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",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"9528d3b1ff011d68022c4fa750b4bc24",bookSignature:"Dr. Kieran Richard Hickey",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8491.jpg",keywords:"Tornadoes Causes, Characteristics, Features, Impacts, Temporal Variability, Spatial Variability, Regional Change, Climate Change, Climatological Context, Trends, Patterns, Projections",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 28th 2020",dateEndSecondStepPublish:"October 26th 2020",dateEndThirdStepPublish:"December 25th 2020",dateEndFourthStepPublish:"March 15th 2021",dateEndFifthStepPublish:"May 14th 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Dr. Kieran R. Hickey is currently Head of the Department of Geography and also Head of the School of the Human Environment at the University College Cork, in addition, he is a Fellow of the Royal Meteorology Society and the Royal Geographical Society.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"17924",title:"Dr.",name:"Kieran",middleName:"Richard",surname:"Hickey",slug:"kieran-hickey",fullName:"Kieran Hickey",profilePictureURL:"https://mts.intechopen.com/storage/users/17924/images/system/17924.jpg",biography:"Dr. Kieran R. Hickey is a Senior Lecturer in Physical Geography in the School of the Human Environment in University College Cork, Rep. of Ireland where he is currently Head of the Department of Geography and also Head of the School of the Human Environment. He earned his B.A. in Geography and Economics in 1986 and his M.A. in Geography in 1990 from University College Cork, Republic of Ireland and his D.Phil from Coventry University, England in 1997. His research is in storms and hurricanes, climate change, historical climatology and climate disasters. He is a Fellow of the Royal Meteorology Society and the Royal Geographical Society. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"16308",title:"Field Estimation through Ray- Tracing for Microwave Links",doi:"10.5772/16373",slug:"field-estimation-through-ray-tracing-for-microwave-links",body:'Engineers using microwave radio links have to address the effects of multipath propagation that arise when several rays arrive at the receiver after travelling along different paths from the transmitter. Rays, along their propagation, undergo reflections at the earth’s surface or at variations in the refractive index or its gradient.
Since the ‘60s, standard ray theories for radio wave applications use effective earth radius concepts, ray bending based on Snell’s law in a layered spherical atmosphere, or analytical method, limited to simple refractive index profiles (Du Castel, 1966; Livingston, 1970). At that time, scientists were interested in statistics of fading, distinguishing between fast or slow fading and the typical results were either nomograms of attenuation as a function of distance for a set of common frequency and height values or cumulative distribution functions representing the fraction of time that the signal was expected to be received at or below a given level (CCIR, 1978). Several techniques were employed to calculate the field strength, such as Cornu\'s spiral derived by the Huygens\' principle together with the introduction of the specular and the diffuse reflection contribution (Hall, 1979). In that approach, the field amplitude was determined assuming the principle of conservation of energy, i.e. the flux of the energy along a ray is the same at every cross section of a narrow tube of rays (Keller, 1957).
Nowadays, radio communications live a renaissance due to the development of mobile and wireless communications and the increasing demand of wideband services. The need of greater rate of transmission is accomplished using higher frequencies for which effects like the tropospheric scatter can affect dramatically the quality of the received signal. Thus, aspects such as analysis of delay power spectra or of potential intersystem interferences require a more realistic modelling. As a matter of fact, local fluctuations in the refractive index n can cause scatter, while its abrupt changes with the height can cause reflection and originate ducting layers, in which the rays are reflected and refracted back in such a way that the field is trapped inside these layers (Bean & Dutton, 1968).
Although the goal of radio engineering is to transmit reliably from the source to the receiver, this is of no use if the received signal is unintelligible due to interference or if the transmission causes interference with other systems. So an analysis of the channel behaviour is mandatory to meet both link design and system requirements. Besides, the availability of geographic databases, digital elevation models and the increasing computing power let us face more realistic description to model the interaction of the propagating wave with the atmosphere and the surrounding scenario (Driessen, 2000; Kurner & Cichon, 1993; Lebherz et al., 1992).
In more recent developments, ray modelling of wave propagation addresses the dispersive effects of perturbed atmosphere on the performance of high-capacity digital radio channel (Akbarpour & Webster, 2005; Sevgi & Felsen, 1998).
Besides telecommunications applications, a proper modelling of atmospheric propagation is of concern in atmospheric sciences with particular focus on radio occultation data analysis for assimilation with numerical weather prediction models (Pany et al., 2001). Also, the decrease of propagation speed related to the atmospheric refractivity causes tropospheric delay, which influences applications of the Global Navigation Satellite System (Eresmaa et al., 2008).
The author presents a widely diffuse technique in the domain of seismic studies that accommodates lateral variations in the medium properties (Farra, 1993). As an asymptotic technique, based on high frequency approximation, it permits fast computation but provides a local solution of propagation problem (Červenŷ et al., 1977). The technique was adapted for application with electromagnetic waves and specifically tailored for signals travelling in the atmosphere. The hypothesis of horizontal uniformity can be removed and no stratification is needed to calculate the ray trajectory. The terrain profile coordinates are mapped over a Cartesian reference through analytical transformation. Refractive index values are given in the same Cartesian reference. Hence, propagation is modelled in a two dimensional range-height scenario over irregular terrain through non-homogeneous atmosphere.
