Mobile Communications/Distance Dependent Attenuation and Shading - Revision history

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Hwang at 10:02, 17 November 2022

2022-11-17T10:02:05Z

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 == # OVERVIEW OF THE FIRST MAIN CHAPTER  # ==
 <br>
-The first main chapter deals with time-variant transmission channels, a property that is of great importance for mobile communication.&nbsp; The description is given throughout in the equivalent low-pass range.
+The first main chapter deals with time-variant transmission channels,&nbsp; a property that is of great importance for mobile communication.&nbsp; The description is given throughout in the equivalent low-pass range.
-It deals in detail with the following topics:
+The chapter deals in detail with the following topics:
-*the distance-dependent attenuation of a radio signal and various path loss models,
+#The&nbsp; &raquo;distance-dependent attenuation of a radio signal&laquo; &nbsp; and various&nbsp; &raquo;path loss models&laquo;,
-*the influence of shadowing&nbsp;, which can be modeled through ''Lognormal fading''&nbsp;
+#the influence of&nbsp; &raquo;shadowing&laquo;,&nbsp; which can be modeled through&nbsp; &raquo;Lognormal fading''&laquo;,
-*the non-frequency selective&nbsp; ''Rayleigh fading'' &nbsp; for channels without "Line of Sight&nbsp; (LoS)",
+#the non-frequency selective&nbsp; &raquo;Rayleigh fading&laquo; &nbsp; for channels without&nbsp; &raquo;line of sight&laquo;&nbsp; $\rm (LoS)$,
-*the consideration of the Doppler effect by the so-called&nbsp; ''Jakes spectrum
+#the consideration of the&nbsp; &raquo;Doppler effect&laquo; &nbsp; by the so-called&nbsp; &raquo;Jakes spectrum&laquo;,
-*the non-frequency selective&nbsp; ''Rice fading'' &nbsp; for channels with direct path&nbsp; (Line of Sight).
+#the non-frequency selective&nbsp; &raquo;Rice fading&laquo; &nbsp; for channels with direct path&nbsp; $($"line of sight$)$.

