Showing papers on "Fading published in 1971"

The Effect of Gaussian Error in Maximal Ratio Combiners

Abstract: In a fading channel, maximal ratio diversity combilling improves the average signal-to-noise ratio over thatof a single branch in proportion to the number of diversity branches combined. However, its main advantage is the reduction of the probability of deep fades. The effect of Gaussian errors in the combiner weighting factors on the probability distribution of the output signal-to-noise ratio is computed. The limits on allowable error for a specified probability of fades below any given level are indicated. The results are applied to a mobile radio example in which the weighting factor is determined from a pilot transmitted along with the signal. To keep the pilot from overlapping the signal, they are separated either in frequency or in time. In this case the Gaussian error is due to decorrelation of the pilot from the signal either because their frequency separation or their time separation is too large.

Feedback equalization for fading dispersive channels

Abstract: Data transmission through a slowly fading dispersive channel is considered. A receiver that linearly operates on both the received signal and reconstructed data is postulated. Assuming an absence of decision errors, the receiver is optimized for a minimum-mean-square-error criterion. Transfer functions are determined and superiority over nonfeedback receivers is indicated. The feedback receiver can be realized in a slowly varying unknown environment by means of an adaptive technique that requires neither test signals nor statistical estimation. The receiver will eliminate timing jitter and Doppler shifts. In addition, the receiver provides a time-diversity effect, as the receiver probability of error averaged over the fading statistics is lower in the presence of dispersion than in its absence.

Optimum Linear Estimation of Stochastic Signals in the Presence of Multiplicative Noise

Abstract: This paper considers optimum (MMSE) linear recursive estimation of stochastic signals in the presence of multiplicative noise in addition to measurement noise. Often problems associated with phenomena such as fading or reflection of the transmitted signal at an ionospheric layer, and also situations involving sampling, gating, or amplitude modulation, can be cast into such formulation. The different kinds of estimation problems treated include one-stage prediction, filtering, and smoothing. Algorithms are presented for discrete time as well as for continuous time estimation.

A comparison of specific space diversity techniques for reduction of fast fading in UHF mobile radio systems

Abstract: Over the past few years a variety of space diversity system techniques have been considered for the purpose of reducing the rapid fading encountered in microwave mobile radio systems. Basic diversity methods are first reviewed in the framework of mobile propagation effects, and then specific techniques are compared from the standpoint of transmitter power required to achieve a certain performance. Criteria of comparison used included baseband SNR while moving and reliability when the vehicle stops at random. System parameters are type and order of diversity and transmission bandwidth. Tradeoffs between performance properties and system parameters are indicated. The calculations show that relatively modest use of diversity techniques can afford savings in transmitter power of 10-20 dB. For example, at a range of 2 mi, to obtain 30-dB baseband SNR while moving and 99.9-percent reliability when stopped requires a transmitted power of 8 W for a conventional FM system with no diversity. Two-branch selection diversity provides the same performance for a transmitter power of only 300 mW.

Multiple-path fading on line-of-sight microwave Radio systems as a function of path length and frequency

Abstract: Transmission over line-of-sight microwave radio paths is analyzed with the aid of a piece-wise linear approximation of the atmospheric index of refraction. The simple model is adequate; it predicts published experimental results. A short path is defined on which no deep fading can occur and the maximum length of such a path is estimated from measured data for New Jersey. Expressions are presented for the worst-case amplitude-frequency response and for the maximum echo delay for short paths. It is shown that if the normal Fresnel-zone clearance is maintained on short paths, no fading will occur due to substandard conditions of propagation. W. T. Barnett's result is also predicted from this model: the distribution of attenuation on long paths is a function of L3/λ where L is the path length and λ is the free space wavelength. The distribution of deep fades on long paths is predicted by this model to have the same slope as the Rayleigh distribution, the slope normally found in measurements of attenuation distributions on long paths.

Statistical behavior of a fading signal

Abstract: A general analysis of the statistical behavior of the envelope of a fading signal V (t)eiϕ(t) is presented in this paper. The statistics include the probability P(V ≤ L) that the amplitude V (t) will fade below a specified signal level L; the expected number N(L) of fades of V (t) below L per unit time; and the average duration t(L) of fades below L. The model for the fading signal is a constant vector plus a random interfering vector which represents the resultant of all the received extraneous signals and noise. The theoretical results agree with three empirically observed power relationships obtained in deep fades of nondiversity signals: P(V ≤ L) ∝ L2, N(L) ∝ L and t(L) ∝ L. The theoretical results are applicable to a wide class of fading problems. The analysis includes the previous works of Rice, Nakagami, Norton, Vogler, Mansfield, and Short as special cases.

