Aufgaben:Exercise 5.9: Selection of OFDM Parameters - Revision history

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	[[Category:Modulation Methods: Exercises\|^5.7 OFDM for 4G Networks^]]		[[Category:Modulation Methods: Exercises\|^5.7 OFDM for 4G Networks^]]
	[[de:Aufgaben:5.~~9_Wahl_der_OFDM–Parameter~~]]		[[de:Aufgaben:Aufgabe 5.9: Wahl der OFDM–Parameter]]

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	'''(3)'''  The required number of useful carriers is given by the following equation:		'''(3)'''  The required number of useful carriers is given by the following equation:
	:$$N_{{\rm{user}}} = \left\lceil {\frac{{R_{{\rm{B}}} \cdot (T + T_{\rm{G}} ')}} {{{\rm{log}_2}(M)}}}\right\rceil		:$$N_{{\rm{user}}} = \left\lceil {\frac{{R_{{\rm{B}}} \cdot (T + T_{\rm{G}} ')}} {{{\rm{log}_2}(M)}}}\right\rceil= \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {25\,\,{\rm µ s}} )}{{{\rm{log}_2}(4)}}}\right\rceil\hspace{0.15cm}\underline {= 61}.$$
	= \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {25\,\,{\rm µ s}} )}
	{{{\rm{log}_2}(4)}}}\right\rceil\hspace{0.15cm}\underline {= 61}.$$

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	[[Category:Modulation Methods: Exercises\|^5.7 OFDM for 4G Networks^]]		[[Category:Modulation Methods: Exercises\|^5.7 OFDM for 4G Networks^]]
			[[de:Aufgaben:5.9_Wahl_der_OFDM–Parameter]]

Guenter at 11:13, 25 January 2022

2022-01-25T11:13:19Z

← Older revision		Revision as of 13:13, 25 January 2022
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	{Determine the required number of useful carriers.		{Determine the required number of useful carriers.
	\|type="{}"}		\|type="{}"}
	$N_{\rm ~~use~~} \ = \ $ { 61 1% }		$N_{\rm user} \ = \ $ { 61 1% }

	{Specify the resulting number of interpolation points of the FFT.		{Specify the resulting number of interpolation points of the FFT.
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	{Using the determined parameters,  determine the number of useful carriers  $N_{\rm use}'$  again.		{Using the determined parameters,  determine the number of useful carriers  $N_{\rm use}'$  again.
	\|type="{}"}		\|type="{}"}
	$N_{\rm ~~use~~}' \ = \ $ { 62 1% }		$N_{\rm user}' \ = \ $ { 62 1% }
	</quiz>		</quiz>

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	'''(3)'''  The required number of useful carriers is given by the following equation:		'''(3)'''  The required number of useful carriers is given by the following equation:
	:$$N_{{\rm{~~use~~}}} = \left\lceil {\frac{{R_{{\rm{B}}} \cdot (T + T_{\rm{G}} ')}} {{{\rm{log}_2}(M)}}}\right\rceil		:$$N_{{\rm{user}}} = \left\lceil {\frac{{R_{{\rm{B}}} \cdot (T + T_{\rm{G}} ')}} {{{\rm{log}_2}(M)}}}\right\rceil
	= \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {25\,\,{\rm µ s}} )}		= \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {25\,\,{\rm µ s}} )}
	{{{\rm{log}_2}(4)}}}\right\rceil\hspace{0.15cm}\underline {= 61}.$$		{{{\rm{log}_2}(4)}}}\right\rceil\hspace{0.15cm}\underline {= 61}.$$
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	'''(8)'''  The recalculation is necessary because the duration of the guard interval may have changed.		'''(8)'''  The recalculation is necessary because the duration of the guard interval may have changed.
	*Compared to subtask '''(3)''',  the provisional length  $T_{\rm{G}} '$  is replaced by  $T_{\rm{G}} $  and a slightly different result is obtained:		*Compared to subtask '''(3)''',  the provisional length  $T_{\rm{G}} '$  is replaced by  $T_{\rm{G}} $  and a slightly different result is obtained:
	:$$N_{\rm ~~use~~}' = \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {26\,\,{\rm µ s}} )} {{{\rm{log_2}}(4)}}}\right\rceil = \left\lceil 61.5\right\rceil\hspace{0.15cm}\underline {= 62}.$$		:$$N_{\rm user}' = \left\lceil {\frac{10^6\,\,{\rm bit/s} \cdot ({97\,\,{\rm µ s}} + {26\,\,{\rm µ s}} )} {{{\rm{log_2}}(4)}}}\right\rceil = \left\lceil 61.5\right\rceil\hspace{0.15cm}\underline {= 62}.$$
	*However, this still gives  $N_{\rm FFT} = 64$.		*However,  this still gives  $N_{\rm FFT} = 64$.

