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A microwave oscillator noise measuring system employing a YIG discriminator has been developed. The resonant frequency of the YIG discriminator is automatically tuned to follow the drift of the carrier frequency of the oscillator under test. This arrangement permits an accurate measurement of FM noise spectra near the carrier frequency as close as several tens of Hz off the carrier. The drift of the carrier frequency is measured over a wide range by monitoring fluctuations of the feedback current in the compensation coil that supports a part of the biasing magnetic field for the YIG discriminator.

The accuracy of a commonly used noise-measuring system at microwave frequencies is calculated under actual measuring conditions. Serious deviations are shown to occur, which impose a lower and upper frequency limit on "double-channel" AM and FM noise measurements, respectively.

A note is described to design digital diode-loaded-line phase shifters. A 75/spl deg/ separation between the loading susceptances has been shown to give the same or better performance in VSWR, loss, and phase-shift setting than a 90/spl deg/ separation.

Measurements of FM noise and the external quality factor Q/sub ex/ of X-band Gunn oscillators are reported which show that both unconverted and intrinsic FM noise vary inversely as Q/sub ex/, if bias voltage, RF power, and frequency are kept constant.

A superior microwave-frequency synthesis technique is treated in this paper, emphasizing improved spectral purity with octave bandwidths in the microwave region. The microwave-frequency synthesizer is discussed in two sections each corresponding to a system unit. The driver unit specifications are analyzed in the first section, showing its voltage-controlled crystal oscillator (VCXO) L(f ) output to be -130 dBc/Hz at 10 kHz. In the second section, the driver VCXO output is translated in the microwave unit to the final X-band frequency by means of a phase-locked loop. An analysis of this phase-locked loop, as described in this paper, shows the final L(f ) equal to -101 dBc/Hz at 10 kHz. Since a worst case situation was assumed, the final L(f ) is quite superior for octave bandwidth microwave-frequency synthesizers.

This paper summarizes several results from a comprehensive study of TE device noise properties. The general noise analysis of Sweet for a TE device in a simple parallel resonant circuit has been extended to include both bias and RF voltage variation of the nonlinear device admittance. The RF components of AM and FM noise become coupled and the video component of FM noise is altered as a result of introducing the RF voltage dependence o This theory has been applied to a particular TE device model interacting with a detailed RF circuit model for an X-band waveguide cavity. The variations of the video and RF components of AM and FM noise have been computed as functions of load conductance, bias voltage, cavity tuning and doping density for uniformly doped devices. This paper includes a brief discussion of the theory and some of the variations of video noise components of AM and FM noise.

A recently developed theoretical analysis has shown that it is possible to measure the Allan variance (a time-domain measure of frequency instability) without any statistical treatment of data from an electronic counter. The measurement is made via high-pass filtering of phase noise with a test set similar to the one used for frequency-domain measurements. The unique test set described in this paper relies on this principle and is capable of measuring the short-term frequency instability of the best quartzcrystal oscillators in both time and frequency domains.

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.

This paper attempts to describe a new method by which periodic signals in noise can be detected easily without the aid of an expensive correlator. In principle, the circuit consists of a delay network which is inserted as a part of a unidirectional loop connected with the main circuit through a hybrid coil. The delay time must be equal to, or an integral multiple of, the signal period to be detected. The delay time also must be longer than the inverse figure of the preceding network bandwidth. Successive noises will be superimposed one after another at random in circulation, while the signals are superimposed in phase. This means an improvement in the signal-to-noise ratio. Theoretically, the ideal basic delayed feedback circuit gives an improvement in the snr of 7.66 db, and in the apparent Q of 9.06. Further improvement can be expected by the use of active circuits. Possible applications are for producing artificial reverberation, a narrow-band filter, and a short-time memory circuit. The response of the delayed feedback circuit is like a comb filter. The circuit also can extract complicated periodic waves without an appreciable distortion.

This paper presents formulations which relate average received signal power, noise density, and bit rate of the to source to the expected probability of bit error in the received information for binary phase modulation systems. The performance of these systems is analyzed for the practical case of demodulation with switching-type phase detectors and the performance is compared with optimal product demodulation. The received signals are assumed corrupted with additive white Gaussian noise. The following modulations are analyzed explicitly: 1) Direct-carrier phase reversal, 2) Squarewave-subcarrier phase reversal, 3) Sinusoidal-subcarrier phase reversal. It is shown that direct-carrier and squarewave-subcarrier phase reversal modulations are optimally demodulated with the switching-type phase detector. The sinuosidal-subcarrier phase reversal modulation, however, is not optimally demodulated by this method. The degradation from optimal product demodulation is slight for modulation indices of 2 radians or less but becomes greater for larger indices.

