Aufgaben:Exercise 3.8: OVSF Codes - Revision history

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

2021-03-23T12:37:53Z

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

Guenter at 09:59, 25 February 2021

2021-02-25T09:59:38Z

Guenter at 15:08, 25 January 2021

2021-01-25T15:08:20Z

Guenter at 14:52, 25 January 2021

2021-01-25T14:52:22Z

Guenter at 14:49, 25 January 2021

2021-01-25T14:49:00Z

Guenter at 14:42, 25 January 2021

2021-01-25T14:42:40Z

Guenter at 14:42, 25 January 2021

2021-01-25T14:42:02Z

Javier: Text replacement - "===Sample solution===" to "===Solution==="

2020-12-16T13:16:09Z

Text replacement - "===Sample solution===" to "===Solution==="

Javier: Text replacement - "Mobile Kommunikation/Die Charakteristika von UMTS" to "Mobile_Communications/Characteristics_of_UMTS"

2020-12-15T14:04:21Z

Text replacement - "Mobile Kommunikation/Die Charakteristika von UMTS" to "Mobile_Communications/Characteristics_of_UMTS"

Oezdemir: /* Musterlösung */

2020-07-10T10:10:46Z

Musterlösung

← Older revision		Revision as of 12:37, 23 March 2021
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−	[[Category:~~Exercises for~~ Mobile Communications\|^3.4 Characteristics of UMTS^]]	+	[[Category:Mobile Communications: Exercises\|^3.4 Characteristics of UMTS^]]

@@ Line 6: / Line 6: @@
 The spreading codes for UMTS should
 *be orthogonal, in order to avoid mutual influence of the participants,
-*at the same time also allow a flexible realization of different spreading factors&nbsp; $J$&nbsp;.
+*at the same time also allow a flexible realization of different spreading factors&nbsp; $J$.
-An example are the&nbsp; "Orthogonal Variable Spreading Factor Codes"&nbsp; $\rm (OVSF)$, which provide the spreading codes of lengths from&nbsp; $J = 4$&nbsp; to&nbsp; $J = 512$&nbsp;.
+An example are the&nbsp; "Orthogonal Variable Spreading Factor Codes"&nbsp; $\rm (OVSF)$, which provide the spreading codes of lengths from&nbsp; $J = 4$&nbsp; to&nbsp; $J = 512$.
-As shown in the graphic, these can be created with the help of a code tree.&nbsp; In doing so, each branching from a code &nbsp; $\mathcal{C}$&nbsp;results in two new codes &nbsp; $(+\mathcal{C}\  +\mathcal{C})$&nbsp; and&nbsp; $(+\mathcal{C} \ –\mathcal{C})$.
+As shown in the graphic, these can be created with the help of a code tree.&nbsp; In doing so, each branching from a code&nbsp; $\mathcal{C}$&nbsp;results in two new codes&nbsp; $(+\mathcal{C}\  +\mathcal{C})$&nbsp; and&nbsp; $(+\mathcal{C} \ –\mathcal{C})$.
 The diagram illustrates the principle given here using the following example&nbsp; $J = 4$.&nbsp; If you number the spreading sequences from&nbsp; $0$&nbsp; to&nbsp; $J -1$, the spreading sequences result
@@ Line 22: / Line 22: @@
 It should be noted that no predecessor or successor of a code may be used by other participants.
-*In the example, four spreading codes with spreading factor&nbsp; $J = 4$&nbsp; could be used, or
+*In the example, four spreading codes with spreading factor $J = 4$&nbsp; could be used, or
-*the three codes highlighted in yellow &ndash; once with&nbsp; $J = 2$&nbsp; and twice with &nbsp; $J = 4$.
+*the three codes highlighted in yellow &ndash; once with $J = 2$&nbsp; and twice with  $J = 4$.
@@ Line 56: / Line 56: @@
 $K \ = \ $ { 5 }
-{The tree structure applies to&nbsp; $J = 32$. &nbsp;Is the following assignment feasible: &nbsp; <br> &nbsp; &nbsp;Twice &nbsp; $J = 4$, once&nbsp; $J = 8$, once&nbsp; $J = 164$&nbsp; and eight times&nbsp; $J = 32$?
+{The tree structure applies to&nbsp; $J = 32$. &nbsp;Is the following assignment feasible: &nbsp;  Twice &nbsp; $J = 4$, once&nbsp; $J = 8$, once&nbsp; $J = 164$&nbsp; and eight times&nbsp; $J = 32$?
 |type="()"}
 + Yes.
@@ Line 66: / Line 66: @@
 {{ML-Kopf}}
-[[File:P_ID2263__Bei_A_4_6a.png|right|frame|OVSF tree structure for&nbsp; $J = 8$]]
+[[File:P_ID2263__Bei_A_4_6a.png|right|frame|OVSF tree structure for $J = 8$]]
 '''(1)'''&nbsp; The following graphic shows the OVSF tree structure for&nbsp; $J = $8&nbsp; users.

