Integrated terrestrial-satellite networks (ITSNs) play an essential role in providing global and ubiquitous connectivity for next generation networks. Spectral efficiency of ITSNs depends on their integrated architecture and the operational strategies, including interference management and resource allocation. This paper proposes an efficient integrated access and backhaul (IAB) architecture for terrestrial-satellite networks considering both uplink (UL) and downlink (DL) communications. We aim to integrate terrestrial access and satellite backhaul networks by developing a novel optimization framework for their joint operation. In particular, in-band access-backhaul transmission is considered for high spectral efficiency, where a reverse time division duplexing is used to prevent both self-interference and interference between access links and backhaul links. In addition, cooperation among gNodeB is taken into account to overcome harsh propagation conditions such as blockage effects and severe pathloss. A framework for joint optimization of cooperative beamforming and resource allocation is developed to maximize the UL-DL rate region of the in-band IAB. The proposed architecture is verified using the 3rd Generation Partnership Project (3GPP) channel models. Numerical results show that the proposed architecture significantly outperforms the classical out-of-band backhauling while approaching an outer bound of the UL-DL rate region.

Integrated satellite-terrestrial networks (ISTNs) are essential for providing ubiquitous mobile ultra-broadband service in beyond 5G networks. The spectral efficiency and reliability of ISTN depend on the integrated architecture and its operational strategies including interference management and resource allocation. Our view is to integrate terrestrial access and satellite backhaul networks and to develop an optimization technique for their joint operation. This paper proposes an efficient integrated access and backhaul (IAB) architecture for satellite-terrestrial networks (STNs) based on reverse time division duplexing (TDD) considering both uplink (UL) and downlink (DL). In particular, in-band backhauling and gNodeB (gNB) cooperation are considered for high spectral efficiency and reliability. A framework for joint optimization of cooperative beamforming and resource allocation is developed to maximize the UL-DL rate region of the in-band IAB. The proposed scheme is verified using the 3rd Generation Partnership Project (3GPP) standard channel models. Results show that the proposed scheme significantly outperforms the conventional wireless backhauling, while approaching to an outer bound of the UL-DL rate region.

Based upon the Fluctuation-Dissipation Theorem of Nyquist-Callen-Welton and the spectrum balancing relationship of Kubo-Martin-Schwinger for operator-valued stochastic noise processes, a two-parameter Quantum Noise-Energy Spectral Density (QN-ESD) is constructed and Fourier-Laplace transformed to obtain its associated Quantum Noise-Autocorrelation Function (QN-ACF). By means of a Taylor series expansion, the quantum thermal noise correlations are linked to Number Theory's Reimann-Zeta function. From this perspective, a panoply of spectral components and their QN correlations are characterized for three disjoint regions located across the Electromagnetic Spectrum (EMS). The second-moment characterizations and frequency boundaries for each region are specified as a function of two frequency dependent design parameters, viz., a normalized temperature dependent frequency and a quantum receiver cutoff frequency. These boundaries define where the quadrature noise correlation projections of the QN-ESD become noticeably asymmetric-in-frequency. For the operator-valued white quantum noise region, various communication system performance metrics are characterized and their limits are presented and compared via interconnecting parameter relations to their classical communications (CC) counterparts. These metrics include Shannon's non-additive, but regularized, zero-error capacity in bits/photon-pair, bits/photon, bits/channel-use and bits/sec, the spectral efficiency in bits/sec/Hz and the error-correcting code rate. For long coded messages, Shannon's capacity quadrature approaches 2π√5/ ln(2) ≈ 20 bits/photon-pair or (10 bits/photon) while for single-photon per channel use transmission it approaches 3 bits/photon-pair. Results are graphically illustrated for the quantum noise spectral density, quantum noise correlations, Shannon's Î-Q̂ capacities and spectral efficiency.

Location awareness is vital for emerging Internet-of-Things applications and opens a new era for Localization-of-Things. This paper first reviews the classical localization techniques based on single-value metrics, such as range and angle estimates, and on fixed measurement models, such as Gaussian distributions with mean equal to the true value of the metric. Then, it presents a new localization approach based on soft information (SI) extracted from intra- and inter-node measurements, as well as from contextual data. In particular, efficient techniques for learning and fusing different kinds of SI are described. Case studies are presented for two scenarios in which sensing measurements are based on: 1) noisy features and non-line-of-sight detector outputs and 2) IEEE 802.15.4a standard. The results show that SI-based localization is highly efficient, can significantly outperform classical techniques, and provides robustness to harsh propagation conditions.