The objectives of this paper are two. The first is to show that a gated phase-locked loop (GPLL) is a tracking device whose operation approximates that of a maximum likelihood estimator of the phase of a pulsed sinusoid imbedded in noise. The second is to determine the behavior of theb loop in the presence of noise. It is found that the loop performance is equivalent to that of a continuous phase-locked loop driven by the same noise, plus a continuous sinusoid which has the same power as the pulsed sinusoid at the input of the GPLL.

The phase-locked loop is a practical device for separating a sinusoidal signal from additive noise. In this device the incoming signal-plus-noise is multiplied by a noise-free sinusoid generated by a voltage-controlled oscillator (vco). The filtered product is used to lock the phase of the vco output to that of the incoming signal, thus producing a relatively clean version of the incoming signal in which the noise manifests itself as a small phase modulation. Analysis of this noise-produced phase modulation is complicated by the presence of the multiplier at the input to the loop. This paper presents a perturbation method which reduces this inherently nonlinear servo analysis problem to the analysis of a series of linear systems, the first of which is related to the linear model used by previous authors. The perturbation technique permits the phase modulation resulting from an arbitrary noise input to be computed to any desired accuracy. This analysis is particularly useful in predicting loop performance when it is used as a narrow-band receiver in a phase-comparison angle-measuring system

This paper describes the frequency spectra of hitherto unobserved excess noise obtained when small signals are applied to transistors and semiconducting diodes and resistors. It is found that this excess noise can be divided into two kinds, one, similar to shot noise, being more or less uniformly distributed over a wide band of frequencies, the other being concentrated in ranges near the frequency of the applied signal. The excess noise is expressed as a ratio of the difference between the noise with and without signals to the noise without signals, Δθ/θ0. The reference quantity θ0 is in most cases independent of frequency, being thermal or shot noise, and even in transistors does not vary greatly with frequency. The ratio Δθ/θ0, plotted as a function of the difference Δf between the applied signal frequency and the frequency at which noise measurements are made, is found to vary in a manner very similar to the flicker effect, varying as 1/Δf. It is also found to vary as the square of the signal strength. It is considered that the excess noise is due to fluctuations in the characteristics of the device under measurement. To enable measurements to be made close to the signal frequency it was necessary to balance out the signal by the use of various bridge circuits. The signal frequency used was 84 kc/s, high enough to be above the frequency at which flicker noise is usually observed and low enough to facilitate the construction of bridge circuits.

In the course of designing an airborne radar system, there is inevitably a requirement that the equipment does not generate microphonic noise over a specified level. The level of interest can be such that accurate measurement can be difficult. This paper compares three measuring systems: a simple microwave bridge system, the commercially available Allscott system, and a coherent system conceived and developed after the above two systems were found inadequate. Also presented are results of tests performed on typical microwave components.

This paper describes a noise measuring system with a high degree of flexibility in regard to video frequency coverage as well as radio frequency coverage. Noise systems for S, X, and Ku-bands were constructed to obtain high sensitivity at spectral frequencies from several Hz to 30 MHz off the carrier. The measured limiting sensitivities of the X-band set over the video range 20 Hz to 325 kHz with an input power of 10 mW are --145 dB for AM noise and 0.02 Hz rms for FM noise in a 100-Hz measuring bandwidth.

In phase-coherent communication systems, where bandpass limiters precede the radio frequency (RF) carrier tracking loop, it is of interest to understand how the noisy RF carrier reference effects system performance. This paper characterizes a model probability distribution for the RF phase error and uses this to predict the performance of phase-shifted keyed and differentially coherent systems. The theory developed is directly applicable to the Mariner- and Pioneer-type communication systems. For these systems two physical situations are considered: 1) system performance when the phase error is constant over the duration of one bit, and 2) system performance when the phase error is allowed to vary over the duration of one bit.