The field amplitude is evaluated by means of a perturbation technique using paraxial rays to observe the wave front structure along the path from the transmitter towards the receiver.
This approach allows to analyze system performance and the channel impulse response in presence of any kind of atmosphere, characterized by local values of refractive index n in the bi-dimensional panel including the antennae and the terrain profile. The variations of the refractive index n along the third dimension are taken equal to zero; nonetheless, the field amplitude is calculated correctly because of the paraxial approximation which takes place in a 3D domain. Median power strength of the numerical results was compared with predictions given by Friis\' Formula (Balanis, 1996).
The proposed ray tracing technique is widely used in seismic for subsoil investigation and it follows an approach based upon the integration of the Eikonal equation with Hamiltonian-Jacobi technique (Kružkov, 1975). According to this formulation, rays are defined by the vector y(τ)=(x(τ), p(τ)), where x(τ) and p(τ) are the position vector and the slowness (inverse of phase velocity) vector along the ray, both function of the integration variable τ and of the initial conditions (launching point and direction). The slowness vector p is defined as
where P and x represent the gradient computed versus the slowness vector and the position vector, respectively. H is the Hamiltonian function describing the wave propagation in the considered medium, i.e. the atmosphere, chosen as follows:
being v (x) the propagation speed of the medium at the position vector x.
The advantage of such an approach is twofold: it takes into account the medium inhomogeneities that originate multipath propagation and wavefronts folding (caustics), and it permits to consider both vertical and long range variations of the atmospheric model, without any approximation like flat-earth model (Hall, 1979). Also, it permits to keep separated the different field contributions due to the different interactions between the rays and the surrounding scenario, which impacts on the phase calculation of the overall received field.
A suitable discussion for ray tracing can be found in (Farra, 1993); nevertheless, in this section some basic concepts and analytical details are reported.
Substituting (2) in (1), one obtains the equations for the vector y(τ):
x and p define the 6D phase-space, where the solution of (3), i.e. the rays, are the characteristic lines of the Eikonal equation, thus enabling the interpolation without ambiguity on a single fold (Vinje et al., 1993). For this reason rays are also called bi-characteristics lines of the wave equation. By choosing as integration variable the ray propagation delay or travel time T, system (3) becomes:
The solution of system (4) describes, under the asymptotic assumption, the propagation in the atmosphere in terms of ray trajectories and time delay.
Anomalous conditions such as medium inhomogeneity or velocity model variations can affect dramatically the wavefront propagation. Under these circumstances the computation based upon the spherical divergence assumption results in erroneous evaluations.
One possible choice is to compute the amplitude through paraxial rays (first order perturbation theory), used to determine the flow tube, whose deformations, together with the theorem of the conservation of the flux along the ray path, allow the calculation of the amplitude A at the time τ.
Let us consider a reference ray with characteristic vector y0(τ)=(x0(τ), p0(τ)). A paraxial ray is obtained from the reference one by applying the first order perturbation theory, so paraxial rays coordinates are defined by:
Tracing paraxial rays consists in finding in the phase-space the canonical perturbation vector δy(τ)=(δx(τ),δp(τ)). These perturbations in the trajectory are due to small changes in the initial conditions of the ray.
The linear system for the calculation of paraxial rays is obtained by inserting the perturbation vector given by (5) in system (1) and developing to the first order:
where
is a 6 6 matrix whose elements are the derivatives of the Hamiltonian function calculated on the reference ray.
Paraxial rays allow to define the flow tube, schematically represented in figure 1.
Flow tube definition through paraxial ray tracing
The deformation of the flow tube along the ray path
where τ is the sampling parameter, θ the elevation angle and ϕ the azimuth angle. The amplitude of the plane wave associated to the ray is computed considering both the deformation of the flow tube and the conservation of power density flow law along the ray path. The volume element of the flow tube can be expressed as
From the conservation of the power density flow along the ray (Keller, 1957) and known the amplitude Ai at τi, it follows that the amplitude Ai+1 at τi+1 is:
Equation (10) shows that the ray amplitude depends on the velocity model. Hence, paraxial rays take into account anomalous propagation conditions.
Sketch of a caustics of the first order: the flow tube looses one dimension
The singularity of the Jacobian J is a singularity, known as caustic, of the plane wave associated to the ray (Kravtsov & Orlov, 1990). Caustics arise when the ray field folds. Caustics are of first order when the flow tube looses one dimension and of the second order when two are the dimensions lost. The wave front folding affects the phase of the field carried by the wave with a phase shift of
The modelling is performed in a 2D panel, as far as the terrain profile and the atmosphere characteristics are concerned, while the ray trajectories are computed in a 3D space.
This assumption is based on the hypothesis that lateral variations in the propagation medium and in the terrain profile are negligible in the third dimension, which does not strictly holds.
Therefore, the propagation occurs in the so called Earth system (s,h), where s is the range measured along the idealized spherical earth and h is the altitude taken along radial direction passing through the Earth centre, respectively. Instead, for sake of simplicity, all calculation are developed in a Cartesian reference system (x,z) related to the Earth by the following transformation relationships:
where R0 is the Earth radius. The transformation from cartographic coordinates (s,h) to absolute coordinates (x,z) is given by the inverse transformation:
being
This way to proceed allows to take into account the actual geometry of the problem without introducing approximations like equivalent Earth radius. Also, it keeps separated the domain in which the radio link characteristics are defined and the computational one, where rays are traced.
