The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

Starting with post World War II studies of fading of radio star sources and continuing with fading of satellite signals of Sputnik, vast quantities of data have built up on the effect of ionospheric irregularities on signals from beyond the F layer. The review attempts to organize the available amplitude and phase scintillation data into equatorial, middle-, and high-latitude morphologies. The effect of magnetic activity, solar sunspot cycle, and time of day is shown for each of these three latitudinal sectors. The effect of the very high levels of solar flux during the past sunspot maximum of 1979-1981 is stressed. During these years unusually high levels of scintillation were noted near the peak of the Appleton equatorial anomaly (∼ ±15° away from the magnetic equator) as well as over polar latitudes. New data on phase fluctuations are summarized for the auroral zone with its sheet-like irregularity structure. One model is now available which will yield amplitude and phase predictions for varying sites and solar conditions. Other models, more limited in their output and use, are also available. The models are outlined with their limitations and data bases noted. New advances in morphology and in understanding the physics of irregularity development in the equatorial and auroral regions have taken place. Questions and unknowns in morphology and in the physics of irregularity development remain. These include the origin of the seeding sources of equatorial irregularities, the physics of development of auroral irregularity patches, and the morphology of F-layer irregularities at middle latitudes.

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Global morphology of ionospheric scintillations

An enigma of equatorial research has been the observed seasonal and longitudinal occurrence patterns of equatorial scintillations (and range-type spread F). We resolve this problem by showing that the seasonal maxima in scintillation activity coincide with the times of year when the solar terminator is most nearly aligned with the geomagnetic flux tubes. That is, occurrence of plasma density irregularities responsible for scintillations is most likely when the integrated E-region Pedersen conductivity is changing most rapidly. Hence the hitherto puzzling seasonal pattern of scintillation activity, at a given longitude, becomes a simple deterministic function of the magnetic declination and geographic latitude of the magnetic dip equator. This demonstrated relationship is consistent with equatorial irregularity generation by the collisional Rayleigh-Taylor instability and irregularity growth enhancement by the current convective and (wind-driven) gradient drift instabilities. Some discrepancies in this relationship, however, have been found in scintillation data obtained at lower radio frequencies (below, say, 300 MHz) that suggest the presence of other irregularity-influencing processes. The role of field-aligned currents, associated with the longitudinal gradient in integrated E-region Pedersen conductivity produced at the solar terminator, in equatorial irregularity generation via the current convective instability has not been discussed previously.

Control of the seasonal and longitudinal occurrence of equatorial scintillations by the longitudinal gradient in integrated E region Pedersen conductivity

Determining the morphology of F-layer irregularities as a function of longitude in the equatorial region is vital for understanding the physics of the development of these irregularities. We aim to lay the observational basis which then can be used to test theoretical models. Theoretical models have been developed, notably in the papers by Tsunoda (1985) and by T. Maruyama and N. Matuura (1984). The question is whether the models are consistent with the morphology as we see it. According to our criteria, the data used should be confined to observations taken near the magnetic equator during quiet magnetic periods and at times within a few hours after sunset. Anomaly region scintillation data have to be used in a limited manner for studying the generation mechanism. The questions to be answered by proposed mechanisms are (1) why do the equinox months have high levels of occurrence over all longitudes and (2) why are there relatively high levels of occurrence in the Central Pacific Sector in the July–August period and in the 0–75° West Sector in the November-December period and (3) why are there very low levels of occurrence in November and December in the Central Pacific Sector and in July and August in the 0–75° West Sector. In the paper by Maruyama and Matuura, the authors have taken observations of topside soundings of spread-F. With this data set in hand, they conclude: “During the northern winter periods, there is maximum enhancement at the Atlantic longitudes of large westward geomagnetic declination and during the northern summer at the Pacific longitude of large eastward declination”. Tsunoda's conclusions from his use of scintillation data is that “scintillation activity appears to maximize at times of the year when the suset nodes occur”. The emphasis of one paper is on the maximum enhancement during the solstices and in the other paper on variations from the equinox as determined by latitude and declination. Each stresses certain characteristics of the morphology. While the two papers explain relatively different morphologies, each makes contributions. However there remain problems to be resolved before certifying a solution as to the physics explaining the longitudinal pattern of F-region irregularities. Satellitein-situ data, scintillation and spread-F observations will be reviewed. The limitation of each data set will be outlined particularly as relevant to the bias produced by the existence of thin versus extended layers of irregularities. A cartoon as to the occurrence pattern, as we see it, as a function of longitude will be shown.

The longitudinal morphology of equatorial F-layer irregularities relevant to their occurrence

Fifth-generation (5G) cellular networks will almost certainly operate in the high-bandwidth, underutilized millimeter-wave (mmWave) frequency spectrum, which offers the potentiality of high-capacity wireless transmission of multi-gigabit-per-second (Gbps) data rates. Despite the enormous available bandwidth potential, mmWave signal transmissions suffer from fundamental technical challenges like severe path loss, sensitivity to blockage, directivity, and narrow beamwidth, due to its short wavelengths. To effectively support system design and deployment, accurate channel modeling comprising several 5G technologies and scenarios is essential. This survey provides a comprehensive overview of several emerging technologies for 5G systems, such as massive multiple-input multiple-output (MIMO) technologies, multiple access technologies, hybrid analog-digital precoding and combining, non-orthogonal multiple access (NOMA), cell-free massive MIMO, and simultaneous wireless information and power transfer (SWIPT) technologies. These technologies induce distinct propagation characteristics and establish specific requirements on 5G channel modeling. To tackle these challenges, we first provide a survey of existing solutions and standards and discuss the radio-frequency (RF) spectrum and regulatory issues for mmWave communications. Second, we compared existing wireless communication techniques like sub-6-GHz WiFi and sub-6 GHz 4G LTE over mmWave communications which come with benefits comprising narrow beam, high signal quality, large capacity data transmission, and strong detection potential. Third, we describe the fundamental propagation characteristics of the mmWave band and survey the existing channel models for mmWave communications. Fourth, we track evolution and advancements in hybrid beamforming for massive MIMO systems in terms of system models of hybrid precoding architectures, hybrid analog and digital precoding/combining matrices, with the potential antenna configuration scenarios and mmWave channel estimation (CE) techniques. Fifth, we extend the scope of the discussion by including multiple access technologies for mmWave systems such as non-orthogonal multiple access (NOMA) and space-division multiple access (SDMA), with limited RF chains at the base station. Lastly, we explore the integration of SWIPT in mmWave massive MIMO systems, with limited RF chains, to realize spectrally and energy-efficient communications.

