Modulation Methods/OFDM for 4G Networks - Revision history

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	{{Display}}		{{Display}}
			[[de:Modulationsverfahren/OFDM_für_4G–Netze]]

Guenter at 13:43, 30 January 2023

2023-01-30T13:43:08Z

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	*and  "frequency-dependent attenuation"  (  "frequency selective fading").		*and  "frequency-dependent attenuation"  (  "frequency selective fading").
	<br clear=all>		<br clear=all>
	[[File:EN_Mod_T_5_7_S2_2neu.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation ~~'''KORREKTUR: arises''']~~]		[[File:EN_Mod_T_5_7_S2_2neu.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation]
	<br><br>The table on the left shows the respective descriptive quantities.  Please note:		<br><br>The table on the left shows the respective descriptive quantities.  Please note:

Guenter at 16:35, 23 January 2023

2023-01-23T16:35:02Z

← Older revision		Revision as of 18:35, 23 January 2023
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	*and  "frequency-dependent attenuation"  (  "frequency selective fading").		*and  "frequency-dependent attenuation"  (  "frequency selective fading").
	<br clear=all>		<br clear=all>
	[[File:~~Mod_T_5_7_S2_2neu2~~.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation '''KORREKTUR: arises''']]		[[File:EN_Mod_T_5_7_S2_2neu.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation '''KORREKTUR: arises''']]
	<br><br>The table on the left shows the respective descriptive quantities.  Please note:		<br><br>The table on the left shows the respective descriptive quantities.  Please note:

Hwang at 11:50, 19 January 2023

2023-01-19T11:50:42Z

← Older revision		Revision as of 13:50, 19 January 2023
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	*and  "frequency-dependent attenuation"  (  "frequency selective fading").		*and  "frequency-dependent attenuation"  (  "frequency selective fading").
	<br clear=all>		<br clear=all>
	[[File:Mod_T_5_7_S2_2neu2.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation]]		[[File:Mod_T_5_7_S2_2neu2.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation '''KORREKTUR: arises''']]
	<br><br>The table on the left shows the respective descriptive quantities.  Please note:		<br><br>The table on the left shows the respective descriptive quantities.  Please note:

Hwang at 11:43, 19 January 2023

2023-01-19T11:43:23Z

← Older revision		Revision as of 13:43, 19 January 2023
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	*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and		*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and
	*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System").		*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System").


	*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.		*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.

Hwang at 11:43, 19 January 2023

2023-01-19T11:43:05Z

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	As a first example,  let's now take a look at the fourth-generation  $\rm (4G)$  mobile communications networks,  which are the successors to the earlier mobile communications networks based on		As a first example,  let's now take a look at the fourth-generation  $\rm (4G)$  mobile communications networks,  which are the successors to the earlier mobile communications networks based on
	*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and		*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and
	*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System")		*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System").


	~~have replaced them~~.

	*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.		*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.

Hwang at 11:37, 19 January 2023

2023-01-19T11:37:28Z

Reed at 14:02, 9 April 2022

2022-04-09T14:02:15Z

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	{{Header		{{Header
	\|Untermenü=Multiple Access Methods		\|Untermenü=Multiple Access Methods
	\|Vorherige Seite=~~Realisierung von~~ OFDM~~-Systemen~~		\|Vorherige Seite=Implementation of OFDM Systems
	\|Nächste Seite=~~Weitere OFDM–Anwendungen~~		\|Nächste Seite=Further OFDM Applications
	}}		}}
	==Multiplexing vs. multiple access methods==		==Multiplexing vs. multiple access methods==

Guenter at 14:57, 31 January 2022

2022-01-31T14:57:25Z

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	*and  "frequency-dependent attenuation"  (  "frequency selective fading").		*and  "frequency-dependent attenuation"  (  "frequency selective fading").
	<br clear=all>		<br clear=all>
	[[File:~~Mod_T_5_7_S2_2neu~~.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation]]		[[File:Mod_T_5_7_S2_2neu2.png \|left\|frame\| Description of time-dependent and frequency-dependent attenuation]]
	<br><br>The table on the left shows the respective descriptive quantities.  Please note:		<br><br>The table on the left shows the respective descriptive quantities.  Please note:

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	[[File: P_ID1652__Mod_T_5_7_S4a_ganz_neu.png \|right\|frame\| Multi-user diversity gain from [Vie17]<ref>Viering, I.:  System Aspects in Communications.  Lecture manuscript, Lehrstuhl für Nachrichtentechnik, TU München, 2017.</ref>.     <br>We thank Ingo Viering for permission to use the diagram.]]		[[File: P_ID1652__Mod_T_5_7_S4a_ganz_neu.png \|right\|frame\| Multi-user diversity gain from [Vie17]<ref>Viering, I.:  System Aspects in Communications.  Lecture manuscript, Lehrstuhl für Nachrichtentechnik, TU München, 2017.</ref>.     <br>We thank Ingo Viering for permission to use the diagram.]]

