Difference between revisions of "Mobile Communications/Characteristics of GSM"

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{{Header
 
{{Header
|Untermenü=Mobilfunksysteme der 2. und 3. Generation – eine Übersicht
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|Untermenü=Mobile Radio Systems of the 2nd and 3rd Generation - an Overview
|Vorherige Seite=Gemeinsamkeiten von GSM und UMTS
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|Vorherige Seite=Similarities Between GSM and UMTS
|Nächste Seite=Die Charakteristika von UMTS
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|Nächste Seite=Characteristics of UMTS
 
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== Systemarchitektur und Basiseinheiten von GSM ==
+
== System architecture and basic units of GSM ==
 
<br>
 
<br>
GSM (<i><b>G</b>lobal <b>S</b>ystem for <b>M</b>obile Communication</i>) ist ein stark hierarchisch gegliedertes System verschiedener Netzkomponenten. Aus der Grafik erkennt man:
+
$\rm GSM$&nbsp; $\rm (G$lobal&nbsp; $\rm S$ystem&nbsp; for&nbsp; $\rm M$obile Communication$)$&nbsp; is a strongly hierarchically structured system of different network components.&nbsp; You can see from the graphic:
*Die Mobilstation (MS) kommuniziert über die Funkschnittstelle mit der nächstgelegenen <i>Base Transceiver Station</i> (BTS, Sende&ndash; und Empfangsbasisstation).<br>
+
[[File:EN_Mob_T_3_3_S1.png|right|frame|GSM system architecture|class=fit]]
 +
*The mobile station&nbsp; $\rm (MS)$&nbsp; communicates via the radio interface with the nearest&nbsp; base transceiver station&nbsp; $\rm (BTS$, transmit and receive base station).<br>
  
*Mehrere solcher BTS werden gebietsweise zusammengefasst und sind gemeinsam einem <i>Base Station Controller</i> (BSC, Kontrollstation) unterstellt.<br>
+
*Several such BTS's are grouped together area by area and are jointly subordinate to a&nbsp; base station controller</i>&nbsp; $\rm (BSC$, control station$)$.<br>
  
*Das <i>Base Station Subsystem</i> (BSS) besteht aus einer Vielzahl von BTS und mehreren BSC. In der Grafik ist ein solches BSS blau umrandet.<br>
+
*The&nbsp; base station sub&ndash;system&nbsp; $\rm(BSS)$&nbsp; consists of a multitude of BTS's and several BSC's.&nbsp; In the graphic such a&nbsp; BSS&nbsp; is framed in blue.<br>
  
*Jeder BSC ist mit einem <i>Mobile Switching Center</i> (MSC, Vermittlungsrechner) verbunden, dessen Funktion mit einem Vermittlungsknoten im Festnetz vergleichbar ist.<br>
+
*Each BSC is connected to a mobile switching center&nbsp; $\rm (MSC$, switching computer$)$, whose function is comparable to a switching node in the fixed network.<br>
  
*Das <i>Gateway Mobile Switching Center</i> (GMSC) ist für die Verbindung zwischen Fest&ndash; und Mobilfunknetz zuständig. Wird zum Beispiel ein Mobilfunkteilnehmer aus dem Festnetz angerufen, so ermittelt das GMSC das zuständige MSC und vermittelt den Ruf weiter.<br>
+
*The gateway mobile switching center&nbsp; $\rm (GMSC)$&nbsp; is responsible for the connection between the fixed and mobile networks.&nbsp; For example, if a mobile subscriber is called from the fixed network, the GMSC determines the responsible MSC and transfers the call.<br>
  
*Das <i>Operation and Maintenance Center</i> (OMC) überwacht einen Teil des Mobilfunknetzes. Daneben übernimmt es auch organisatorische Aufgaben wie Steuerung des Verkehrsflusses, Gebührenerfassung, Sicherheitsmanagement, usw..<br>
+
*The operation and maintenance center</i>&nbsp; $\rm (OMC)$&nbsp; monitors a part of the mobile network.&nbsp; It also takes on organizational tasks such as traffic flow control, charging, security management, etc.<br>
  