The nominal 4-kc telephone channel is by far the most dominant parameter of contemporary telecommunication networks. It is, directly or otherwise, underwritten by a world-wide investment of the order of fifty billion dollars. The engineering of present and future global communication networks must therefore provide for working with and into such channels, concomitantly with finding avenues out of their limitations as a device for partitioning and and utilizing communications space. This paper is a characterization of the telephone channel to a first order of approximation-its loss, phase and noise characteristics and some related operational factors.

The paper deals with a theoretical analysis of the random noise characteristics of a pulse-length-modulated system of communication. The result is demonstrated by two different methods, one of which is rigorous and based on the frequency spectrum of a rectangular pulse, while the other is an approximation based upon calculation of the average value of the pulse waveform, plus noise, integrated over a period of time that is short compared with a cycle of the a.f. cut off frequency.

In this paper we exhibit the effect of the data sequence on the reconstruction of the reference (pilot) tone for a quadrature phase-shift keying (Q-PSK) system. This is a binary digital transmission system in which the phase of one quadrature component of the carrier tone is keyed, while the phase of the other component is unkeyed. The integration of several previous keying intervals provides a reference phase. A scheme of this type, called Kathryn, has been built by General Atronics Corporation. We find that the performance of a Q-PSK system is limited by self-noise unless certain message sequences can be avoided. It is concluded that a Q-PSK system can be used effectively only in a decision-directed mode which is also analyzed.

This paper is concerned with the problem of detecting a weak sine wave and measuring its parameters in the presence of arbitrary gain fluctuations and additive Gaussian noise. The parameters considered are frequency, phase, and signal-to-noise power ratio. Some practical methods are presented for detecting the weak sine wave and measuring its parameters. The methods are simple to implement, insensitive to gain fluctuations, and relatively accurate. The implementations have, inherently, a wide dynamic range.

The purpose of this paper is to provide an insight into low frequency divergent noises with spectral density |f|?, where ? ? -1, and into their effect on physical measurements, with special reference to 1/|f| noise. This class of noise is widespread in nature, and it presents unique limitations to the measurement accuracy. In an attempt to present a picture of this class of noise with regard to the measurements of observable physical quantities, the questions about generation of noise, its divergence, correlation properties and measurements of variance are discussed. A statistical model for generation of low frequency divergent noises is used to consider the divergence problem in both the frequency and time domain. It is shown that 1/|f| noise is "weakly divergent," and that power limitation presents no reason to impose a low frequency limit within time intervals observable in nature. Correlation properties are discussed in terms of the time-dependent correlation function, using an ideal impulse response which generates low frequency noise from white noise. Two general models for generation of 1/|f| noise are summarized and discussed. Generation of 1/|f| noise from white noise over a limited frequency range by distributed and lumped-parameter filters is described. It is shown that the variance (i.e. mean square noise) is determined by the frequency limits of the observation method.

The testing of radio systems for data communication through the atmospheric burst error channel requires a laboratory source of the burst form of atmospheric radio noise. The paper describes the design, construction and testing of such an instrument. This noise burst generator employs hybrid circuits and, through circuitry, realizes, for the artificial noise bursts, all the observed statistical amplitude and time characteristics of the natural noise bursts in the burst form of the noise in the frequency range 0·1–10 MHz.

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.

Phase-locked loops (PLL) with pulse-type (sawtooth) phase comparators find many applications in digital transmission systems. In this paper, the results available on the pull-in performance of the second-order PLL with sawtooth phase comparator are summarized. Then a generalized phase comparator, called a phase-and-frequency comparator, is shown to improve PLL acquisition performance significantly. Several circuit implementations are discussed in detail.

Because Pulse Frequency Modulation (PFM) provides a high degree of immunity to noise, it is presently of interest in many modern communication and control systems. This paper presents a quantitative statistical analysis of PFM systems with a noise input (namely, white noise). Some concepts of the Impulse process and the first passage time problems of diffusion process are introduced, which are analogous to the noise transmission of PFM systems. The autocorrelation and spectral density functions are determined for the output of the PFM system with a white noise input. A comparison between the analytical and experimental results is presented.

This paper supplements an earlier report which describes a recommended standard resistor-noise test system. It treats the nature and the magnitude of the errors associated with the use of the test system. The sources and types of errors are discussed for different operating procedures. Means are provided in summary form for estimating accuracy of current-noise measurements under a broad range of operating conditions.