The two reference systems: cartographic coordinates (s,h) and absolute ones (x,z).
The characteristics of the atmosphere are taken into account in terms of its propagation velocity using several quantities that are generally function of the position vector x:
where c is the speed of the light and n(x) is the refractive index of the atmosphere, which usually is expressed in terms of the refractivity N:
N is a dimensionless quantity but in literature it is often measured in N-units or in parts per million (ppm). Its value depends upon the altitude and the range locally according to the atmospheric pressure P, the vapour pressure PV and the temperature T as in the following (Bean and Dutton, 1968) :
Besides the variations in the refractive index, or its gradient, rays along their propagation undergo reflections and diffraction at the earth’s surface. At the present stage of the modelling, neither the diffraction mechanisms nor any scattering features are included except reflection.
The trajectory of the reflected ray is given by the Snell’s law under the hypothesis that locally the ground acts as a perfect smooth surface. The initial conditions with which the reflected ray is traced depend both on the geometric characteristics of the terrain profile and on the ray direction of incidence. The amplitude and the phase of the rays reflected from the ground are computed according to the chosen ground parameterization, i.e. the electric soil properties. These determine the value of the ground impedance η, which is a function of both soil permittivity εr and conductivity σ (Ulaby, 1999):
being ε0 and ω the free space permittivity and the angular frequency respectively.
Once that the rays trajectories are computed, together with their complex amplitudes - weighted by the antenna pattern - and the travel times, they are classified into different wave fronts and then interpolated on the locations where the field is desired. The total field is obtained by addition of the single contribution of each wave front.
The field reconstruction is described by means of a pilot example of a 4.5 GHz point-to-point radio link 80 km long affected by multipath. The aim of the technique is to evaluate the vertical electric field (or the received power) intensity at the receiver range. According to the considered geometry, this leads to the prediction of the vertical profile of the electric field E(h) (or P(h)), where h is the receiver height ranging between
The modelled atmospheric condition is indicated in the panel of figure 4, while figure 5 shows the vertical profile of N at few chosen distances. The N value is comprised between 280 and 360 N-units and it shows variations in both dimensions. This atmospheric model -taken from (Bean and Dutton, 1968), p.325 - let us focus on several kind of interactions and their effects on the propagating signal that could possible occur in actual conditions.
panel of the atmosphere charachteristics. Contour lines report the value of the refractivity index N
To appreciate the role of the variations in the refractivity, and without loss of generality, the ground profile was chosen as a plane surface characterized by the values of permittivity εr = 3 and conductivity σ = 0.001 [S/m] in the frequency band of interest.
Vertical profile at 5 chosen range distances.
The top image in figure 6 shows the trajectories of the rays belonging to a chosen elevation angular sector (-0.5 ÷ 0.5 with respect to the local horizon) traced in the cartographic system. The transmitter is in the origin of abscissas axis at 100 m above the ground. Besides the wavefront that carries the direct arrival of the signal, one may observe that several wavefronts are involved, resulting from the inhomogeneities of the atmosphere and ground reflection.
Ray pattern (top) and wavefronts (bottom)
The bottom image of figure 6 shows the rays pertaining to the 30 wavefronts that results from the ray tracing process. The first step consists in grouping rays in different wave fronts, each characterized by the same history such as same number and location of caustics or reflections. Wavefronts are numbered and rays belonging to the same wavefront can be used to interpolate the field. As a matter of fact, rays arrive at the receiver range at discrete values so that the vertical profiling of the field intensity involves three steps: wavefronts separation; interpolation of the ray comb belonging to the same wavefront; coherent addition of the wavefronts themselves.
The first criterion of wavefront separation that could come in mind is that of the travel time arrivals. Figure 7a shows the multi-valued behaviour of the wavefront delay of arrivals at different heights, while figure 7b shows how the parameterization of the wavefronts in the ray launching angle resolves the ambiguity: working in the angle domain seems the natural way for unfolding multi-valued ray fields (Operto et al., 2000).
The wavefronts separation is based on a broad and on a narrow selection process applied consecutively. The broad selection process involves the ray history: as for example, two rays belong to two different wavefronts if they are reflected a different number of times. The narrow selection process uses as criterion the angular distance: if two rays are reflected the same number of times they belong to the different wavefronts when their elevation starting angles difference is greater than δθ. This angular distance has the role of guarantee the proper accuracy in the interpolation of the ray field and it depends on the velocity model of the medium (Sun, 1992).
The results of the wavefront separation process are organized in a database whose structure is schematically represented in figure 8. Wavefronts and rays are organized in a record frame that gives for the kth wavefront the propagation delay τk, the amplitude Ak and the phase ϕk obtained by interpolation of the travel time Tik, aik and φik of the rays at their arrival height, where i pertains to the individual rays in the wavefront k.
Wavefronts time delay dispersion (a) and launching angle distribution (b)
Ray field database: the arrivals are organized according to their wavefronts
Each ray record refers is composed of the following parameters: the height of arrival, the travel time, which depend on the ray history; the amplitude and the phase, which depend on the ray history, on the reflection coefficients and on the system parameters.