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 We assume an unmodulated oscillation of the frequency&nbsp; $f_{\rm S}$&nbsp; or of the wavelength&nbsp; $\lambda= c/f_{\rm S}$&nbsp; where&nbsp; $c = 3 \cdot 10^8\ \rm m/s$&nbsp; indicates the ''speed of light''&nbsp;, the signal power is&nbsp; $P_{\rm S}$.<br>
-[https://en.wikipedia.org/wiki/Harald_T._Friis $\text{Harald Friis}$]&nbsp; gave an equation in 1944 for the reception '''KORREKTUR: received''' power&nbsp; $P_{\rm E}(d)$&nbsp; from the distance&nbsp; $d$&nbsp; (this equation, however, is only valid in a vacuum):
+[https://en.wikipedia.org/wiki/Harald_T._Friis $\text{Harald Friis}$]&nbsp; gave an equation in 1944 for the received power&nbsp; $P_{\rm E}(d)$&nbsp; from the distance&nbsp; $d$&nbsp; (this equation, however, is only valid in a vacuum):
 ::<math>P_{\rm E}(d) = \frac{P_{\rm S} \cdot G_{\rm S} \cdot G_{\rm E} \cdot \lambda^2}{16 \cdot  \pi^2 \cdot d^2 \cdot V_{\rm add}} =
@@ Line 81: / Line 81: @@
 *The equation only applies in the far field of the antenna&nbsp; $(d > d_{\rm F})$.&nbsp; Here&nbsp; $d_{\rm F} = 2 D^2/\lambda$&nbsp; the so-called &nbsp;&raquo;'''Fraunhofer distance'''&laquo;.&nbsp; For&nbsp; $D$&nbsp; the largest physical dimension of the transmitting antenna must be used.<br>
-*The equation does not apply to&nbsp; $d \to 0$.&nbsp; This would result in the limit value&nbsp; $K_{\rm FR} \to 0$, and it would result independently from&nbsp; $P_{\rm S}$&nbsp; always an infinite receiving '''KORREKTUR: received?''' power&nbsp; $P_{\rm E}(d \to 0)$.<br>
+*The equation does not apply to&nbsp; $d \to 0$.&nbsp; This would result in the limit value&nbsp; $K_{\rm FR} \to 0$, and it would result independently from&nbsp; $P_{\rm S}$&nbsp; always an infinite received power&nbsp; $P_{\rm E}(d \to 0)$.<br>
 *The free-space attenuation&nbsp; $K_{\rm FR}(d)$&nbsp; increases  quadratically with increasing distance&nbsp; $d$&nbsp;  and also quadratically with increasing signal frequency&nbsp; $f_{\rm S}$, that is, with decreasing wavelength&nbsp; $\lambda$.<br>
@@ Line 93: / Line 93: @@
 == Common path loss model ==
 <br>
-In contrast to satellite and radio relay links, in the case of land mobile radio in addition to free-space attenuation, other disturbing effects  must be taken into account which also contribute to a reduction in reception '''KORREKTUR: received?''' power, namely:
+In contrast to satellite and radio relay links, in the case of land mobile radio in addition to free-space attenuation, other disturbing effects  must be taken into account which also contribute to a reduction in received power, namely:
-*&raquo;'''Reflections'''&laquo;: &nbsp; By superimposing the transmitted signal with a signal component reflected on the ground or on other large smooth surfaces, cancellations can occur which cause a decrease in the reception '''KORREKTUR: received?''' power up to the fourth power of the distance&nbsp; $d$&nbsp; between transmitter and receiver.&nbsp; For more information, see&nbsp; [Zan05]<ref name = 'Zan05'>Zangl, J.:&nbsp; Multi-Hop-Netze mit Kanalcodierung und Medium Access Controll (MAC).&nbsp; Düsseldorf: VDI Verlag, Reihe 10, Nummer 761, 2005.</ref>&nbsp; and&nbsp; [PA95]<ref name = 'PA95'>Pahlavan, K.; Allen, L.:&nbsp; Wireless Information Networks.&nbsp; New York: John Wiley & Sons, Wiley Series in Telecommunications and Signal Processing, 1995.</ref>.<br>
+*&raquo;'''Reflections'''&laquo;: &nbsp; By superimposing the transmitted signal with a signal component reflected on the ground or on other large smooth surfaces, cancellations can occur which cause a decrease in the received power up to the fourth power of the distance&nbsp; $d$&nbsp; between transmitter and receiver.&nbsp; For more information, see&nbsp; [Zan05]<ref name = 'Zan05'>Zangl, J.:&nbsp; Multi-Hop-Netze mit Kanalcodierung und Medium Access Controll (MAC).&nbsp; Düsseldorf: VDI Verlag, Reihe 10, Nummer 761, 2005.</ref>&nbsp; and&nbsp; [PA95]<ref name = 'PA95'>Pahlavan, K.; Allen, L.:&nbsp; Wireless Information Networks.&nbsp; New York: John Wiley & Sons, Wiley Series in Telecommunications and Signal Processing, 1995.</ref>.<br>
 *&raquo;'''Diffraction'''&laquo;: &nbsp; This is when the signal is not reflected but deflected from its direction of propagation, for example at the edge of a building.&nbsp; A physical explanation can be found again in&nbsp; [Zan05]<ref name = 'Zan05'></ref>.<br>
@@ Line 100: / Line 100: @@
 *&raquo;'''Dispersion'''&laquo;: &nbsp; If the connection&nbsp; transmitter &ndash; receiver&nbsp; is interrupted by several objects with irregular surfaces&nbsp; (for example trees or bushes)&nbsp; the signal arrives at the receiver in the form of many scattered signals with slightly different propagation times.&nbsp; The size of the obstacle determines whether it is to be interpreted as a reflecting or as a scattering object.<br><br>
-The effects mentioned here are responsible for the fact that mobile radio can be operated without direct line of sight&nbsp; $\rm (LOS)$, and thus one of the bases for the economic success of mobile radio systems.&nbsp; Negatively, these effects are caused by a lower reception '''KORREKTUR: received?''' power, which must be taken into account by a larger exponent than&nbsp; $\gamma = 2$&nbsp;.&nbsp; We then no longer speak of&nbsp; "free-space attenuation",&nbsp; but generally of&nbsp; "path attenuation factor":
+The effects mentioned here are responsible for the fact that mobile radio can be operated without direct line of sight&nbsp; $\rm (LOS)$, and thus one of the bases for the economic success of mobile radio systems.&nbsp; Negatively, these effects are caused by a lower  received power, which must be taken into account by a larger exponent than&nbsp; $\gamma = 2$&nbsp;.&nbsp; We then no longer speak of&nbsp; "free-space attenuation",&nbsp; but generally of&nbsp; "path attenuation factor":
 ::<math>K_{\rm P}(d) = K_{\rm P}(d_0) \cdot (d/d_0)^\gamma \hspace{0.05cm}.</math>
@@ Line 256: / Line 256: @@
 *The input signal of the mobile radio channel is a cosine oscillation with the amplitude&nbsp; $A = 1$&nbsp; and the frequency&nbsp; $f_{\rm T}$.&nbsp; We refer to this harmonic oscillation as the&nbsp; "transmitted signal"&nbsp; $s_{\rm BP}(t)$.&nbsp; This band-pass signal is shown in red in the upper graphic.<br>
-*The output signal&nbsp; $r_{\rm BP}(t)$&nbsp; of the mobile radio channel &ndash; in the following called&nbsp; "reception '''KORREKTUR: received''' signal"&nbsp; &ndash; may differ from&nbsp; $s_{\rm BP}(t)$&nbsp; both in amplitude&nbsp; (envelope)&nbsp; and in phase &nbsp; &rArr; &nbsp; lower graph, red.<br>
+*The output signal&nbsp; $r_{\rm BP}(t)$&nbsp; of the mobile radio channel &ndash; in the following called&nbsp; "received signal"&nbsp; &ndash; may differ from&nbsp; $s_{\rm BP}(t)$&nbsp; both in amplitude&nbsp; (envelope)&nbsp; and in phase &nbsp; &rArr; &nbsp; lower graph, red.<br>
 *Furthermore, we mostly look at the mobile radio channel in the&nbsp; [[Signal_Representation/Equivalent_Low-Pass_Signal_and_its_Spectral_Function#Motivation_for_describing_in_the_equivalent_low-pass_range| $\text{equivalent low-pass range}$]].&nbsp; (German:&nbsp; Tiefpass,&nbsp; $\rm TP$).&nbsp; The&nbsp; "transmitted signal"&nbsp; is then&nbsp; $s_{\rm TP}(t) = 1$&nbsp; and thus real &nbsp; &rArr; &nbsp; blue horizontal in the upper graphic.<br>
@@ Line 263: / Line 263: @@
 {{BlaueBox|TEXT=
-$\text{Conclusion:}$&nbsp; For the&nbsp; &raquo;'''physical signal at the output of the mobile radio channel'''&laquo;&nbsp; &rArr; &nbsp; &raquo;'''band-pass reception '''KORREKTUR: received?''' signal'''&laquo;&nbsp; always applies in the following:
+$\text{Conclusion:}$&nbsp; For the&nbsp; &raquo;'''physical signal at the output of the mobile radio channel'''&laquo;&nbsp; &rArr; &nbsp; &raquo;'''band-pass received  signal'''&laquo;&nbsp; always applies in the following:
 ::<math>r_{\rm BP}(t) = a(t) \cdot \cos \big [2\pi f_{\rm T} t + \phi(t)\big ]\hspace{0.3cm}\Rightarrow \hspace{0.3cm} a(t) = \vert r_{\rm BP}(t)\vert\hspace{0.05cm}, \hspace{0.2cm}  \phi(t) = {\rm arc}\hspace{0.15cm} r_{\rm BP}(t)\hspace{0.05cm}.</math>}}