	[[File:~~P_ID1653__Mod_T_5_7_S5_neu~~.png \|right\|frame\| Cross-layer scheduler ~~'''KORREKTUR''': higher layers ...~~]]		[[File:EN_Mod_T_5_7_S5.png \|right\|frame\| Cross-layer scheduler]]

	*In principle,  it can be said that the robustness decreases with increasing  ${\rm log_2}(M)$,  since this reduces the spacing of the possible signal space points.		*In principle,  it can be said that the robustness decreases with increasing  ${\rm log_2}(M)$,  since this reduces the spacing of the possible signal space points.

← Older revision		Revision as of 13:43, 19 January 2023
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	*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and		*$\rm TDMA/FDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_GSM\|$\rm GSM$]]  ("Global System for Mobile Communications"),  and
	*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System").		*$\rm CDMA$, see  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_UMTS\|$\rm UMTS$]]  ("Universal Mobile Telecommunications System").


	*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.		*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.

← Older revision		Revision as of 15:47, 16 March 2026
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	:$$T_{\rm R} \ll T_{\rm coh}.$$		:$$T_{\rm R} \ll T_{\rm coh}.$$
	*Frequency selective fading  (within a subcarrier)  is avoided if the bandwidth of all carriers  $(≈ f_0)$  is significantly smaller than the coherence bandwidth  $f_{\rm coh}$:		*Frequency selective fading  (within a subcarrier)  is avoided if the bandwidth of all carriers  $(≈ f_0)$  is significantly smaller than the coherence bandwidth  $f_{\rm coh}$:
	:$$f_0 = {1}/{T} \ll f_{{\rm{coh}}} = {1}/{{T_{\rm{D}} }} \approx {1}/{{T_{\rm{G}} }}		:$$f_0 = {1}/{T} \ll f_{{\rm{coh}}} = {1}/{{T_{\rm{D}} }} \approx {1}/{{T_{\rm{G}} }}\hspace{1.0cm}({\rm e.g.\hspace{0.12cm} for }\hspace{0.15cm} \tau_{\rm min}= 0,\hspace{0.12cm}\tau_{\rm max}= T_{\rm G}\hspace{0.12cm}{\rm applies}).$$
	\hspace{1.0cm}({\rm e.g.\hspace{0.12cm} for }\hspace{0.15cm} \tau_{\rm min}= 0,\hspace{0.12cm}\tau_{\rm max}= T_{\rm G}\hspace{0.12cm}{\rm applies}).$$
	*Both requirements can be summarized by the following inequality with respect to the symbol duration  $T$:		*Both requirements can be summarized by the following inequality with respect to the symbol duration  $T$:
	:$$T_{\rm{G}} \ll T \ll T_{{\rm{coh}}} - T_{\rm{G}}.$$		:$$T_{\rm{G}} \ll T \ll T_{{\rm{coh}}} - T_{\rm{G}}.$$
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	::$$T_{\rm opt} = \sqrt { {T_{\rm G} }' \cdot (T_{\rm coh} - {T_{\rm G} }') }.$$		::$$T_{\rm opt} = \sqrt { {T_{\rm G} }' \cdot (T_{\rm coh} - {T_{\rm G} }') }.$$
	*The required number  $N_{\rm user}$  of subcarriers  – and thus the minimum FFT support number –  is obtained from this together with the data rate  $R$  and the number  $M$  of signal space points of the mapping used after rounding up:		*The required number  $N_{\rm user}$  of subcarriers  – and thus the minimum FFT support number –  is obtained from this together with the data rate  $R$  and the number  $M$  of signal space points of the mapping used after rounding up:
	:$$N_{ {\rm{user} } } = \left\lceil {\frac{ {R \cdot (T + {T_{\rm G} }') } } { { {\rm{log}_2}(M)} } } \right\rceil \hspace{0.3cm}\Rightarrow \hspace{0.3cm}		:$$N_{ {\rm{user} } } = \left\lceil {\frac{ {R \cdot (T + {T_{\rm G} }') } } { { {\rm{log}_2}(M)} } } \right\rceil \hspace{0.3cm}\Rightarrow \hspace{0.3cm}N_{ {\rm{FFT} } } = 2^{\left\lceil { {\rm{log}_2} (N_{ {\rm{use} } } )} \right\rceil }.$$
	N_{ {\rm{FFT} } } = 2^{\left\lceil { {\rm{log}_2} (N_{ {\rm{use} } } )} \right\rceil }.$$