The various quantities calculated by the ray tracing are referred to as Green’s function attributes. Figure 9 shows among the attributes those that directly contribute to the field calculation.
Green’s function attributes for the field calculation: from bottom to top: delay(a), amplitude (b), caustic phase (c), caustic +reflection phase (H polarization), caustic + reflection phase (V polarization)
The field calculation along the vertical profile at the receiver range is performed through the interpolation of the different wavefronts contribution. Let K be the number of the wavefronts, each including Nk arrivals, the electric field associated to the ith arrival of the kth wavefront is:
where f is the frequency of operation of the link. The contribution of the kth wavefront to the total field is obtained through interpolation of the travel times, of the amplitudes and of the phases in the following way:
where gk is a generic interpolating function and h is the height. As result, the interpolation of local values returns the field intensity in the target zone. Finally, the overall field is computed adding coherently all the wavefronts contributions:
The vertical profile of the received power is obtained by applying locally the Poynting\'s theorem to a spherical surface with radius R:
being η the medium impedance and R the receiver range.
The solid line in the leftmost panel of figure 10 shows the power profile due to the direct arrival, while the dotted line represents the theoretical values predicted by Friis’ formula (Balanis, 1996). Here, the vertical power profile is shown along the entire computational domain, from 0 up to 300 m, in order to show the effects of the tropospheric multipath on the received signal. The panel in the middle and the rightmost one of figure 10 show the power profile computed adding all the wavefront contribution at vertical (V) and horizontal (H) polarization.
Received Power vertical profile, from left to right: direct arrival contribution (solid line) and theoretical arrive (Friis); direct + reflected contribution (vertical polarization); direct + reflected contribution (horizontal polarization)
The aim of time domain approach is to estimate the radio channel response to a transmitted pulse with a given waveform
where H represents the Hilbert transform operator. The corresponding pass band signal, which is transmitted on radio channel, is obtained with a frequency shift:
The channel pulse response can be written as a sequence of ideal shifted pulses of the transmitted waveform with their own amplitude and phase:
where the amplitudes, the phases and the propagation delays have been calculated, respectively, through interpolation of aik, φik and Tik at height h. These procedure has low computational cost as the ray trajectories and propagation delay τk do not depend on the frequency and they can be computed once for all. In equation (23) some quantities such as amplitudes Ak and phases ϕk depends on the frequency of operation but using a narrow band approximation one can assume that amplitude and phase variations are negligible within the signal bandwidth. Under these hypothesis, the pass band received signal
The received base band signal
whose real part gives the received signal
The panel in figure 11 reports the estimated field and the time delay as a function of height ranging between
Impulse response panel (left). The image on the right shows the channel response to the transmitted Nyquist wavelet at four height values, sketched as a dotted white line in the panel on the left.
The computation of the electric field in the target zone for a given frequency f0 as reported in §3.2 strictly holds under the hypothesis of the transmission of a sinusoidal signal, which has an infinite duration and an infinitesimal band. As radio systems transmit signals with finite duration and band, there is the need to evaluate the response of the radio channel to the effects of frequency variation inside the system bandwidth of operation.
Let us assume that the radio link is transmitting a signal with bandwidth B around the carrier frequency f0. Therefore, given the frequency f and using the equation (17) principle, the received electric field expression is:
Applying equation (27) for each frequency in the interval spanning from
Frequency domain approach can lead also to a characterization of radio channel in the time domain applying Fourier transform to the radio channel transfer function provided by equation (27). However, when the bandwidth of the transmitted signal is narrow, that is when f0 >> B, this procedure leads to a waste of computational resources. A more efficient way to manage narrow band channels is to face the problem in the time domain.
The transfer function of the radio channel is shown in figure 12 together with the frequency behaviour computed at the same four height levels highlighted in the time domain analysis. Again the target zone is comprised between 100 and 150 m and the signal has vertical polarization. One can notices how the transfer function may change from a smooth behaviour, panel c) to a sharper one with a notch deepness of about 30 dB, panel a).
Transfer function panel (left). The image on the right shows the channel response to the transmitted Nyquist wavelet at four height values, sketched as a dotted white line in the panel on the left.
The ray tracing technique was developed to set up a prediction tool that is operative both as a MATLAB-based package and a C++ executable code. Unfortunately, beside an industrial application whose results are not available for publication at this stage, the computed field and power vertical profiles were not validated against measurements. Nevertheless the quality of the prediction performance can be observed when compared against canonical scenarios or other authors reference solutions.
Usually, when developing solver codes, one starts with the comparison of the predicted results with analytical or assessed solutions to check the correctness of the implementation. If this is the proper choice at that stage, it could lead to a flat and formal exposition of the methodology under study when describing the single steps towards the overall result. That is why the particular example chosen to illustrate the technique throughout §3 and §4 is far complicated, as it appears from the number and variety of wavefronts and from the aspects of the radio link characteristics both in time and in frequency domain. As the complexity could conceal errors or misevaluations, the author chose as reference solution an example in which a standard atmosphere model describes the velocity of the propagation medium over a flat perfect electric conductor ground. Even in such a simple example, the importance of the wave front discrimination could induce in errors when reconstructing the field.