H.F. data transmission using chirp signals

Abstract: Swept-frequency or chirp signals are currently under investigation for data-transmission applications. In particular, long-range air/ground communication in the h.f. band may benefit from the use of these wideband signals owing to the inherent protection chirp signals offer against fading in a time-varying multipath channel. The theory of pulse compression and data transmission using chirp signals is outlined, and an experimental communication system is described with measured error rates in noise and carrier interference.

An improved microspectrofluorimeter with automatic digital data logging: Construction and operation

Abstract: SUMMARY This paper describes an instrument for microspectrofluorimetry, based on the Leitz microspectrograph. Important features are monochromatic epi-illumination, a reference channel and a measuring system using photon counting with automatic recording of data in digital form. To minimize fading, measurements of fluorescence intensity can be made within as little as 200 msec from the commencement of irradiation.

Radio system with feedback for fading compensation

Abstract: A nondiversity radio system provides compensation for multipath fading by means of continuous amplitude feedback. Intelligence is transmitted from one station by means of frequency modulation, while amplitude modulation is caused by the fading en route. At the other station the received amplitude envelope is fed back as part of a frequency modulated, return intelligence signal. The feedback envelope is used at the first station to amplitude modulate the subsequent transmission to precompensate for the anticipated fade and produce fade-free reception at the other station. The system is especially well suited for mobile radio telephone applications since fading can be eliminated at a relatively simple, single branch mobile station.

FM Noise With Fading Channels and Diversity

Abstract: The response of an FM discriminator to a fading signal is derived, taking into account the below-threshold noise and the effect of various diversity techniques. The effect of muting the discriminator output at low signal levels is considered and shown to achieve only marginal improvement. The diversity techniques considered are maximal-ratio combining, selection diversity, and equalgain combining. Only predetection combining is considered for the maximal-ratio and equal-gain techniques. The average SNR at the discriminator output is derived for each form of diversity, assuming that each diversity branch is independent of the others and subject to fading with a Rayleigh envelope distribution. Curves of average SNR plotted against the mean CNR in one branch are presented for various numbers of diversity branches and ratios of IF bandwidth and baseband bandwidth. The curves presented are for maximal-ratio combining only, but it is shown that the results for selection diversity and equal-gain combining may be obtained from these curves by simply applying a correction to the mean CNR. The theoretical results are supported by experimental measurements that show very close agreement with theory.

Spectral and angular covariance of scintillation for propagation in a randomly inhomogeneous medium.

Abstract: Based on a multiple transform approach, it is shown that it is possible to compute the statistics of propagation in a randomly inhomogeneous medium without invoking the small scattering angle approximation. This technique also makes it possible to compute the cross-statistics between two waves with different wavelengths or traveling in slightly different directions. The spectral covariance of log-amplitude and the spectral phase, and wave-structure functions are evaluated for horizontal propagation (i.e., for the statistics of turbulence not changing over the path). They are found to vary very slowly with separation of wavenumber. The angular covariance of log-amplitude and the angular-phase and wave-structure functions are formulated, but only the angular variance of log-amplitude is evaluated. It is found that the variance decreases very rapidly. Correlation only extends over an angular range of +/-0.2(4/zk)((1/2)), where z is the path length and k is the wavenumber. Comments concerning the application of these results to several problems are presented. These problems include: (1) the use of spectral diversity techniques in optical communications; (2) the possibility of turbulence garbling optical communications; (3) the cause of chromatic scintillation of stars; and (4) the scintillation and fading of laser illuminated targets, etc.

Fading techniques and concept learning in children

Abstract: The utility of stimulus fading as a training technique for attainment of concepts was questioned. Fading on a cue which focused attention toward the criterial aspect of the stimuli (axis of symmetry) produced no better performance than standard discrimination procedures, while fading on an extrinsic dimension yielded significantly poorer performance than did the standard. Possible explanations were discussed in terms of “blocking” effects.