The paper is concerned with the causes and characteristics of threshold behavior in pulse-averaging and phase-coherent (``phase-locked loop'') FM subcarrier discriminators. An analytical discussion of the basic elements of each form of discriminator is first presented, leading to a comparison of the devices for input modulation indices of one and five, in the presence of noise. For the first time in the literature, the effect of additional output filtering following the ideal phase-coherent loop is discussed. Finally, the requisite modulation characteristics for an improved threshold in a phase-locked loop discriminator are presented, followed by a brief description of the approaches which may be taken in the design of such a system.

In this paper, the output of a differentially coherent detector using the phase of the k th previous bit as a reference is derived under noise free conditions for binary differential phase shift keyed signals, where k = 1, 2, 3 ... or ally integer. This is then related to the output of a conventional differentially coherent detector ( k = 1 ). In the presence of noise, this output relationship changes depending on which detector has made an error in detection. This property can be used to reduce the error rate for differentially coherent systems. A receiver consisting of a first-order (conventional) and second-order detectors, where the references are the phase of the previous and second previous bits, respectively, is analyzed theoretically. The result shows that the amount of improvement in error rate due to the addition of the second-order detector depends on the percentage of single errors in the conventional detector. If the error rate of a conventional differentially coherent system is close to the optimum, the theoretical improvement using the additional detector is small (≃ 0.2 dB). However, it is shown experimentally that if the original performance is poor due to intersymbol interference, then considerable improvement is possible with an additional detector (≃ 1.6 dB). In addition to error rate improvement, the circuit also provides error rate information that can be used for in-service performance monitoring and as a sensor for automatic equalizers.

The aim of this paper is to discuss some elementary properties of a type of noise which has been called ?Gaussian? or ?random.? The power spectrum is discussed and its relation to the autocorrelation function is pointed out. Two probability distributions associated with the noise are described.

This paper considers the response of Van der Pol’s oscillator to random excitation. It is shown that the output of the oscillator consists of a periodic term, plus a narrow band noise term centered at the natural frequency of the oscillator. The root-mean-square amplitude of this noise term is shown to be proportional to the square root of the spectral density of the excitation, and inversely proportional to the amplitude of self-oscillation.

In this paper a model for a carrier plus narrowband noise is presented, and with its aid the expected number of cycle slipping events per second for a first-order phase-locked loop (PLL) driven by a narrowband noise corrupted carrier, both with and without a limiter, is determined. Experimental data are presented which indicate the extreme accuracy of the results obtained with the use of this model. The noise model, which is based on the hypothesis that steps of \pm2\pi in phase exist when a carrier is added to narrowband noise, yields not only computational simplicity in calculating the expected number of cycle slipping events per second in a PLL, but also a good deal of insight into the basic threshold improvement mechanism of the PLL. In particular it is shown that a cycle slipping event, or equivalently a PLL output "click" occurs not when the PLL "loses lock," but rather when it tracks a step of \pm2\pi appearing at its input.

The problem of the phase noise generated by nonlinear effects and chromatic dispersion can limit the transmission distance and the bit rate for phase-shift-keying modulation formats. In this paper, the compensation of the nonlinear and linear effects by a midspan optical phase conjugation (OPC) is studied. First, we show the impacts of chromatic dispersion in an OD8PSK systems (Optical Differential 8-Level Phase-Shift Keying), then a long-haul differential 8-Level Phase-Shift Keying (OD8PSK) transmission simulation is studied in order to compare both the performance of the dispersion compensating fiber (DCF) and the midspan optical phase conjugation. OPC allow to obtain a best recovered of transmitted information especially when compared to a «conventional» transmission system; the latter uses dispersion compensating fiber (DCF). OPC performs better even if we increase the bit rate and the distance. Key words : alternative modulation formats; Optical Differential 8-Level Phase-Shift Keying (OD8PSK); dispersion compensation; fiber optics communications; nonlinear phase noise; optical phase conjugation; spectral inversion.

A wave analyzer capable of measuring noise spectra in the video-frequency range is described. Part I of the paper discusses requirements in noise-analyzer design. Part II is a detailed description of a practical instrument. A frequency range of 50 kc to 10 Mc is covered, without bandswitching, at virtually constant sensitivity. The width of the analyzing pass band, 33 kc, remains constant over the measuring range. The lowest spectral level that can be measured is 7 microvolts per root kilocycle.