@@ Line 66: / Line 66: @@
 {{ML-Kopf}}
-[[File:P_ID2263__Bei_A_4_6a.png|right|frame|OVSF tree structure for $J = 8$]]
+[[File:P_ID2263__Bei_A_4_6a.png|right|frame|OVSF tree structure for&nbsp; $J = 8$]]
-'''(1)'''&nbsp; The following graphic shows the OVSF tree structure for $J = $8 users.
+'''(1)'''&nbsp; The following graphic shows the OVSF tree structure for&nbsp; $J = $8&nbsp; users.
 *From this it can be seen that the <u>solutions 1, 3 and 4</u> apply, but not the second.
 '''(4)'''&nbsp;  We denote
-*$K_{4} = 2$ as the number of spreading sequences with $J = 4$,
+*$K_{4} = 2$&nbsp; as the number of spreading sequences with&nbsp; $J = 4$,
-*$K_{8} = 1$ as the number of spreading sequences with $J = 8$,
+*$K_{8} = 1$&nbsp; as the number of spreading sequences with&nbsp; $J = 8$,
-*$K_{16} = 2$ as the number of spreading sequences with $J = 16$,
+*$K_{16} = 2$&nbsp; as the number of spreading sequences with&nbsp; $J = 16$,
-*$K_{32} = 8$ as the number of spreading sequences with $J = 32$,
+*$K_{32} = 8$&nbsp; as the number of spreading sequences with&nbsp; $J = 32$,
@@ Line 88: / Line 91: @@
 :$$K_4 \cdot \frac{32}{4} + K_8 \cdot \frac{32}{8} +K_{16} \cdot \frac{32}{16} +K_{32} \cdot \frac{32}{32} \le 32\hspace{0.3cm}
 \Rightarrow \hspace{0.3cm} K_4 \cdot8 + K_8 \cdot 4 +K_{16} \cdot 2 +K_{32} \cdot1 \le 32 \hspace{0.05cm}.$$
-*Because $2 \cdot 8 + 1 \cdot 4 + 2 \cdot 2 + 8 = 32$ the desired assignment is just allowed  &nbsp; &rArr; &nbsp;  <u>The answer is YES</u>.
+*Because&nbsp; $2 \cdot 8 + 1 \cdot 4 + 2 \cdot 2 + 8 = 32$&nbsp; the desired assignment is just allowed  &nbsp; &rArr; &nbsp;  <u>The answer is YES</u>.
-*For example, providing the $J = 4$ twice blocks the upper half of the tree, after providing a $J = 8$ spreading code, $3$ of the $8$ branches remain to be occupied at the $J = 8$ level, and so on and so forth.
+*For example, providing the&nbsp; $J = 4$&nbsp; twice blocks the upper half of the tree, after providing a&nbsp; $J = 8$&nbsp; spreading code,&nbsp; $3$&nbsp; of the&nbsp; $8$&nbsp; branches remain to be occupied at the&nbsp; $J = 8$&nbsp; level, and so on and so forth.
 {{ML-Fuß}}

@@ Line 41: / Line 41: @@
 <quiz display=simple>
-{Construct the tree diagram for&nbsp; $J = 8$. What are the resulting OVSF codes?
+{Construct the tree diagram for&nbsp; $J = 8$.&nbsp; What are the resulting OVSF codes?
 |type="[]"}
 + $\langle c_\nu^{(1)}\rangle = +\hspace{-0.05cm}1 \ +\hspace{-0.08cm}1 \ +\hspace{-0.08cm}1 \ +\hspace{-0.08cm}1 \ -\hspace{-0.08cm}1 \ -\hspace{-0.08cm}1 \ -\hspace{-0.08cm}1 \ -\hspace{-0.08cm}1$,
@@ Line 56: / Line 56: @@
 $K \ = \ $ { 5 }
-{The tree structure applies to&nbsp; $J = 32$. &nbsp;Is the following assignment feasible: &nbsp; <br>twice &nbsp; $J = 4$, once&nbsp; $J = 8$, once&nbsp; $J = 164$&nbsp; and eight times&nbsp; $J = 32$?
+{The tree structure applies to&nbsp; $J = 32$. &nbsp;Is the following assignment feasible: &nbsp; <br> &nbsp; &nbsp;Twice &nbsp; $J = 4$, once&nbsp; $J = 8$, once&nbsp; $J = 164$&nbsp; and eight times&nbsp; $J = 32$?
 |type="()"}
 + Yes.