	*The value  $N_{\rm FFT}$  takes into account that the number of interpolation points of the FFT must be a power of two.  The unused carriers due to the FFT adjustment are used as an additional guard band at the edges of the spectrum.		*The value  $N_{\rm FFT}$  takes into account that the number of interpolation points of the FFT must be a power of two.  The unused carriers due to the FFT adjustment are used as an additional guard band at the edges of the spectrum.
	*The resulting guard interval must now be adjusted to the new parameters:		*The resulting guard interval must now be adjusted to the new parameters:
	:$$T_{\rm{G} } = N_{\rm{G} } \cdot \frac{{T_{{\rm{opt} } } } } { {N_{ {\rm{FFT} } } }} \quad {\rm{with}}		:$$T_{\rm{G} } = N_{\rm{G} } \cdot \frac{{T_{{\rm{opt} } } } } { {N_{ {\rm{FFT} } } }} \quad {\rm{with}}\quad N_{\rm{G} } = \left\lceil {\frac{ { {T_{\rm G} }' } } { {T_{ {\rm{opt} } } } } \cdot N_{ {\rm{FFT} } } } \right\rceil.$$
	\quad N_{\rm{G} } = \left\lceil {\frac{ { {T_{\rm G} }' } } { {T_{ {\rm{opt} } } } } \cdot N_{ {\rm{FFT} } } } \right\rceil.$$

	*The frame duration is given by  $T_{\rm R} = T + T_{\rm G}$  and the total number of samples in a frame is given by  $N_{\rm total} = N_{\rm FFT} + N_{\rm G}$.		*The frame duration is given by  $T_{\rm R} = T + T_{\rm G}$  and the total number of samples in a frame is given by  $N_{\rm total} = N_{\rm FFT} + N_{\rm G}$.
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	<br>When implementing a channel-adaptive scheduler,  however,  information from higher layers should also be included,  since long waiting times   (large delays)  must be avoided depending on the  "Quality of Service"  $\rm (QoS)$  requirements and traffic type.  The diagram on the right shows a schematic representation of such a   "cross–layer approach".		<br>When implementing a channel-adaptive scheduler,  however,  information from higher layers should also be included,  since long waiting times   (large delays)  must be avoided depending on the  "Quality of Service"  $\rm (QoS)$  requirements and traffic type.  The diagram on the right shows a schematic representation of such a   "cross–layer approach".
	*The scheduler is located in the MAC layer  ("Medium Access Control Layer")  and communicates with the other  (not necessarily neighboring)  layers.  It should be noted that this approach contradicts the modularity principle envisaged in the OSI model.		*The scheduler is located in the MAC layer  ("Medium Access Control Layer")  and communicates with the other  (not necessarily neighboring)  layers.  It should be noted that this approach contradicts the modularity principle envisaged in the OSI model.
	*A similar approach has already been implemented as part of the extension of the UMTS network to include the [[Examples_of_Communication_Systems/~~Weiterentwicklungen_von_UMTS~~#~~High.E2.80.93Speed_Downlink_Packet_Access~~\|$\rm HSDPA$]]  ("High Speed Downlink Packet Access") standard,  which has increased the maximum data rate in the 3G network  (downstream)  from  $\text{384 kbit/s}$  to the theoretical value  $\text{14.4 Mbit/s}$.		*A similar approach has already been implemented as part of the extension of the UMTS network to include the [[Examples_of_Communication_Systems/Further_Developments_of_UMTS#High–Speed_Downlink_Packet_Access\|$\rm HSDPA$]]  ("High Speed Downlink Packet Access") standard,  which has increased the maximum data rate in the 3G network  (downstream)  from  $\text{384 kbit/s}$  to the theoretical value  $\text{14.4 Mbit/s}$.

← Older revision		Revision as of 13:37, 19 January 2023
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	have replaced them.		have replaced them.

	*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX WiMAX]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.		*Another name often used synonymously with  "4G"  is  [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard\|$\rm LTE$]]  ("Long Term Evolution").  Like  [https://en.wikipedia.org/wiki/WiMAX $\text{WiMAX}$]  ("Worldwide Interoperability for Microwave Access"),  LTE uses  [https://www.techtarget.com/searchnetworking/definition/orthogonal-frequency-division-multiple-access-OFDMA  $\rm OFDMA$]  ("Orthogonal Frequency Division Multiple Access")  as its multiple access method.

	*The main difference between a pure  "$\rm multiplexing \; method$"  $($TDM,  FDM,  CDM,  OFDM$)$  and a  "$\rm multiple \; access \; method$"  $($TDMA,  FDMA,  CDMA,  OFDMA$)$  is the user separation realized by resource allocation.  In the case of OFDMA,  this means that not only time slots  (TDMA)  or spreading codes  (CDMA)  are allocated to the individual subscribers,  but also different and  "preferably"  orthogonal subcarriers.		*The main difference between a pure  "$\rm multiplexing \; method$"  $($TDM,  FDM,  CDM,  OFDM$)$  and a  "$\rm multiple \; access \; method$"  $($TDMA,  FDMA,  CDMA,  OFDMA$)$  is the user separation realized by resource allocation.  In the case of OFDMA,  this means that not only time slots  (TDMA)  or spreading codes  (CDMA)  are allocated to the individual subscribers,  but also different and  "preferably"  orthogonal subcarriers.

