Aufgaben:Exercise 1.2: Lognormal Channel Model - Revision history

Javier at 14:58, 2 July 2021

2021-07-02T14:58:26Z

Javier: Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

2021-03-23T12:37:11Z

Text replacement - "Category:Exercises for Mobile Communications" to "Category:Mobile Communications: Exercises"

Javier: Text replacement - "===Solutions===" to "===Solution==="

2020-12-15T14:11:21Z

Text replacement - "===Solutions===" to "===Solution==="

Javier: Text replacement - "Mobile Kommunikation/Distanzabhängige Dämpfung und Abschattung" to "Mobile_Communications/Distance_Dependent_Attenuation_and_Shading"

2020-12-15T13:55:06Z

Text replacement - "Mobile Kommunikation/Distanzabhängige Dämpfung und Abschattung" to "Mobile_Communications/Distance_Dependent_Attenuation_and_Shading"

Guenter at 13:40, 16 November 2020

2020-11-16T13:40:52Z

Oezdemir at 15:33, 1 November 2020

2020-11-01T15:33:55Z

Oezdemir at 20:39, 30 July 2020

2020-07-30T20:39:57Z

Guenter at 08:57, 26 July 2020

2020-07-26T08:57:24Z

Guenter at 08:56, 26 July 2020

2020-07-26T08:56:16Z

Guenter at 08:51, 26 July 2020

2020-07-26T08:51:43Z

@@ Line 37: / Line 37: @@
 <quiz display=simple>
-{Would&nbsp; $P_{\rm E}$&nbsp;  be sufficient without consideration of the lognormal&ndash;fading?
+{Would&nbsp; $P_{\rm E}$&nbsp;  be sufficient if the loss $V_S$ due to shadowing is not present?
 |type="()"}
 + Yes,

← Older revision		Revision as of 12:37, 23 March 2021
Line 105:		Line 105:


−	[[Category:~~Exercises for~~ Mobile Communications\|^1.1 Distance-Dependent Attenuation^]]	+	[[Category:Mobile Communications: Exercises\|^1.1 Distance-Dependent Attenuation^]]

@@ Line 55: / Line 55: @@
 </quiz>
-===Solutions===
+===Solution===
 {{ML-Kopf}}
 '''(1)'''&nbsp; The correct answer is <u>YES</u>:

← Older revision		Revision as of 13:55, 15 December 2020
Line 1:		Line 1:
−	{{quiz-Header\|Buchseite=~~Mobile Kommunikation~~/~~Distanzabhängige Dämpfung und Abschattung~~	+	{{quiz-Header\|Buchseite=Mobile_Communications/Distance_Dependent_Attenuation_and_Shading
	}}		}}

@@ Line 77: / Line 77: @@
 '''(3)'''&nbsp; The received power is too low&nbsp; $($less than $&ndash;80 \ \rm dBm)$&nbsp; if the power loss due to the lognormal&ndash;term is&nbsp; $40 \ \rm dB$&nbsp; or more.
-[[File:EN_Mob_A_1_2c.png|right|frame|loss due to lognormal fading]]
+[[File:EN_Mob_A_1_2c.png|right|frame|Loss due to lognormal fading]]
 *The distance-dependent path loss $V_{\rm S}$ must therefore not be greater than&nbsp; $20 \ \rm dB$.

← Older revision		Revision as of 15:33, 1 November 2020
Line 105:		Line 105:


−	[[Category:Exercises for Mobile Communications\|^1.1 Distance-~~dependent attenuation~~^]]	+	[[Category:Exercises for Mobile Communications\|^1.1 Distance-Dependent Attenuation^]]

@@ Line 30: / Line 30: @@
 :$${\rm Q}(1) \approx 0.16\hspace{0.05cm},\hspace{0.2cm} {\rm Q}(2) \approx 0.02\hspace{0.05cm},\hspace{0.2cm}
   {\rm Q}(3) \approx 10^{-3}\hspace{0.05cm}.$$
-* Or use the interaction module&nbsp; [[Applets:Applets:Complementary_Gaussian_Error_Functions|Complementary Gaussian Error Functions]]&nbsp; provided by&nbsp; $\rm LNTwww$.
+* Or use the interaction module&nbsp; [[Applets:Complementary_Gaussian_Error_Functions|Complementary Gaussian Error Functions]]&nbsp; provided by&nbsp; $\rm LNTwww$.