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A Comprehensive Survey on Millimeter Wave Communications for Fifth-Generation Wireless Networks: Feasibility and Challenges

Boundary layer dynamics play an important role in determining precipitation structure during convective processes. The radar reflectivity profiles which depend on the sixth moment of rain drop size distribution (DSD) can be employed to sense the precipitation processes. The height profiles of DSD significantly depend on the vertical wind velocity. The observations with a micro rain radar (MRR), an FMCW radar, over Kolkata, have been utilized to study the drop size distribution and its relationship with radar reflectivity at Ka-band. A sharp decrease of radar reflectivity in the height range 1–2 km corresponds to an increase of downdraft velocity observed around the same height range. This indicates that the increased downdraft causes breakup of rain drops into smaller sizes. The split in the Doppler spectrum, known as aliasing effect, is most prominent near the boundary layer height and has been employed to estimate downward wind velocity.

Rain Radar Studies of Boundary Layer Dynamics at a Tropical Location

Raindrop size distribution (DSD) parameters need to be estimated to determine rainfall from radar measurements of backscattered signals in the precipitating medium and to study microphysics of precipitation under varying atmospheric conditions. A technique is proposed to estimate the DSD parameters from Global Precipitation Measurement (GPM) dual-frequency products at Ku and Ka bands, which has been validated with ground-based disdrometer measurements obtained during the five-year period 2014–2018 over a tropical location, Kolkata (<inline-formula> <tex-math notation="LaTeX">$22^{\circ }54^{\prime} \text{N}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$88^{\circ }35^{\prime} \text{E}$ </tex-math></inline-formula>), India. The present method yields the three parameters of the DSD model in terms of a gamma function, namely, intercept (<inline-formula> <tex-math notation="LaTeX">$N_{0}$ </tex-math></inline-formula>), shape (<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>), and slope (<inline-formula> <tex-math notation="LaTeX">$\Lambda$ </tex-math></inline-formula>). Based on a proposed optimization technique, the most appropriate <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\Lambda $ </tex-math></inline-formula> relationship is determined during a GPM satellite pass to obtain the DSD parameters. The derived parameters have yielded mass-weighted mean diameter (<inline-formula> <tex-math notation="LaTeX">$D_{m}$ </tex-math></inline-formula>) data that show much better agreement with ground-based DSD measurements than that provided by GPM dual-frequency precipitation radar (DPR) product. This method has also been used to obtain the height profiles of DSD that broadly correlate with ground-based micro rain radar (MRR) observations, showing how DSD varies at different altitudes. The present results demonstrate that the proposed technique is effective in obtaining three-parameter DSDs over a tropical location and offers a useful method to study the microstructure of rain using space-borne radar.

Three-Parameter Rain Drop Size Distributions From GPM Dual-Frequency Precipitation Radar Measurements: Techniques and Validation With Ground-Based Observations

Probability density functions of measured fade slope for a tropical location are analyzed and found to very close to Van De Kamp distribution model. Cumulative distributions of the measured fade slope closely follows ITU-R model. The fade-slope technique is adopted to predict time series of rain attenuation of Ku band signal during rain events for the tropical location. A good matching is obtained between measured and predicted attenuations.

Modeling of Fade-Slope for a Tropical Region and Time Series Prediction of Attenuation Based on Fade-Slope

The characteristics of high velocity small drops (super-terminal) are observed during different types of rain in a tropical region, Kolkata. Measurements using a Laser Precipitation Monitor (LPM) for several rain events spanning the monsoon season of 2013 at Kolkata, India, shows that the presence of high velocity small drops is significant in tropical convection. Additionally, the fraction of super-terminal drops in natural rain is found to decrease with increasing rain rate. The decrease of superterminal drops in high rain intensities, implies increase in rain drop coalescence over drop break up.

Characteristics of high velocity small drops in tropical convective rain

Rainfall information is important in various fields such as agriculture, water resource management, and weather forecast. A proper and efficient forecast of precipitation occurrences and rainfall amounts is important in this connection. Information on the different phases of atmospheric water is necessary to characterize the impending precipitation. A multi-frequency microwave radiometer is capable of continuous monitoring of the brightness temperature of atmospheric emissions which is capable of sensing water vapour, liquid water and their evolution towards forming rain structures with different microphysical properties.

Animesh Maitra

Papers

Rain Radar Studies of Boundary Layer Dynamics at a Tropical Location

Three-Parameter Rain Drop Size Distributions From GPM Dual-Frequency Precipitation Radar Measurements: Techniques and Validation With Ground-Based Observations

Modeling of Fade-Slope for a Tropical Region and Time Series Prediction of Attenuation Based on Fade-Slope

Characteristics of high velocity small drops in tropical convective rain

Identification and Estimation of Rainfall Intensity using Microwave Radiometric Measurements