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Report presents theoretical and experimental analysis of noise in coherent optical phase-locked loop. Optical phase-locked loop being considered for use in heterodyne reception of binary pulse-position modulation at data rate of 100 Kb/s in optical communication system in which transmitter also includes frequency-stabilized laser.
In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many communications or storage systems cannot easily accommodate an increased symbol size, e.g., M-ary frequency shift keying (FSK) and photon-counting pulse-position modulation demand a fixed symbol size. A technique for sharing redundancy among many different Reed-Solomon codewords to achieve the efficiency attainable in long Reed-Solomon codes without increasing the symbol size is described. Techniques both for calculating the performance of these new codes and for determining their encoder and decoder complexities is presented. These complexities are usually found to be substantially lower than conventional Reed-Solomon codes of similar performance.
The NASA Lewis Research Center in Cleveland, Ohio, has developed the electronics for a free-space, direct-detection laser communications system demonstration. Under the High-Speed Laser Integrated Terminal Electronics (Hi-LITE) Project, NASA Lewis has built a prototype full-duplex, dual-channel electronics transmitter and receiver operating at 325 megabit S per second (Mbps) per channel and using quaternary pulse-position modulation (QPPM). This paper describes the integration and testing of the transmitter portion for future application in free-space, direct-detection laser communications. A companion paper reviews the receiver portion of the prototype electronics. Minor modifications to the transmitter were made since the initial report on the entire system, and this paper addresses them. The digital electronics are implemented in gallium arsenide integrated circuits mounted on prototype boards. The fabrication and implementation issues related to these high-speed devices are discussed. The transmitter's test results are documented, and its functionality is verified by exercising all modes of operation. Various testing issues pertaining to high-speed circuits are addressed. A description of the transmitter electronics packaging concludes the paper.
The performance improvement obtained through the use of adaptive optics for deep-space communications in the presence of atmospheric turbulence is analyzed. Using simulated focal-plane signal-intensity distributions, uncoded pulse-position modulation (PPM) bit-error probabilities are calculated assuming the use of an adaptive focal-plane detector array as well as an adaptively sized single detector. It is demonstrated that current practical adaptive optics systems can yield performance gains over an uncompensated system ranging from approximately 1 dB to 6 dB depending upon the PPM order and background radiation level.
The photon-starved channel for optical communications from deep space requires the development of detector technology that can achieve photon-counting sensitivities with high bandwidth. In this article, a near-infrared enhanced photomultiplier tube (PMT) with a quantum e.ciency of 0.08 at a 1.06- m wavelength is characterized in the laboratory. A Polya distribution model is used to compute the probability distribution function of the emitted secondary photoelectrons from the PMT. The model is compared with measured pulse-height distributions with reasonable agreement. The model accounts for realistic device parameters, such as the individual dynode stage gains and a shape parameter that is representative of the spatial uniformity of response across the photocathode and dynodes. Bit-error rate (BER) measurements also are presented for 4- and 8-pulse-position modulation (PPM) modulation schemes with data rates of 20 to 30 Mb/s. A BER of 10-2 is obtained for a mean of 8 detected photons.
An avalanche photodiode (APD) array for ground-based optical communications receivers is investigated for the reception of optical signals through the turbulent atmosphere. Kolmogorov phase screen simulations are used to generate realistic spatial distributions of the received optical field. It is shown that use of an APD array for pulse-position modulation detection can improve performance by up to 4 dB over single APD detection in the presence of turbulence, but that photon-counting detector arrays yield even greater gains.
The maximum likelihood decision statistic for detection of pulse-position modulated signals with an avalanche photodiode is derived, using the more accurate Webb density rather than Poisson or Gaussian approximations for the distribution of avalanche photodiode output electrons. It is shown that for Webb-distributed output electtrons, the maximum likelihood rule is to choose the PPM word corresponding to the slot with the maximum electron count.
Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.
An inter-symbol guard time has been proposed as a means of synchronizing the symbol and slot clocks of an optical pulse-position modulation (PPM) receiver with the symbol and slot periods of an incoming optical PPM signal.The proposal is applicable to the low-flux case in which the receiver photodetector operates in a photon-counting mode and the count can include contributions from incidental light sources and dark current.