:[[File:P ID2203 Mob T 3 3 S1 v1.png|GSM–Systemarchitektur|class=fit]]<br>
 
  
Genauere Informationen zur GSM&ndash;Systemarchitektur und zu den einzelnen Netzkomponenten finden Sie im Kapitel 3.1 des Buches &bdquo;Beispiele von Nachrichtensystemen&rdquo;.
+
More detailed information on GSM system architecture and the individual network components can be found in the chapter&nbsp; [[Examples_of_Communication_Systems/General_Description_of_GSM|"General Description of GSM"]]&nbsp; of the book "Examples of Communication Systems".
 +
<br clear=all>
 +
== Multiple access with GSM ==
 +
<br>
 +
[[File:EN_Mob_T_3_3_S2_v2.png|right|frame|Realization of FDMA and TDMA with "GSM 900"|class=fit]]
 +
 
 +
GSM uses two multiple access methods in parallel:
 +
*$\text{Frequency Division Multiple Access}$ &nbsp; $\rm (FDMA)$,<br>
 +
*$\text{Time Division Multiple Access}$ &nbsp; $\rm (TDMA)$.
 +
 
 +
 
 +
The graphic and the following description is valid for the original system "GSM 900" (in the following:&nbsp; "GSM&ndash;D").&nbsp;
  
== Vielfachzugriff bei GSM ==
+
For "GSM/DCS 1800"&nbsp; &rArr; &nbsp;  "GSM&ndash;E" comparable statements apply.
 +
 
 +
*With "GSM&ndash;D", a bandwidth of&nbsp; $25\ \rm MHz$&nbsp; is provided for uplink and downlink respectively&nbsp; $($duplex spacing:&nbsp; $45\ \rm MHz)$.&nbsp; This is called&nbsp; "Frequency Division Duplex"&nbsp; $\rm (FDD)$.&nbsp; For "GSM&ndash;E", the bandwidth is&nbsp; $75\ \rm MHz$&nbsp; and the duplex spacing is&nbsp; $95\ \rm MHz$.<br>
 +
 
 +
*Uplink and downlink bands are divided into frequency bands of width&nbsp; $200\ \rm kHz$.&nbsp; Taking into account the protection areas at the respective edges, there are&nbsp; $N_{\rm F} = 124$&nbsp; (GSM&ndash;D) or&nbsp; $N_{\rm F} = 374$&nbsp; (GSM&ndash;E) frequency channels.
 +
 
 +
*Each cell is assigned a subset of the frequencies &nbsp; &#8658; &nbsp; "Cell Allocation".&nbsp; Neighboring cells usually work at different frequencies, for example with the reuse&ndash;factor &nbsp;$3$, as in section&nbsp; [[Mobile_Communications/Similarities_Between_GSM_and_UMTS#Cellular_architecture|"Cellular architecture"]] indicated by the colors white, yellow, and blue.<br>
 +
 
 +
*The&nbsp; $124$&nbsp; GSM frequency channels are further divided by time division multiplexing&nbsp; $\rm (TDMA)$.&nbsp; Each FDMA channel is divided into TDMA frames, which each comprise&nbsp; $N_{\rm T} = 8$&nbsp; time slots.
 +
 
 +
*The slots are periodically assigned to the individual GSM users and each contain a so-called&nbsp; [[Mobile_Communications/Characteristics_of_GSM#Data_and_frame_structure_for_GSM|$\text{Burst}$]].&nbsp; Each user has a time slot available in each TDMA frame.&nbsp; A bundling (maximum six per user) is only possible with GPRS/EDGE.<br>
 +
 
 +
*The TDMA frames of the uplink are sent delayed by three slots compared to the downlink: &nbsp; "Time Division Duplex"&nbsp; $\rm (TDD)$.&nbsp; The hardware of the mobile station can thus be used for sending and receiving a message simultaneously.
 +
 
 +
 
 +
== Data and frame structure for GSM ==
 
<br>
 
<br>
Bei GSM werden zwei Vielfachzugriffsverfahren parallel verwendet:
+
The mapping of logical to physical channels is done using the GSM frame structure.&nbsp; Here we only look to traffic channels and to the mapping in time.&nbsp; In this case, each multi&ndash;frame of &nbsp; $120 \ \rm ms$&nbsp;  duration is divided into&nbsp; $26$&nbsp; TDMA frames (two of them for control channels) of&nbsp; $4.615\ \rm ms$&nbsp;  duration.&nbsp; Thus, the duration of a time slot is approximately&nbsp; $T_{\rm Z} = 576.9\ \rm &micro; s$.<br>
*Frequenzmultiplex (<i>Frequency Division Multiple Access</i>, FDMA), und<br>
 