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 The following conditions therefore apply with immediate effect:
-*The input signal of the mobile radio channel is a cosine oscillation with the amplitude&nbsp; $A = 1$&nbsp; and the frequency&nbsp; $f_{\rm T}$.&nbsp; We refer to this harmonic oscillation as the&nbsp; "transmission signal"&nbsp; $s_{\rm BP}(t)$.&nbsp; This band-pass signal is shown in red in the upper graphic.<br>
+*The input signal of the mobile radio channel is a cosine oscillation with the amplitude&nbsp; $A = 1$&nbsp; and the frequency&nbsp; $f_{\rm T}$.&nbsp; We refer to this harmonic oscillation as the&nbsp; "transmitted signal"&nbsp; $s_{\rm BP}(t)$.&nbsp; This band-pass signal is shown in red in the upper graphic.<br>
 *The output signal&nbsp; $r_{\rm BP}(t)$&nbsp; of the mobile radio channel &ndash; in the following called&nbsp; "reception '''KORREKTUR: received''' signal"&nbsp; &ndash; may differ from&nbsp; $s_{\rm BP}(t)$&nbsp; both in amplitude&nbsp; (envelope)&nbsp; and in phase &nbsp; &rArr; &nbsp; lower graph, red.<br>
-*Furthermore, we mostly look at the mobile radio channel in the&nbsp; [[Signal_Representation/Equivalent_Low-Pass_Signal_and_its_Spectral_Function#Motivation_for_describing_in_the_equivalent_low-pass_range| $\text{equivalent low-pass range}$]].&nbsp; (German:&nbsp; Tiefpass,&nbsp; $\rm TP$).&nbsp; The&nbsp; "transmission signal"&nbsp; is then&nbsp; $s_{\rm TP}(t) = 1$&nbsp; and thus real &nbsp; &rArr; &nbsp; blue horizontal in the upper graphic.<br>
+*Furthermore, we mostly look at the mobile radio channel in the&nbsp; [[Signal_Representation/Equivalent_Low-Pass_Signal_and_its_Spectral_Function#Motivation_for_describing_in_the_equivalent_low-pass_range| $\text{equivalent low-pass range}$]].&nbsp; (German:&nbsp; Tiefpass,&nbsp; $\rm TP$).&nbsp; The&nbsp; "transmitted signal"&nbsp; is then&nbsp; $s_{\rm TP}(t) = 1$&nbsp; and thus real &nbsp; &rArr; &nbsp; blue horizontal in the upper graphic.<br>
 *The low-pass output signal&nbsp; $r_{\rm TP}(t)$&nbsp; is generally complex, where the envelope is given by&nbsp; $a(t)$&nbsp; and the phase&nbsp; $\phi(t)$&nbsp; is noticeable by shifts in the zero crossings &nbsp; &rArr; &nbsp; blue envelope in the lower graph.<br><br>

