Aufgaben:Exercise 4.2: UMTS Radio Channel Basics - Revision history

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Guenter at 14:33, 24 January 2023

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Guenter: Guenter moved page Aufgaben:Aufgabe 4.2: Grundlegendes zum UMTS-Funkkanal to Aufgaben:Exercise 4.2: UMTS Radio Channel Basics

2023-01-24T14:31:45Z

Guenter moved page Aufgabe 4.2: Grundlegendes zum UMTS-Funkkanal to Exercise 4.2: UMTS Radio Channel Basics

@@ Line 4: / Line 4: @@
 }}
-[[File:EN_Bei_A_4_2.png|right|frame|Path loss,&nbsp; frequency&ndash;selective and time&ndash;selective fading '''Korrektur''']]
+[[File:EN_Bei_A_4_2_v2.png|right|frame|Path loss,&nbsp; frequency/time&ndash;selective fading ]]
 UMTS also has quite a few effects leading to degradation that must be taken into account during system planning:
 *${\rm Interference}$:&nbsp; Since all users are simultaneously served in the same frequency band,&nbsp; each user is interfered by other users.

@@ Line 4: / Line 4: @@
 }}
-[[File:P_ID1931__Bei_A_4_2.png|right|frame|Path loss,&nbsp; frequency&ndash;selective and time&ndash;selective fading '''Korrektur''']]
+[[File:EN_Bei_A_4_2.png|right|frame|Path loss,&nbsp; frequency&ndash;selective and time&ndash;selective fading '''Korrektur''']]
 UMTS also has quite a few effects leading to degradation that must be taken into account during system planning:
 *${\rm Interference}$:&nbsp; Since all users are simultaneously served in the same frequency band,&nbsp; each user is interfered by other users.

@@ Line 66: / Line 66: @@
 {{ML-Kopf}}
-'''(1)'''&nbsp; According to the sketch, the breakpoint is at $d_{0} = 100 \ \rm m$.
+'''(1)'''&nbsp; According to the sketch,&nbsp; the breakpoint is at&nbsp; $d_{0} = 100 \ \rm m$.
-*For $d ≤ d_{0}$, the path loss is equal to $\alpha_{0} \cdot (d/d_{0})^{-2}$. For $d = d_{0} = 100 \ \rm m$ holds:
+*For&nbsp; $d ≤ d_{0}$,&nbsp; the path loss is equal to&nbsp; $\alpha_{0} \cdot (d/d_{0})^{-2}$.&nbsp; For $d = d_{0} = 100 \ \rm m$&nbsp; holds:
-:$${\rm path loss} = \alpha_0 = 10^{-5}\hspace{0.5cm}\Rightarrow\hspace{0.5cm}{50\,{\rm dB}}.$$
+:$${\rm path\ loss} = \alpha_0 = 10^{-5}\hspace{0.5cm}\Rightarrow\hspace{0.5cm}{50\,{\rm dB}}.$$
 *Different frequency components are delayed and attenuated differently by the channel.
 *This results in attenuation and phase distortion.
-*Because $\tau_{\rm max} = 1 \ \rm &micro; s$ (simplifying $\tau_{\rm min} = 0$ is set) further results in
+*This results in attenuation and phase distortion.
 :$$B_{\rm K} = \frac{1}{\tau_{\rm max}- \tau_{\rm min}} = 1\,{\rm MHz}\ \ll \ B_{\rm S} \hspace{0.15cm}\underline {= 5\,{\rm MHz}}.$$
-'''(3)'''&nbsp; Correct is <u>statement 2</u>.
+'''(3)'''&nbsp; Correct is&nbsp; <u>statement 2</u>.
-*Statements 1 and 3, on the other hand, are valid for frequency-selective fading &ndash; see subtask '''(2)'''.
+*Statements 1 and 3,&nbsp; on the other hand,&nbsp; are valid for frequency-selective fading &ndash; see subtask&nbsp; '''(2)'''.

