Weight vector fluctuations in adaptive antenna arrays with nonlinear function in a feedback loop

We present the results of statistical analysis of adaptive antenna arrays with nonlinear function in the feedback loop, which are adjusted by an algorithm for recurrent inversion of a sample estimate of the input-signal correlation matrix with allowance for the weight-coefficient fluctuations. Using the perturbation-theory methods in the first (Born) approximation, we obtain expressions for the correlation function and power of the output signal of an adaptive antenna array and a formula for the covariance matrix of the weight-coefficient vector. The weight-coefficient fluctuations are shown to result in signal distortions at the antenna-array output and appearance of additional terms in the statistical characteristics of the antenna array. These terms are second-order infinitesimals with respect to adaptation coefficient. Fluctuations are first-order infinitesimals and, thus, are much greater in an antenna array without nonlinear function in the feedback loop. It is also shown that the weight-vector fluctuations are anisotropic, i.e., they are absent in the constraint direction, minimal in the interference direction, and maximal in all other directions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 2, pp. 164–172, February 2006.     

Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 520–544, June, 2000.     

Spectral correlation characteristics of an adaptive Antenna array tuned by the Hebb algorithm with allowance for the weight-vector fluctuations

In this paper, we present the results of statistical analysis of the characteristics of an adaptive antenna array tuned by the Hebb algorithm with allowance for the weight-vector fluctuations in the case where signals with different levels of autocorrelatedness of the input-signal readouts arrive at the antenna array. Expressions for the correlation function of the output signal and the power spectral density at the antenna-array output are obtained. It is shown that fluctuations lead to distortions of the output signal of the adaptive antenna array and appearance of additional terms in the formulas for these characteristics.     

Measurement of the frequency fluctuations of a laser with a nonlinear-absorbing cell using the Bershtein method

We propose to use the method of I. L. Bershtein for measuring the frequency fluctuations of an arbitrary type oscillator from the error signal at the output of the phase locking system for a laser with internal absorbing cell. The spectral density of the frequency fluctuations of a single-frequency He-Ne/CH₄ laser was measured. It is shown that in this case the method allows us to measure the low-frequency technical fluctuations of the laser frequency, which determine the width of the laser emission line. The measurements can be performed in the case of both suppression of low-frequency fluctuations of the laser frequency due to the phase locking system and the regime that is close to that of free generation. It is also shown that an increase in the operating frequency band of the phase locking system makes sense only in the case in which the reference spectral density of the laser frequency fluctuations multiplied by the slope of the frequency discriminator conversion (in this case, the power and photoreceiver peak) exceeds the noise level at the system input. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 11, pp. 1487–1494, November, 1998.     

Statistical characteristics of adaptive antenna arrays

Using the method of successive approximations, we obtain expressions for the spectral and correlation characteristics of the output signal of adaptive antenna arrays under the stationary operation regime in the first-order approximation, which is also called Born’s approximation. We show that the fluctuations of the weight coefficients result in distortions of the output-signal spectrum, such as its broadening and the appearance of a “trough” in a band that is somewhat narrower than the input-signal spectrum width. N. I. Lobachevsky State University, Nizhniy Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 10, pp. 1013–1024, October 1999.     

Radiation noise of an active interferometer

 An investigation of the behaviour of amplitude and frequency noise of radiation of an active interferometer in the regime of amplified optical bistability is presented. The phenomenon of non-amplification of external signal noise at sharp amplification of the external signal is established. The impact of strong amplitude fluctuations is studied. Our results have shown that the active interferometer allows an effective separation of the valid signal from the amplitude noise. The spectral density of a fluctuation of the field frequency in the active interferometer is shown to fall sharply in comparison with the “quantum limit”. The linewidth of radiation is determined by the spectral density at zero frequency and is equal to the natural linewidth of the external signal. The influence of quantum noise of the amplifying and absorbing media of the active interferometer is discussed. Received: 26 January 1996     

Transformation of the radiation fluctuations of a low-coherence source in a two-arm interferometer

We consider fluctuations of the radiation of a low-coherence source transmitted through a two-arm interferometer and transformed by a square-law detector. It is assumed that the output radiation of the source is a stationary Gaussian narrow-band random process. The fluctuation process at the detector output is presented as the sum of the intensity noise and the interference-component noise. We calculate the relationships between the spectral densities of these components and the degree of their correlation for different delays between the interferometer arms. We show theoretically and confirm experimentally that the power of interference-component fluctuations is nonzero even if the delay between the interferometer arms exceeds the correlation time of the process at the source output. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 350–356, September., 2000     

