The asymptotically optimum simultaneous estimation of the phase and frequency of MPSK signals in AWGN channel is derived at low SNRs under the maximum-likelihood criterion. Its performance is superior to those of previously published methods, in particular at large frequency uncertainty.

The design and performance of indoor communication systems are strongly dependent on the delay spread in the impulse response of the channel. The delay spread is due to the abundance of the multipath reflections in the indoor environment. Judicious system design can derive benefit from the availability of the multipath signal to improve the system performance. Such potential improvement is due mainly to the fact that the various multipath components are very weakly dependent on each other, while fading, and a natural temporal diversity situation occurs. For system performance evaluation it is desirable to have an estimate of how the delay spread varies while the received power decreases with increasing transmitter-receiver distance. The simplest possible model that retains the essentials of a dense multipath environment is proposed and analyzed. It assumes that the direct path is blocked and that only scattered signals are received. A small ellipse of focal distance r/sub min/ about the transmitter and receiver is assumed to be free of scatterers. The scatterers are assumed to be Lambertian uncorrelated point-scatterers, uniformly distributed in 2-dimensional space. Secondary reflections are neglected and primary reflections are assumed not to be hampered by the presence of the other point scatterers. This is basically the wide sense stationary uncorrelated scatterers (WSSUS) model often used in communications analysis.

The capacity C(/spl rho//sub a/, /spl rho//sub p/) of the discrete-time quadrature additive Gaussian channel (QAGC) with inputs subjected to (normalized) average and peak power constraints, /spl rho//sub a/ and /spl rho//sub p/ respectively, is considered. By generalizing Smith's results for the scalar average and peak-power-constrained Gaussian channel, it is shown that the capacity achieving distribution is discrete in amplitude (envelope), having a finite number of mass-points, with a uniformly distributed independent phase and it is geometrically described by concentric circles. It is shown that with peak power being solely the effective constraint, a constant envelope with uniformly distributed phase input is capacity achieving for /spl rho//sub p//spl les/7.8 (dB 4.8 (dB) per dimension). The capacity under a peak-power constraint is evaluated for a wide range of /spl rho//sub p/, by incorporating the theoretical observations into a nonlinear dynamic programming procedure. Closed-form expressions for the asymptotic (low and large /spl rho//sub a/ and /spl rho//sub p/) capacity and the corresponding capacity achieving distribution and for lower and upper bounds on the capacity C(/spl rho//sub a/, /spl rho//sub p/) are developed. The capacity C(/spl rho//sub a/, /spl rho//sub p/) provides an improved ultimate upper bound on the reliable information rates transmitted over the QAGC with any communication systems subjected to both average and peak-power limitations, when compared to the classical Shannon formula for the capacity of the QAGC which does not account for the peak-power constraint. This is in particular important for systems that operate with restrictive (close to 1) average-to-peak power ratio /spl rho//sub a///spl rho//sub p/ and at moderate power values.>

pg 100 diversity coding, as introduced in Ayanoglu et al. (1990), is a method of protection against failures in a communication network or a storage system, which is based on introducing a digital error-correcting code across independent links. This technique makes efficient use of the extra network capacity needed for coding and has the additional advantages of being nearly instantaneous, not requiring a feedback channel, rerouting, or resynchronization. In high-speed (multi Gbps) networks, digital coding will be difficult to implement, and the purpose of the present paper is to demonstrate how diversity coding may be implemented in the analog domain using the discrete fourier transform (DFT). In particular, the authors show that the DFT is a continuous-amplitude maximum-distance separable code over the field of complex numbers when the transform kernel is a prime root of unity. This code can be used to generate self-healing or fault-tolerant communication networks for continuous- or discrete-amplitude signals, as long as continuous-amplitude parity channels are available. The authors describe electrical and optoelectronic implementations, and a signal estimation approach to combat channel noise and thereby improve the performance of the analog diversity coding system. The most important advantage of this technique is in greatly simplifying the encoders and decoders of diversity coding systems for high-speed networks, such as fiber-optic wavelength division multiplexed networks. Application of analog diversity coding to systems with analog sources, such as telemetry systems is also possible.>

