Which propagation model is used when reflection from the earth’s surface takes place? Deduce the total electric field considering the constant K.
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Which propagation model is used when reflection from the earth’s surface takes place? Deduce the total electric field considering the constant K.
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Answer:
Explanation:
This chapter introduces propagation characteristics and models for cellular systems. It summarizes important notions, and expands on aspects of fixed-versus-mobile and indoor-versus-outdoor propagation modeling. 1
Before studying details of propagation we need to define a few notation conventions, which will require the reader to be familiar with the following general concepts of electromagnetic field and wave theory.
Wireless communications signals of interest are electromagnetic waves, and may be derived in free space from the electric field E⃗.
The power density of the electromagnetic wave may be written in the form of the Poynting vector: ⃗P = ⃗E ×H⃗. The power density is the modulus of the Poynting vector Pd = |⃗P|.
In free space the electric and magnetic field strength are related by |⃗
E| = η0| ⃗
H|, and the power density of the electromagnetic wave is proportional to the modulus squared of the electric field: Pd = |E|2∕η0, where η0 ≈ 377 Ω is the impedance of the vacuum (and by approximation of air). 2
The electric field may be identified with the transmitted signal S(t) = s(t) ⋅ exp(j2πft), where s(t) is the (real) user encoded information to transmit, and f is the carrier frequency. S(t) is a complex function which real part Re{S(t)} = s(t)⋅cos(2πft) is the physical quantity of interest; although the complex function S(t) is usually used for simpler mathematical treatment, one should remember that its real part is the meaningful quantity. 3
Similarly, we identify the received signal with the received electric field; we denote the received signal: R(t) = r(t) ⋅ exp(j2πft).
Given the above, received power densities are given by the expression Pd(t) = |R(t)|2∕η0.
Actual received power Pr also depends on the effective area of the receiving antenna Pr(t) = AePd(t) = Ae|R(t)|2∕η0 (see further details in §3.2).
Some details of E-field propagation will be studied later with ray tracing; but most of the remainder of the section deals with very simple expressions of power levels for paths loss modeling.
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