Guenter at 11:08, 25 January 2022

2022-01-25T11:08:10Z

Hwang at 14:50, 29 December 2021

2021-12-29T14:50:58Z

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Guenter at 16:01, 14 December 2021

2021-12-14T16:01:30Z

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	[[Category:Modulation Methods: Exercises\|^5.7 OFDM ~~für 4G–Netze~~^]]		[[Category:Modulation Methods: Exercises\|^5.7 OFDM for 4G Networks^]]

Guenter: Guenter moved page Aufgaben:Aufgabe 5.9: Wahl der OFDM–Parameter to Aufgaben:Exercise 5.9: Selection of OFDM Parameters

2021-12-14T16:00:41Z

Guenter moved page Aufgaben:Aufgabe 5.9: Wahl der OFDM–Parameter to Aufgaben:Exercise 5.9: Selection of OFDM Parameters

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	<quiz display=simple>		<quiz display=simple>
	{Bestimmen Sie die minimal sinnvolle Dauer  $T_{\rm G}'$  des "vorläufigen Guard–Intervalls~~”~~.		{Bestimmen Sie die minimal sinnvolle Dauer  $T_{\rm G}'$  des "vorläufigen Guard–Intervalls".
	\|type="{}"}		\|type="{}"}
	$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$		$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$

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	<quiz display=simple>		<quiz display=simple>
	{Bestimmen Sie die minimal sinnvolle Dauer  $T_{\rm G}'$  des ~~&bdquo;~~vorläufigen Guard–Intervalls”.		{Bestimmen Sie die minimal sinnvolle Dauer  $T_{\rm G}'$  des "vorläufigen Guard–Intervalls”.
	\|type="{}"}		\|type="{}"}
	$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$		$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$

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	[[File:P_ID1668__Mod_A_5_9.png\|right\|frame\|Time-dependent attenuation curve		[[File:P_ID1668__Mod_A_5_9.png\|right\|frame\|Time-dependent attenuation curve
	of two mobile radio channels]]		of two mobile radio channels]]
	In this exercise, some OFDM parameters of a mobile radio system are to be determined.		In this exercise,  some OFDM parameters of a mobile radio system are to be determined.

	The following assumptions are made:		The following assumptions are made:
	* The coherence time of the channel is  $T_{\rm coh} = 0.4 \ \rm ms$.		* The coherence time of the channel is  $T_{\rm coh} = 0.4 \ \rm ms$.
	* The maximum path delay is  $τ_{\rm max} = 25 \ \rm µ s$.		* The maximum path delay is  $τ_{\rm max} = 25 \ \rm µ s$.
	* The data rate (bit rate) is  $R_{\rm B} = 1 \ \rm Mbit/s$.		* The data rate  (bit rate)  is  $R_{\rm B} = 1 \ \rm Mbit/s$.
	* All subcarriers are  $\rm 4–QAM$ modulated.		* All subcarriers are  $\rm 4–QAM$ modulated.