Optical response of a cold-electron bolometer array

A multielement bolometric receiver system has been developed to measure the power and polarization of radiation at a calculated frequency of 345 GHz. Arrays of ten series-parallel connected cold-electron bolometers have been pairwise integrated into orthogonal ports of a cross-slot antenna. Arrays are connected in parallel in the high-frequency input signal and in series in the output signal, which is measured at a low frequency, and in a dc bias. Such an array makes it possible to increase the output resistance by two orders of magnitude as compared to an individual bolometer under the same conditions of high-frequency matching and to optimize the matching with the JFET amplifier impedance up to dozens of megohms. Parallel connection ensures matching of the input signal to the cross-slot antenna with an impedance of 30 Ω on a massive silicon dielectric lens. At a temperature of 100 mK, a response to the thermal radiation of a thermal radiation source with an emissivity of 0.3, which covers the input aperture of the antenna and is heated to 3 K, is 25 μV/K. Taking into account real noise, the optical fluctuation dc sensitivity is 5 mK, the estimated sensitivity corresponding to the noise of the amplifier is about 10⁻⁴ K/Hz^1/2, and the noise-equivalent power is about (1–5) × 10⁻¹⁷ W/Hz^1/2.     

A TERAHERTZ PHASE FREQUENCY CHANGER WITH THE CRYSTAL QUARTZ PHASE SECTIONS

A phase frequency changer (PFC) for quasi-optical transmission line with phase sections made of crystal quartz and polarizers executed on the basis of small-period wire gratings has been considered. The PFC is intended for operation in terahertz (THz) frequency region. It has been examined at the frequency f _o= 0.89THz. The influence of the differential phase shift deviation in the sections on the output signal spectrum and the influence of the sections mismatch on the reflection signal spectrum have been considered. In the frequency region ± 10% f _o the levels of the spurious spectral components of output signal are less than −40 dB with regard to the level of the useful signal of the shifted frequency. The levels of all spectral components of the reflection signal are less than −60 dB with regard to the level of the useful component of the PFC output signal.     

Optical design of a high power mode-cleaner for AIGO

Laser beam geometry variations such as beam jitter and frequency fluctuations are a critical source of noise in the output signal of a laser interferometer gravitational wave detector. In order to minimise this noise a resonant vibration isolated optical filter or mode-cleaner is required. For advanced gravitational wave detectors such a mode-cleaner is required to be able to handle transmitted power ∼100 W, and an internal circulating power of 45 kW. This paper addresses the design requirements of such a mode-cleaner. We characterise the mode-cleaner requirements and the effects of high laser power on the optics and its consequence on the suppression of higher order modes.     

Stochastic resonance in parabolic—bistable potential system with an additive colour noise

We propose a new model (parabolic bistable system) with a colour noise source. In the presence of periodic input signal, we investigate the output signal to-noise ratio and the power spectral density of output signal, in which the self-correlation time may be an arbitrary value with no restriction. We find that the curves of signal-to-noise ratio versus the noise intensity D exhibits a bell-shape behaviour. The peak height increases with the increasing value of amplitude A_0 of the input signal. However, the position of peak does not shift. Moreover, the signal-to-noise ratio is insensitive to the modulation frequency Ω, which completely differs from result of Ref.[6]. The power spectral density also has similar behaviour.     

Characterization of the noise in continuously operating mode-locked lasers

An experimental and theoretical investigation of the fluctuations of the pulses from continuous-wave mode-locked lasers is presented. It is shown that these fluctuations can be detected and quantitatively characterized from measurements of the power spectrum of the light intensity. Such power spectra can be measured with great accuracy by shining the laser output on a suitable photodetector and by processing the detector signal with the use of an electronic spectrum analyzer. Different types of noise such as fluctuations of the pulse energy, pulse repetition time, and pulse duration, can be readily recognized from their characteristic spectral signature. Experimental results of noise measurements are presented for a synchronously mode-locked dye laser pumped by an acousto-optically mode-locked argon ion laser, and also for a colliding pulse passively mode-locked dye laser.     

Origin of laser-output noise of cataphoretic HeSe+ lasers

We investigated noise and fluctuations of the output power of cataphoretic HeSe⁺ lasers in positive column plasma. Direct coupling of laser output power noise and fluctuations of the local population inversion was found. An investigation of the positive column plasma showed moving striations being responsible for the gain fluctuations. Whereas the local plasma properties are dominated by high frequency striations in the 100 kHz range, integrated quantities such as laser gain per pass are most strongly influenced by low-frequency waves with a continuous noise spectrum below 200 kHz. External modulation of the discharge voltage or current at a frequency near thehf striations reduces laser noise and increases laser output power.     