@@ Line 33: / Line 33: @@
 *This exercise belongs to the chapter&nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS|"General Description of UMTS"]].
-*Reference is made in particular to the sections &nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Properties_of_the_UMTS_radio_channel|"Properties of the UMTS radio channel"]] &nbsp; and &nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Frequency. E2.80.93_and_time.E2.80.93selective_fading|"Frequency- and time-selective fading"]].
+*Reference is made in particular to the sections &nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Properties_of_the_UMTS_radio_channel|"Properties of the UMTS radio channel"]] &nbsp; and &nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Frequency.E2.80.93selective_and_time.E2.80.93selective_fading|"Frequency-selective and time-selective fading"]].
 *For UMTS,&nbsp; the bandwidth:&nbsp; $B_{\rm S} = 5 \ \rm MHz$&nbsp; and the chip duration:&nbsp; $T_{\rm C} \approx 0.26 \ \rm &micro; s$.

@@ Line 16: / Line 16: @@
 In the book&nbsp; "[[Mobile Communications]]"&nbsp; these effects have already been discussed in detail. The diagrams convey only a few pieces of information regarding
-*<u>Path loss:</u>&nbsp; Path loss indicates the decrease in received power with distance&nbsp; $d$&nbsp; from the transmitter. Above the so-called&nbsp; ''break point''&nbsp; applies approximately to the received power:
+*<u>Path loss:</u>&nbsp; Path loss indicates the decrease in the received power with distance&nbsp; $d$&nbsp; from the transmitter.&nbsp; Above the so-called&nbsp; "break point"&nbsp; applies approximately to the received power:
-:$$\frac{P(d)}{P(d_0)} = \alpha_0 \cdot \left ( {d}/{d_0}\right )^{-4}.$$
+::$$\frac{P(d)}{P(d_0)} = \alpha_0 \cdot \left ( {d}/{d_0}\right )^{-4}.$$
 :According to the upper graph&nbsp; $\alpha_{0} = 10^{-5}$&nbsp; $($correspondingly&nbsp; $50 \ \rm dB)$&nbsp; and&nbsp; $d_{0} = 100 \ \rm m$.
+*For UMTS,&nbsp; the bandwidth:&nbsp; $B_{\rm S} = 5 \ \rm MHz$&nbsp; and the chip duration:&nbsp; $T_{\rm C} \approx 0.26 \ \rm &micro; s$.
@@ Line 45: / Line 44: @@
 <quiz display=simple>
-{Calculate - starting from the top graph on the information page - the path loss&nbsp; $($in&nbsp; $\rm dB)$&nbsp; for&nbsp; $d = \rm 5 \ km$.
+{Starting from the top graph on the information page,&nbsp; calculate the path loss&nbsp; $($in&nbsp; $\rm dB)$&nbsp; for&nbsp; $d = \rm 5 \ km$.
 |type="{}"}
-${\rm path loss} \ = \ $ { 118 3% } $\ \rm dB $.
+${\rm path\ loss} \ = \ $ { 118 3% } $\ \rm dB $.
-{What statements are true regarding frequency selective fading?
+{What statements are true regarding frequency-selective fading?
 |type="[]"}
 + This is caused by multipath reception.
 - It is caused by movement of transmitter and/or receiver.
 + Different frequencies are attenuated differently.
-+ An echo at a distance&nbsp; $1\ \rm &micro; s$&nbsp; results in frequency selective fading.
++ An echo at a distance&nbsp; $1\ \rm &micro; s$&nbsp; results in frequency-selective fading.
 {What statements are true regarding time-selective fading?

