Aufgaben:Exercise 5.3Z: Realization of a PN Sequence - Revision history

Guenter at 16:32, 20 December 2021

2021-12-20T16:32:25Z

Guenter at 13:46, 13 December 2021

2021-12-13T13:46:21Z

Guenter at 13:35, 13 December 2021

2021-12-13T13:35:13Z

Guenter at 13:33, 13 December 2021

2021-12-13T13:33:59Z

Hwang at 15:44, 10 December 2021

2021-12-10T15:44:48Z

Hwang at 15:43, 10 December 2021

2021-12-10T15:43:56Z

Hwang at 13:28, 10 December 2021

2021-12-10T13:28:46Z

Hwang at 13:25, 10 December 2021

2021-12-10T13:25:31Z

Guenter at 10:25, 1 December 2021

2021-12-01T10:25:29Z

Guenter: Guenter moved page Aufgaben:Aufgabe 5.3Z: Realisierung einer PN–Sequenz to Aufgaben:Exercise 5.3Z: Realization of a PN Sequence

2021-12-01T10:20:42Z

Guenter moved page Aufgabe 5.3Z: Realisierung einer PN–Sequenz to Exercise 5.3Z: Realization of a PN Sequence

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 }}
-[[File:EN_Mod_Z_5_3.png|right|frame|Two PN generator realizations]]
+[[File:EN_Mod_Z_5_3neu.png|right|frame|Two PN generator realizations]]
 The diagram shows two possible generators for generating PN sequences in unipolar representation: &nbsp; $u_ν ∈ \{0, 1\}$.
 *The upper generator with the coefficients

@@ Line 39: / Line 39: @@
 |type="[]"}
 - The number of&nbsp; "zeros"&nbsp; and&nbsp; "ones"&nbsp; is the same.
-+ In each period there are&nbsp; "ones"&nbsp; more than&nbsp; "zeros".
++ In each period there is one more&nbsp; "ones"&nbsp; than&nbsp; "zeros".
 + The maximum number of consecutive&nbsp; "ones"&nbsp; is &nbsp;$G$.
 + The sequence &nbsp;$1 0 1 0 1 0$ ... &nbsp; is not possible.
@@ Line 62: / Line 62: @@
-'''(3)'''&nbsp; <u>Solutions 2, 3 and 4</u> are correct:
+'''(3)'''&nbsp; <u>Solutions 2, 3 and 4</u>&nbsp; are correct:
-*The maximum number of consecutive ones is&nbsp; $G$&nbsp; (whenever there is a one in all&nbsp; $G$&nbsp; memory cells).
+*The maximum number of consecutive&nbsp; "ones"&nbsp; is&nbsp; $G$&nbsp; (whenever there is a&nbsp; "one"&nbsp; in all&nbsp; $G$&nbsp; memory cells).
-*On the other hand, it is not possible that all memory cells are filled with zeros&nbsp; (otherwise only zeros would be generated).
+*On the other hand,&nbsp; it is not possible that all memory cells are filled with zeros&nbsp; (otherwise only zeros would be generated).
-*Therefore, there is always one more one than zeros.
+*Therefore,&nbsp; there is always one more&nbsp; "ones"&nbsp; than zeros.
-*The period length of the last sequence is&nbsp; $P = 2$.&nbsp; For an M-sequence&nbsp; $P = 2^G –1$.&nbsp; For no value of&nbsp; $G$&nbsp; is&nbsp; $P = 2$&nbsp; possible.
+*The period length of the sequence&nbsp; "$1 0 1 0 1 0$ ..." &nbsp; is&nbsp; $P = 2$.&nbsp; For an M-sequence&nbsp; $P = 2^G –1$.&nbsp; For no value of&nbsp; $G$:&nbsp; &nbsp; $P = 2$&nbsp; is possible.
-'''(4)'''&nbsp; If all memory cells are occupied with ones, the generator with the octal identifier&nbsp; $(17)$&nbsp; returns a&nbsp; $1$ again:
+'''(4)'''&nbsp; If all memory cells are occupied with ones,&nbsp; the generator with the octal identifier&nbsp; $(17)$&nbsp; returns a&nbsp; $1$&nbsp; again:
 :$$u_{\nu} \big [ u_{\nu-1} + u_{\nu-2} + u_{\nu-3} \big ] \,\,{\rm mod} \,\,2 =1 \hspace{0.05cm}.$$
-*Since this does not change the memory allocation, all further binary values generated will also be&nbsp; $1$&nbsp; each &nbsp; ⇒ &nbsp; $\underline{P = 1}$.
+*Since this does not change the memory allocation,&nbsp; all further binary values generated will also be&nbsp; $1$&nbsp; each &nbsp; ⇒ &nbsp; $\underline{P = 1}$.
-'''(5)'''&nbsp; <u>Answer 1</u> is correct:
+'''(5)'''&nbsp; <u>Answer 1</u>&nbsp; is correct:
 *One speaks of an M-sequence only if&nbsp; $P = 2^G –1$&nbsp; holds.
-*Here, "M" stands for "maximum".
+*Here,&nbsp; "M"&nbsp; stands for "maximum".
 {{ML-Fuß}}

@@ Line 39: / Line 39: @@
 |type="[]"}
 - The number of&nbsp; "zeros"&nbsp; and&nbsp; "ones"&nbsp; is the same.
-+ In each period there are&nbsp; "ones"&nbsp; more one than&nbsp; "zeros".
++ In each period there are&nbsp; "ones"&nbsp; more than&nbsp; "zeros".
 + The maximum number of consecutive&nbsp; "ones"&nbsp; is &nbsp;$G$.
 + The sequence &nbsp;$1 0 1 0 1 0$ ... &nbsp; is not possible.