The transmitter, in the origin of the abscissa axis, is at 150 m above the ground and the receiver range is 50 km apart. The atmospheric model is a standard exponential one with a gradient of 40 ppm in the first 1000m. Figure 13 shows the trajectories together with the two wavefront, one associated with the direct arrival and another with the reflected one. The ground is a perfect conductor with reflection coefficient equal to -1.
The two arrivals, direct and reflected, are shown in figure 14: on the leftmost panel the wavefront time delay dispersion results in 2 distinct contribution at the same instant. As in §3.1, the parameterization in the angular domain nicely unfolds the integration path (rightmost panel).
The predicted vertical received power profile is reported in figure 15, together with the direct arrival contributions given by Friis’ formula. One can notice the typical pattern of zero and maxima of reception due to the rotating in-phase and counter-phase summation of the two arrivals.
Finally, figure 16 shows the impulse response panel calculated for the two ray model and vertical polarization. Again, the received signal shows different behaviour due to the atmospheric multipath as a function of the height.
Ray pattern (top) and wavefronts (bottom)
Wavefronts time delay dispersion (a) and launching angle distribution (b)
Received Power vertical profile (solid line) and direct arrival (dotted line)
Impulse response panel (left). The image on the right shows the channel response to the transmitted Nyquist wavelet at three height values, sketched as a white line in the panel on the left.
The ray tracing technique based on the resolution of the Eikonal equation with Hamilton-Jacobi technique is well suited to model the dispersive effects of perturbed atmosphere on the performance of high-capacity digital radio channel.
The advantage of such an approach is the possibility of describing the medium with its variation in the lateral domain in presence of atmospheric multipath and of non uniform terrain profile.
The field profiling at the receiving site is obtained through 2,5D propagation as, notwithstanding all variations in the third dimension are taken equal to zero, the field amplitude is calculated correctly because of the paraxial approximation which takes place in a 3D domain.
At the time of writing the author is refining the code towards a full 3D implementation, which requires a reformulation in spherical coordinates, and the modelling of the mechanism of ground scattering and diffraction.
The author would like to thank Professor Giuseppe Drufuca (Politecnico di Milano) for his useful comments and suggestions and Simone Re (former research associate, Politecnico di Milano) for his contribution to the code development and calculations.
Entrepreneurship as an academic field and societal trend appears to be growing. The field of entrepreneurship is defined as “…the study of sources of opportunities; the processes of discovery, evaluation, and exploitation of opportunities [1].” Entrepreneurs are “…individuals who discover, evaluate, and exploit them [opportunities] ([1], p. 217).” Entrepreneurs may be of nearly any age from school age children to older adults.
Despite the reality that there are entrepreneurs of all ages, far too many of us automatically imagine that the entrepreneur is an adult in their early 20s to mid-30s, college educated, and has launched a technological venture. One study found that the mean age for launching a company is in the late 30s to early 40s [2]. The Kaufmann Foundation [3] found that the most frequent ages of entrepreneurs in descending order in 2019 were the following: 20–34 (27.2%); 55–64 (25.1%); 45–54 (24.8%); and 35–44 (22.9%). This age breakdown reflects a change from 1996 during which it was found that as age increased, the rate of new entrepreneurs decreased. The Kaufmann Foundation is missing two age cohorts: entrepreneurs under the age of 20 and entrepreneurs 65 and older. This chapter will focus on entrepreneurs along the age continuum.
Regardless of the age of the entrepreneur, there are both common challenges and unique challenges. Furthermore, there are also common and unique opportunities. This chapter will first frame entrepreneurship from a developmental theoretical frame and then review the literature on the relationship between age and entrepreneurship. This literature review will not be exhaustive due to space limitations. After theorizing about entrepreneurship and reviewing the pertinent literature, the challenges and opportunities experienced by entrepreneurs at different ages will be described. These challenges and opportunities will be discussed not just from the lens of the entrepreneur but entrepreneurial ecosystems. Toward the end of this chapter, recommendations will be presented for entrepreneurs of specific age groups and entrepreneurship support organizations (ESOs). Next, a research agenda with specific hypotheses will also be presented for academics to include age as a key variable in research. Finally, recommendations will be formulated for entrepreneurship educators in formal and informal educational settings.
The theoretical frame in this chapter is grounded in a developmental perspective drawing upon Amartya Sen’s capability approach. Sen equates human development with the enlargement of positive freedoms [4]. A related concept of Sen’s capability approach is agency. Agency is “a person’s ability to pursue and realize the goals that he or she values…the opposite of a person with agency is someone who is forced, oppressed, or passive ([4], p. 3).” Moreover, human agency is a central concept among motivation theories [5].
This capability approach is reinforced with a lifespan developmental approach drawing upon Baltes [6]. According to Baltes [6], “Lifespan developmental psychology involves the study of constancy and change in behavior throughout the life course (ontogenesis), from conception to death (p. 611).” The behavior of focus in this chapter is entrepreneurial activity. A team of researchers [7] assert citing the body of research, “Individuals’ orientation toward entrepreneurial activities differs depending on where they stand in their lifespans (p. 1).” Our lifespans are typically measured by age and occasionally by developmental periods such as adolescence.
