Aufgaben:Exercise 5.4Z: OVSF Codes - Revision history

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	[[Category:Modulation Methods: Exercises\|^5.3 Spread Sequences for CDMA^]]		[[Category:Modulation Methods: Exercises\|^5.3 Spread Sequences for CDMA^]]
	[[de:Aufgaben:5.~~4Z_OVSF–Codes~~]]		[[de:Aufgaben:Aufgabe 5.4Z: OVSF–Codes]]

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	Then the following condition must be satisfied:		Then the following condition must be satisfied:
	:$$K_4 \cdot \frac{32}{4} + K_8 \cdot \frac{32}{8} +K_{16} \cdot \frac{32}{16} +K_{32} \cdot \frac{32}{32} \le 32 \hspace{0.3cm}		:$$K_4 \cdot \frac{32}{4} + K_8 \cdot \frac{32}{8} +K_{16} \cdot \frac{32}{16} +K_{32} \cdot \frac{32}{32} \le 32 \hspace{0.3cm}\Rightarrow \hspace{0.3cm} K_4 \cdot8 + K_8 \cdot 4 +K_{16} \cdot 2 +K_{32} \cdot1 \le 32 \hspace{0.05cm}.$$
	\Rightarrow \hspace{0.3cm} K_4 \cdot8 + K_8 \cdot 4 +K_{16} \cdot 2 +K_{32} \cdot1 \le 32 \hspace{0.05cm}.$$

	*Because of  $2 · 8 + 1 · 4 + 2 · 2 + 8 = 32$,  the desired occupancy is just allowed   ⇒   <u>answer YES</u>.		*Because of  $2 · 8 + 1 · 4 + 2 · 2 + 8 = 32$,  the desired occupancy is just allowed   ⇒   <u>answer YES</u>.

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	[[Category:Modulation Methods: Exercises\|^5.3 Spread Sequences for CDMA^]]		[[Category:Modulation Methods: Exercises\|^5.3 Spread Sequences for CDMA^]]
			[[de:Aufgaben:5.4Z_OVSF–Codes]]

Hwang at 16:13, 1 November 2022

2022-11-01T16:13:58Z

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	{Construct the tree diagram for  $J = 8$.  What are the resulting OVSF codes?		{Construct the tree diagram for  $J = 8$.  What are the resulting OVSF codes?
	\|type="[]"}		\|type="[]"}
	+ '''~~Codeword~~ 1:'''   $ \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:'''   $ \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:'''   $ \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:'''   $ \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:'''   $ \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:'''   $ \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:'''   $ \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:'''   $ \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}$.

Guenter at 15:23, 13 December 2021

2021-12-13T15:23:36Z

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	'''(3)'''  When three subscribers are served by  $J = 4$  only two subscribers can still be served by a spreading sequence with  $J = 8$  (see exemplary yellow background in the diagram ~~above~~)   ⇒   $K\hspace{0.15cm}\underline{ = 5}$.		'''(3)'''  When three subscribers are served by  $J = 4$ <br>  ⇒   only two subscribers can still be served by a spreading sequence with  $J = 8$  (see exemplary yellow background in the diagram)   ⇒   $K\hspace{0.15cm}\underline{ = 5}$.


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	*Because of  $2 · 8 + 1 · 4 + 2 · 2 + 8 = 32$,  the desired occupancy is just allowed   ⇒   <u>answer YES</u>.		*Because of  $2 · 8 + 1 · 4 + 2 · 2 + 8 = 32$,  the desired occupancy is just allowed   ⇒   <u>answer YES</u>.
	*For example, supplying the spreading factor  $J = 4$  twice blocks the upper half of the tree.		*For example,  supplying the spreading factor  $J = 4$  twice blocks the upper half of the tree.
	*After providing one spreading  $J = 8$, three of the eight branches remain to be occupied on the  $J = 8$ level, and so on.		*After providing one spreading  $J = 8$,  three of the eight branches remain to be occupied on the  $J = 8$  level, and so on.