The month’s regular papers issue covers machine learning at the wireless network edge, soft-informationbased localization techniques, and Antenna-in-Package technology.

This paper studies the concatenation of turbo codes and Reed-Solomon (RS) codes. The error patterns of turbo codes are first analyzed. Since error patterns of turbo codes are much different than those of convolutional codes, the design rules for a matched interleaver between turbo codes and RS codes are provided. As an application to digital video broadcasting by satellite (DVB-S), the performance of Forney interleavers with different spreading abilities is studied for a fixed turbo code. For a (34,6) Forney interleaver, the performance of turbo codes with different block sizes is also studied. A delay and performance tradeoff can be made via simulation results.

This paper focuses on the modeling and analysis of phase-locked loops in the presence of continuous wave (CW) interference such that the operating vulnerability to CW jamming and interference can be accessed. The loop phase error is characterized, and the conditions under which the loop remains locked in frequency to the desired carrier are presented. Analysis is conducted for arbitrary offsets of carrier and interferer signal frequencies relative to the quiescent voltage-controlled oscillator (VCO) frequency. The results show that loop performance depends not only on the frequency difference between the desired signal and interferer, but also on the frequency offset between the quiescent VCO oscillation and desired carrier. The vulnerability of the loop to the presence of interference increases if interferer and desired signal spectral locations are in opposite sides of quiescent VCO frequency.

A unified treatment is presented for the problem of detecting binary data transmitted over an L-fold diversity complex non-Gaussian channel further disturbed by additive white Gaussian noise. The data is extracted using a quadratic form detector driven by the outputs from a cross-correlation detector matched to the transmitted signals. By employing a probability density function (PDF) expansion technique, the bit error probability is decomposed into a Gaussian and a non-Gaussian component. Our results, being valid for the doubly dispersive (space and time) channels, are reduced to expressions which characterize the performance for other channel types, viz., the wide-sense stationary uncorrelated scattering (WSSUS), the temporally-dispersive spatially-nondispersive, the temporally-nondispersive spatially-dispersive, and the totally nondispersive channel. A coherence matrix is defined which allows us to treat three types of diversity reception, vis., noncoherent, partially coherent, and coherent detection with a noisy phase reference. Detailed performance analysis of the noncoherent case is presented and used to numerically evaluate system performance over a non-Gaussian channel modeled by the Middleton (1977) class A PDF.>

Advanced modulation/demodulation techniques which are robust in the presence of phase and frequency uncertainties continue to be of interest to communication engineers. The authors are particularly interested in techniques which accommodate slow channel phase and frequency variations with minimal performance degradation and which alleviate the need for phase and frequency tracking loops in the receiver. They investigate the performance sensitivity to frequency offsets of a modulation technique known as binary double differential phase shift keying (DDPSK) and compare it to that of classical binary differential phase shift keying (DPSK). They also generalize their analytical results to include n/sup -th/ order, M-ary DPSK. The DDPSK (n=2) technique was first introduced in the Russian literature circa 1972 and was studied more thoroughly in the late 1970s by Pent and Okunev. They present an expression for the symbol error probability that is easy to derive and to evaluate numerically. They also present graphical results that establish when, as a function of the signal energy-to-noise ratio and normalized frequency offset, binary DDPSK is preferable to binary DPSK with respect to performance in additive white Gaussian noise. Finally, they provide insight into the optimum receiver from a detection theory viewpoint.>

The author of the original article (ibid., vol.42, p.2672, no.9, 1994) is concerned with the use of the averaged conditional phase-error variance, as a performance measure for a PLL operating in the presence of CW interferers. He correctly points out that the variance of the random variable /spl phi/ can be obtained using the equation given; however, the physics of the problem suggests that the average of the conditional variance used by Lindsey and Yoon (1982) is perhaps the more meaningful performance measure for use in loop design and performance evaluation. The author discusses this issue further in his reply.

New and unifying analytical tools are developed and used to evaluate the bit error probability, false alarm and detection probabilities that result when binary information is communicated through a random channel further disturbed by additive white Gaussian noise. The class of channels modeled here are those which envelop the received electric field with an arbitrary space-time complex envelope. The complex Gaussian envelope, being a special case, yields the Rayleigh and Rice fading statistics. Considerable insight into the problem of communicating through a complex non-Gaussian fading channel is obtained by decomposing the performance measures into the sum of two terms, viz., one attributable to the usually assumed complex Gaussian envelope plus a residual performance term expressed as a series expansion in terms of multidimensional Hermite polynomials whose coefficients are the channel quasi-moments. Finally, a numerical example is presented in which the theory is applied to a specific non-Gaussian channel.>