Yet, age is a more commonly used marker of human development. There are two categories of age: chronological and subjective. Chronological age is marked by date of birth or the number of years alive. Varying patterns of entrepreneurship have been documented regarding chronological age [8]. In contrast to chronological age, subjective age is how young or old an individual experience themselves to be [9]. Beyond chronological age, age-related factors such as a future time perspective account for changes in motivation [10]. Hence, age is objective and subjective as well as static and dynamic.
Age is not the only marker of the development of human development and entrepreneurship. It was empirically found that entrepreneurial activity varies by age, yet this relationship is mediated by perceived opportunities and perceived skills [11]. As it relates to opportunities, it was found that entrepreneurial intent among high school students was positively influenced by parents first, peers second, and the neighbors third [12]. Hence, entrepreneurs are embedded in a social context. The impact of context on the development of entrepreneurial behavior is well established [13]. Furthermore, in one study, it was empirically demonstrated that entrepreneurs embedded in a supportive social context are more likely to translate their entrepreneurial intent into an actual startup [14].
Any discussion of development circles back to the nature/nurture debate. The nature/nurture debate will not be resolved here. Yet, the evidence is clear that the chances of a child becoming an entrepreneur is increased by 60% if one of the parents is an entrepreneur [15]. This finding does not address the degree to which entrepreneurship is influenced by genetics. Obschonka [16] writes, “Recent research in behavioral genetics suggests that entrepreneurship has a substantial genetic component (p. 196).” Regardless of the relative contributions of nature or nurture, Obschonka [16] concludes that, “…adolescence is a crucial developmental phase in entrepreneurial development (p. 200).” Another period of an increase in entrepreneurial activity is job loss of individuals over the age of 50 as described by Moulton and Scott [17]: “We find that job loss shows a strong association into self-employment, particularly less desirable forms of self-employment (p. 1539).” This finding is important because it demonstrates that entrepreneurship or self-employment is not inherently desirable.
Returning to the nature/nurture debate, entrepreneurship educators assume that entrepreneurship can be learned [18]. As such, this assumption suggests that entrepreneurship can be nurtured along the age continuum. One such entrepreneurship education program targeting primary/elementary school children described the effects of such education as follows:
“The implementation of this EE model from September 2009 to June 2014 allowed us to conclude that children can be entrepreneurs and can open, operate, and close a small enterprise in the short term, thanks to the experience transmitted by the tutors and advisers ([19], p. 303).”
However, there is a dearth of literature on entrepreneurship education targeting older adults over the age of 50. Moreover, most of these programs target younger entrepreneurs [20]. Hantman and Gimmon [21] describe an entrepreneurship incubator in which 70% of the 22 participants, all of whom were 55 or older, launched a new venture over the 12-meeting training program.
It is beyond the scope here to review the body of literature on the relationship between age and entrepreneurship. The research to date is mixed regarding the relationship between age and entrepreneurship. The UK (United Kingdom) government [22] defines older entrepreneurship as any entrepreneur 50 and older.
Past research has shown an inverted U-shaped relationship between age and entrepreneurship [7]. It has also been argued that there is a negative relationship between age and engaging in entrepreneurship [11, 23]. In an empirical study examining high-growth companies, it was found that founders under the age of 25 are strongly disadvantaged at creating high growth companies with a surge in creating such companies after the age of 35 and another surge after the age of 46 until plateauing at age 60 [24]. As for business ownership, individuals over the age of 55 represent one-third of all firms although this same age cohort launches 15 percent of new firms [25].
The type of business launched also vary by age. Personal services, retail and restaurants are more likely launched by entrepreneurs in the 35–53 age cohort [25]. In contrast, entrepreneurs 55 and older are more likely to launch high-tech manufacturing, real estate, metal & machinery, and health care services [25]. Entrepreneurial ventures can be categorized into four segments: financed growth; organic growth; stable small employer; and stable micro [25]. Financed growth firms were defined as those with at least $400,000 in financing cash inflows and organic growth firms were defined as those with less than $400,000 in financing cash inflows [25]. The other segments are the following: stable small employer and stable micro. The difference is that the stable small employer is defined as having over $500,000 in expenses primarily payroll and the stable micro has no or very few employees with less than $500,000 in expenses [25]. It was found that younger entrepreneurs 35 and under were less likely to own financed growth and stable small employer ventures [25]. Yet, the 35–54 age cohort were overall overrepresented across all firms based upon a population comparison. Among the older entrepreneurs 55 and older, they were more likely to be in the stable small employer and micro segment [25].
As for exits, it was found that “a founder at age 50 is approximately twice as likely to experience a successful exit compared to a founder at age 30 ([24], p. 74).” Yet, founders 55 and older are the least likely to employ others although the most likely to survive [25].
Another finding emerging from the growing body of literature on age and entrepreneurship is that entrepreneurs of different ages manifest different goals related to what it means to be an entrepreneur [7]. To this point, younger and older entrepreneurs are more likely to launch ventures which are more socially oriented than middle age entrepreneurs [7]. These types of ventures fall under the category of social entrepreneurship.