On the Similarity of the Statistical Characteristics of Spontaneous Radiation of a Quantum Amplifier at Different Gain Factors

The transformation laws governing the statistical properties of the quantum noise of an optical amplifier when its gain factor and spectral line profile are varied are considered. The correlation functions of quantum noise both at the amplifier output and after nonlinear transformation normalized to the correlation time of quantum noise at the amplifier output were found to be independent of the amplifier gain provided that it exceeds 10 for the Gaussian spectral line profile and 10³ for the Lorentzian profile. The spectral density of quantum noise transformed in a nonlinear system was shown to possess the same similarity property. It was found that the statistical characteristics possess a similarity property even in the case of variation of the spectral line profile from Gaussian to Lorentzian. It was concluded that such a characteristic of quantum noise of an optical amplifier as the correlation time bears virtually all information on the above-mentioned statistical properties at a reasonably large amplifier gain. The similarity property revealed has an important application. It allows finding the matching condition between the optical signal spectrum and the gain profile of the optical quantum amplifier to achieve the highest sensitivity of signal detection by the amplifier.     

Measurement of high-power microwave pulse under intense electromagnetic noise

KALI-1000 pulse power system has been used to generate single pulse nanosecond duration high-power microwaves (HPM) from a virtual cathode oscillator (VIRCATOR) device. HPM power measurements were carried out using a transmitting-receiving system in the presence of intense high frequency (a few MHz) electromagnetic noise. Initially, the diode detector output signal could not be recorded due to the high noise level persisting in the ambiance. It was found that the HPM pulse can be successfully detected using wide band antenna, RF cable and diode detector set-up in the presence of significant electromagnetic noise. Estimated microwave peak power was ∼59.8 dBm (∼1 kW) at 7 m distance from the VIRCATOR window. Peak amplitude of the HPM signal varies on shot-to-shot basis. Duration of the HPM pulse (FWHM) also varies from 52 ns to 94 ns for different shots.     

Some problems of spectral estimation

The main problems of spectral estimation are considered. It is shown that these problems arise from sample limitation and finiteness of the frequency band. We suggest that the signal spectrum composition should be described by the distribution function of oscillation density instead of the traditionally used complex spectrum and spectral power density. Siberian Physical and Technical Institute of Tomsk State University, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp.925–930, July, 1997.     

Noise spectrum of a multicircuit oscillator

We study the inherent power fluctuations in multicircuit self-oscillating systems, which can be represented by an oscillating circuit with a nonlinear element connected in series, and by a multiresonance linear system. We obtain in a general form the expressions for the spectral density of power fluctuations. We show that the shape of the spectral line of a multicircuit self-oscillator is, in general, asymmetric, and the pedestal has a number of maxima. The structure of the pedestal is determined by the roots of the characteristic stability equation. An estimate of the width of the spectral line is given. As examples, we consider the line shape of two- and three-circuit frequency stabilization systems. We take into account the noise contributions of separate circuits at various temperatures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 71–78, January, 1984.In conclusion, the authors express their gratitude to I. I. Minakova for the useful discussions of the results of the paper.     

Temperature resolution of microwave radiometers

We consider the quantum limits of the radiometer sensitivity in power and spectral density measurements of the radio emission. It is shown that taking into account zero-point field fluctuations makes it possible to resolve some paradoxes in the theory of an ideal radiometer. We estimate the limiting temperature resolution achieved when the entire spectrum of thermal radio emission is integrated. The sensitivity of a detector radiometer is analyzed with allowance for the thermal noise of the nonlinear element. The results of calculations are compared with the experimental data. State University of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 824–835, July, 1997.     

Noise characteristics of a high-power ytterbium-doped fibre amplifier at 1083 nm

Experimental results are reported for the noise characteristics of an Yb-doped fibre amplifier pumped at 975 nm, used as a booster of a low-noise narrow-linewidth single-frequency 1083-nm wavelength laser diode. The maximum output power of the amplifier is 1.2 W with a gain larger than 30 dB. An increase of the intensity-noise spectral density relative to the signal, by approximately 6.5 dB, is introduced by the amplification process, due to signal-amplified spontaneous-emission (ASE) beat noise. A remarkable increase of the noise level with decreasing frequency is observed below ≈35 kHz, probably due to technical noise of the amplifier pump diodes. The spectral broadening due to amplifier phase noise was measured to be less than 300 Hz with a 5-kHz-linewidth Nd:YAG laser and that for the 300-kHz-linewidth diode laser at 1083 nm is therefore expected to be in the same range. Received: 5 October 1999 / Revised version: 2 December 1999 / Published online: 24 March 2000     

Frequency-stabilized Nd:YVO4 thin-disk laser

We have developed a Nd:YVO₄ thin-disk laser at 914 nm with single-frequency operation and active frequency stabilization to a low-finesse reference cavity. The spectral density of laser frequency noise is analysed by means of noise measurements at the error point of the frequency control loop. To address the 3¹S₀→3³P₁ magnesium intercombination line at 457 nm, we use an external frequency doubling stage based on periodically poled KTiOPO₄ for the generation of more than 150-mW output power at 457 nm. Optical beat signal measurements at 457 nm with a frequency-stable dye laser show a short-time line width of the thin-disk laser of less than 100 kHz. PACS 42.55.Xi; 42.60.Lh; 42.62.Fi; 42.65.Ky