@@ Line 9: / Line 9: @@
 *$V_0$&nbsp; takes into account the distance-dependent path loss which is assumed to be constant:&nbsp; $V_0 = 80 \ \rm dB$&nbsp;.
-*The loss&nbsp; $V_{\rm S}$&nbsp; is due to shadowing caused by the lognormal&ndash;distribution with the probability density function (PDF)
+*The loss&nbsp; $V_{\rm S}$&nbsp; is due to shadowing caused by the lognormal distribution with the probability density function (PDF)
 :$$f_{V_{\rm S}}(V_{\rm S}) =  \frac {1}{ \sqrt{2 \pi }\cdot \sigma_{\rm S}}  \cdot {\rm e }^{ - { (V_{\rm S}\hspace{0.05cm}- \hspace{0.05cm}m_{\rm S})^2}/(2 \hspace{0.05cm}\cdot \hspace{0.05cm}\sigma_{\rm S}^2) },$$
@@ Line 71: / Line 71: @@
 '''(2)'''&nbsp; Lognormal fading with&nbsp; $\sigma_{\rm S} = 0 \ \rm dB$&nbsp; is equivalent to a constant received power&nbsp; $P_{\rm E}$.
 *Compared to the subtask&nbsp; '''(1)'''&nbsp; this is&nbsp; $m_{\rm S} = 20 \ \ \rm dB$&nbsp; smaller &nbsp; &#8658; &nbsp; $P_{\rm E} = \ &ndash;60 \ \ \rm dBm$.
-*But it is still greater than the specified limit value&nbsp; ($-80 \ \rm dBm$).
+*But it is still greater than the specified limit value&nbsp; $(-80 \ \rm dBm)$.
-*It follows: &nbsp; The system is (almost) <u>100% functional</u>.&nbsp; "Almost" because with a Gaussian random quantity there is always a (small) residual uncertainty.
+*It follows: &nbsp; The system is (almost)&nbsp; <u>100% functional</u>.&nbsp; "Almost" because with a Gaussian random quantity there is always a (small) residual uncertainty.
-'''(3)'''&nbsp; The received power is too low (less than $&ndash;80 \ \rm dBm$) if the power loss due to the lognormal&ndash;term is $40 \ \rm dB$ or more.
+'''(3)'''&nbsp; The received power is too low&nbsp; $($less than $&ndash;80 \ \rm dBm)$&nbsp; if the power loss due to the lognormal&ndash;term is&nbsp; $40 \ \rm dB$&nbsp; or more.
-*The variable portion $V_{\rm S}$ must therefore not be greater than $20 \ \rm dB$.
+[[File:EN_Mob_A_1_2c.png|right|frame|loss due to lognormal fading]]
 *So it follows:
 :$${\rm Pr}({\rm "System\hspace{0.15cm}does\hspace{0.15cm}not\hspace{0.15cm}work"})= {\rm Q}\left ( \frac{20\,\,{\rm dB}}{\sigma_{\rm S} = 10\,{\rm dB}}\right )
-   = {\rm Q}(2) \approx 0.02\hspace{0.3cm}
+   = {\rm Q}(2) \approx 0.02$$
-\Rightarrow \hspace{0.3cm}{\rm Pr}({\rm "System\hspace{0.15cm}works"})= 1-  0.02 \hspace{0.15cm} \underline{\approx 98\,\%}\hspace{0.05cm}.$$
+:$$\Rightarrow \hspace{0.3cm}{\rm Pr}({\rm "System\hspace{0.15cm}works"})= 1-  0.02 \hspace{0.15cm} \underline{\approx 98\,\%}\hspace{0.05cm}.$$
 The graphic illustrates the result.
-*The probability density $f_{\rm VS}(V_{\rm S})$ of the path loss due to shadowing (Longnormal&ndash;Fading) is shown here.
+*The probability density&nbsp; $f_{\rm VS}(V_{\rm S})$&nbsp; of the path loss due to shadowing&nbsp; (Longnormal Fading)&nbsp; is shown here.
 *The probability that the system will fail is marked in red.
-<br clear=all>
-'''(4)'''&nbsp; From the availability probability $99.9 \%$ follows the failure probability $10^{\rm &ndash;3} \approx \ {\rm Q}(3)$.
 *If the distance-dependent path loss $V_0$ is reduced by $10 \ \ \rm dB$ to $\underline {70 \ \rm dB}$, a failure will only occur when $V_{\rm S} &#8805; 50 \ \ \rm dB$.
 *This would achieve exactly the required reliability, as the following calculation shows:
 :$${\rm Pr}({\rm "System\hspace{0.15cm} does\hspace{0.15cm} not\hspace{0.15cm} work\hspace{0.15cm}"})=