Decision variables in numerous practical systems can frequently be characterized using a Hermitian quadratic form in complex Gaussian variates. Performance analysis involving these variates requires a complete description of the statistical distribution of the quadratic form. Such a complete description is presented. The method used is based on inverting the characteristic function of the quadratic form by solving a number of convolution integrals. The results presented include two forms for the probability density function (PDF), an expression for the cumulative distribution function (CDF), and expressions for the distribution moments and cumulants. These results are shown to reduce to previously known results for some special cases. Relations of the quadratic form and its CDF to the noncentral chi /sup 2/ (chi-square) and the complex noncentral Wishart distributions are exposed. Evaluation of the CDF at the origin is shown to reduce to the doubly noncentral F-distribution due to R. Price (1962, 1964). A generalization of the Marcum Q-function is also identified and suggested.>

A decision-directed, digitally implemented carrier synchronizer for channels with both frequency and phase uncertainty is presented. This combined algorithm and its derivatives are analyzed with respect to the achievable carrier acquisition time and the resulting bit error probability. For certain data rates (approximately 50 MSps or less), this algorithm can be implemented using CMOS gate array technology. As examples BPSK and QPSK modulation formats are studied herein and compared to their differentially coherent counterparts of DPSK and DQPSK.>

The tracking performance of three conventional carrier tracking loops in the presence of intersymbol interference (ISI) is analyzed. The closed-form expressions for the squaring losses of BPSK (binary phase-shift-keyed) low-SNR (signal-to-noise ratio), BPSK high-SNR, and QPSK (quaternary phase-shift-keyed) low-SNR loops are derived. ISI is shown to affect the BPSK high-SNR loop as much as the I-Q loop despite the nonlinear effect of the hard-limiter. For the QPSK carrier tracking loop, the degradation is shown to be greater due to the modulation of both components of the carrier. In this case, ISI, in addition to modifying the coefficients in the squaring loss, adds a new term not present in wideband channels. In all cases, a unity squaring loss could not be achieved because of the irreducible error due to pattern noise. This noise is only present in band-limited channels and is dependent on the data model used.>

The problem of time and frequency transfer between remotely located clocks is investigated for the case when internal and external disturbances are present. A model based on the maximum-likelihood (ML) estimation of the carrier phase and the transmission path delay in the face of white Gaussian noise is suggested. In this model, path delay estimation and, consequently, clock synchronization is achieved by tracking a pseudonoise (PN) code phase-modulated onto the carrier. Phase and frequency estimation are obtained through a closed-loop phase tracking model. The performance of the maximum-likelihood model under high and low signal-to-noise ratio (SNR) is established in terms of probability density functions of the phase increment processes in space and time. Factors which influence performance include external and internal disturbances. These include additive thermal noise, range delay, clock drift, etc. Numerical results are presented to explain the influence of system parameters on performance.>

Results are presented concerning the noise-free false lock problem in quadriphase receivers with unequal I-channel and Q-channel data rates. It is shown that false lock may occur when the incoming carrier frequency and the loop VCO (voltage-controlled oscillator) frequency differ by an amount that is a linear combination of a quarter of I-channel and Q-channel data rates. General expressions for the false lock performance of quadriphase receivers are given for random as well as periodic data patterns. Specific closed-form expressions for the false lock margin are derived when the arm filters of the quadriphase receivers are single-pole Butterworth filters, and the format of the random data is NRZ (nonreturn-to-zero). Numerical evaluations of false lock margin as a function of the product of 3 dB arm-filter bandwidth and symbol duration are carried out for random data using various arm filters and for different periodic I-channel and Q-channel data patterns.>

Quadrature amplitude-shift keying (QASK) is often used for transmitting two digital data streams in bandwidth-constrained communication systems. Previous analyses of the tracking performance of a decision-feedback carrier tracking loop, which can be used to provide a carrier reference for a QASK signal set, have neglected the effects of the self-noise in the derivation of the loop resonance. The authors incorporate the effects of the self-noise will only result in a conservative assessment of the system's performance, contrary to what might be expected. All results obtained are in closed form and can easily be evaluated numerically for performance prediction purposes.>

Two types of master-slave networks are investigated: oneway and two-way master-slave networks. The one-way master-slave System is a generalization of the well-known hierarchical master-slave tree system. The two-way master-slave system is a novel concept. Sufficient stability conditions are given for both network types. After synchronization is achieved, the frequency drift rate of all oscillators in the network approaches the frequency drift rate of the master oscillator. The steady-state frequency differences between the oscillators and their variances are computed for six network configurations of practical interest. A performance comparison for different network connectivities shows that the two-way master-slave system with a star configuration has the best performance.