There has been a considerable interest recently in the attenuation of a microwave signal when it traverses an ionized exhaust plume of a rocket motor. A closely related and sometimes more serious guidance problem is the introduction of amplitude-modulated (AM) or phase-modulated (PM) noise onto the transmitted signal by the rocket exhaust plume. This paper reports the results of a set of measurements wherein X-band attenuation was measured simultaneously with AM/PM noise for seven different double-base propellant systems and a single rubber-base system. The method and limitations of the measurements are discussed. Results are reported for total attenuation and AM/PM noise, together with spectral distributions of the noise, generally between 3.9 and 40 kc. Peak attenuation and noise levels occurred in the aft regions of the plume. Noise and attenuation varied markedly with changes in propellant composition, the more severe levels of each resulting from the more highly aluminized systems. A correlation existed between the level of attenuation and the levels of AM/PM noise. Causes of the induced noise were explained using a model based on turbulent scattering of the radar beam.

In a medium in which noise and signal propagate with different velocities, a detection scheme making use of the crosscorrelation between the received waveforms at two different locations offers a number of distinct advantages over one making use of ordinary autocorrelation of the received waveform. These advantages arise from the resultant relative shift between the noise and signal autocorrelation functions, allowing for separation of noise and signal when the noise characteristics or statistics are unknown, and even where the processes are nonstationary. Ramifications of the correlation shift are an improvement in signal‐to noise ratio (even when noise characteristics are known), and capability for measurement of velocity, signal‐source direction, and signal and noise and channel characteristics. With the current interest in detection of underground nuclear explosions, this paper is directed toward detection of seismic disturbances wherein effective use can be made of the multivelocity properties of the...

One of the problems in the reception of television images is to provide satisfactory synchronization in the presence of noise. During the past several years considerable experience has been gained with respect to this problem under various receiving conditions. The system of synchronization which has given satisfactory results up to the present time has depended for its operation on the reception and separation of individual pulses. In general, it can be said that with this system satisfactory synchronization can be obtained from those signals which will in all other respects provide an entirely acceptable picture. However, for limiting conditions of service, particularly during early operation where field strength may be low, an improvement in synchronization will be effective and desirable provided that it does not involve other complications or disadvantages. This paper describes a synchronizing means at the receiver that employs a new principle in the field of synchronization. The principle is automatic frequency and phase control of the saw-tooth scanning voltages. In such a system, synchronization depends on the average of many regularly recurring synchronizing pulses. Noise has insufficient energy at the scanning frequencies to effect control through the direct-current link from which all but relatively long-time variations are filtered out. Experimental receivers, in which automatic phase and frequency control of the scanning oscillators has been incorporated, have operated with high immunity to noise. The degree of immunity is of a different order of magnitude from that found in conventional synchronizing systems. Noise cannot affect horizontal resolution or interlacing.

In this paper we start from our Quantum Noise IV model of a homogenously broadened maser and specialize to the case in which the number of photons and the population difference are the slowest changing variables. In spite of the high coherence of the system, we find that by eliminating all other variables adiabatically we obtain the usual rate equations plus a set of noise sources with precisely those moments appropriate to shot noise. Thus we justify McCumber's model for amplitude noise in a laser, and after making a quasi-linear approximation obtain his amplitude spectrum. Comparison with exact calculations of Hempstead and Lax for the rotating wave van der Pol oscillator suggests that quasi-linear methods are accurate except within a factor 10 (in photon number) of threshold.

Precision quartz oscillators have three main sources of noise contributing to frequency fluctuations: thermal noise in the oscillator, additive noise contributed by auxiliary circuitry such as AGC, etc., and fluctuations in the quartz frequency itself as well as in the reactive elements associated with the crystal, leading to an f-1type of power spectral density in frequency fluctuations. Masers are influenced by the first two types of noise, and probably also by the third. The influence of these sources of noise on frequency fluctuation vs. averaging time measurements is discussed. The f-1-spectral density leads to results that depend on the length of time over which the measurements are made. An analysis of the effects of finite observation time is given. The characteristics of both passive and active atomic standards using a servo-controlled oscillator are discussed. The choice of servo time constant influences the frequency fluctuations observed as a function of averaging time and should be chosen for best performance with a given quartz oscillator and atomic reference. The conventional methods of handling random signals, i.e., variances, autocorrelation, and spectral densities, are applied to the special case of frequency and phase fluctuations in oscillators, in order to obtain meaningful criteria for specifying oscillator frequency stability. The interrelations between these specifications are developed in the course of the paper.