@@ Line 32: / Line 32: @@
 ''Notes:''
-*This task belongs to the chapter&nbsp; [[Modulation_Methods/Spreizfolgen_für_CDMA|Spreading Sequences for CDMA]].
+*This task belongs to the chapter&nbsp; [[Modulation_Methods/Spreizfolgen_für_CDMA|Spreading sequences for CDMA]].
-*Particular reference is made to the page&nbsp; [[Modulation_Methods/Spreizfolgen_für_CDMA#Codes_mit_variablem_Spreizfaktor_.28OVSF.E2.80.93Code.29|Codes mit variablem Spreizfaktor (OVSF–Code)]].
+*Particular reference is made to the page&nbsp; [[Modulation_Methods/Spreading_Sequences_for_CDMA#Codes_with_variable_spreading_factor_.28OVSF_codes.29|Codes with variable spreading factor]].

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Mob_A_3_9.png|right|frame|Tree diagram to construct <br>a OVSF–Code]]
+[[File:EN_Mob_A_3_9.png|right|frame|Tree diagram to construct <br>an OVSF–Code]]
 The spreading codes for UMTS should
 *be orthogonal, in order to avoid mutual influence of the participants,
@@ Line 9: / Line 9: @@
-An example are the&nbsp;''orthogonal Variable Spreading Factor''&nbsp;(OVSF),which provide the spreading codes of lengths from&nbsp; $J = 4$&nbsp; to&nbsp; $J = 512$&nbsp;.
+An example are the&nbsp; "Orthogonal Variable Spreading Factor Codes"&nbsp; $\rm (OVSF)$, which provide the spreading codes of lengths from&nbsp; $J = 4$&nbsp; to&nbsp; $J = 512$&nbsp;.
-As shown in the graphic, these can be created with the help of a code tree. In doing so, each branching from a code &nbsp; $\mathcal{C}$&nbsp;results in two new codes &nbsp; $(+\mathcal{C}\  +\mathcal{C})$&nbsp; and&nbsp; $(+\mathcal{C} \ –\mathcal{C})$.
+As shown in the graphic, these can be created with the help of a code tree.&nbsp; In doing so, each branching from a code &nbsp; $\mathcal{C}$&nbsp;results in two new codes &nbsp; $(+\mathcal{C}\  +\mathcal{C})$&nbsp; and&nbsp; $(+\mathcal{C} \ –\mathcal{C})$.
-The diagram illustrates the principle given here using the following example&nbsp; $J = 4$. If you number the spreading sequences from&nbsp; $0$&nbsp; to&nbsp; $J –1$&nbsp; through, the spreading sequences result
+The diagram illustrates the principle given here using the following example&nbsp; $J = 4$.&nbsp; If you number the spreading sequences from&nbsp; $0$&nbsp; to&nbsp; $J -1$, the spreading sequences result
 :$$\langle c_\nu^{(0)}\rangle = \ {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm},$$
 :$$ \langle c_\nu^{(1)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.05cm},$$
@@ Line 19: / Line 19: @@
 :$$ \langle c_\nu^{(3)}\rangle = {+\hspace{-0.05cm}1}\hspace{0.15cm} {-\hspace{-0.05cm}1} \hspace{0.15cm} {-\hspace{-0.05cm}1}\hspace{0.15cm} {+\hspace{-0.05cm}1} \hspace{0.05cm}.$$
-According to this nomenclature, for the spreading factor&nbsp; $J = 8$&nbsp; there are the spreading sequences&nbsp; $\langle c_\nu^{(0)}\rangle, \text{...} ,\langle c_\nu^{(7)}\rangle.$
+According to this nomenclature, there are the spreading sequences&nbsp; $\langle c_\nu^{(0)}\rangle, \text{...} ,\langle c_\nu^{(7)}\rangle$&nbsp; for the spreading factor&nbsp; $J = 8$.&nbsp;
 It should be noted that no predecessor or successor of a code may be used by other participants.
 *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; $J = 4$.
+*the three codes highlighted in yellow &ndash; once with&nbsp; $J = 2$&nbsp; and twice with &nbsp; $J = 4$.

@@ Line 63: / Line 63: @@
 </quiz>
-===Sample solution===
+===Solution===
 {{ML-Kopf}}

← Older revision		Revision as of 14:04, 15 December 2020
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−	{{quiz-Header\|Buchseite=~~Mobile Kommunikation~~/~~Die Charakteristika von UMTS~~	+	{{quiz-Header\|Buchseite=Mobile_Communications/Characteristics_of_UMTS
	}}		}}