	{{ML-Fuß}}		{{ML-Fuß}}

Guenter at 15:18, 13 December 2021

2021-12-13T15:18:53Z

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

Guenter at 15:16, 13 December 2021

2021-12-13T15:16:24Z

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

Guenter at 15:13, 13 December 2021

2021-12-13T15:13:26Z

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	}}		}}

	[[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]]
	of an OVSF code]]
	The spreading codes for  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|UMTS]]  should		The spreading codes for  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|UMTS]]  should
	* all be orthogonal to each other in order to avoid mutual interference between subscribers,		* all be orthogonal to each other in order to avoid mutual interference between subscribers,
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	One example of this is the so-called  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|Orthogonal Variable Spreading Factor ~~codes~~]],  which provide spreading codes with lengths from  $J = 4$  to  $J = 512$.		One example of this is the so-called  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|"Orthogonal Variable Spreading Factor" code]],  which provide spreading codes with lengths from  $J = 4$  to  $J = 512$.

	These can be created using a code tree, as shown in the diagram.  In this process, two new codes  $+C \ +C$  and  $+C \ -C$ are created from a code $C$  at each branching.		These can be created using a code tree,  as shown in the diagram.  In this process,  two new codes  $(+C \ +C)$  and  $(+C \ -C)$  are created from a code  $C$  at each branching.

	The diagram illustrates the principle given here with the example  $J = 4$:		The diagram illustrates the principle given here with the example  $J = 4$:
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	:$$\langle c_\nu^{(0)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(1)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$$		:$$\langle c_\nu^{(0)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(1)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$$
	:$$\langle c_\nu^{(2)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(3)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm}.$$		:$$\langle c_\nu^{(2)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},\hspace{0.3cm} \langle c_\nu^{(3)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm}.$$
	*According to this nomenclature, for the spreading factor  $J = 8$  there are the spreading sequences  $\langle c_\nu^{(0)}\rangle $, ... , $\langle c_\nu^{(7)}\rangle $.		*According to this nomenclature,  for the spreading factor  $J = 8$  there are the spreading sequences  $\langle c_\nu^{(0)}\rangle $,  ... ,  $\langle c_\nu^{(7)}\rangle $.

	*Note that no predecessor and successor of a code may be used for another participant.		*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  $J = 4$  could be used or the three codes highlighted in yellow – once with  $J = 2$  and twice with  $J = 4$.		*So,  in the example,  four spreading codes with spreading factor  $J = 4$  could be used or the three codes highlighted in yellow – once with  $J = 2$  and twice with  $J = 4$.





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	''Notes:''		Notes:
	*The exercise belongs to the chapter  [[Modulation_Methods/Spreizfolgen_für_CDMA\|Spreading Sequences for CDMA]].		*The exercise belongs to the chapter  [[Modulation_Methods/Spreizfolgen_für_CDMA\|Spreading Sequences for CDMA]].
	*Reference is made in particular to the section  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|Codes with variable spreading factor (OVSF codes)]]  in the theory part.		*Reference is made in particular to the section  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|Codes with variable spreading factor (OVSF codes)]]  in the theory part.
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	$K \ = \ $ { 5 }		$K \ = \ $ { 5 }

	{Assume a tree structure for  $J = 32$.   Is the following assignment feasible:<br>Twice  $J = 4$, once  $J = 8$, twice  $J = 16$  and eight times  $J = 32$?		{Assume a tree structure for  $J = 32$.   Is the following assignment feasible:<br>Twice  $J = 4$,  once  $J = 8$,  twice  $J = 16$  and eight times  $J = 32$?
	\|type="()"}		\|type="()"}
	+ Yes.		+ Yes.

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

← Older revision		Revision as of 12:26, 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 17:16, 13 December 2021
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	*The exercise belongs to the chapter  [[Modulation_Methods/Spreizfolgen_für_CDMA\|Spreading Sequences for CDMA]].		*The exercise belongs to the chapter  [[Modulation_Methods/Spreizfolgen_für_CDMA\|Spreading Sequences for CDMA]].
	*Reference is made in particular to the section  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|Codes with variable spreading factor (OVSF codes)]]  in the theory part.		*Reference is made in particular to the section  [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29\|Codes with variable spreading factor (OVSF codes)]]  in the theory part.
	* We would also like to draw your attention to the ~~interaction~~ module  [[Applets:OVSF-Codes_(Applet)\|OVSF]].		* We would also like to draw your attention to the  (German language)  interactive SWF module  [[Applets:OVSF-Codes_(Applet)\|OVSF]].