An improved method has been devised for controlling the DC bias applied to an electro-optical crystal that is part of a Mach-Zehnder modulator that generates low-duty-cycle optical pulses for a pulse-position modulation (PPM) optical data-communication system. In such a system, it is desirable to minimize the transmission of light during the intervals between pulses, and for this purpose, it is necessary to maximize the extinction ratio of the modulator (the ratio between the power transmitted during an "on" period and the power transmitted during an "off" period). The present method is related to prior dither error feedback methods, but unlike in those methods, there is no need for an auxiliary modulation subsystem to generate a dithering signal. Instead, as described below, dither is effected through alternation of the polarity of the modulation signal. The upper part of Figure 1 schematically depicts a Mach-Zehnder modulator. The signal applied to the electro-optical crystal consists of a radio-frequency modulating pulse signal, VRF, superimposed on a DC bias Vbias. Maximum extinction occurs during the off (VRF = 0) period if Vbias is set at a value that makes the two optical paths differ by an odd integer multiple of a half wavelength so that the beams traveling along the two paths interfere destructively at the output beam splitter. Assuming that the modulating pulse signal VRF has a rectangular waveform, maximum transmission occurs during the "on" period if the amplitude of VRF is set to a value, V , that shifts the length of the affected optical path by a half wavelength so that now the two beams interfere constructively at the output beam splitter. The modulating pulse signal is AC-coupled from an amplifier to the electro-optical crystal. Sometimes, two successive pulses occur so close in time that the operating point of the amplifier drifts, one result being that there is not enough time for the signal level to return to ground between pulses. Also, the difference between the optical-path lengths can drift with changes in temperature and other spurious effects. The effects of both types of drift are suppressed in the present method, in which one takes advantage of the fact that when Vbias is set at the value for maximum extinction, equal-magnitude positive and negative pulses applied to the electro-optical crystal produce equal output light pulses.
A recently developed algorithm for demodulation and decoding of a pulse-position- modulation (PPM) signal is suitable as a basis for designing a single hardware decoding apparatus to be capable of handling any PPM order. Hence, this algorithm offers advantages of greater flexibility and lower cost, in comparison with prior such algorithms, which necessitate the use of a distinct hardware implementation for each PPM order. In addition, in comparison with the prior algorithms, the present algorithm entails less complexity in decoding at large orders. An unavoidably lengthy presentation of background information, including definitions of terms, is prerequisite to a meaningful summary of this development. As an aid to understanding, the figure illustrates the relevant processes of coding, modulation, propagation, demodulation, and decoding. An M-ary PPM signal has M time slots per symbol period. A pulse (signifying 1) is transmitted during one of the time slots; no pulse (signifying 0) is transmitted during the other time slots. The information intended to be conveyed from the transmitting end to the receiving end of a radio or optical communication channel is a K-bit vector u. This vector is encoded by an (N,K) binary error-correcting code, producing an N-bit vector a. In turn, the vector a is subdivided into blocks of m = log2(M) bits and each such block is mapped to an M-ary PPM symbol. The resultant coding/modulation scheme can be regarded as equivalent to a nonlinear binary code. The binary vector of PPM symbols, x is transmitted over a Poisson channel, such that there is obtained, at the receiver, a Poisson-distributed photon count characterized by a mean background count nb during no-pulse time slots and a mean signal-plus-background count of ns+nb during a pulse time slot. In the receiver, demodulation of the signal is effected in an iterative soft decoding process that involves consideration of relationships among photon counts and conditional likelihoods of m-bit vectors of coded bits. Inasmuch as the likelihoods of all the m-bit vectors of coded bits mapping to the same PPM symbol are correlated, the best performance is obtained when the joint mbit conditional likelihoods are utilized. Unfortunately, the complexity of decoding, measured in the number of operations per bit, grows exponentially with m, and can thus become prohibitively expensive for large PPM orders. For a system required to handle multiple PPM orders, the cost is even higher because it is necessary to have separate decoding hardware for each order. This concludes the prerequisite background information. In the present algorithm, the decoding process as described above is modified by, among other things, introduction of an lbit marginalizer sub-algorithm. The term "l-bit marginalizer" signifies that instead of m-bit conditional likelihoods, the decoder computes l-bit conditional likelihoods, where l is fixed. Fixing l, regardless of the value of m, makes it possible to use a single hardware implementation for any PPM order. One could minimize the decoding complexity and obtain an especially simple design by fixing l at 1, but this would entail some loss of performance. An intermediate solution is to fix l at some value, greater than 1, that may be less than or greater than m. This solution makes it possible to obtain the desired flexibility to handle any PPM order while compromising between complexity and loss of performance.