@@ Line 4: / Line 4: @@
 }}
-[[File:P_ID1931__Bei_A_4_2.png|right|frame|Path loss, frequency&ndash; and time&ndash;selective fading]]
+[[File:P_ID1931__Bei_A_4_2.png|right|frame|Path loss,&nbsp; frequency&ndash;selective and time&ndash;selective fading '''Korrektur''']]
 UMTS also has quite a few effects leading to degradation that must be taken into account during system planning:
-*${\rm Interference}$:&nbsp; Since all users are simultaneously served in the same frequency band, each user is interfered by other users.
+*${\rm Interference}$:&nbsp; Since all users are simultaneously served in the same frequency band,&nbsp; each user is interfered by other users.
-*${\rm Path\:loss}$:&nbsp; The received power&nbsp; $P_{\rm E}$&nbsp; of a radio signal decreases with distance&nbsp; $d$&nbsp; by a factor&nbsp; $d^{- \gamma}$&nbsp;.
-*${\rm Multipath\:reception}$:&nbsp; The signal reaches the mobile receiver not only through the direct path, but through several paths &ndash; differently attenuated and differently delayed.
+*${\rm Path\:loss}$:&nbsp; The received power&nbsp; $P_{\rm E}$&nbsp; of a radio signal decreases with distance &nbsp; $d$ &nbsp; by a factor&nbsp; $d^{- \gamma}$.
-*${\rm Doppler\:effect}$:&nbsp; If transmitter and/or receiver move, frequency shifts can occur depending on direction (Which angle? Towards each other? Away from each other?) and speed.

@@ Line 42: / Line 42: @@
 <quiz display=simple>
-{Berechnen Sie – ausgehend von der oberen Grafik auf der Angabenseite – den Pfadverlust&nbsp; $($in&nbsp; $\rm dB)$&nbsp; für&nbsp; $d =   \rm 5 \ km$.
+{Calculate - starting from the top graph on the information page - the path loss&nbsp; $($in&nbsp; $\rm dB)$&nbsp; for&nbsp; $d = \rm 5 \ km$.
 |type="{}"}
-${\rm Pfadverlust} \ = \ $ { 118 3% } $\ \rm dB $
+${\rm path loss} \ = \ $ { 118 3% } $\ \rm dB $.
-{Welche Aussagen gelten bezüglich des frequenzselektiven Fadings?
+{What statements are true regarding frequency selective fading?
 |type="[]"}
-+ Dieses entsteht durch Mehrwegeempfang.
++ This is caused by multipath reception.
-- Es entsteht durch Bewegung von Sender und/oder Empfänger.
+- It is caused by movement of transmitter and/or receiver.
-+ Verschiedene Frequenzen werden unterschiedlich gedämpft.
++ Different frequencies are attenuated differently.
-+ Ein Echo im Abstand&nbsp; $1\ \rm &micro; s$&nbsp; führt zu frequenzselektivem Fading.
++ An echo at a distance&nbsp; $1\ \rm &micro; s$&nbsp; results in frequency selective fading.
-{Welche Aussagen gelten bezüglich des zeitselektiven Fadings?
+{What statements are true regarding time-selective fading?
 |type="[]"}
-- Dieses entsteht durch Mehrwegeempfang.
+- This arises due to multipath reception.