There is a wide array of reasons why ventures fail to launch, why ventures fail to generate a profit, why ventures fail to survive, and why ventures fail to exit. One of the more common challenges has to do with managing the finances of entrepreneurial ventures regardless of the age of the entrepreneur. Competence in accounting practices has been found to be a challenge for entrepreneurs between the ages of 18 to 59 and a predictor of small business failure [26]. Working capital has always represented a challenge for small businesses [26]. Lack of liquidity has become even more of a challenge given the impact of COVID-19 [27]. Although this is not the only challenge, this challenge is more than likely related to the survival of the entrepreneurial venture.
A common challenge may revolve around stereotype bias and entrepreneurs especially those who are under the age of 18 and even over the age of 50. This type of bias may present roadblocks to those seeking to become entrepreneurs because they do not fit the “mental model” of the appropriate age of an entrepreneur. Related to both age groups is an increasing degree of interdependence among others. Specifically, for those entrepreneurs under the age of 18, it is likely that parental involvement will be higher. For those over the age of 50, it is likely that involvement with children and even aging parents will be higher. In fact, empirical evidence is emerging about the U-shaped curve of age discrimination in the workplace [28]. This empirical work has to be extended to entrepreneurial settings until researchers being to investigate bias and stereotyping in entrepreneurship using age as a variable in addition to the numerous studies investigating gender.
Younger and older entrepreneurs may benefit from a different set of resources. Regarding entrepreneurship, it was found that a focus on opportunity seeking is central to venture growth among entrepreneurs from 24 to 74 [29]. Of all the generations, the millennial generation is more interested in digital entrepreneurship than previous generations [33].
Regarding specific opportunity sets for entrepreneurs, it is conceivable that younger entrepreneurs have greater physical resources such as enhanced cognitive function and are also less encumbered with family and other responsibilities [24]. As for older entrepreneurs, it is conceivable that they have greater access to capital of all types including financial, social, and human [24]. Mental health is a key moderator between the age of the entrepreneur and a focus on opportunities [29]. Intergenerational entrepreneurship represents another opportunity for entrepreneurs of all ages. This ranges from launching firms together to intergenerational entrepreneurship education [30].
The role of formal and informal organizations in shaping and supporting entrepreneurship is critical [31]. Yet, the type of support may vary given the heterogeneity of entrepreneurs. Bohlmann et al. [11] found that entrepreneurs of different ages need different types of support. Furthermore, the current entrepreneurship ecosystem has been critiqued by Bohlmann et al. [11] “These programs do not accurately take the needs and motivation of different ages into account (p. 8).”
Brieger et al. [7] recommend that high quality entrepreneurship support organizations offer services appropriate for specific life phases.
As an example, Gielnik et al. [29] based upon their study on the role of mental health for maintaining a high level focus on opportunities suggest that policy makers should invest in maintaining or improving mental health and invest in increasing learning & development opportunities targeting older entrepreneurs.
Entrepreneurship research is increasingly taking a development approach. Even further, research is increasingly investigating older entrepreneurs who are 55 and older [21]. Future research ideally will draw upon a range of theories including developmental theories. Yet, researchers have eleven theoretical perspectives from which to frame future research beyond developmental theories. Eleven perspectives include the following: negative relationship personal health; rigidity; time allocation; risk propensity; discrimination; positive relationship human capital; social capital; financial capital; emotion; family obligation; and gender stereotype.
Beyond the theoretical base of future research, different research designs are recommended including cross-sectional and longitudinal designs. Given the focus on age and entrepreneurship, cohort based, and panel research designs are also worth pursuing among future researchers. The challenge for researchers may be to collaborate with researchers from other disciplines such as developmental psychology, family systems, sociology, and gerontology [32].
This line of research should go beyond age and also examine cohort effects by generation. To this point, the call for such research has been made, “It is critical that scholars of international entrepreneurship explore millennial entrepreneurs and contrast them across generations and countries ([33], p. 9).” Given the social context of younger and older entrepreneurs in particular, intersectionality as a construct is warranted [34].
This research should be grounded in qualitative, quantitative, mixed methods and even deploy big data analytic models. Much of the research should be hypothesis driven but not all of the research due to the nascent aspects of the nexus between age and entrepreneurship as well as generation and entrepreneurship. The following hypotheses represent a starting point to engage researchers in contributing to the dearth on aging and entrepreneurship. These hypotheses are by no means exhaustive.
H1: There are differences in entrepreneurial intent among entrepreneurs across the age continuum.
H2: There are differences in entrepreneurial motivation among entrepreneurs across the age continuum.
H3: There are differences in “push” and “pull” factors among entrepreneurs across the age continuum.
H4: There are differences in opportunities in entrepreneurial financing among entrepreneurs across the age continuum.
H5: There are differences in entrepreneurial exits among entrepreneurs across the age continuum.
It has previously been mentioned that the ideal entrepreneur and most entrepreneurship education program are not inclusive by age. In fact, they target younger entrepreneurs often under the age of 30. Following this trend, there appears to be a lot of focus on weaving entrepreneurship education into primary/elementary school and secondary/high school not to mention colleges/universities. These efforts should continue but ought to be expanded to include other age groups over the age of 30 up to retirement age or older.