Bit synchronization in the presence of asymmetric channel noise has not appeared in the open literature. It is the purpose of this paper to study the tracking performance (clock jitter and cycle slip rate) of a popular digital clock synchronizer, the digital data transition tracking loop (DTTL), in the presence of asymmetric noise. Related parameters of interest, the transition density and data asymmetry, are also included. Acquisition performance (frequency acquisition time) is discussed in the absence of noise. A comparison of the DTTL and crossspectrum synchronization loop (CSSL) is also provided. Numerical results are Presented for the design of a bit synchronizer in this environment.

Network synchronization deals with the problem of distributing time and frequency among spatially remote locations. Network synchronization is an integral part of any large communication system, such as the telephone network. It also plays an important role in many diverse applications like navigation and position determination, computer communication, data gathering, control and command systems, and phased-array antennas. The purpose of this paper is to introduce the reader to the subject of network synchronization by organizing and presenting a tutorial of the theoretical work accomplished to date. Since the subject material is scattered, disconnected, and couched in different notations, the authors have long felt that it would be significant to organize the material and present the reader with an overview of the growth of the subject. A by-product of such a review should serve as an aid to set direction for future studies and research work. The paper begins by providing the classification of networks into plesiochronous (asynchronous) and synchronous. Further breakdown of this basic classification into a tree-structure hierarchy is presented. Since the time and frequency waveforms transmitted between nodes experience propagation delay, some form of ranging system application is usually required in order to compensate for these delays. Several delay compensation techniques are described and incorporated into a more detailed classification of the synchronization systems. This is then followed by presenting functional network models from which a generic and unified mathematical model is formulated. Network performance measures are defined and the mathematical model is used to characterize the synchronization behavior of the network in terms of these measures. Emphasis is placed on characterizing and understanding network stability, steady-state behavior, effects of clock phase noise, and channel thermal noise. The nonlinear behavior of synchronization systems is also explored. Numerous applications are pointed out and a rather complete list (unfortunately nonexhaustive) of the references is provided for the purpose of directing future research work.

Accurate phase and frequency transfer between mutually synchronized oscillators is a problem of current interest. This paper addresses a system of two mutually synchronized oscillators with inherently sinusoidal phase detectors. The system is studied in the context of nonlinear phase-locked loop theory. This is accomplished by Statistically characterizing the "time" and "space and time" increments of the phase processes generated by the two oscillators. The characterization of these increment processes is obtained in the form of steady-state probability density functions (pdf's). The effects of such disturbances as noise, transmission path delays, and oscillator frequency instabilities on the system are studied through their effects on these pdf's. Gaussian approximations for these pdf's (which simplify the extraction of the effects of the disturbances on the system) are also developed. Additionally, the stability of the time intervals and time interval errors generated by the oscillators are studied in the context of cycle slipping phenomena.

This paper presents the results of the modeling and analysis of the bit error probability performance of pseudonoise (PN) spread-spectrum satellite communication systems subject to the worst case continuous wave (CW) tone interference. The mathematical model for the band-limited nonlinear satellite repeater is formulated and the bit error probability is evaluated using classical moment techniques. Accordingly, this paper develops a simple scheme for computing the required moments and for efficient utilization of the moment approach to the evaluation of bit error probability performance. In addition, new numerical results are given for situations of practical interests.

This note demonstrates that the behavior of two mutually synchronized phase-locked oscillators using delay compensation is equivalent to that of a first-order loop with the loop parameters degraded by the residual uncompensated delays of the system. In particular, the probability density of phase differences between the two oscillators is derived and the numerical results are also presented. The cycle slipping rate is easily obtained from this density.

This paper discusses the principle of operation of a phaselocked loop using a vector diagram approach. From this diagram the acquisition, tracking, and frequency stability performance measures are introduced without the need of a loop mathematical model and associated loop analysis. Designers of phase-lock technology should find this tutorial discussion useful in understanding and writing specifications to meet system performance and testing requirements. On the other hand, users should find this discussion useful in interfacing with phase-locked loop designers. Additionally, those who wish to obtain an oveview of the phase-lock technical parlance should also find this paper of interest.

This paper presents the results of an investigation concerning the performance degradation of a phase-locked loop (PLL) due to continuous wave (CW) interference and additive white Gaussian noise. The performance measures evaluated include the probability density function (pdf) of phase error and the cycleslipping rate. The measures are characterized in terms of the ratio of interference to the desired signal power and the loop signal-to-noise ratio. Since the interference term in the loop phase error signal is periodic, the conditional pdf of the phase error process is cyclostationary. A Fourier series expansion is applied as an approach to obtain a solution to the cyclostationary process. Linear performance results are derived and compared to the analytic results.