The capacity of the M-user binary adder channel, subjected to various restrictions of physical nature, is investigated. The underlying propagation media considered are (i) fiber-optic, with lossless coupling and Poisson statistics, (ii) radio, under Rayleigh fading, and (iii) radio with constant amplitudes and random phases. Whereas the capacity of the unrestricted (ideal) model for the binary adder channel is known to increase without limit with the number of users, it is shown in the present paper that, for each of these cases, the total capacity is upper-bounded by a constant independent of the number of users: in case (i) by 1.7Q/sub T/ bits per channel use, where Q/sub T/ is the parameter of the Poisson process, in case (ii) by 4.33 bits per channel use, and in case (iii) by 4.27 bits per channel use.>

Consider M-Choose-T communications: T users or less, out of M potential users, are chosen at random to simultaneously transmit binary data over a common channel. A method for constructing codes that achieve error-free M-Choose-T communication over the noiseless adder channel (AC), at a nominal rate of 1/T bits per channel symbol per active user, is described and an efficient decoding procedure is presented. The use of such codes is referred to as forward collision resolution (FCR), as it enables correct decoding of collided messages without retransmissions. For any given T a code is available that yields a stable throughput arbitrarily close to 1 message/slot. Furthermore, if the occurrence of collisions is made known to the transmitters, such a throughput can be maintained for arbitrary T,T>

Abstract In this paper, we present a construction of Euler circuits for some circular multistage interconnection networks, which have a uniform structure between consecutive stages.

Techniques are presented that can cancel ghosts in received analog TV (for IDTV, EDTV, and HDTV) signals. The authors utilize the fact that there are short periods of time without the analog signal (the horizontal flyback interval between the lines) to periodically cleanse a finite impulse response (FIR) or an infinite impulse response (IIR) equalizer. This line-by-line processing (cleansing) overcomes the limitations of standard equalizers to allow adequate suppression of ghosts, even with nulls in the spectrum.>

A lower bound on the cutoff rate R/sub O/ of a dispersive Gaussian channel with peak- rather than average-power-limited input is evaluated and compared to the lower bound on capacity under the same input constraints. It is assumed that the input symbols are independent and uniformly distributed. Both bounds exhibit the same behavior as a function of an appropriately defined signal-to-noise ratio (SNR), with a discrepancy of 1.68 dB to the disadvantage of R/sub O/, at high SNRs. The lower bound on R/sub O/ is evaluated for peak- and slope-limited signals that model magnetic recording systems and is compared to the lower bound on capacity.>

Techniques that can cancel ghosts in received analog TV (for improved-definition TV, extended-definition TV, and high-definition TV) signals are presented. The fact that there are short periods of time without the analog signal (the horizontal flyback interval between the lines) is utilized to periodically cleanse a finite impulse response (FIR) or an infinite impulse response (IIR) equalizer. This line-by-line processing (cleansing) overcomes the limitation of standard equalizers to allow for 40-50 dB of suppression of ghosts, even with nulls in the spectrum, as long as the ghost delay is less than the period of time without the analog signal. Furthermore, by using time inversion in combination with line-by-line processing, the stability problem of the conventional IIR equalizer can be eliminated. It is shown that it may be possible to implement this IIR equalizer on a single digital integrated circuit. Alternatively, an FIR equalizer can be used; although it requires multiple chips (i.e. more taps), it can acquire and adapt to the ghosted channel more rapidly than an IIR equalizer.>

A multiconnected ring is a ring-structured network in which each node is also connected by chords to other nodes of the ring. The span of a chord is the number of nodes counted between the endpoints of the chord (only one endpoint is included). A multiconnected ring is defined as being nested if it is rotationally symmetric and if the span of each chord is an integral multiple of the spans of each of the shorter chords. For local and metropolitan area networks, a nested multiconnected ring (NMCR) can be implemented as a multifiber ring network in which each node receives and transmits on a subset of the fibers in a bundle or cable. Because of the rotational symmetry, NMCRs permit an identical connector to be used at each node. A NMCR is one of several intermediary networks between a ring and a fully connected network. Under a performance criterion that takes throughput, equipment cost, and complexity into account, an optimized NMCR outperforms both its extreme counterparts. Although ShuffleNet multiconnected rings can provide higher throughput per node than NMCRs, the rotational symmetry and identical connectors of NMCRs make them preferable for applications with many nodes and lower throughput-per-node requirements.>