*Zeitmultiplex (<i>Time Division Multiple Access</i>, TDMA).<br>
 
  
[[File:P ID2204 Mob T 3 3 S2 v2.png|Realisierung von FDMA und TDMA bei GSM 900|class=fit]]<br>
+
[[File:EN_Mob_T_3_3_S2_v3.png||right|frame|Data and frame structure for GSM|class=fit]]
  
Die Grafik und die folgende Beschreibung gilt für das ursprüngliche System GSM 900 (D&ndash;Netz). Für GSM/DCS 1800 (E&ndash;Netz) gelten vergleichbare Aussagen.
+
You can see from this graphic:
*Im D&ndash;Netz werden für Uplink und Downlink jeweils eine Bandbreite von 25 MHz bereit gestellt (Duplexabstand: 45 MHz). Man spricht von <i>Frequency Division Duplex</i> (FDD). Beim E&ndash;Netz beträgt die Bandbreite jeweils 75 MHz und der Duplexabstand ist 95 MHz.<br>
+
*In each time slot one "burst" is transmitted, whose duration corresponds to&nbsp; $156.25$&nbsp; bits.&nbsp; The bit duration is&nbsp; $T_{\rm B} = 576.9\ \rm &micro; s/156.25 \approx 3.692 \ \rm &micro;s$&nbsp; and for the total gross data rate:
  
*Uplink&ndash; und Downlinkband werden in Frequenzbänder der Breite 200 kHz unterteilt. Unter Berücksichtigung von Schutzbereichen an den jeweiligen Rändern stehen somit <i>N</i><sub>F</sub> = 124 (D&ndash;Netz) bzw. <i>N</i> = 374 (E&ndash;Netz) Frequenzkanäle zur Verfügung.<br>
+
::<math>R_{\rm total} = {1}/{T_{\rm B}}= 270.833\,{\rm kbit/s}\hspace{0.05cm}.</math>
  
*Jeder Zelle wird  eine Teilmenge dieser Frequenzen zugewiesen &nbsp;&#8658;&nbsp; <i>Cell Allocation</i>. Benachbarte Zellen arbeiten meist bei unterschiedlichen Frequenzen, zum Beispiel mit dem Reuse&ndash;Faktor 3, wie im [http://en.lntwww.de/Mobile_Kommunikation/Gemeinsamkeiten_von_GSM_und_UMTS#Zellulare_Architektur Kapitel 3.2] durch die Farben Weiß, Gelb und Blau angedeutet.<br>
+
*The&nbsp; &raquo;'''gross data rate'''&laquo; &nbsp;of each user is&nbsp; $R_{\rm gross} = 33.854 \ \rm kbit/s$.&nbsp; But since in every normal burst only&nbsp; $2 &middot; 57 = 114$&nbsp; data bits (highlighted blue in the graphic) are transmitted, it results in the lower &nbsp;&raquo;'''net data rate'''&laquo;&nbsp; $R_{\rm net} = 22.8 \ \rm kbit/s$.<br>
  
*Die 124 GSM&ndash;Frequenzkanäle werden durch Zeitmultiplex (TDMA) weiter unterteilt. Jeder FDMA&ndash;Kanal wird in so genannte TDMA&ndash;Rahmen aufgeteilt, die ihrerseits jeweils <i>N</i><sub>T</sub> = 8 Zeitschlitze (<i>Time&ndash;Slots</i>) umfassen.<br>
+
*This net data rate also takes the channel coding into account.&nbsp; In the case of a speech signal, for every&nbsp; $20\ \rm kbit/s$&nbsp; speech frame&nbsp; $456$&nbsp; bits are transmitted, which results in exactly the rate&nbsp; $R_{\rm net} = 22.8 \ \rm kbit/s$. &nbsp; Without channel coding, the data rate would be only&nbsp; $13 \ \rm kbit/s$.<br>
  
*Die Slots werden periodisch den einzelnen GSM&ndash;Nutzern zugeordnet und beinhalten jeweils einen sog. [http://en.lntwww.de/Mobile_Kommunikation/Die_Charakteristika_von_GSM#Daten.E2.80.93_und_Rahmenstruktur_bei_GSM Burst.] Jedem Nutzer steht in jedem TDMA&ndash;Rahmen ein Zeitschlitz zur Verfügung. Eine Bündelung (maximal 6 pro User) ist nur bei GPRS/EDGE möglich.<br>
+
*In addition to the traffic data, a&nbsp; &raquo;'''normal burst'''&laquo;&nbsp; also contains
 +
:&ndash; &nbsp; twice three tailbits (red, during this time the channel is remeasured),
 +
:&ndash; &nbsp; two signaling bits (green),
 +
:&ndash; &nbsp; the "Guard Period"&nbsp; $\rm (GP)$&nbsp; with&nbsp; $8.25$&nbsp; bit duration $($grey, ca.&nbsp; $30.5 \ \rm &micro; s)$,
 +
:&ndash; &nbsp; $26$&nbsp; bit for a training sequence (for channel estimation and synchronization).
  