-+ Es entsteht durch Bewegung von Sender und/oder Empfänger.
++ It results from movement of transmitter and/or receiver.
-- Verschiedene Frequenzen werden unterschiedlich gedämpft.
+- Different frequencies are attenuated differently.
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Entsprechend der Skizze liegt der Breakpoint bei $d_{0} = 100 \ \rm m$.
+'''(1)'''&nbsp; According to the sketch, the breakpoint is at $d_{0} = 100 \ \rm m$.
-*Für $d ≤ d_{0}$ ist der Pfadverlust gleich $\alpha_{0} \cdot (d/d_{0})^{–2}$. Für $d = d_{0} = 100 \ \rm m$ gilt:
+*For $d ≤ d_{0}$, the path loss is equal to $\alpha_{0} \cdot (d/d_{0})^{-2}$. For $d = d_{0} = 100 \ \rm m$ holds:
-:$${\rm Pfadverlust} = \alpha_0 = 10^{-5}\hspace{0.5cm}\Rightarrow\hspace{0.5cm}{50\,{\rm dB}}.$$
+:$${\rm path loss} = \alpha_0 = 10^{-5}\hspace{0.5cm}\Rightarrow\hspace{0.5cm}{50\,{\rm dB}}.$$
-*Oberhalb von $d_{0}$ ist der Pfadverlust gleich  $\alpha_{0} \cdot (d/d_{0})^{–4}$. Somit erhält man in $5 \ \rm km$ Entfernung:
+*Above $d_{0}$, the path loss is equal to $\alpha_{0} \cdot (d/d_{0})^{-4}$. Thus, at $5 \ \rm km$ distance, one obtains:
-:$${\rm Pfadverlust} = 10^{-5}\cdot 50^{-4} = 1.6 \cdot 10^{-12}\hspace{0.5cm}\Rightarrow\hspace{0.5cm}\underline{118\,{\rm dB}}.$$
+:$${\rm path loss} = 10^{-5}\cdot 50^{-4} = 1.6 \cdot 10^{-12}\hspace{0.5cm}\rightarrow\hspace{0.5cm}\underline{118\,{\rm dB}}.$$
-'''(2)'''&nbsp; Richtig sind die <u>Aussagen 1, 3 und 4</u>:
+'''(2)'''&nbsp; Correct <u>statements 1, 3, and 4</u>:
-*Das frequenzselektive Fading ist auf Mehrwegeempfang zurückzuführen. Das bedeutet:
+*Frequency selective fading is due to multipath reception. This means:
-*Unterschiedliche Frequenzanteile werden durch den Kanal unterschiedlich verzögert und gedämpft.
+*Different frequency components are delayed and attenuated differently by the channel.
-*Dadurch entstehen  Dämpfungs– und Phasenverzerrungen.
+*This results in attenuation and phase distortion.
-*Wegen $\tau_{\rm max} = 1 \ \rm &micro; s$ (vereinfachend wird $\tau_{\rm min} = 0$ gesetzt) ergibt sich weiter
+*Because $\tau_{\rm max} = 1 \ \rm &micro; s$ (simplifying $\tau_{\rm min} = 0$ is set) further results in
-:$$B_{\rm K} = \frac{1}{\tau_{\rm max}- \tau_{\rm min}} = 1\,{\rm MHz}\  \ll \ B_{\rm S} \hspace{0.15cm}\underline {= 5\,{\rm MHz}}.$$
+:$$B_{\rm K} = \frac{1}{\tau_{\rm max}- \tau_{\rm min}} = 1\,{\rm MHz}\ \ll \ B_{\rm S} \hspace{0.15cm}\underline {= 5\,{\rm MHz}}.$$
-'''(3)'''&nbsp; Richtig ist die <u>Aussage 2</u>.
+'''(3)'''&nbsp; Correct is <u>statement 2</u>.
-*Die Aussagen 1 und 3 gelten dagegen für frequenzselektives Fading &ndash; siehe Teilaufgabe '''(2)'''.
+*Statements 1 and 3, on the other hand, are valid for frequency-selective fading &ndash; see subtask '''(2)'''.