This paper presents the analysis and evaluation of bit error probabilities of coherent MPSK nonlinear satellite communication systems, in which there is uplink noise, downlink noise, and CW tone interference with random phase uniformly distributed over the interval [0, 2π]. The evaluation of bit probabilities also includes intersymbol interference whose statistical distribution is constructed through a two-dimensional moment technique. This moment technique is as effective and accurate as the standard Gauss quadrature formulas (GQF), yet more versatile than GQF for evaluating an expectation over random variables. Some numerical examples for the performance of satellite channels are illustrated.

Synchronization is a fundamental problem in digital cornmunications systems. In radar, sonar, and navigation systems, synchronization is connected with the objectives of measuring range, velocity, and position. This Special Issue is devoted specifically to the synchronization problem as it relates to digital communications engineering and technology. In the implementation of digital communication systems, one must distinguish among several types of synchronization. Some of these are: 1 ) carrier synchronization, 2) clock synchronization. 3) codeword and node synchronization, 4) frame synchronization, and 5) network synchronization. This Special Issue provides papers which address each of the above synchronization types. Additionally, special problems related to the operation and performance of synchronizers which employ the phase-lock principle are provided. A brief overview of the content of this Special Issue is presented.

This paper presents a unified mathematical model for studying the behavior of various network synchronization techniques, e.g., plesiochronous or independent clocks, hierarchical master-slave, delay-compensated and uncompensated network models are presented in the form of a set of nonlinear space-time matrix equations in which network interconnection matrices are manifested. Each equation in the set characterizes the diffusion of phase (time) and frequency generated at each network node. The matrices of this model define the topological structure of the network. The time-frequency model is used to characterize the timefrequency stability of the network clock ensemble. Expressions for the steady-state network frequency and the time differences between nodal clocks are derived and compared for plesiochronous, delay compensated and uncompensated networks. A network frequency stability measure is introduced, evaluated and performance comparisons are made for specific network configurations. Finally, we illustrate the steady-state frequency stability achievable whenMsubnetworks are connected to form a larger network.

Structure functions are introduced into the theory of correlative tracking systems and how frequency and phase instability enters naturally into the system performance equations is shown. Both the\tau-domain andf-domain peformance is characterized and a Mellin transform theory relating the two is given. The theory is applied to first-, second-, and third-order systems containing arbitrary phase detectors.

This paper uses MAP estimation techniques to obtain carrier reconstruction circuits for unbalanced QPSK signals. In addition, the performance analysis of these circuits is carried out to the extent that a loop design can proceed. Optimal weighting coefficients in the receiving system are identified as functions of theI-Qpower and data rate splits. Finally, numerical results are presented in order to demonstrate the utility of the theory developed. This signal design will be used in the development of the Tracking and Data Relay Satellite System (TDRSS) and the Navigation Satellite Timing and Ranging Global Positioning System (NAVSTAR GPS).

This paper develops the theory for assessing the tracking performance and designing carrier synchronization loops which are to be matched to an unbalanced QPSK signal design. It is assumed that the power split and theIandQchannel data rates are arbitrary. Bit synchronization is assumed unavailable for both carrier reconstruction techniques which have been suggested via MAP estimation theory. Numerical results are presented along with their comparison with results given in Part I where bit timing was assumed known.

This paper is concerned with new results on data related false lock of Costas loops caused by arm filter distortion of the data. The false lock phenomena is demonstrated to occur for random as well as periodic data and the relative levels of lock are predicted. It is shown that, for the case of random data with Manchester symbols, strong lock points exist when the incoming carrier frequency and the loop VCO frequency differ bynR_{s}/2 (n = 1, 2, 3, ...)Hz where Rsis the data symbol rate. In addition to the loop error signal the lock detection signal(I^{2}Q^{2})is also analyzed for false lock effects. The theory also applies to the case of NRZ data symbols with the main result being strong false lock points also occur at VCO frequency offsets ofnR_{s}/2 (n = l, 2, 3, \ldot)but at different levels than the Manchester data. The results of these analyses lead to schemes capable of detecting false lock.