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Mod_Z_5_3.png|right|frame|Two possible realizations for PN generators]]
+[[File:EN_Mod_Z_5_3.png|right|frame|Two PN generator realizations]]
 The diagram shows two possible generators for generating PN sequences in unipolar representation: &nbsp; $u_ν ∈ \{0, 1\}$.
 *The upper generator with the coefficients
 :$$ g_0 = 1 \hspace{0.05cm}, \hspace{0.2cm}g_1 = 0 \hspace{0.05cm}, \hspace{0.2cm}g_2 = 1 \hspace{0.05cm}, \hspace{0.2cm}g_3 = 1 \hspace{0.05cm}$$
-:is denoted by the octal identifier &nbsp; $(g_3, g_2, g_1, g_0)_{\rm octal} = (15)$.&nbsp;
+:is denoted by the octal identifier &nbsp; $(g_3,\ g_2,\ g_1,\ g_0)_{\rm octal} = (15)$.&nbsp;
-*Accordingly, the octal identifier of the second PN generator is equal to &nbsp;$(17)$.
+*Accordingly,&nbsp; the octal identifier of the second PN generator is &nbsp;$(17)$.
 *One speaks of an M-sequence if for the period length of the sequence &nbsp; $〈u_ν〉$&nbsp;  holds:
 :$$P = 2^G – 1.$$
-:Here &nbsp; $G$&nbsp; denotes the degree of the shift register, which is equal to the number of memory cells.
+:Here,&nbsp; $G$&nbsp; denotes the degree of the shift register,&nbsp; which is equal to the number of memory cells.
 Notes:
 *The exercise belongs to the chapter&nbsp;  [[Modulation_Methods/Spreading_Sequences_for_CDMA|Spreading Sequences for CDMA]].
-*However, reference is also made to the chapter&nbsp;  [[Theory_of_Stochastic_Signals/Erzeugung_von_diskreten_Zufallsgr%C3%B6%C3%9Fen |Generation of Discrete Random Variables]]&nbsp; in the book "Theory of Stochastic Signals".
+*Reference is also made to the chapter&nbsp;  [[Theory_of_Stochastic_Signals/Erzeugung_von_diskreten_Zufallsgr%C3%B6%C3%9Fen |Generation of Discrete Random Variables]]&nbsp; in the book "Theory of Stochastic Signals".
-* We would also like to draw your attention to the learning video&nbsp; [[Erläuterung_der_PN–Generatoren_an_einem_Beispiel_(Lernvideo)|Explanation of PN generators using an example]].&nbsp;
+* We would also like to draw your attention to the&nbsp;  (German language)&nbsp;  learning video <br> &nbsp; [[Erläuterung_der_PN–Generatoren_an_einem_Beispiel_(Lernvideo)|Erläuterung der PN–Generatoren an einem Beispiel]] &nbsp; &rArr;&nbsp;  "Explanation of PN generators using an example".&nbsp;
@@ Line 37: / Line 32: @@
 $G \ = \ $  { 3 }
-{Give the period length &nbsp;$P$&nbsp; of the PN generator with the octal identifier &nbsp;$(15)$&nbsp; an.
+{Give the period length &nbsp;$P$&nbsp; of the PN generator with the octal identifier &nbsp;$(15)$.
 |type="{}"}
 $P\ = \ $  { 7 }
@@ Line 43: / Line 38: @@
 {Which of the following statements are true for each M-sequence?
 |type="[]"}
-- The number of zeros and ones is the same.
+- The number of&nbsp; "zeros"&nbsp; and&nbsp; "ones"&nbsp; is the same.
-+ In each period there is one more one than zeros.
++ In each period there are&nbsp; "ones"&nbsp; more one than&nbsp; "zeros".
-+ The maximum number of consecutive ones is &nbsp;$G$.
++ The maximum number of consecutive&nbsp; "ones"&nbsp; is &nbsp;$G$.
 + The sequence &nbsp;$1 0 1 0 1 0$ ... &nbsp; is not possible.
-{Specify the period length &nbsp;$P$&nbsp; of the PN generator with the octal identifier&nbsp;$(17)$&nbsp; an.
+{Specify the period length &nbsp;$P$&nbsp; of the PN generator with the octal identifier&nbsp;$(17)$.
 |type="{}"}
 $P\ = \ $ { 1 }

@@ Line 23: / Line 23: @@
-''Note:''
+''Notes:''
 *The exercise belongs to the chapter&nbsp;  [[Modulation_Methods/Spreading_Sequences_for_CDMA|Spreading Sequences for CDMA]].
 *However, reference is also made to the chapter&nbsp;  [[Theory_of_Stochastic_Signals/Erzeugung_von_diskreten_Zufallsgr%C3%B6%C3%9Fen |Generation of Discrete Random Variables]]&nbsp; in the book "Theory of Stochastic Signals".

← Older revision		Revision as of 13:28, 10 December 2021
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−	{{quiz-Header\|Buchseite=~~Modulationsverfahren~~/~~Spreizfolgen für CDMA~~	+	{{quiz-Header\|Buchseite=Modulation_Methods/Spreading_Sequences_for_CDMA
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← Older revision		Revision as of 10:25, 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^]]