A computer program has been written as a tool for developing optical pulse-position- modulation (PPM) receivers in which photodetector outputs are fed to analog-to-digital converters (ADCs) and all subsequent signal processing is performed digitally. The program can be used, for example, to simulate an all-digital version of the PPM receiver described in Parallel Processing of Broad-Band PPM Signals (NPO-40711), which appears elsewhere in this issue of NASA Tech Briefs. The program can also be translated into a design for digital PPM receiver hardware. The most notable innovation embodied in the software and the underlying PPM-reception concept is a digital processing subsystem that performs synchronization of PPM time slots, even though the digital processing is, itself, asynchronous in the sense that no attempt is made to synchronize it with the incoming optical signal a priori and there is no feedback to analog signal processing subsystems or ADCs. Functions performed by the software receiver include time-slot synchronization, symbol synchronization, coding preprocessing, and diagnostic functions. The program is written in the MATLAB and Simulink software system. The software receiver is highly parameterized and, hence, programmable: for example, slot- and symbol-synchronization filters have programmable bandwidths.
A method of computing channel capacities and error rates in multipulse pulse-position modulation (multipulse PPM) has been developed. The method makes it possible, when designing an optical PPM communication system, to determine whether and under what conditions a given multipulse PPM scheme would be more or less advantageous, relative to other candidate modulation schemes. In conventional M-ary PPM, each symbol is transmitted in a time frame that is divided into M time slots (where M is an integer >1), defining an M-symbol alphabet. A symbol is represented by transmitting a pulse (representing 1) during one of the time slots and no pulse (representing 0 ) during the other M 1 time slots. Multipulse PPM is a generalization of PPM in which pulses are transmitted during two or more of the M time slots.
A method of coherent detection of high-rate pulse-position modulation (PPM) on a received laser beam has been conceived as a means of reducing the deleterious effects of noise and atmospheric turbulence in free-space optical communication using focal-plane detector array technologies. In comparison with a receiver based on direct detection of the intensity modulation of a PPM signal, a receiver based on the present method of coherent detection performs well at much higher background levels. In principle, the coherent-detection receiver can exhibit quantum-limited performance despite atmospheric turbulence. The key components of such a receiver include standard receiver optics, a laser that serves as a local oscillator, a focal-plane array of photodetectors, and a signal-processing and data-acquisition assembly needed to sample the focal-plane fields and reconstruct the pulsed signal prior to detection. The received PPM-modulated laser beam and the local-oscillator beam are focused onto the photodetector array, where they are mixed in the detection process. The two lasers are of the same or nearly the same frequency. If the two lasers are of different frequencies, then the coherent detection process is characterized as heterodyne and, using traditional heterodyne-detection terminology, the difference between the two laser frequencies is denoted the intermediate frequency (IF). If the two laser beams are of the same frequency and remain aligned in phase, then the coherent detection process is characterized as homodyne (essentially, heterodyne detection at zero IF). As a result of the inherent squaring operation of each photodetector, the output current includes an IF component that contains the signal modulation. The amplitude of the IF component is proportional to the product of the local-oscillator signal amplitude and the PPM signal amplitude. Hence, by using a sufficiently strong local-oscillator signal, one can make the PPM-modulated IF signal strong enough to overcome thermal noise in the receiver circuits: this is what makes it possible to achieve near-quantum-limited detection in the presence of strong background. Following quantum-limited coherent detection, the outputs of the individual photodetectors are automatically aligned in phase by use of one or more adaptive array compensation algorithms [e.g., the least-mean-square (LMS) algorithm]. Then the outputs are combined and the resulting signal is processed to extract the high-rate information, as though the PPM signal were received by a single photodetector. In a continuing series of experiments to test this method (see Fig. 1), the local oscillator has a wavelength of 1,064 nm, and another laser is used as a signal transmitter at a slightly different wavelength to establish an IF of about 6 MHz. There are 16 photodetectors in a 4 4 focal-plane array; the detector outputs are digitized at a sampling rate of 25 MHz, and the signals in digital form are combined by use of the LMS algorithm. Convergence of the adaptive combining algorithm in the presence of simulated atmospheric turbulence for optical PPM signals has already been demonstrated in the laboratory; the combined output is shown in Fig. 2(a), and Fig. 2(b) shows the behavior of the phase of the combining weights as a function of time (or samples). We observe that the phase of the weights has a sawtooth shape due to the continuously changing phase in the down-converted output, which is not exactly at zero frequency. Detailed performance analysis of this coherent free-space optical communication system in the presence of simulated atmospheric turbulence is currently under way.