An analytical simulation package called LinCsim has been developed by LinCom Corporation for analytical verification of bit error rate and tracking service performance for bothS- andKu-band Shuttle user service through the Tracking and Data Relay Satellite System (TDRSS). The purpose of this effort was to provide a tool to assess overall system performances as well as the sensitivity to key subsystem parameters and to ensure compatibility of TDRSS and Shuttle transponder performance specifications. The evaluation is based on an analytical simulation, i.e., a combination of simulation techniques and analytical performance evaluation. This allows the use of a more realistic signal format than is possible with a purely analytical approach and maintains the advantage of short computation time. The Shuttle forward and return link models and the main features of the simulation are described. Sample results of the computer runs are provided for current power budgets and system design parameters.

A general "phase-plane" technique for investigating the stability of nonlinear difference equation is described and applied to determine the stability criterion of a first-order digital phase-locked loop (DPLL). If the loop is stable, it is shown that acquisition behavior can be modeled as a first passage time problem. Using this model, one can evaluate the acquisition probability and the mean time to acquire, from the appropriate Chapman-Kolmogorov (C-K) equation describing the transition of the phase error sequence. This approach is verified by direct simulation.

This paper investigates a new method of compensating for the transmission delays encountered in communications networks employing mutual synchronization. The compensation technique suggested belongs to the category of the single-ended methods in the sense that all the phase measurements affecting the control signal supplied to the local oscillator are carried out at that particular node; however, each oscillator does get signals which reflect, to some extent, the phase relationships between the signals received and the local oscillator at all other nodes in the network. The steady-state frequency of theNnodal network is found for general phase detector characteristics in order to demonstrate the profitable properties of the returnable timing system. The effects of mismatched phase detectors and imperfect delay compensation on the network steady-state frequency is given.

The purpose of this paper is to present a theory which can be used to determine the effects which phase noise sources produce on the bit error probability performance of phase coherent links. The paper begins by presenting typical math models for phase noise sources known to exist in frequency generators. These phase and frequency instability models are then incorporated into equivalent loop models known to characterize the performance of CW and Costas loops. From these equivalent loop models a general analysis is presented which can be used to: (1) determine optimum tracking performance (minimum phase-error jitter) and (2) evaluate bit error probability degradations due to combined phase noise sources. This paper concludes with an example which applies the theory presented to assess the impact on link performance due to phase noise sources generated in the ShuttleS-band payload interrogator. By careful design and control of the power spectral densities of the phase noise sources one can design a system so that the phase noise has a small effect on bit error probability performance.

The false (sideband) lock problem in Shuttle Costas loop receivers, in the presencse of noise, is assessed in this paper. False lock margin is defined depending on symbol signal-to-noise ratio rather than in the absence of noise as reported earlier in [4], [5]. Closed form results are given when the arm filters of the Costas loop are one-pole Butterworth filters as used in the Shuttle receivers. However, the approach taken is also general enough to cover filters of arbitrary characteristics. As part of the development of the false lock margin, it is shown that the false lock phenomenon of the squaring loop is identical to that of the Costas loop.

A classical problem in digital frequency-shifted keyed (FSK) demodulation is the evaluation of the bit error probability performance when an estimator-correlator that incorporates a phaselocked loop (PLL) is employed. Although some attention has been devoted to this problem in the past, an accurate account of the mechanism which produces decision errors has not yet been advanced. This paper examines a special case, viz., a first-order PLL preceded by a wideband IF filter, of the above problem using a new approach which is based upon the renewal Markov process theory and the Meyr distribution. In particular, the ad hoc approach of invoking the Gaussian assumption on the decision variable and patching it with a correction term based on Rice's click theory is not used. Rather, the effective noise is properly characterized by unfolding the renewal Markov process associated with the loop phase error. As a slight extension of the results, the performance of the above PLL detector operating on low data rate PSK is given and demonstrated to be approximately 3 dB superior to that of FSK reception. The theory and analysis presented herein apply to the special case where the bandwidth of the IF filter preceding the first-order PLL is required to be several times the data rate because of frequency uncertainties due to channel Doppler and oscillator instabilities, but the frequency deviation to data rate ratio may be chosen small (if desired) to optimize system error probability performance. In addition to presenting results for the case where the oscillator instabilities are assumed absent and channel Doppler is prefectly tuned out at the receiver oscillator, the effects of small residual Doppler on bit error probability performance is considered. In all cases tested, excellent agreement was obtained between theory and computer simulation results.