	*The realization of a suitable allocation mechanism is a non-trivial problem which can only be dealt with very superficially here.  It makes sense that a method is not limited to only one  (physical)  layer,  but works across layers.  The term  "layer"  is to be understood here in the sense of the  [https://en.wikipedia.org/wiki/OSI_model OSI reference model].		*The realization of a suitable allocation mechanism is a non-trivial problem which can only be dealt with very superficially here.  It makes sense that a method is not limited to only one  (physical)  layer,  but works across layers.  The term  "layer"  is to be understood here in the sense of the  [https://en.wikipedia.org/wiki/OSI_model $\text{OSI reference model}$].

	*This is also necessitated by the changing requirements of a mobile communications network.  Whereas  '''connection-oriented'''  services such as voice telephony were in the foreground at the beginning of mobile communications,  today  '''packet-oriented'''  applications such as  "Voice over IP" (VoIP),  "video telephony"  or  "mobile data services"  represent the main traffic load and are the cause of the increased demand on the available data rates.		*This is also necessitated by the changing requirements of a mobile communications network.  Whereas  »'''connection-oriented'''«  services such as voice telephony were in the foreground at the beginning of mobile communications,  today  »'''packet-oriented'''«  applications such as  "Voice over IP" (VoIP),  "video telephony"  or  "mobile data services"  represent the main traffic load and are the cause of the increased demand on the available data rates.

	==Some characteristics of mobile radio systems==		==Some characteristics of mobile radio systems==
	<br>		<br>
	First of all,  the special features of the mobile radio channel will be discussed very briefly.  The figure shows a typical mobile radio scenario.  More detailed information on this subject can be found in the book  [[Mobile_Communications/Distance_Dependent_Attenuation_and_Shading\|Mobile Communications]].		First of all,  the special features of the mobile radio channel will be discussed very briefly.  The figure shows a typical mobile radio scenario.  More detailed information on this subject can be found in the book  [[Mobile_Communications/Distance_Dependent_Attenuation_and_Shading\|"Mobile Communications"]].

	[[File:EN_Mob_T1_1_S1.png \|right\|frame\| Characteristics of the mobile communications channel]]		[[File:EN_Mob_T1_1_S1.png \|right\|frame\| Characteristics of the mobile communications channel]]
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	*The coherence bandwidth  $f_{\rm coh}$  is not the reciprocal of the coherence time  $T_{\rm coh}$,  although one might assume this due to comparable naming.		*The coherence bandwidth  $f_{\rm coh}$  is not the reciprocal of the coherence time  $T_{\rm coh}$,  although one might assume this due to comparable naming.

	* $f_{\rm coh}$  is a parameter for the frequency-dependent attenuation and results as the reciprocal of the  [https://en.wikipedia.org/wiki/Delay_spread delay spread].		* $f_{\rm coh}$  is a parameter for the frequency-dependent attenuation and results as the reciprocal of the  [https://en.wikipedia.org/wiki/Delay_spread $\text{delay spread}$].

	* $T_{\rm coh}$  on the other hand,  describes the time-dependent attenuation and is the reciprocal of the  [https://en.wikipedia.org/wiki/Fading Doppler spread].		* $T_{\rm coh}$  on the other hand,  describes the time-dependent attenuation and is the reciprocal of the  [https://en.wikipedia.org/wiki/Fading $\text{Doppler spread}$].
	<br clear=all>		<br clear=all>
	==Determination of some OFDM parameters==		==Determination of some OFDM parameters==
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	The aim of a suitable  '''scheduling procedure'''  is now,		The aim of a suitable  »'''scheduling procedure'''«  is now,
	*transmit only when the channel is good,  and		*transmit only when the channel is good,  and
	*to serve other subscribers during the dips in attenuation.		*to serve other subscribers during the dips in attenuation.


	The gain in system throughput that can be achieved in this way is often referred to as  [https://en.wikipedia.org/wiki/Diversity_scheme "multi-user diversity gain"].		The gain in system throughput that can be achieved in this way is often referred to as  [https://en.wikipedia.org/wiki/Diversity_scheme $\text{multi-user diversity gain}$].

	The diagram on the right shows the procedure.  The blue line represents the desired  "riding on the peaks"  for the case of eight participants  (eight fading processes).		The diagram on the right shows the procedure.  The blue line represents the desired  "riding on the peaks"  for the case of eight participants  (eight fading processes).