*Die TDMA&ndash;Rahmen des Uplinks werden gegenüber denen des Downlinks um drei Slots verzögert gesendet: <i>Time Division Duplex</i> (TDD). Die Hardware der Mobilstation kann somit gleichermaßen zum Senden und Empfangen einer Nachricht verwendet werden.<br><br>
+
These bits increase the data rate from&nbsp; $22.8$&nbsp; to&nbsp; $33.854 \ \rm kbit/s$.
  
== Daten– und Rahmenstruktur bei GSM ==
+
''Note:''
 +
*In GSM, besides the "Normal Burst" there are  some other&nbsp; [[Examples_of_Communication_Systems/Radio_Interface#The_different_burst_types_in_GSM|$\text{types of bursts}$]]:&nbsp; Frequency Correction Burst,&nbsp; Synchronization Burst,&nbsp; Dummy Burst,&nbsp; Access Burst, ... .
 +
*All these bursts have a uniform length of&nbsp; $156.25$&nbsp; bit durations.&nbsp; This is discussed in more detail in the&nbsp; [[Aufgaben:Exercise_3.2:_GSM Data Rates|"Excercise 3.2"]].
 +
 
 +
== Modulation method for GSM==
 
<br>
 
<br>
Durch die GSM&ndash;Rahmenstruktur erfolgt die Abbildung der logischen Kanäle auf physikalische Kanäle. Hier beschränken wir uns  auf Verkehrskanäle und auf die Abbildung in der Zeit. In diesem Fall wird jeder Multiframe von 120 ms Dauer in 26 TDMA&ndash;Rahmen (davon zwei für Kontrollkanäle) der Dauer 4.615 ms unterteilt. Damit ergibt sich für die Dauer eines Zeitschlitzes näherungsweise <i>T</i><sub>Z</sub> = 577 &mu;s.<br>
+
With GSM, only a bandwidth of&nbsp; $B = 200 \ \rm kHz$&nbsp; is available per frequency channel, in which a total data rate (for eight users) of&nbsp; $R_{\rm total} = 270.833 \ \rm kbit/s$&nbsp; must be transmitted.&nbsp; Required is therefore a modulation method with a bandwidth efficiency of at least
 +
 
 +
::<math>\beta \ge {R_{\rm total}}/{B} \approx 1.35 \,\,{\rm bit/s/Hz}.</math>
 +
 
 +
GSM uses the very bandwidth-efficient modulation method&nbsp; [[Examples_of_Communication_Systems/Radio_Interface#Gaussian_Minimum_Shift_Keying_.28GMSK.29| $\text{Gaussian Minimum Shift Keying}$]]&nbsp; $\rm (GMSK)$.&nbsp; It should again be expressly mentioned that this modulation method, just like the FDMA/TDMA multiple access, is exclusively based on the air interface between the mobile station&nbsp; $\rm (MS)$&nbsp; and the base transceiver station &nbsp; $\rm (BTS)$, which is highlighted in yellow in the&nbsp; [[Mobile_Communications/Characteristics_of_GSM#System_architecture_and_basic_units_of_GSM|$\text{system architecture graphic}$]]&nbsp; at the beginning of the chapter. <br>
 +
 
 +
GMSK has already been described in chapter&nbsp; [[Modulation_Methods/Non-Linear_Digital_Modulation#Properties_of_non-linear_modulation_methods| "Properties of nonlinear modulation methods"]]&nbsp; of the book "Modulation Methods".&nbsp; The most important properties are briefly summarized here.
 +
*GMSK is a special form of binary&nbsp; [[Modulation_Methods/Non-Linear_Digital_Modulation#FSK_.E2.80.93_Frequency_Shift_Keying| $\text{Frequency Shift Keying}$]]&nbsp; $\rm (FSK)$.&nbsp; A prerequisite for the orthogonality between the two waveforms is that the modulation index&nbsp; $h$&nbsp; is a multiple of&nbsp; $0.5$&nbsp;. For integer values of&nbsp; $h$&nbsp; the demodulation can also be performed non-coherently.<br>
 +
 
