channel can support while operating at a given BER. For the particular case studied, the capacity-maximizing PPM order is near 2048 for nighttime reception and 16 for daytime reception. Reed-Solomon codes can handle background levels 2.3 to 7.6 dB below the ultimate level that can be handled by codes operating at the Shannon limit.
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