In this paper we consider the problem of using signals received at three or four antennas to estimate the direction from which radio-frequency (RF) radiation is arriving. Though the results are couched in the terminology of angle measurements, they are applicable to any ambiguous measurements for which the number of ambiguities is inversely proportional to the accuracy. For an interferometric system the effect of receiver noise is examined. Then the optimum way to process the received waveforms, and the best spacing for the antennas, is determined. Next, signal-to-noise ratio (SNR) requirements are determined which must be met to insure that, with a given probability, the final unambiguous measurement is not in error by more than some specified amount. Finally, a comparison is made between a system which uses unambiguous measurements and a system which uses ambiguous measurements and then resolves the ambiguities.

This paper presents the basic characteristics of impulse noise and its effects on various types of binary data transmission systems. The sources and properties of such impulsive noise, in contrast to Gaussian noise, are discussed. A method is described for the experimental comparative evaluation of bit error rates in the presence of additive impulse noise. The method is shown to permit unique comparison among the three modulation schemes tested, namely, on/off carrier, frequency shift, and phase reversal keying.

The noise properties of amplifiers and oscillators are critical in systems applications. This paper describes a system for the measurement of AM noise in amplifiers and oscillators pulsed on for durations on the order of a microsecond or less. Such a system is useful in measuring AM noise in pulsed solid-state microwave devices such as avalanche- and Gunn-diode simplifiers and oscillators, where heat-dissipation limitations sometimes make continuous operation impossible.

Two parameters which are important in the theory and design of phase-lock loop systems are lock range and threshold. In this paper these parameters are carefully defined and the results of an experimental study to determine the effects of the modified n thorder tanlock class of phase detector characteristics upon these parameters are presented. Lock range as a function of signal-to-noise ratio (SNR) is of particular interest. It is shown that when the SNR is high, the lock range of phase-lock systems with modified n th-order tanlock phase detector characteristics exceeds that of systems employing a sinusoidal phase detector. However, as threshold is approached, the lock range of the tanlock systems falls off faster than the lock range of conventional sinusoidal systems. When compared to systems with sinusoidal phase detectors and normalized with respect to equivalent noise bandwidth the tanlock systems are shown to exhibit a higher threshold, but when normalized to lock range the tanlock systems have a slightly lower threshold. The series of curves which summarize the study may be used as an aid in the design of phase-lock loop systems.

This paper presents radio noise measurements made near overhead power lines from 2.4 to 345 kV in the frequency range of 60 Hz to 1 GHz and on radio noise measurements made on 7.2, 345, 525, 735, and 765-kV ac lines and on an 800-kV dc test line up to 10 GHz. The measurements and their analysis show the important radio noise factors involved in the development and use of prediction techniques for the evaluation of communication site performance in the vicinity of overhead power lines.

The paper gives results obtained in synchronizing an X-band reflex klystron oscillator to a source of power at a similar frequency. The power is fed through an isolator to the oscillator so that synchronization is attempted in one direction only. The results show the variation of control range and power output with various parameters of the system. A number of applications of the phenomenon are discussed. The valve used in the work was the K302 with an output of about 20 mW. An incident power of less than 1 ?W is sufficient to lock this valve. In addition, the energy distribution of the noise in a small bandwidth in the range 3?80 kc/s from the carrier was investigated for both locked and unlocked oscillator. Brief mention is made of the method of measurement. Using a source of locking power with a narrow energy distribution the relationship between this energy distribution and that of the locked oscillator is discussed as a function of incident power. It is shown that the amplitude-modulation noise distribution of the locked oscillator becomes identical to that of the locking source independently of the locking power, always provided that it remains locked and that the frequency-modulation noise distribution is a function of the locking power, being identical to that of the source for large locking powers and degenerating as the locking power is reduced. This provides a means of improving the noise distribution of a noisy reflex oscillator. The f.m. noise spectrum is measured in terms of the r.m.s. deviation in a small bandwidth at some distance from the carrier. It is shown that for a small deviation ratio (?) the power in the bandwidth of measurement is given by ??2, relative to the carrier power. The contribution of the local-oscillator noise spectrum to the noise spectrum of the i.f. output from a balanced mixer is investigated and is shown to be as important as that of the noise distribution in the signal.