To optimize the threshold of a pseudonoise (PN) spread spectrum modem for use over an aircraft/satellite communications link at SHF, the effects of Doppler must be taken into account. Reconstitution of carrier phase by a Costas loop to coherently demodulate the PSK data and also the delay-lock error voltage has typically been the practice in PN modems intended for ground applications. To accommodate the platform dynamics, the Costas loop must have a relatively wide bandwidth, and this implies a significant threshold degradation. An alternate implementation employs a noncoherent carrier tracking loop which maintains frequency lock rather than phase lock. Now, the delay-lock error voltage is noncoherently demodulated. For the airborne application, analysis and simulations show this implementation will extend the receiver's tracking threshold significantly (up to 6 dB) for the worst case dynamics profile. An experimental project was undertaken to modify an existing ground PN modem (AN/USC-28, ADM version) for flight test. A software implementation of the digital tracking algorithms was selected where a HP-2100A minicomputer controls carrier frequency and PN code phase via digital phase shifters. The Costas demodulator for extracting PSK data resides entirely in software, and is completely segregated from PN tracking. In laboratory testing of the receiver with simulated dynamics and in actual flight tests, the demonstrated performance was found to approach closely the goals established by the analyses and simulations.

The performance of suppressed carrier receivers with Costas loop tracking is optimized by proper choice of loop arm filter bandwidth. In particular, it is shown that for a variety of passive arm filter types, there exists, for a given data rate and data signal-signal-to-noise ratio, an optimum filter bandwidth in the sense of minimizing the loop's squaring loss. For the linear theory case, this is equivalent to minimizing the loop's tracking jitter. When symbol synchronization is known, it is shown that by replacing the passive arm filters with active filters, i.e., integrate-and-dump circuits, one can achieve an improvement in carrier-to-noise ratio of as much as 4 to 6 dB depending on the passive arm filter type used for comparison and the value of data signal-to-noise ratio (SNR).

The implementation and tracking performance of symbol synchronizers for Manchester coded data is presented with motivation provided by maximum a posteriori (MAP) estimation theory. In particular, it is shown herein that for uncoded data symbols, with, however, arbitrary data transition probabilities, certain physically realizable closed-loop structures, which are readily implemented in practice, are suggested by the theory. The tracking performance of these loops is optimized and comparisons are made among the various configurations over a wide range of system parameters. Although not the major intent of the paper, the acquisition problem is briefly addressed.

The complete statistical description of a first-order correlative tracking system with periodic nonlinearity is shown to be embedded in a renewal process. The time-dependent probability density function of the phase error, as well as the distribution of the cycle slips, is computed. The use of the renewal process approach makes it possible for the first time to compute the distribution of the positive and negative number of cycle slips within a given time interval. This information is sufficient to determine the probability density function of the absolute phase error.

Mutual synchronization between two geographically separated phase-locked oscillators is investigated for two different interconnection methods. This includes the so-called single-ended (uncompensated delay) and the double-ended (compensated delay) methods. Explicit formulas for determining the steady-state frequency and phase errors are developed for both methods. Necessary conditions for the existance of a synchronous state are derived in terms of basic system parameters. Finally, a comparison Of the methods of oscillator interconnection is made as a function of the uncompensated channel delays. Graphical results are presented which are useful in determining steadystate system performance.

In a variety of practical problems involving random processes, it is necessary to have statistical information on their level-crossing properties. This paper presents a survey of known results on certain aspects of this problem and provides a basis for further study in the area. The goal has been to give a broad view of the problems considered in the literature and a brief indication of the techniques used in their solution. Much material of a more or less historical nature has been included since, to the authors' knowledge, no other survey of this nature exists.

This paper is concerned with the problem Of obtaining time-dependent solutions to a class of Fokker-Planck equations that arise in the analysis and synthesis of a variety of first-order synchronization systems employing the phase-lock principle. These include the classical sinusoidal phase-locked loop, squaring and Costas loops, data-aided loops, hybrid loops, various symbol synchronizer mechanizations, and tunnel-diode oscillators. By analyzing the spectral properties of the associated time-dependent Fokker-Planck boundary value problem, eigenfunction expansions of the reduced modulo-2 \piphase-error-transition probability-density function are developed for a class of first-order synchronization systems. Whereas previous work treated the steady-state probability density function, this approach yields a complete statistical description of the phase-error process reduced modulo-2 \pi.

The tracking loops presented herein exploit the coherency of the observed data sidebands at the carrier frequency for improvements in phase-coherent tracking, telemetry, and command system performance. The loop is motivated by one aspect of generalized harmonic analysis, viz., the so-called cross spectrum. The basic idea of the loop centers around using the power in the composite received signal (sidebands including cross-modulation components) to enhance the signal-to-noise ratio in the carrier tracking loop, thereby reducing the noisy reference loss and ultimately the subcarrier reference jitter, the symbol sync jitter, and the error probability of the data detector. The modulation from the extracted sidebands is removed in such a way that the coherence power in the data sidebands can be used for tracking at the carrier frequency.