If indeed entrepreneurship educators offer targeted entrepreneurship curricula that is age appropriate, then this education ought to also embrace an inter-generational element rather than “segregating” the target audiences by age cohorts. Yet, the case can be made for exclusive entrepreneurship education targeting specific age cohorts given the unique challenges and opportunities facing entrepreneurs at different ages and developmental periods.
The case for targeting specific age cohorts and even generational cohorts can be further subdivided into types of entrepreneurs within a given age cohort and generational cohort. As an illustration, it was found that there are eight types of entrepreneurs in the Baby Boom Generation (born between 1946 and 1964) [35]. This typology categorizes entrepreneurs into these categories or types: new versus existing, new opportunity versus new necessity, full-time versus part-time, and incorporated versus unincorporated entrepreneurs [35]. The author of this study argues “Understanding baby boomer entrepreneurs better and assisting them to develop entrepreneurship could be an effective strategy for our aging population ([35], p. 70).”
The recommendations set forth for entrepreneurs are presented from the lens of offering tailor made recommendations for different age groups across the developmental continuum.
School age entrepreneurs are deeply embedded in a family context and increasingly a school context with a rise in entrepreneurship educational programs targeting school age entrepreneurs. The degree to which these ventures are actually family firms is subject to further discovery, but the role of parents, other relatives and others is critical to the success of school age entrepreneurs. The current legal and regulatory system not to mention societal norms may impose unique barriers for school age entrepreneurs because they have not achieved the age of majority. Hence, stakeholders in the entrepreneurship ecosystem should continue to design and deliver tailored solutions for school age entrepreneurs while at the same time advocating to relax some legal and regulatory barriers.
College age entrepreneurs are increasingly warmly embraced by colleges and universities which offer degree and certificate programs in entrepreneurship. These efforts should continue along with the hackathons and business plan competitions. Likewise, research should continue involving college age entrepreneurs yet educational, programming and research investments need to be more inclusive of other age groups beyond the college age entrepreneurs. In most nations, college attendance and graduation are the exception not the rule. As such, attention should be paid to those who are college but decide not to attend college and start ventures in the skilled trades, retail, and food/beverages as well as gig workers.
Young adult entrepreneurs have decided to choose a particular path in life regarding their occupational identify and way to earn an income. At some point, during young adult, these entrepreneurs will make a commitment as a partner and even add the role of a parent. As such, greater attention is warranted to look at the varying roles for young adults and how they balance the tasks associated with these roles as well as the challenges of launching a new venture often without steady cash flow to ensure survival.
Middle age entrepreneurs are often ignored by the entrepreneurship ecosystem except to include them as mentors and financiers. These entrepreneurs often select entrepreneurship after some adverse life event ranging from a health event to a job loss event. Hence, programming ought to focus upon not just launching a venture but also managing grief and other emotions associated with a sudden loss of stability. Similar to young age entrepreneurs, these middle age entrepreneurs with aging parents may be part of the “sandwich generation” requiring different types of programming, support, and advocacy.
Older age entrepreneurs are nearly invisible in the entrepreneurship ecosystem as participants. Proactive steps must be taken to include older entrepreneurs to counter the bias and stereotyping which occurs among older entrepreneurs. This step will require that leaders and decision makers in the entrepreneurship ecosystem look at their own biases and stereotypes and rid their organizations of such biases which become part of the culture, policies, and procedures.
Although these recommendations are presented as if they are separate, they are not. Leading organizations dedicated to enhancing entrepreneurship along the lifespan should seek to be “friendly” and “serve” entrepreneurs of all age or differentiate based upon serving entrepreneurs of a certain age group.
Furthermore, the designers, funders and evaluators of entrepreneurship programs targeting entrepreneurs at various ages must also consider the differences among the opportunity versus the necessity entrepreneurs. This categorization is similar to the push/pull framework [36]. This framework suggests that some entrepreneurs are pushed into entrepreneurship for such reasons as a lack of other career alternatives and others are pulled into entrepreneurship to pursue opportunities.
Entrepreneurship is all too often considered a more viable career option for those who are younger. Yet, as discussed above, the empirical evidence including a meta-analysis conclude that the opposite is true. Specifically, older entrepreneurs are more likely to succeed than younger entrepreneurs [37]. A central theme throughout this chapter is to challenge some assumptions that the general public, the media, academics and other stakeholders in the entrepreneurship ecosystem have about who is an entrepreneur, who seeks to be an entrepreneur out of necessity or opportunity seeking, and who should be served by entrepreneurship support organizations. The empirical evidence suggests a quite different picture that what is imagined in the eyes of most about the prototypical entrepreneur.
Fundamentally, entrepreneurship is a choice that individuals make at various stages of their life’s journey. This choice sometimes arises out of identifying an opportunity, sometimes arises out of needing to earn income, and sometimes arises out of the existential need to “chart your own course.” Regardless of the origins of the choice, entrepreneurship may occur at nearly any age from 10 to 100. The age and generational diversity of entrepreneurs is a reality that must be embraced by policy makers, entrepreneurship educators, entrepreneurship support organizations, and entrepreneurship researchers. Embracing the age and generational diversity of entrepreneurs begins with you and your beliefs about who aspires to and currently is an entrepreneur.
The authors declare no conflict of interest.
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