In this paper a useful and mathematically rigorous method is presented for exactly evaluating the error-probability performance of a binary differentially coherent phase-shift-keyed (DPSK) system in the presence of both thermal noise and intersymbol interference. The channel filter and the receiver input signal-to-noise ratio are assumed to be given. This method suggests, first, to calculate the probability of error induced by both the thermal noise and the large interfering samples whose normalized amplitudes with respect to noise standard deviation are greater than unity, and then, to add the correction terms due to the presence of the other intersymbol interference samples. If the normalized interference amplitudes with respect to the noise standard deviation are less than unity (although the total interference power may still be greater than total noise power), then this method simply becomes that which first evaluates the error probability induced by thermal noise alone and then adds the correction terms due to the presence of intersymbol interference. For numerical computations, various recurrence relations are developed so that the probability of error can be easily obtained on a digital computer. These relations have been utilized in an example to calculate the performance of certain practical PSK and DPSK systems.

Employing techniques similar to the averaging methods of Krylov and Bogoliubov, an approximate noise analysis of the phase-locked loop with signal clipping is presented. The validity of the method is demonstrated by comparing the stationary probability density function for the phase error, generated by a system simulation, with the derived theoretical results. The latter portion of the paper discusses the relation of the phase-locked loop to Kalman-Bucy filter theory and presents a demodulator design that illustrates the self-adaptive properties attainable in phase-locked loops with signal clipping.

This paper describes a theoretical comparison of the noise immunity of direct-detection binary single-channel with direct-detection binary twin-channel optical digital communication systems. The conclusion is that a simple ON-OFF single-channel system is usually superior to twin-channel systems (such as polarization modulation and differentially coherent phase-shift systems) in noise immunity as well as simplicity. This result is quite different from the radio frequency case where twin-channel systems exhibit up to 6-dB advantage relative to single-channel systems.

In this paper are calculated the informational capacities and the optimum statistics of communication systems consisting of an amplitude- and/or phase-modulated transmitter; a medium, which may include the rf and IF portions of the receiver, and in which white thermal noise of the same bandwidth as the transmitted signal is added to the latter; and a receiver responding to the amplitude and/or phase of this received signal. Restriction of the transmitted signal or receiver response to amplitude modulation alone or to phase modulation alone reduces the informational capacity of the system below the full channel capacity found by Shannon, C = W log (1+r2), with W the bandwidth in cps and r the rms signal-to-noise ratio. It is found that at very high signal-to-noise ratios the capabilities of AM alone and of PM alone each account for half this full informational capacity of the channel. When the signal-to-noise ratio is much less than unity, however, PM has 79% of the full channel capacity, while AM can transmit no more than about 17% of the full channel capacity. If a receiver is used which responds to both amplitude and phase, on the other hand, the capacity at low signal-to-noise ratios equals the full channel capacity whatever type of transmitter is used. An AM signal received on a PM receiver is found to be able at low signal-to-noise ratios to convey as much information as a PM signal.

A direct approach to the design of PM communications systems utilizing phase-locked demodulators is developed, and the design procedure is illustrated by example. In addition to the new design techniques, two other ideas are emphasized. First, the output signal-to-noise ratio (SNR) is defined as the ratio of the mean information power output to the total mean-square closed-loop phase error, which includes the effect of signal distortion on the design. Second, the safety margin is defined as the ratio of the total mean-square phase error diminished by the mean-square phase error due to signal distortion to the quantity representing the nominal or expected mean-square phase error due to additive noise. Although the design techniques developed in this paper are applicable for information waveforms having a flat power spectrum, a similar approach can be used for sine-wave modulation. The equations representing the output SNR for sine-wave modulation are included. An experimental PM communications system has been constructed, and the results of initial tests show good agreement with the predicted performance.

The paper describes a.m. and f.m. direct-detection and superheterodyne noise spectrum measurements on various types of backward-wave oscillator and reflex klystron. A procedure has been developed by which the individual a.m., f.m. and background noise components can be separated. The results show that the predominant component at low sideband frequencies is f.m. noise and at high sideband frequencies is background noise. The a.m. noise is not a significant component. The presence of positive ions in the beam of a backward-wave oscillator causes noise peaks at frequencies near 1 Mc/s and an increase of modulation noise over a wide frequency range. Positive ions can be relatively easily removed by transverse ion drainage. Large noise peaks may also be generated at frequencies near those of spurious oscillations. The results of measurements of carrier frequency deviation, and of correlation between a.m. and f.m. noise, and between modulation and beam noise are also given.