A study of the relationship between multipath distortion and wavenumber spectrum of refractive index in radio links

Abstract: The study reported here is concerned with relating the multipath and frequency selective fading characteristics of radio links caused by scatter phenomena to the statistical spatial characteristics of the refractive index. Two specific antenna configurations are studied in detail: the LOS (line-of-sight) case where the two antennas are pointed concentrically and the OTH (over-the-horizon) case where the antennas point along a great circle path. For each of these antenna configurations two scatter situations are considered: isotropic scatter with the propagation medium controlling the focusing of energy and locally isotropic scatter with narrow-beam antennas. In all cases single scattering theory is used and narrow-band signal transmission is assumed. It is found that when multipath is of any importance in causing signal distortion for a LOS link, the scatter portion of the channel may be modeled as a continuum of uncorrelated scatterers. Also OTH links are found to be characterizable in the same way. Single integrals and specific analytic and numerical examples are given relating frequency correlation functions and delay power spectra to the wavenumber spectra of assumed refractive index fluctuations. It is shown that a measurement of the frequency correlation function or delay power spectrum can yield an estimate of the wavenumber spectrum of the refractive index fluctuations.

Cochannel interference rejection in a mobile radio space diversity system

Abstract: Diversity is often used in radio systems to alleviate the problem of fading. It is shown here that the use of diversity in a mobile radio system also will result in better utilization of the frequency spectrum. In a system which reuses channels in physically separated areas, probability distributions of signal-to-cochannel interference ratios in 1-, 2-, and 4-branch diversity systems are developed by Monte Carlo methods. We consider two cases: first, we assume signal strength to be Rayleigh distributed, which is a valid model for reception within a small localized area; second, we take shadow losses into account by assuming a more realistic long-term fading model. The effect of using diversity in a mobile radio system is considerable with either model. Assuming a hexagonal cell pattern of frequency reuse, it is shown that frequencies may be reassigned more often in a diversity system than in a system which does not use diversity. The conclusion, therefore, is that a diversity system utilizes the frequency spectrum more efficiently than an equivalent nondiversity system.

The Error Probability of a Wide-Band FSK Receiver in the Presence of Multipath Fading

Abstract: Calculations are made for the probability of error of a wide-band FSK receiver of the type used in space telemetry when multipath reflections off the planetary surface cause signal fading. The error probability is found for both low and high fading bandwidths and for small or large reflected path delays.

Rain outage performance of tandem and path diversity 18-GHz short hop radio systems

Abstract: The performance with respect to rain outage time of dual path diversity and non-path diversity (tandem) arrangements for 18-GHz short hop radio systems is computed and compared. The analysis is based on two extrapolations of R. A. Semplak's1 three-year average of the measured probability distributions for rain attenuation at 18.5 GHz on a 6.4-km hop in New Jersey. The effects of merge hops and joint fading between hops in the diversity system, dependence of the rain attenuation distribution on hop length, and uncertainty in the tail of the distribution are included. The results show that (i) the performance of tandem systems relative to diversity systems increases as the system length increases, (ii) the difference in the number of repeaters per unit length required for short and long tandem systems is small, (iii) the performance of the diversity system is strongly dependent on the amount of joint fading between parallel paths, and (iv) the performance of the tandem system is strongly dependent on the tail of the attenuation distribution. Neither of the latter two factors is known from rain attenuation measurements, but if the joint attenuation probabilities are sufficiently high, then diversity shows no advantage over tandem for either of the assumed extrapolations. The uncertainty in the tail of the attenuation distribution and the sensitivity of the tandem system performance to it emphasize the need for reliable attenuation measurements out to a probability of about 10−7.

Signal design for fast-fading Gaussian channels

Abstract: The design of signals for digital communication over fast-fading Gaussian channels is considered; the emphasis is on nonorthogonal signaling schemes. A discrete channel model is used. Necessary and sufficient conditions on the transmitted signals are found that make the Bayes receiver independent of the channel parameters. By using a geometric interpretation of the resultant receiver a heuristic design criterion is developed. Then union bounds for particular nonorthogonal signaling schemes are evaluated. Nonorthogonal schemes based on modulation similar to differential-phase-shift-keyed (DPSK) modulation are found to use substantially less bandwidth than equivalent schemes based on generalized frequency-shift-keyed modulation.

Mutual interference between linear crosspolarised radio channels at 11 GHz

Abstract: Preliminary findings are presented from a study to determine the mutual interference between linear crosspolarised radio channels at 11 GHz over an 8½-mile path. In particular, severe crosspolarising effects were encountered when antenna primary-feed apertures were artificially wetted or allowed to become wet during rain and snow. Significantly improved values of isolation between channels have been measured under heavy rainfall with the antennas protected from rain.

