Random Phase Distortions Research Articles

Partially Coherent Compressive Phase Retrieval for Millimeter-Wave Massive MIMO Channel Estimation

Channel estimation is challenging for millimeter-wave (mmWave) massive MIMO systems. Leveraging the spatial sparsity of mmWave channels, compressive sensing (CS) based channel estimation been extensively studied. However, the mmWave hardware imperfections may introduce random phase distortions to the received pilots, which makes the conventional CS methods fail to estimate the channel. The compressive phase retrieval (CPR) method can be employed to solve this challenging problem. In this paper, we exploit the partial coherence in hybrid mmWave systems, i.e., the pilots sent from different radio frequency (RF) chains share the same phase distortion in the same time frame, while the phase distortions are different across different time frames. Based on this property, we propose an on-grid partially coherent CPR (PC-CPR) algorithm for mmWave channel estimation in the presence of severe phase distortions. Unlike the existing coherent channel estimation schemes that require perfect phase information or the noncoherent channel estimation schemes that ignore the phases of measurements, the proposed on-grid PC-CPR algorithm exploits the partial coherence property to estimate the sparse angle-domain channel vector. Furthermore, to solve the resolution limitation of the on-grid PC-CPR algorithm, we propose an off-grid PC-CPR algorithm that directly estimates the parameters of channel paths. The proposed partially coherent channel estimation framework subsumes the existing coherent and noncoherent channel estimation methods as special cases. Simulation results show that under the presence of random phase distortions, the proposed PC-CPR algorithms outperform noncoherent channel estimation methods with higher reliability and lower pilot overhead by leveraging the partial coherence.

Reconstruction of wavefront distorted by atmospheric turbulence using a Shack-Hartman sensor

The reconstruction of a wave front containing random phase distortions of the light field is considered. The reconstruction is performed by a Hartmann method based on the approximation of the wave function by Zernike polynomials using estimates of local slopes. The slope values depend on the algorithms by which they are determined. The number of slopes is proportional to the number of focal spots recorded in the plane of the receiving device, which varies depending not only on the raster dimension, but also on the parameters of turbulence, design features of the receiving devices, as well as being restricted by the orthogonality of Zernike polynomials. Results of numerical experiments are given, which will be taken into account when creating adaptive optics systems for correcting strong turbulent distortions of the optical radiation.

Statistical Model of a Laser Beam with Random Phase Distortions of the Field Inside an Unstable Resonator

The dependence of the correlation function of output laser radiation on statistical characteristics of spatially distributed random phase distortions in an unstable resonator has been theoretically studied. The intra-resonator field is considered in the geometric optics approximation. The applicability conditions of the optical-geometrical approach are formulated. The main condition is as follows: within the boundaries of a separate, arbitrarily isolated wavefront inhomogeneity, the amplitude of wavefront distortions should be much smaller than the regular distortion introduced into the field due to the reflection from nominally spherical resonator mirrors. The power distribution for a focused resonance laser beam as a function of the resonator characteristics and field phase distortions is studied. In the Fresnel approximation, it is shown that a focused beam can be represented by the sum of diffraction-limited and scattered components. The power of the components is determined by the phase distortion dispersion. The divergence of the scattered component depends on the dispersion of wavefront tilt angles and the dispersion of the field phase distortions. The specific features of the optimization model of an optical laser transmitter with an unstable resonator have been investigated. Under typical conditions, for an annular output beam, the intensity of the focused radiation is maximum when the laser output power is lower than the maximum value by a factor of 1.2 to 1.9.

A multiscale approach to a synthetic aperture radar in dispersive random media

We consider synthetic aperture radar (SAR) image formation in the situation when the propagation medium is random and dispersive. The propagation model is the Klein–Gordon equation with a random index of refraction and a random dispersive term. We show via a multiscale analysis how medium heterogeneities and dispersion affect the image. In fact, in a situation with a strong source chirp signal, the main effect of the medium heterogeneities is to introduce random phase distortions in the SAR data. We carry out a novel scaling analysis that gives a precise characterization of this canonical phase perturbation and how it affects image resolution and stability. The main effect of the phase perturbation is to reduce the azimuthal resolution and the signal-to-noise ratio and we quantify this performance degradation.

Adaptive correction of distortions in a multichannel optical system

Results of modern investigations of multichannel laser systems are analyzed; sources of aberrations in such systems and the methods of their active and passive compensation are described. Simulation results of combined beam propagation are also presented; a possibility of long-range energy transfer in systems of such a type is considered. Effects of random phase incursions and atmospheric turbulence on beam parameters in the plane of observations are studied. The use of the multidither algorithm for correction of random phase distortions in multichannel systems is considered.

Statistical View on Phase and Magnitude Information in Signal Processing

Statistical View on Phase and Magnitude Information in Signal ProcessingIn this work the problem of reconstruction of an original complex-valued signalot,t= 0, 1, …,n- 1, from its Discrete Fourier Transform (DFT) spectrum corrupted by random fluctuations of magnitude and/or phase is investigated. It is assumed that the magnitude and/or phase of discrete spectrum values are distorted by realizations of uncorrelated random variables. The obtained results of analysis of signal reconstruction from such distorted DFT spectra concern derivation of the expected values and bounds on variances of the reconstructed signal at the observation moments. It is shown that the considered random distortions in general entail change in magnitude and/or phase of the reconstructed signal expected values, which together with imposed random deviations with finite variances can blur the similarity to the original signal. The effect of analogous random amplitude and/or phase distortions of a complex valued time domain signal on band pass filtration of distorted signal is also investigated.

Adaptive compensation of phase distortions in synthetic-aperture radars

It is shown that the criterion of the maximum sharpness applied in incoherent adaptive optics can be used for compensation of random phase distortions in synthetic-aperture radars under the condition of effective range averaging of the sharpness function. Theoretical validation is confirmed by the results of simulation.

Hartmann test in atmospheric research

The problem of the reconstruction of random phase distortions from Hartmann test data is discussed. A statistical approach allowing calculation of reconstruction errors associated with the discrete character of the data is developed. It is shown that the correct choice of both the experimental scheme and the method of data reduction can significantly improve the results. Some practical recommendations presented allow one to choose the main parameters of the experimental scheme in such a way that the errors of the retrieved phase distortions are minimal. The results obtained can be applied for both atmospheric and adaptive optics.

Numerical modeling of a linear wavefront reversal system utilizing a spatial phase filter

The possibilities of compensating random small-scale phase distortions in a linear wavefront reversal system utilizing a spatial phase filter were analyzed by numerical methods. It was found that for an appropriate choice of the parameters of the system it is possible to compensate effectively such distortions in the variance range 0.1–1.3 rad2. The improvement in the axial light intensity depends on the spatial spectrum of the distortions and can be as high as a factor of ten. The permissible misalignments of the system are estimated and recommendations are given on the choice of its parameters.

Passage of a light beam through a thin layer with nonlinear and random phase distortions. Possibility of compensation

The degree of compensation of regular and random phase distortions of optical radiation traversing a layer of nonlinear medium is analyzed. Additive systems are considered, capable of compensating a finite number of random and regular aberrations. Dispersions and correlations of random aberration modes are determined. Expressions are obtained for evaluation of the effectiveness of compensation of regular and random distortions. Conditions under which beam distortions due to nonlinear interaction with the medium dominate over distortion produced by turbulence are determined. Conditions for effective tracking of phase fluctuations are found.