Digital communication networks used for the distribution of high-speed digital information are currently the subject of design studies for many civil and military applications. This paper presents results that are useful in such studies as well as in network planning. In particular, the paper is concerned with the problems of carrier synchronization and noisy reference detection of polyphase signals. Reconstruction of coherent references for the detection of polyphase [N-ary phase-shift-keyed (PSK)] signals is considered and analyzed for three carrier reconstruction loops, namely,Nth power (multiply-and-divide) loops, generalized Costas (I-Q) loops, and extensions of data-aided (modulation wipeoff) loops. General expressions for the error probability are developed when the reconstructed reference signals are noisy. These expressions are evaluated numerically for cases of practical interest and compared with differentially coherent reception.

This paper investigates the detail capabilities and performance characterization of systems that employL-orthogonal signaling techniques.L-orthogonal signals represent a unified set of signals wherein the polyphase and orthogonal (biorthogonal) signal sets are included as special cases. This fact is important since orthogonal (biorthogonal) and polyphase signaling sets represent opposing forces as far as tradeoffs between error probability, energy-to-noise ratio, and bandwidth requirements are concerned. Bounds on the performance of the optimum receiver and the performance of various suboptimum (practical) receiver structures are given. Coherent and differentially encoded signals are also pursued. Various comparisons and tradeoffs are made by means of numerical evaluation of the error-probability expressions.

Any digital communication system that employs coherent detection requires coherent reference signals for proper operation. This paper is concerned with the transmission and detection of differentially encoded multiple phase-shift-keyed (MPSK) signals and the ambiguity resolution problem that results from suppression of the transmitted carrier. In particular, the paper presents the analysis and performance of differentially encoded coherent MPSK systems that reconstruct coherent reference signals by means of generalized Costas orNth power loops. The performance of such systems is then compared with that of ideal reception of MPSK signals and differentially coherent detection of differentially encoded MPSK signals. Emphasis is placed upon the special cases of quadriphase and octaphase signaling.

Variation of coherent correlation receiver performance characteristics caused by transmitted signal corrupted by Rician fading phenomena and additive Gaussian noise

The problem of computing error probabilities for multi-channel communications using an incoherently terminated receiver is analyzed. The signaling alphabet is composed of two equal-energy, equiprobable, correlated waveforms and the multichannel model is presumed to be of the slowly fading "Rician" type, i.e., each subchannel is presumed to be composed of a fixed or specular component and a scatter-like or Rayleigh fading component. The main result of this paper is a generalization (21) of an earlier result derived by Helstrom. Novel by-products of this generalization include, as special cases, results derived by Turin, Pierce, Price, and Lindsey. Also closed-form solutions to very general integrals (22) (heretofore seemingly unknown) involving Bessel function products are presented as part of the main result. These integrals are known to arise in the analysis of multichannel adaptive communication systems. Numerical computations for the error probabilities are given for special values of the signal cross-correlation coefficient\lambdaand multi-channel order. These results graphically illustrate that the optimum set of equal-energy binary signals which minimize the error rate for the Rayleigh fading multichannel are orthogonal. Specifically, to maintain the same error probability in two systems, one employing nonorthogonal signals having correlation coefficient\lambda, the other employing orthogonal signals, the transmitter power must be increased in the former. In fact, for large SNR's, the graphical data indicate that the required increase in transmitter power is approximately10 \log_{10}(1 - \lambda^{2})^{-1}dB.

Performance characteristics are derived for two different forms of multireceivers (the coherent and noncoherent) which are used with binary andN-ary signaling through the Rician fading multichannel. The coherent multireceiver is capable of perfectly measuring the channel amplitudes and phases whereas, at the other extreme, the noncoherent multireceiver implies a receiver which requires no channel measurement whatsoever. The multichannel model presumes that each transmission mode supports a specular or fixed component and a random or scatter component which fades according to the Rayleigh distribution. Heretofore, performance analyses of multichannel links have assumed that the fading obeys the Rayleigh law. This multichannel model is sufficiently general to include four practical types: the Rician and the Rayleigh fading multichannels, multichannels whose propagation modes do not fade, and those which simultaneously contain Rician and Rayleigh fading propagation paths or the so called mixed-mode multichannel. Error probabilities are graphically illustrated and compared for various multichannel models. It is found that the effectiveness of multichannel reception is highly dependent on the strength of the specular channel component relative to the mean squared value of the random channel component. In particular, multichannel reception is more effective when applied to the completely random multichannel. For special cases the error-rate expressions reduce to well-known results.