It is well known that in cases of unlimited channel bandwidth and unconstrained signal spectrum, a constant-envelope constraint on the signal does not reduce the capacity of an additive Gaussian channel, as compared to its capacity with the optimum signals of similar average power. For band-limited channels of bandwidth B, however, the constant-envelope constraints does reduce the capacity, even if the signals themselves are allowed arbitrarily rapid alternations (transitions). Here, using a recently introduced technique, it is shown that the capacity is further drastically reduced if, in addition to the channel limitation, the constant-envelope signal is itself restricted to a small fractional out-of-band power epsilon . Ideal lowpass and bandpass channel filters are considered, and upper bounds on the capacity are derived. The out-of-band power restrictions can be met, for example, by restricting the average rate of transitions rho of the binary input signal. It is shown that in this case, epsilon>

The multiple-access problem is addressed from the combined standpoint of both coding and scheduling to arrive at a stable, highly efficient access scheme for the binary adder channel. The authors define a system model that includes the channel and the coding mechanism and explain the M-choose-T communication mode which is fundamental to their method. They then address the system's performance and show that high throughput (arbitrarily close to 1) is achieved while the access remains stable. They also investigate the average message delay.>

A model for magnetic recording is proposed which uses two parameters to describe the limitations on the remanent magnetization in the medium: the dimensionless peak value A/sub m/ and the steepest slope B(s/sup -1/). A low-pass bandwidth restriction W(s/sup -1/) due to read circuits is also included. Lower and upper bounds on the achievable transmission rates are derived in terms of the signal-to-noise ratio. For the case of ideal low-pass restriction with B>

The Gilbert-Elliott channel, a varying binary symmetric channel, with crossover probabilities determined by a binary-state Markov process, is treated. In general, such a channel has a memory that depends on the transition probabilities between the states. A method of calculating the capacity of this channel is introduced and applied to several examples, and the question of coding is addressed. In the conventional usage of varying channels, a code suitable for memoryless channels is used in conjunction with an interleaver, with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel. The transmission rate is limited by the capacity of this memoryless channel, which is often considerably less than the capacity of the original channel. A decision-feedback decoding algorithm that completely recovers this capacity loss is introduced. It is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie-aided channel, the capacity of which equals that of the original channel. The calculated random coding exponent of the genie-aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel.>

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N/sub 0/B) for P/(N/sub 0/B)>>1, where P is the peak power of the input signal and N/sub 0//2 is the double-sided power spectral density of the additive white Gaussian noise.>

The authors provide mathematical justification, using classical detection theory, for the observed superior performance of coherent dual optical detection over single-diode detection and establish a rationale for determining the intensity of the local oscillator. Viewing the dual detector as an optical channel with one input and two outputs, they show that in the limit of large local oscillator intensity, the optimal processor uses the difference of the two detector outputs, and consequently no bias subtraction needs to be carried out. Since phase is a major problem in applications of coherent optical communication, the authors propose modulation and detection formats that can possibly trade the effects of phase noise for the often less objectionable additive noise.>

The validity of the click noise method of S.O. Rice (1963) for describing the performance of an analog threshold-extending receiver is established within the scope of a simulated environment. The significance of the received signal envelope for enhancing the detection of clicks is examined, and it is shown that a reliable click detector must make use of signal memory. A 'genie-aided' errorless click detector could lower the FM threshold by at least 6 dB. Threshold extension of 2.75 dB is observed under simulated conditions, with a realizable, clicks-cancelling receiver at a modulation index of five.>