Single-receiver diversity system for reducing the effect of fast fading in mobile radio

Abstract: A 2-aerial diversity system suitable for combating fast fading is described. It is easily applied to a conventional v.h.f. or u.h.f. area-coverage receiver, and is therefore of particular interest in the mobile-radio field. Some initial results from laboratory tests are given.

On the recognition of time-varying patterns using learning procedures

Abstract: Some recognizers for stochastic time-varying patterns with additive noise are studied. As in binary communication channels with fading, it is supposed that the fluctuation of a pattern (or signal) may be approximated by a stationary Gaussian autoregressive process with known parameters. Each measurement belongs to either of two classes: the pattern plus noise or noise alone. Under these assumptions, optimum dichotomizers with supervized learning are discussed. To the nonsupervised problems, the decision-directed approach and the modified-decision-directed approach are applied. Also some experimental results are presented.

Measurement of the coherence and fading of long-range acoustic signals

Abstract: A series of underwater acoustic experiments has been performed to measure the effects of fading and partial coherence upon array performance after long-range transmission through the ocean. Measurements were made of the complex demodulates of signals that were generated by a bottom-fixed source off Eleuthera operating at 367 Hz and received by the hydrophones of a bottom-fixed array in the Bermuda area about 700 nmi away. The fading spectra of the signals showed a strong modulation at the ocean wave frequency of 0.08 Hz that is a distinctive characteristic of surface scattering. Slower variations were observed in the data that are probably due to changes in the scattering by the inhomogeneities of the sound velocity structure of the ocean caused by temperature change. The scattering strongly affected the coherence properties of the multipath signal and there was a severe degradation in the signal gain of the array that was obtained with plane-wave steering. The degradation was due to both the distortion of the average signal wavefront from planarity and the reduced level of coherence over the aperture of the array. The severity of these two effects was found to increase for averaging times sufficiently long to include the slower changes that were found in the scattering.

Channel Coding with a Sequential Algebraic Coding Scheme

Abstract: In this paper a simple coding scheme utilizing both sequential and algebraic coding is proposed, and bounds on its performance are derived using theoretical bounds on the performance of sequential decoding. These bounds are compared with bounds on a similar, though more complex, scheme proposed by Falconer [2]. Except for sequential rates in a range strictly above R_{comp}, the bounds on the present scheme are shown to be superior.

Dependency of scintillation fading of oppositely polarized VHF signals

Abstract: Under the effects of ionospheric scintillations, the fading of RH and LH circularly polarized 136 MHz signals is observed to be perfectly correlated. Polarization diversity reception will not improve the reliability of VHF space communications through the turbulent ionosphere.

Probability of error for binary permutation modulation on a fading Gaussian channel

Abstract: The probability of error for binary permutation modulation with diversity on fading Gaussian channels is considered. Upper bounds on the probability of error are found in a simple manner. These bounds indicate that the probability of error decreases exponentially with increasing transmitter memory as long as the transmitter's rate is less than the ratio of average received signal power to noise power per unit bandwidth. This asymptotic behavior is true for any form of binary permutation modulation with the proper order of diversity. Furthermore, orthogonal signals are found to be the most efficient form of binary permutation modulation.

Fading of prompts in learning sequences

Abstract: Whenever a fixed series of steps must be learned, the question arises as to the order in which they should be brought to mastery and any prompts used in the lesson withdrawn. Reinforcement theorists argue that responses in a chain should be mastered in retrogressive order, but experiments have not supported this argument. Furthermore the argument ignores the differential practice of responses which retrogressive chaining entails. It is proposed that the differing extent to which responses should be practised is indicated by the classical serial position effect. Fading of prompts should proceed from the middle to the ends of the chain. For retention of series of complex instructions, this fading sequence is superior (in terms of re‐learning errors) to retrogressive fading.

The Application of Information Feedback to an Amplitude-Modulated Laser Communications System

Abstract: The application of information feedback to amplitudemodulated (AM) laser communication systems used to transmit the value, of a continuous parameter is considered. The laser system is assumed to be quantum-noise limited. The particular information feedback technique used is here termed feedback averaging. It is found that the use of this technique improves the accuracy of the estimate of the parameter at the receiver over a corresponding one-way system. The effect of a multiplicative error (slow fading for example), background shot noise, and the fluctuation in the photon arrivals at the receiver due to the laser itself are considered. Both experimental and simulation results bear out the analysis. A Chebyshev bound for the probability of error is derived for the special case of an M -ary AM system, both with and without feedback.