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Beispiele von Nachrichtensystemen/Allgemeine Beschreibung von UMTS
+{{quiz-Header|Buchseite=Examples_of_Communication_Systems/General_Description_of_UMTS
 }}
-[[File:P_ID1931__Bei_A_4_2.png|right|frame|Pfadverlust, frequenz&ndash; und zeitselektives Fading]]
+[[File:P_ID1931__Bei_A_4_2.png|right|frame|Path loss, frequency&ndash; and time&ndash;selective fading]]
-Auch bei UMTS gibt es etliche zu Degradationen führende Effekte, die man bereits bei der Systemplanung berücksichtigen muss:
+UMTS also has quite a few effects leading to degradation that must be taken into account during system planning:
-*${\rm Interferenzen}$:&nbsp; Da alle Nutzer gleichzeitig im gleichen Frequenzband versorgt werden, wird jeder Nutzer durch andere Nutzer gestört.
+*${\rm Interference}$:&nbsp; Since all users are simultaneously served in the same frequency band, each user is interfered by other users.
-*${\rm Pfadverlust}$:&nbsp; Die Empfangsleistung&nbsp; $P_{\rm E}$&nbsp; eines Funksignals nimmt mit der Entfernung&nbsp; $d$&nbsp; um den Faktor&nbsp; $d^{- \gamma}$&nbsp; ab.
+*${\rm Path\:loss}$:&nbsp; The received power&nbsp; $P_{\rm E}$&nbsp; of a radio signal decreases with distance&nbsp; $d$&nbsp; by a factor&nbsp; $d^{- \gamma}$&nbsp;.
-*${\rm Mehrwegeempfang}$:&nbsp; Das Signal erreicht den mobilen Empfänger nicht nur über den direkten Pfad, sondern auf mehreren Wegen &ndash; unterschiedlich gedämpft und verschieden verzögert.
+*${\rm Multipath\:reception}$:&nbsp; The signal reaches the mobile receiver not only through the direct path, but through several paths &ndash; differently attenuated and differently delayed.
-*${\rm Dopplereffekt}$:&nbsp; Bewegen sich Sender und/oder Empfänger, so kann es abhängig von Richtung (Welcher Winkel? Aufeinander zu? Voneinander weg?) und Geschwindigkeit zu Frequenzverschiebungen kommen.
+*${\rm Doppler\:effect}$:&nbsp; If transmitter and/or receiver move, frequency shifts can occur depending on direction (Which angle? Towards each other? Away from each other?) and speed.
-Im Buch&nbsp; [[Mobile Kommunikation]]&nbsp; wurden diese Effekte bereits im Detail behandelt. Die Diagramme vermitteln nur einige wenige Informationen bezüglich
+In the book&nbsp; "[[Mobile Communications]]"&nbsp; these effects have already been discussed in detail. The diagrams convey only a few pieces of information regarding
-*<u>Pfadverlust:</u>&nbsp; Der Pfadverlust gibt die Verminderung der Empfangsleistung mit der Entfernung&nbsp; $d$&nbsp; vom Sender an. Oberhalb des so genannten&nbsp; ''Break Points''&nbsp; gilt für die Empfangsleistung näherungsweise:
+*<u>Path loss:</u>&nbsp; Path loss indicates the decrease in received power with distance&nbsp; $d$&nbsp; from the transmitter. Above the so-called&nbsp; ''break point''&nbsp; applies approximately to the received power:
 :$$\frac{P(d)}{P(d_0)} = \alpha_0 \cdot \left ( {d}/{d_0}\right )^{-4}.$$
-:Nach der oberen Grafik gilt&nbsp; $\alpha_{0} = 10^{–5}$&nbsp; $($entsprechend&nbsp; $50 \ \rm dB)$&nbsp; und&nbsp; $d_{0} = 100 \ \rm m$.
+:According to the upper graph&nbsp; $\alpha_{0} = 10^{-5}$&nbsp; $($correspondingly&nbsp; $50 \ \rm dB)$&nbsp; and&nbsp; $d_{0} = 100 \ \rm m$.
-*<u>Frequenzselektives Fading:</u>&nbsp; Die Leistungsübertragungsfunktion&nbsp; $|H_{\rm K}(f)|^{2}$&nbsp; zu einem gegebenen Zeitpunkt gemäß der mittleren Grafik verdeutlicht frequenzselektives Fading. Die blau–gestrichelt eingezeichnete Horizontale kennzeichnet dagegen nichtfrequenzselektives Fading.
+*<u>Frequency-selective fading:</u>&nbsp; The power transfer function&nbsp; $|H_{\rm K}(f)|^{2}$&nbsp; at a given time according to the middle graph illustrates frequency-selective fading. The blue-dashed horizontal line, on the other hand, indicates non-frequency-selective fading.
-::Ein solches frequenzselektives Fading entsteht, wenn die Kohärenzbandbreite&nbsp; $B_{\rm K}$&nbsp; sehr viel kleiner als die Signalbandbreite&nbsp; $B_{\rm S}$&nbsp; ist. Dabei gilt mit der&nbsp; ''Mehrwegeverbreiterung''&nbsp; (englisch:&nbsp; ''Delay Spread''&nbsp;)&nbsp; $T_{\rm V}$ &nbsp; &rArr; &nbsp;  Differenz zwischen der maximalen und der minimalen Verzögerungszeit:
+::Such frequency-selective fading occurs when the coherence bandwidth&nbsp; $B_{\rm K}$&nbsp; is much smaller than the signal bandwidth&nbsp; $B_{\rm S}$&nbsp;. Here, with the&nbsp; ''delayspread''&nbsp; $T_{\rm V}$ &nbsp; &rArr; &nbsp; difference between the maximum and minimum delay times:
 :$$B_{\rm K}\approx \frac{1}{T_{\rm V}}= \frac{1}{\tau_{\rm max}- \tau_{\rm min}}.$$
-*<u>Zeitselektives Fading:</u>&nbsp; Die untere Grafik zeigt  die Leistungsübertragungsfunktion&nbsp; $|H_{\rm K}(t)|^{2}$&nbsp; für eine feste Frequenz&nbsp; $f_{0}$. Die Skizze ist "schematisch" zu verstehen, weil für das hier betrachtete zeitselektive Fading genau der gleiche Verlauf gewählt wurde wie in der mittleren Grafik für das frequenzselektive Fading (reine Bequemlichkeit des Autors).
+*<u>Time-selective fading:</u>&nbsp; The bottom graph shows the power transfer function&nbsp; $|H_{\rm K}(t)|^{2}$&nbsp; for a fixed frequency&nbsp; $f_{0}$. The sketch is to be understood "schematically", because for the time-selective fading considered here exactly the same course was chosen as in the middle diagram for the frequency-selective fading (pure convenience of the author).
-::Hier entsteht eine so genannte Dopplerverbreiterung&nbsp; $B_{\rm D}$, definiert als Differenz zwischen der maximalen und der minimalen Dopplerfrequenz. Der Kehrwert&nbsp; $T_{\rm D} = 1/B_{\rm D}$&nbsp; wird als&nbsp; ''Kohärenzzeit''&nbsp; oder auch als&nbsp; ''Korrelationsdauer''&nbsp; bezeichnet. Bei UMTS tritt immer dann zeitselektives Fading auf, wenn&nbsp; $T_{\rm D} \ll T_{\rm C}$&nbsp; (Chipdauer) ist.
+::Here a so-called Doppler spread&nbsp; $B_{\rm D}$ arises, defined as the difference between the maximum and the minimum Doppler frequency. The inverse&nbsp; $T_{\rm D} = 1/B_{\rm D}$&nbsp; is called&nbsp; ''coherence time''&nbsp; or also&nbsp; ''correlation duration''&nbsp;. In UMTS, time-selective fading occurs whenever&nbsp; $T_{\rm D} \ll T_{\rm C}$&nbsp; (chip duration) is.
@@ Line 29: / Line 29: @@
-''Hinweise:''
+Hints:
-*Die Aufgabe gehört zum Themengebiet von&nbsp; [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS|Allgemeine Beschreibung von UMTS]].
+*This exercise belongs to the subject area of&nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS|"General Description of UMTS"]].
-*Bezug genommen wird insbesondere auf die Seiten&nbsp; [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS#Eigenschaften_des_UMTS-Funkkanals|Eigenschaften des UMTS-Funkkanals]]&nbsp; sowie&nbsp; [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS#Frequenz.E2.80.93_und_zeitselektives_Fading|Frequenz&ndash; und zeitselektives Fading]].
+*Reference is made in particular to the pages&nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Properties_of_the_UMTS_radio_channel|"Properties of the UMTS radio channel"]]&nbsp; and&nbsp; [[Examples_of_Communication_Systems/General_Description_of_UMTS#Frequency. E2.80.93_and_time.E2.80.93selective_fading|"Frequency- and time-selective fading"]].
-*Bei UMTS beträgt die Bandbreite&nbsp;  $B_{\rm S} = 5 \ \rm MHz$&nbsp; und die Chipdauer ist&nbsp; $T_{\rm C} \approx 0.26 \  \rm &micro; s$.
+*For UMTS, the bandwidth is&nbsp; $B_{\rm S} = 5 \ \rm MHz$&nbsp; and the chip duration is&nbsp; $T_{\rm C} \approx 0.26 \ \rm &micro; s$.
-===Fragebogen===
+===Questions===
 <quiz display=simple>

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−	[[Category:Examples of Communication Systems: Exercises\|^4.1 ~~Allgemeine Beschreibung von~~ UMTS	+	[[Category:Examples of Communication Systems: Exercises\|^4.1 General Description of UMTS
	^]]		^]]

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