@@ Line 258: / Line 258: @@
 *The output signal&nbsp; $r_{\rm BP}(t)$&nbsp; of the mobile radio channel &ndash; in the following called&nbsp; "reception '''KORREKTUR: received''' signal"&nbsp; &ndash; may differ from&nbsp; $s_{\rm BP}(t)$&nbsp; both in amplitude&nbsp; (envelope)&nbsp; and in phase &nbsp; &rArr; &nbsp; lower graph, red.<br>
-*Furthermore, we mostly look at the mobile radio channel in the&nbsp; [[Signal_Representation/Equivalent_Low_Pass_Signal_and_Its_Spectral_Function#Motivation| $\text{equivalent low-pass range}$]].&nbsp; (German:&nbsp; Tiefpass,&nbsp; $\rm TP$).&nbsp; The&nbsp; "transmission signal"&nbsp; is then&nbsp; $s_{\rm TP}(t) = 1$&nbsp; and thus real &nbsp; &rArr; &nbsp; blue horizontal in the upper graphic.<br>
+*Furthermore, we mostly look at the mobile radio channel in the&nbsp; [[Signal_Representation/Equivalent_Low-Pass_Signal_and_its_Spectral_Function#Motivation_for_describing_in_the_equivalent_low-pass_range| $\text{equivalent low-pass range}$]].&nbsp; (German:&nbsp; Tiefpass,&nbsp; $\rm TP$).&nbsp; The&nbsp; "transmission signal"&nbsp; is then&nbsp; $s_{\rm TP}(t) = 1$&nbsp; and thus real &nbsp; &rArr; &nbsp; blue horizontal in the upper graphic.<br>
 *The low-pass output signal&nbsp; $r_{\rm TP}(t)$&nbsp; is generally complex, where the envelope is given by&nbsp; $a(t)$&nbsp; and the phase&nbsp; $\phi(t)$&nbsp; is noticeable by shifts in the zero crossings &nbsp; &rArr; &nbsp; blue envelope in the lower graph.<br><br>

