There is interest in space-based wireless optical networks with nonsynchronous multiple access capability. Since space links are usually power-limited, pulsing is necessary to accomplish the multiple accessing and data transmission. In this paper, a nonsynchronous pulsed multiple-access optical-space system using code sequences for identifying stations is considered. Both OOK and PPM data encoding is considered and the link data rates and bit error probabilities (PE) are examined. It is shown that the achievable data rates are limited by the multiple access coding and the link SNR, while the PE can be either crosstalk or power-limited. It appears that moderate data rates (tens of Mb/s) are feasible with networks of about 5-20 stations even with low-link SNR.>

Several studies have explored the feasibility and systems performance aspects of a code division multiple access (CDMA) format for fiberoptic networks. Previously discussed CDMA architectures would either have to tolerate a high bit error rate or be forced to use long code sequences in networks with even a moderate number of simultaneous users. The use of long sequences lowers the maximum achievable bit rate or places unrealistic requirements on the system hardware. This paper examines some of the possible improvements to system performance that could be realized by combining the CDMA format with external error correcting codes (ECCs) or a PPM format. It is determined that ECCs can be highly effective in lowering the BER, and/or increasing the achievable information bit rate and number of network users. The results are sufficiently encouraging to conclude that one should seriously consider including ECCs in any practical fiberoptic CDMA network.>

A basic low-probability of intercept (LPI) study for a pulsed-laser pulse position modulated (PPM) optical link with a colocated direct detection intercepting receiver is presented. The latter is considered to be a form of optical radiometer using continuous threshold testing to detect the presence of the transmitting laser. The various design alternatives for the coded PPM link, and their effect on the communication and LPI performance, are examined. It is shown that the use of optical pulse power spreading via multiple frame symbol coding is vital for avoiding interception. It can be achieved by transmitting message symbols as repeated PPM symbols using a laser pulse of sufficiently low peak power so that the detected pulse energy is much less than the detected background energy. The possibility of the use of both wideband and narrowband radiometers by the interceptor further limits the communicator's code design choices. Some equations defining effective LIP gain parameters for the communication link are developed.>

The effect of oscillator phase noise on noncoherent data detection is considered with the objective of relating more specifically than in prior studies the phase noise key parameters (bandwidth, spectral slopes, upper and lower cutoffs, spectral height). The concentration is on binary frequency-shift keying (FSK) and differential phase-shift keying (DPSK). Expressions that relate decoding error probability to the phase noise spectra are derived. It is shown that decoding degradation can be accurately approximated by relatively simple integrals involving the phase noise structure function (the latter obtained directly from the phase spectrum). Examples with reported crystal and cesium oscillator noise are presented. The key phase noise parameters are the spectral bandwidth relative to the bit rate, and the gain level of the phase noise (the latter being dependent on the carrier frequency to which the oscillator is multiplied). Separate results are derived for FSK and DPSK, but the order of the degradation is comparable in both cases.>

Synthesizer transient and spur effects in an frequency-shift-keying frequency-hopped system are investigated. Models for transient analysis are developed, and resulting degradations to performance are computed. Compensation methods, such as ping-ponging multiple synthesizers and gating symbol detectors, are considered. A spur analysis is presented, and the overall output effects on hopping spectrum and demodulation are shown. Methods to bound degradation in terms of number and strength of spur lines are presented.>

The most efficient way to encode laser diodes for maximum data rate is studied. Three different system architectures are considered, with combining achieved by dichroic mirrors operating in conjunction with a pulse-position-modulated (PPM) format. The basic criterion is to maximize the data rate with increasing number of diodes, while maintaining diode power constraints and decoding bit error probability. The three systems are: power combining into a single pulse, followed by PPM encoding; parallel channels, in which each diode is separately PPM encoded; and color coding, in which diodes are encoded over a common wavelength-time slot alphabet. Data rate equations are presented as a function of the number of diodes, mirror combining losses, PPM alphabet size, and the operating optical signal-to-noise ratio.>

In pulse position modulation (PPM) communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission. This sequence must have PPM structure (one pulse per frame) and desirable autocorrelation properties for its detection. The problem of finding aperiodic PPM acquisition sequences having the minimum possible autocorrelation for all off-shifted positions is investigated. Sequences with the maximum possible number of frames have been found up to frame size15. Examples are given for every frame length up to88, and powers of two up to1024. An interesting relation between the PPM sequence problem, Costas and sonar arrays, and Golomb's ruler is explored.

Maintaining slot clock synchronization in a baseband pulse position modulated (PPM) communication link is vital to its performance. This paper examines the slot clocking design associated with a direct detection, photodetecting optical PPM system. Although theoretical PPM synchronizers for optical links have been derived in the past, there is still interest in finding more practical, simpler, and easier-to-implement clocking subsystems. In this paper several types of practical slot synchronizers are considered. A basic design involving analog correlators and slot gating is presented, along with an indication of its performance. Several alternative designs are also presented, including digital synchronizers in which time samples are used for loop control. The advantage in digital systems is that more extensive processing can be handled in software, allowing the loop to perform closer to the ideal. Design procedures for digital clocking are presented, and optimal laser pulse shaping and filtering are discussed. Performance in terms of loop models and tracking error variance is included.

Consideration is presently being given to an optical-RF relay deep space communication link that transmits optical PPM data from spacecraft to orbital relay, then retransmits the data via microwave to ground. It is generally advantageous to use Reed-Solomon (RS) encoding over the PPM optical link for improved error correction. In this paper several demodulating schemes are considered for generating the RS symbols at the relay photodetector output, and the effect of each on overall RS decoding performance is computed. Both Poisson and Gaussian optical noise models are used in the evaluation. The effect on performance of bit errors in the relay downlink is also examined.

The design and performance of optical PPM communication systems with ideal (rectangular) pulses have been well documented. However, many optical channels (fibers, atmosphere, clouds) are extremely dispersive to narrow pulses, producing receiver pulses that are spread (stretched) in time. This stretching produces interslot interference within a PPM frame, and if severe enough, can stretch over several frames (intersymbol interference). In this paper, laser pulse stretching in optical PPM formats is investigated in terms of performance degradation and decoder design alternatives. Several methods are considered for combating the pulse stretching, including pulse equalization, extended pulse integration, and pulse shape matching. Performance of these methods is compared for the case of exponential stretching and Gaussian statistics.

Pulse position modulation (PPM) is a popular signaling format in pulsed optical communication links. PPM encoding is extended to include block pulse encoding over multiple PPM frames. Maximum likelihood decoding operations associated with this encoding are developed for both shot-noise limited and thermal-noise limited optical receiver models. Both ideal (Poisson) and avalanche photodetectors are considered, and it is shown that optimal block decoders involve combinations of linear and quadratic operations. Error probability bounds are presented, showing the relative improvement in detectability that appears possible by resorting to block encoding over multiple frames.

Costas loops are invariably designed in conjunction with an automatic gain control (AGC) loop for stabilizing performance. In such systems an inherent coupling between the AGC and Costas loops develops, complicating the standard phase referencing analysis. This coupling is further emphasized if the gain control amplifier introduces an AM/PM conversion, which causes power variations to enter the Costas loop as phase variations. In this paper the coupling effect between AGC and Costas loops is developed, leading to a pair of joint, interconnected dynamical tracking loops. Some degree of solution is attainable by assuming a first order AGC loop, and resorting to quasi-stationary analysis for evaluating the phase referencing generation. Results with and without AM/PM are presented, and illustrate how an improper AGC may in fact degrade the phase referencing from the expected performance.

The output voltage of an optical receiver is statistically a mixture random variable, composed of the sum of a discrete count variable and a continuous Gaussian thermal noise variable. Based on some computer analyses, it is shown here that threshold crossing probabilities using the mixture density can be reliably approximated by integrations of an equivalent continuous Gaussian density. The conditions for this approximation and an accurate assessment of its error are derived.

In systems employing relay satellites there is invariably a strict requirement for maintaining frequency and phase coherence throughout the system. Although frequency lock can generally be attained by tracking loops and Doppler correction, phase coherency is often destroyed by phase noise, frequency offsets, and differential phase shifts. To evaluate the degree of phase instability, and its effect on decoding and Doppler tracking, it is necessary to perform an accurate phase noise analysis, accounting for all phase noise sources and the manner in which they interact. In relay satellite systems this analysis is further complicated by the interconnection of many tracking loops among ground, satellite and user. In this paper the basic procedures for generating phase stability models are presented and are applied to general forms of relay satellite systems. Consideration is given to both forward and return channel effects, including the use of pilot tone links for satellite referencing. Such phase noise models aid in pinpointing most significant sources, and often suggest design procedures relating to implementation alternatives and bandwidth selection.

In this paper the optimal Bayes detector for a general periodic waveform having uniform delay and additive white Gaussian noise is examined. It is shown that the detector is much more complex than that for the we!l-known cases of pure sine waves (i.e., classical noncoherent detection)and narrow-hand signals. An interpretation of the optimal processor is presented, and several implementations are discussed.

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. In this report 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.

The use of digital transmission with narrow light pulses appears attractive for data communications, but carries with it a stringent requirement on system bit timing. The effects of imperfect timing in direct-detection (noncoherent) optical binary systems are investigated using both pulse-position modulation (PPM) and on-off keying for bit transmission. Particular emphasis is placed on specification of timing accuracy and an examination of system degradation when this accuracy is not attained. Bit error probabilities are shown as a function of timing errors from which average error probabilities can be computed for specific synchronization methods. Of significance is the presence of a residual or irreducible error probability in both systems, due entirely to the timing system, which cannot be overcome by the data channel.

In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.

In many applications a Poisson shot noise (PSN) process is said to statistically "represent" its intensity process. In this paper an investigation is made of the relationship between a PSN process and its intensity, when the latter is a sample function of a continuous stochastic process. The difference of the moments and the mean-square difference between the two processes are examined. The continuity assumption on the intensity permits the development of a sequence of moment relationships in which the effect of the PSN parameters can be seen. The results simplify and afford some degree of physical interpretation when the component functions of the PSN are "rectangular," or when the intensity process does not vary appreciably over their time width. An integral equation is derived that defines the component function that minimizes the mean-square difference between the two processes. It is shown that a "degenerate" form of component function induces complete statistical equality of the two processes. The problem has application to optical communication systems using photodetectors.

Sequential analysis has been used in the literature for analyzing a radar search system. The procedure is to continually sample a given range "bin" until a yes-no decision concerning the presence of a target is made. The results, however, do not provide for the possibility of a target emerging into the bin during the sampling process. In this report we consider a likelihood-ratio test for detecting emerging targets by sequential sampling. It is shown that the decisioning threshold must be continually increased in order to maintain a fixed false alarm rate at each sample. An upper bound on the average number of samples required to detect an emerging target is computed, and the results are significant in that this bound may become quite large. A test using a fixed threshold in which the average false alarm rate is constrained is investigated and shown to be inferior to the variable threshold test. A suboptimum test using only a finite number of past samples is also considered. The results of this study are equally applicable to the converse problem, i.e., detecting when a known target exits from the bin, which is important in target tracking.