Using T.E. Duncan's theorem (1970) on the relation between mutual information and the mean-square error of the optimum causal estimator of a random signal in additive white Gaussian noise (AWGN), the maximum achievable information transfer over the AWGN channel is derived with the random telegraph wave input. The information transfer is bounded and symptotically determined for the Wiener phase-modulated process input at large signal-to-noise ratio (SNR). Both results are compared to the information transfer for the capacity-achieving Gauss-Markov input process. For both the Wiener phase-modulated and the Gauss-Markov processes the information transfer increases asymptotically as the square root of SNR, but for the random telegraph wave it increases only as its logarithm.>

The so-called click-and-Gaussian-noise model for the output of a limiter-discriminator receiver for frequency-modulated signals, first proposed by S.O. Rice in 1963, is reviewed. A short survey is presented of the subsequent research that it generated and of some practical applications that it motivated. A more detailed analysis of parameters encountered in the Rice model is carried out with emphasis on their pertinence to click detection. These results are applied to the understanding of the limitations and to the interpretation of the performance of several noise threshold extension techniques for analog modulations and of error reduction techniques for digital modulations that depend on click detection and elimination.>

A "slowly" fluctuating target is assumed to keep its radar cross section constant for the duration of several(M)dwells on target. To resolve multiple range and/or Doppler ambiguities, the received signal, which is presumably coherently processed (i.e., predetection integrated or matched filtered) over each dwell, must often be tested against a threshold, {\em independently} of those on other dwells. Such a procedure is referred to as {\em multiple detection}. A technique for the evaluation of a tight lower bound on the multiple-detection probabilityP_{M}, under Swerling case I statistics for the cross section, is presented in term of an infinite series and worked out in detail forP_{2}andP_{3}. Estimates on the computation error due to the truncation of the series are derived. Numerical results indicate thatP_{3}comes much closer toP_{1}than top_{1}^{3}or even toP_{1}P_{2}; at an expected signal-to-noise ratio of13dB and atP_{1} = 0.51, it obtains thatP_{3} \geq 0.40, whereasP_{1}P_{2} = 0.23andp_{1}^{3} = 0.17.

A two-parameter tracking loop that mutually locks the phases and delays of two noise-contaminated replicas of a randomly phase-modulated signal, received via different channels, is analyzed. It is shown that, at high SNR, i.e., small tracking errors, the twoparameter loop can be considered as two uncoupled single parameter loops, provided the signals are beaten down to zero center frequency. Special emphasis is put on the delay error variance; it is found that, in general, the broadening of the phase loop bandwidth (provided for more rapid acquisition) induces larger delay-tracking errors. Also, such broadening decreases the expected time to loss of delay lock; the influence of the location of the absorbing boundaries for this problem is investigated. Quantitative results for a typical configuration are presented in Figs. 1-9.

A direct-detection photon-limited optical communication channel that uses pulse position modulation (PPM) under a pulsewidth constraint is considered. Overlapping PPM (OPPM) allows multiple positions per pulsewidth, as well as fractional modulation indices (number of pulsewidths per frame) requiring more refined timing than that needed for conventional disjoint PPM (DJPPM). It is shown that even at moderate values of the expected photon count per pulse(Q)--such as needed for high data rates--OPPM outperforms on-off keying (OOK) in both capacity and cutoff rate, even though OOK is uniformly superior to DJPPM. Moreover, efficient use of OPPM is possible with equiprobable input symbols, whereas OOK requires inconvenient asymmetrical inputs to achieve capacity and high cutoff rate efficiencies (nats/ photon). At lower data rates, where capacity efficiency is the prime criterion, a significant advantage (- 20 percent) over DJPPM can be achieved up to efficiencies of about 0.7 nats/ photon. The M-ary photon-limited OPPM channel can be viewed as an ambiguity and erasure channel, in the sense that some channel outputs are ambiguous in only some input symbols and only if no photons are counted is there ambiguity in all input symbols. For largeMambiguities cause bursts of erasures of data symbols. Massey's interlaced encoding, as well as conventional encoding followed by interleaving, are adaptable to this bursty channel, and effect an increase in its cutoff rate comparable to the increase obtainable with DJPPM by the same techniques.

The mean-square error of the delay estimate of a photon pulse is known to decrease asQ^{-1}if the pulse envelope is smooth, but asQ^{-2}if it has sharp edges, thereby belonging to "nonregular" estimation cases (Qdenotes the expected photon count). The transition from theQ^{-1}to theQ^{-2}law is investigated for trapezoidal pulse models, and is found to occur in the region where the standard deviation of the error is on the order of the width of the pulse slopes. Thus for values ofQbelow this region, practical pulses are effectively rectangular, and their estimation problem may be qualified as "nonregular."

Orthogonal quantization is a partition of signal space that is achieved by independent quantization of each of itsMorthogonal axes. A closed form expression is derived for the quantized channel cutoff rate and for the optimum orthogonal quantization similar to the one that has been derived for binary signaling. While orthogonal quantization is natural for communication systems in which the transmitted signals are themselves orthogonal, it can also be profitably applied to other signals, e.g., a simplex set in a lower dimensional space. Though orthogonal quantization is inferior to optimal quantization, it is essentially simpler and does not incur great loss in performance. A numerical example illustrates the relative merits of optimal and orthogonal quantization for the simplex set in the plane.

Sampling performed in conjunction with hard-limiting of a narrow band signal in band-limited white Gaussian noise increases the loss in output signal-to-noise ratio over that incurred by hardlimiting the original time-continuous signal. The largest increase in noise is by a factor of\pi^{2}/8in both the band-pass and the base-band cases, and occurs when the input signal-to-noise ratio is low and sampling is at Nyquist rate. Increase in the sampling rate gradually reduces the additional loss in both cases.

This paper presents data and criteria to assess and guide the design of modems for coded noncoherent communication systems subject to practical system constraints of powerS, bandwidthW, noise spectral density N0, coherence time Tc, and number of orthogonal signalsM. Three basic receiver types are analyzed for the noncoherent multifrequency-shift keying (MFSK) additive white Gaussian noise channel: hard decision, unquantized (optimum), and quantized (soft decision). Channel capacity and computational cutoff rate Rcompare computed for each type and presented as functions of the predetection signal-to-noise ratioST/N_{0}and the number of orthogonal signalsM = 2TW. This relates the channel constraints of power, bandwidth, coherence time, and noise power to the optimum choice of signal durationT \leq T_{c}and signal numberM.

The stochastic process at the output of a matched filter, when the latter is excited by its proper signal in additive white noise, has a mean function proportional to its covariance function. Sample path properties of a Gaussian process with the mean proportional to the covariance, conditioned such that it assumes a given value at the instant of the peak in the mean, are independent of signal amplitude. Formal and rigorous proofs and a detection-theoretical interpretation of this result are presented. It is then applied to the calculation of the detection probability of a rectangular signal of unknown time of arrival and to bounding the threshold effect in the estimation of the time of arrival. A novel passage time result is derived in the Appendix.

The types of ambiguities that preclude the possibility of recovering the sample functions of a Gaussian process from their zero-crossings are illustrated by a simple example.

The minimum-mean-square-error (rose) estimation of the delay of a coherent pulse of photons by a direct-detection receiver is shown to depend on the shape of the pulse envelope. Whereas with smooth envelopes the minimum mse decreases only as the expected energy in the pulse, with sharp-edged envelopes it decreases as its square, provided the optimum estimator is used. Occurrence of photoelectrons due to additive noise increases the rose by an additional term, proportional to the expected intensity of the noise. It approximately equals the photon-limited term at a signal-to-noise power ratio of 17 dB in the case of rectangular envelopes.

Expressions for the error probabilities in the detection of binary coherent orthogonal equienergy optical signals of random phase in thermal background noise are derived. They converge to the classical expressions at high densities. Poisson models for background noise, however, lead to singular detection at high densities.