← Older revision		Revision as of 13:22, 19 January 2023
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−	However, such channel changes are very slow due to shading.   Often the conditions remain the same for several seconds and one speaks here of  "Long Term Fading"  in contrast to fast fading like  [[Mobile_Communications/Probability density of Rayleigh fading#A very general description of the mobile communication channel\|$\text{Rayleigh fading}$]]  and  [[Mobile_Communications/Non-~~frequency_selective_fading_with_direct component~~#~~Kanalmodell_und_Rice.E2.80.93WDF~~\|$\text{Rice fading}$]].<br>	+	However, such channel changes are very slow due to shading.   Often the conditions remain the same for several seconds and one speaks here of  "Long Term Fading"  in contrast to fast fading like  [[Mobile_Communications/Probability density of Rayleigh fading#A very general description of the mobile communication channel\|$\text{Rayleigh fading}$]]  and  [[Mobile_Communications/Non-Frequency_Selective_Fading_With_Direct_Component#Channel_model_and_Rice_PDF\|$\text{Rice fading}$]].<br>

	== Lognormal channel model==		== Lognormal channel model==

← Older revision		Revision as of 13:19, 19 January 2023
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−	The effects of shadowing can be ~~summarised~~ as follows:	+	The effects of shadowing can be summarized as follows:
	*For stationary transmitters and receivers, the shadowing is to be considered deterministic.  It causes the path loss due to the shadowing to change by a constant value  $V_{\rm S}$  (in dB):		*For stationary transmitters and receivers, the shadowing is to be considered deterministic.  It causes the path loss due to the shadowing to change by a constant value  $V_{\rm S}$  (in dB):

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 == Other, more accurate path loss models ==
 <br>
-The relatively simple path loss model shown on the last page is well suited for macro cells, but requires high base station antennas.&nbsp; It was used, for example, as a reference&ndash;scenario for the standardization of&nbsp; [[Mobile_Communications/General information on the LTE mobile communications standard|Long Term Evolution]]&nbsp; $\rm (LTE)$.<br>
+The relatively simple path loss model shown in the last section is well suited for macro cells, but requires high base station antennas.&nbsp; It was used, for example, as a reference&ndash;scenario for the standardization of&nbsp; [[Mobile_Communications/General information on the LTE mobile communications standard|Long Term Evolution]]&nbsp; $\rm (LTE)$.<br>
 Of course, this very simple two&ndash;parameter model&nbsp; $(V_0, \ \gamma)$&nbsp; cannot reproduce all use cases with sufficient accuracy.&nbsp; A large number of other models for power attenuation can be found in the literature, which are more precisely adapted to specific boundary conditions&nbsp; (neighbourhood)&nbsp; and also take different cell sizes into account.&nbsp; Well-known are for example, see&nbsp; [Gol06]<ref name='Gol06'>Goldsmith, A.:&nbsp; Wireless Communications.&nbsp; Cambridge University Press, Cambridge, UK, 2006.</ref>: