Aufgaben:Exercise 5.4Z: OVSF Codes - Revision history

Hwang at 16:13, 1 November 2022

2022-11-01T16:13:58Z

Guenter at 15:23, 13 December 2021

2021-12-13T15:23:36Z

Guenter at 15:18, 13 December 2021

2021-12-13T15:18:53Z

Guenter at 15:16, 13 December 2021

2021-12-13T15:16:24Z

Guenter at 15:13, 13 December 2021

2021-12-13T15:13:26Z

Hwang at 14:52, 10 December 2021

2021-12-10T14:52:16Z

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Guenter at 10:26, 1 December 2021

2021-12-01T10:26:49Z

Guenter: Guenter moved page Aufgaben:Aufgabe 5.4Z: OVSF–Codes to Aufgaben:Exercise 5.4Z: OVSF Codes

2021-12-01T10:23:41Z

Guenter moved page Aufgabe 5.4Z: OVSF–Codes to Exercise 5.4Z: OVSF Codes

Guenter at 16:54, 26 November 2021

2021-11-26T16:54:31Z

Javier: Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

2021-03-23T12:50:31Z

Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

@@ Line 38: / Line 38: @@
 {Construct the tree diagram for &nbsp;$J = 8$.&nbsp; What are the resulting OVSF codes?
 |type="[]"}
-+ '''Codeword 1:''' &nbsp; $ \langle c_\nu^{(1)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$
++ '''Code word 1:''' &nbsp; $ \langle c_\nu^{(1)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$
-- '''Codeword 3:''' &nbsp; $ \langle c_\nu^{(3)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1}$ ,
+- '''Code word 3:''' &nbsp; $ \langle c_\nu^{(3)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1}$ ,
-+ '''Codeword 5:''' &nbsp; $ \langle c_\nu^{(5)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm}$,
++ '''Code word 5:''' &nbsp; $ \langle c_\nu^{(5)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm}$,
-+ '''Codeword 7:''' &nbsp; $ \langle c_\nu^{(7)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm}$.
++ '''Code word 7:''' &nbsp; $ \langle c_\nu^{(7)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm}{+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm}$.

@@ Line 69: / Line 69: @@
-'''(3)'''&nbsp; When three subscribers are served by&nbsp; $J = 4$&nbsp; only two subscribers can still be served by a spreading sequence with&nbsp; $J = 8$&nbsp; (see exemplary yellow background in the diagram above) &nbsp; ⇒ &nbsp; $K\hspace{0.15cm}\underline{ = 5}$.
+'''(3)'''&nbsp; When three subscribers are served by&nbsp; $J = 4$ <br>&nbsp; &rArr; &nbsp; only two subscribers can still be served by a spreading sequence with&nbsp; $J = 8$&nbsp; (see exemplary yellow background in the diagram) &nbsp; ⇒ &nbsp; $K\hspace{0.15cm}\underline{ = 5}$.
@@ Line 85: / Line 85: @@
 *Because of &nbsp;$2 · 8 + 1 · 4 + 2 · 2 + 8 = 32$,&nbsp; the desired occupancy is just allowed &nbsp; ⇒ &nbsp; <u>answer YES</u>.
-*For example, supplying the spreading factor &nbsp;$J = 4$&nbsp; twice blocks the upper half of the tree.
+*For example,&nbsp; supplying the spreading factor &nbsp;$J = 4$&nbsp; twice blocks the upper half of the tree.
-*After providing one spreading &nbsp;$J = 8$, three of the eight branches remain to be occupied on the &nbsp;$J = 8$ level, and so on.
+*After providing one spreading &nbsp;$J = 8$,&nbsp; three of the eight branches remain to be occupied on the&nbsp; $J = 8$&nbsp; level, and so on.
 {{ML-Fuß}}

@@ Line 60: / Line 60: @@
 ===Solution===
 {{ML-Kopf}}
-[[File:P_ID1892__Mod_Z_5_4a.png|right|frame|OVSF Tree Structure for &nbsp;$J = 8$]]
+[[File:P_ID1892__Mod_Z_5_4a.png|right|frame|OVSF tree structure for &nbsp;$J = 8$]]
-'''(1)'''&nbsp; The diagram shows the OVSF tree structure for &nbsp;$J = 8$ users.&nbsp; From this it can be seen that <u> solutions 1, 3 and 4</u> apply, but not the second one.
+'''(1)'''&nbsp; The diagram shows the OVSF tree structure for &nbsp;$J = 8$ users.&nbsp; From this it can be seen that&nbsp; <u>solutions 1, 3 and 4</u>&nbsp; apply,&nbsp; but not the second one.

@@ Line 29: / Line 29: @@
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Spreizfolgen_für_CDMA|Spreading Sequences for CDMA]].
 *Reference is made in particular to the section&nbsp; [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29|Codes with variable spreading factor (OVSF codes)]]&nbsp; in the theory part.
-* We would also like to draw your attention to the interaction module &nbsp;[[Applets:OVSF-Codes_(Applet)|OVSF]].&nbsp;
+* We would also like to draw your attention to the&nbsp; (German language)&nbsp; interactive SWF module &nbsp;[[Applets:OVSF-Codes_(Applet)|OVSF]].&nbsp;

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Mod_Z_5_4.png|right|frame|Tree structure for the construction
+[[File:EN_Mod_Z_5_4.png|right|frame|Construction of an OVSF code]]
 The spreading codes for &nbsp;[[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS|UMTS]]&nbsp; should
 * all be orthogonal to each other in order to avoid mutual interference between subscribers,
@@ Line 10: / Line 9: @@
-One example of this is the so-called &nbsp;[[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29|Orthogonal Variable Spreading Factor codes]],&nbsp; which provide spreading codes with lengths from &nbsp;$J = 4$&nbsp; to &nbsp;$J = 512$.&nbsp;
+One example of this is the so-called &nbsp;[[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29|"Orthogonal Variable Spreading Factor" code]],&nbsp; which provide spreading codes with lengths from &nbsp;$J = 4$&nbsp; to &nbsp;$J = 512$.&nbsp;
-These can be created using a code tree, as shown in the diagram.&nbsp; In this process, two new codes &nbsp;$+C \ +C$&nbsp; and &nbsp;$+C \ -C$ are created from a code&nbsp;$C$&nbsp; at each branching.
+These can be created using a code tree,&nbsp; as shown in the diagram.&nbsp; In this process,&nbsp; two new codes &nbsp;$(+C \ +C)$&nbsp; and &nbsp;$(+C \ -C)$&nbsp; are created from a code&nbsp; $C$&nbsp; at each branching.
 The diagram illustrates the principle given here with the example &nbsp;$J = 4$:&nbsp;
@@ Line 18: / Line 17: @@
 :$$\langle c_\nu^{(0)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(1)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$$
 :$$\langle c_\nu^{(2)}\rangle  =  {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(3)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm}.$$
-*According to this nomenclature, for the spreading factor &nbsp;$J = 8$&nbsp; there are the spreading sequences &nbsp;$\langle c_\nu^{(0)}\rangle $, ... , $\langle c_\nu^{(7)}\rangle $.
+*According to this nomenclature,&nbsp; for the spreading factor &nbsp;$J = 8$&nbsp; there are the spreading sequences &nbsp;$\langle c_\nu^{(0)}\rangle $,&nbsp; ... ,&nbsp; $\langle c_\nu^{(7)}\rangle $.
 *Note that no predecessor and successor of a code may be used for another participant.
-*So, in the example, four spreading codes with spreading factor &nbsp;$J = 4$&nbsp; could be used or the three codes highlighted in yellow – once with &nbsp;$J = 2$&nbsp; and twice with &nbsp;$J = 4$.
+*So,&nbsp; in the example,&nbsp; four spreading codes with spreading factor &nbsp;$J = 4$&nbsp; could be used or the three codes highlighted in yellow – once with &nbsp;$J = 2$&nbsp; and twice with &nbsp;$J = 4$.
@@ Line 31: / Line 26: @@
-''Notes:''
+Notes:
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Spreizfolgen_für_CDMA|Spreading Sequences for CDMA]].
 *Reference is made in particular to the section&nbsp; [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29|Codes with variable spreading factor (OVSF codes)]]&nbsp; in the theory part.
@@ Line 57: / Line 52: @@
 $K \ = \ $ { 5 }
-{Assume a tree structure for &nbsp;$J = 32$.&nbsp;&nbsp;  Is the following assignment feasible:<br>Twice &nbsp;$J = 4$, once &nbsp;$J = 8$, twice &nbsp;$J = 16$&nbsp; and eight times &nbsp;$J = 32$?
+{Assume a tree structure for &nbsp;$J = 32$.&nbsp;&nbsp;  Is the following assignment feasible:<br>Twice &nbsp;$J = 4$,&nbsp; once &nbsp;$J = 8$,&nbsp; twice &nbsp;$J = 16$&nbsp; and eight times &nbsp;$J = 32$?
 |type="()"}
 + Yes.

← Older revision		Revision as of 10:26, 1 December 2021
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−	[[Category:Modulation Methods: Exercises\|^5.3 ~~Spreizfolgen für~~ CDMA^]]	+	[[Category:Modulation Methods: Exercises\|^5.3 Spread Sequences for CDMA^]]

← Older revision	Revision as of 10:23, 1 December 2021
(No difference)

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1891__Mod_Z_5_4.png|right|frame|Baumstruktur zur Konstruktion <br>eines OVSF–Codes]]
+[[File:EN_Mod_Z_5_4.png|right|frame|Baumstruktur zur Konstruktion <br>eines OVSF–Codes]]
 Die Spreizcodes für &nbsp;[[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS|UMTS]]&nbsp; sollen
 * alle zueinander orthogonal sein, um eine gegenseitige Beeinflussung der Teilnehmer zu vermeiden,

← Older revision		Revision as of 12:50, 23 March 2021
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−	[[Category:~~Aufgaben zu Modulationsverfahren~~\|^5.3 Spreizfolgen für CDMA^]]	+	[[Category:Modulation Methods: Exercises\|^5.3 Spreizfolgen für CDMA^]]