	To ensure some robustness of the system to time and frequency selective fading, the following inequality must be satisfied:		To ensure some robustness of the system to time and frequency selective fading,  the following inequality must be satisfied:
	:$$T_{\rm{G}} \ll T \ll T_{{\rm{coh}}} - T_{\rm{G}}.$$		:$$T_{\rm{G}} \ll T \ll T_{{\rm{coh}}} - T_{\rm{G}}.$$
	Overall, the following procedure should be followed:		Overall,  the following procedure should be followed:
	* Preliminary determination of the guard interval  $(T_{\rm G}')$,		* Preliminary determination of the guard interval duration  $(T_{\rm G}')$,
	* Determination of the optimal core symbol duration  $(T)$,		* Determination of the optimal core symbol duration  $(T)$,
	* corresponding determination of the number of sampling points of the  $\rm FFT$.		* corresponding determination of the number of sampling points of the  $\rm FFT$.


	After that, it may be necessary to redetermine some system quantities due to the rounding performed during the calculations.		After that,  it may be necessary to redetermine some system quantities due to the rounding performed during the calculations.

	The diagram shows two exemplary attenuation curves of mobile radio systems in logarithmic representation.		The diagram shows two exemplary attenuation curves of mobile radio systems in logarithmic representation.
	*In the case of the blue curve, the changes over time occur relatively slowly, while in the case of the red curve they occur four times as fast.		*In the case of the blue curve,  the changes over time occur relatively slowly,  while in the case of the red curve they occur four times as fast.
	*Consequently, the blue channel has a four times larger coherence time than the red channel.		*Consequently,  the blue channel has a four times larger coherence time than the red channel.


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	''Notes:''		Notes:
	*The exercise belongs to the chapter  [[Modulation_Methods/OFDM_für_4G–Netze\|OFDM for 4G Networks]].		*The exercise belongs to the chapter  [[Modulation_Methods/OFDM_für_4G–Netze\|OFDM for 4G Networks]].
	*Reference is made in particular to the ~~page~~  [[Modulation_Methods/OFDM_for_4G_Networks#Determination_of_some_OFDM_parameters\|Determination of some OFDM parameters]].		*Reference is made in particular to the section  [[Modulation_Methods/OFDM_for_4G_Networks#Determination_of_some_OFDM_parameters\|Determination of some OFDM parameters]].
	* Further information on the topic can be found in the ~~LNTww~~ book  [[Mobile Communications]].		* Further information on the topic can be found in the LNTwww book  [[Mobile Communications]].


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	<quiz display=simple>		<quiz display=simple>
	{Determine the minimum reasonable duration  $T_{\rm G}'$  of the "preliminary guard interval".		{Determine the minimum reasonable duration  $T_{\rm G}'$  of the  "preliminary guard interval".
	\|type="{}"}		\|type="{}"}
	$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$		$T_{\rm G}' \ = \ $ { 25 3% } $\ \rm µ s$
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	$N_{\rm FFT} \ = \ $ { 64 1% }		$N_{\rm FFT} \ = \ $ { 64 1% }

	{Calculate the number  $N_{\rm G}$  of time samples of the guard interval and from this the new resulting guard ~~time~~  $T_{\rm G}$.		{Calculate the number  $N_{\rm G}$  of time samples of the guard interval and from this the new resulting guard duration  $T_{\rm G}$.
	\|type="{}"}		\|type="{}"}
	$N_{\rm G} \ = \ $ { 17 1% }		$N_{\rm G} \ = \ $ { 17 1% }
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	$N_{\rm total} \ = \ $ { 81 1% }		$N_{\rm total} \ = \ $ { 81 1% }

	{Using the determined parameters, determine the number of useful carriers  $N_{\rm use}'$  again.		{Using the determined parameters,  determine the number of useful carriers  $N_{\rm use}'$  again.
	\|type="{}"}		\|type="{}"}
	$N_{\rm use}' \ = \ $ { 62 1% }		$N_{\rm use}' \ = \ $ { 62 1% }