A method of sequence detection has been proposed to mitigate the effects of inter-slot interference and inter-symbol interference (both denoted ISI) in the reception of M-ary pulse-position modulation (PPM) optical signals. The method would make it possible to reduce the error rate for a given slot duration, to use a shorter slot duration (and, hence, to communicate at a higher rate) without exceeding a given error rate, or to use a lower-bandwidth (and, hence, less-expensive) receiver to receive a signal of a given slot width without exceeding a given error rate. In M-ary PPM, a symbol period is divided into M time slots, each of duration T(sub s), and a symbol consists of a binary sequence ones and zeros represented by pulses or the absence of pulses, respectively, in the time slots. At the transmitter, the bit stream is used to modulate a laser, the output of which is constant (either full power or zero power, representing 1 or 0, respectively) during each time slot. However, the signal becomes attenuated (signal photons are lost) in propagation from the transmitter to the receiver and noise enters at the receiver, complicating the problem of determining the timing of the symbol periods and slots and identifying the symbols.
A method of adaptive setting of a threshold level for the detection of pulses in a pulse-position modulation (PPM) free-space optical communication system has been developed. In simplified terms, it is desirable to set a threshold value high enough to greatly reduce the probability (PFA as defined below) of erroneously detecting noise as signal pulses but not so high as to greatly reduce the probability (PD as defined below) of detecting any signal pulses that may be present along with noise. In the present method, the threshold level is varied with time, in response to changing conditions in the optical-communication channel, in an effort to maintain a balance between the aforesaid competing requirements. An integral part of this adaptation scheme is a scheme for estimating key parameters of the optical-communication channel in particular, parameters that describe the fading and total attenuation in the channel, and parameters that characterize spreading of pulses by atmospheric and other effects. The method can be implemented by software processing of digitized optoelectronic-detector output, and has been tested by computational simulation. In the first stage of processing by this method, the digitized values of the detector output during noise-only time slots of received PPM symbols are averaged to obtain a background level. This background level is subtracted from the detector output in the hope of reducing or eliminating the noise component in the remaining signal. (This background level should not be confused with the detection threshold, which is computed in the last stage of processing.) Next, the remaining signal - in effect, a vector of pulse samples - is normalized by dividing it by its L1 norm (in general, the L1 norm of a vector is defined as the sum of absolute magnitudes of its orthogonal components).
A paper discusses the optimization of the parameters of a high-rate, deep-space optical communication link that utilizes pulse-position modulation (PPM) and an error-correcting code (ECC). The parameters in question include the PPM order (number of pulse time slots in one symbol period), the ECC rate, and the uncoded symbol error rate. In simple terms, the optimization problem is to choose the combination of these parameters that maximizes the throughput data rate at a given bit-error-rate (BER), subject to several constraints, including limits on the average and peak power and possibly a limit on the uncoded symbol error rate. This is a complex, multidimensional optimization problem, the solution of which involves computation of channel capacities for various combinations of the parameters. The paper presents extensive theoretical analyses and numerical predictions that elucidate the many facets of the optimization problem. It shows how a nearly optimum solution can be obtained by choosing the optimum PPM order for the desired number of bits per slot and concatenating the PPM mapping with an error-correction code so that the decoded bits satisfy some BER threshold.
The potential development of large aperture groundbased "photon bucket" optical receivers for deep space communications, with acceptable performance even when pointing close to the sun, is receiving considerable attention. Sunlight scattered by the atmosphere becomes significant at micron wavelengths when pointing to a few degrees from the sun, even with the narrowest bandwidth optical filters. In addition, high quality optical apertures in the 10-30 meter range are costly and difficult to build with accurate surfaces to ensure narrow fields-of-view (FOV). One approach currently under consideration is to polish the aluminum reflector panels of large 34-meter microwave antennas to high reflectance, and accept the relatively large FOV generated by state-of-the-art polished aluminum panels with rms surface accuracies on the order of a few microns, corresponding to several-hundred micro-radian FOV, hence generating centimeter-diameter focused spots at the Cassegrain focus of 34-meter antennas. Assuming pulse-position modulation (PPM) and Poisson-distributed photon-counting detection, a "polished panel" photon-bucket receiver with large FOV will collect hundreds of background photons per PPM slot, along with comparable signal photons due to its large aperture. It is demonstrated that communications performance in terms of PPM symbol-error probability in high-background high-signal environments depends more strongly on signal than on background photons, implying that large increases in background energy can be compensated by a disproportionally small increase in signal energy. This surprising result suggests that large optical apertures with relatively poor surface quality may nevertheless provide acceptable performance for deep-space optical communications, potentially enabling the construction of cost-effective hybrid RF/optical receivers in the future.