In above-threshold communication situations, the estimation bias and hence the modulation suppression are practically negligible; so that the output signal-to-noise ratio (SNR) is numerically very close to the reciprocal of the normalized mean-square error (MSE). The two last performance measures are, however, conceptually distinct as well as numerically widely different below threshold. Whereas in estimation and control problems the latter is of primary interest, much effort having been invested in its calculation and bounding, the former is very often more meaningful when transmitting sampled continuous data. This paper purports to review the relations between the previously mentioned quantities in time-discrete communications; to conjecture a functional dependence of bias and MSE on the value of the transmitted parameter, that simplifies these relations; to present some results of a Monte-Carlo simulation that tests these conjectures and provides performance curves for the maximum a posteriori probability, the (minimum-MSE-optimal) conditional mean and other derived estimators; and finally to speculate about the relative merits of these averaging type estimators as compared with the discriminator types in a frequency-position-modulation system, from the point of view of the aural character of the output noise below threshold.

An expression for the expectation of level crossings of a class of nondifferentiable shot processes that involve impulse responses having discontinuities is derived. Its first term is essentially the Rician formula [l, pp. 51-53] except that the random variables(y_o, \dot{y}_o)in the integrand are conditioned on nonoccurrence of discontinuities and can be interpreted as yielding the contribution of "smooth" crossings; the second term then describes the direct contribution of the jumps. The moments of(y_o, \dot{y}_o)reflect the influence, at the points of continuity of the processy(t), of the jumps at its points of discontinuity. Whereas in differentiable processes(y, \dot{y})are orthogonal, here(y_o, \dot{y}_o)are correlated; furthermore, althoughy_oconverges in distribution toyandE[\dot{y}_o]is finite and nonzero in general, evidently\dot{y}has no finite moments. In the Gaussian limit of large densities of counts of the underlying Poisson process, an explicit formula is obtained in terms of known parameters. The Rician term is slightly altered by the correlation betweeny_oand\dot{y}_o. On the other hand, the additional term has a component that increases as the square root of the average number of counts. In various practical cases either the bounded Rician or the diverging term can be dominant. An example of particular interest is examined in detail.

By "Poisson regime" we mean a model in which intelligence is communicated by random discrete occurrences in time that obey Poisson statistics of arbitrarily time-varying mean, as for example when modulated electromagnetic radiation and background radiation at optical frequencies is incoherently detected by photon-sensitive surfaces. The problems of optimal detection of signals of arbitrary shape and of the estimation of signal amplitude and delay are treated under a maximum-likelihood criterion. Detection probabilities, delay estimation errors, and the probability of "noise threshold" in delay estimation, are derived. Some results are basically different from those of parallel problems treating known signals in Gaussian noise. The treatment is based on a representation of nonstationary Poisson processes in which the observables are the instants of the occurrences rather than their numbers in given intervals of time.

The measurement of linear time-varying systems and the mapping of densely distributed radar targets provide the motivation for the problem of estimation of linear multidimensional weighting functions in Gaussian noise. The assumption that the weighting function to be estimated is a sample of a Gaussian process of known autocorrelation function, and the adoption of either a maximum a posteriori probability or a minimum mean-square error criterion for the excellence of the estimate reduces the estimation problem to that of the solution of a Fredholm equation, the kernel of which is a generalization of Woodward's ambiguity function. A unique solution is assured if the statistics involved have sufficiently short correlation intervals. Closed-form solutions to the Fredholm equation, in particular two-dimensional cases of time- and frequency-shifted signals, are obtained over infinite domains of the weighting function by using Fourier and Wiener-Hopf techniques, and over finite domains by solving the eigenvalue problem of the ambiguity function. Generally speaking, the estimation error decreases with the decrease in the domain area; within a domain of unit area, perfect reproduction can be approached by increasing the SNR, in agreement with previous resuits on strictly noiseless measurement of linear systems. The appropriate "optimum" signal processor performs on the received signal a linear operation that is, essentially, an "inversion" of the eigenvalue spectrum of the ambiguity function; the extent of inversion is,limited:by its accentuation of the additive noise of the interference from neighboring areas of the domain. Only under extreme circumstances of constant eigenvalue spectra or of vanishing signal-to-noise ratios is the optimum processor equivalent to a "matched filter." The performances of the optimum processor and of the matched filter are compared in several examples.