 +
*For GSM you use the smallest possible modulation index&nbsp; $h = 0.5$.&nbsp; A higher value would require a much larger bandwidth.&nbsp; Such an FSK with&nbsp; $h = 0.5$&nbsp; is also called [[Modulation_Methods/Non-Linear_Digital_Modulation#MSK_.E2.80.93_Minimum_Shift_Keying|$\text{Minimum Shift Keying}$]]&nbsp;&nbsp; $\rm (MSK)$.&nbsp; However, a coherent demodulation is then required.<br>
  
[[File:P ID2205 Mob T 3 3 S3a v2.png|Daten– und Rahmenstruktur bei GSM|class=fit]]<br>
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*A very narrow spectrum, however, is only obtained if the phase values at the symbol boundaries are matched to each other, thus avoiding phase jumps, which is given with MSK.&nbsp; Such methods are referred to as&nbsp; [[Modulation_Methods/Nonlinear_Digital_Modulation#General_Description_of_Continuous_Phase_Modulation|$\text{Continuous Phase Frequency Shift Keying}$]]&nbsp; $\rm (CP&ndash;FSK)$.&nbsp;<br>
  
Weiter erkennt man aus der Grafik:
+
*For GSM, a low-pass filter with Gaussian characteristic is inserted before the frequency modulator &nbsp; &#8658; &nbsp; [[Modulation_Methods/Nonlinear_Digital_Modulation#GMSK_.E2.80.93_Gaussian_Minimum_Shift_Keying|$\text{Gaussian Minimum Shift Keying}$]]&nbsp; $\rm (GMSK)$, which further reduces the bandwidth and improves bandwidth efficiency.<br><br>
*In jedem Zeitschlitz wird ein so genannter <i>Burst</i> übertragen, dessen Zeitdauer einheitlich 156.25 Bitdauern entspricht. Daraus folgt für die Bitdauer <i>T</i><sub>B</sub> = 576.9 &mu;s/156.25 &asymp; 3.692 &mu;s und für die Gesamt&ndash;Bruttodatenrate
 
  
::<math>R_{\rm ges} = \frac{1}{T_{\rm B}}= 270.833\,{\rm kbit/s}\hspace{0.05cm}.</math>
+
Regarding the topic treated here&nbsp; (coherent or non-coherent demodulation of FSK)&nbsp; we refer to two exercises in the book "Digital Signal Transmission":
 +
*[[Aufgaben:Aufgabe_4.16:_Binary_Frequency_Shift_Keying|Excercise 4.16: &nbsp; Binary Frequency Shift Keying]],<br>
  
*Die Bruttodatenrate eines jeden Nutzers beträgt somit <i>R</i><sub>Brutto</sub> = 33.854 kbit/s. Da in jedem <i>Normal Burst</i> aber nur 2 &middot; 57 = 114 Datenbit (in der Grafik blau hinterlegt) übertragen werden, ergibt sich für die Nettodatenrate mit  <i>R</i><sub>Netto</sub> = 22.8 kbit/s ein kleinerer Wert.<br>
+
*[[Aufgaben:Aufgabe_4.18Z:_BER_von_kohärenter_und_nichtkohärenter_FSK| Excercise 4.18Z: &nbsp; BER of coherent and non-coherent FSK]].<br><br>
  
*Diese Nettodatenrate berücksichtigt auch die Kanalcodierung. Bei einem Sprachsignal werden pro Sprachrahmen von 20 ms Dauer 456 Bit übertragen, woraus sich genau die Rate 22.8 kbit/s ergibt. Ohne Kanalcodierung wäre die Datenrate nur 13 kbit/s.<br>
 
  
*Neben den Verkehrsdaten enthält ein <i>Normal Burst</i> noch zweimal drei Tailbits (rot, in dieser Zeit wird der Kanal neu vermessen), zwei Signalisierungsbits (grün), 26 Bit für die Trainingssequenz (erforderlich für die Kanalschätzung und Synchronisation) sowie die <i>Guard Period</i> (GP) mit 8.25 Bitdauern (grau, ca. 30.5 &mu;s), wodurch sich die Datenrate von 22.8 auf 33.854 kbit/s erhöht.<br><br>
+
{{GraueBox|TEXT=  
 +
$\text{Example 1:}$&nbsp; The following graphic is to clarify the previous statements:
  
Anzumerken ist, dass bei GSM neben dem <i>Normal Burst</i> auch noch andere [http://en.lntwww.de/Beispiele_von_Nachrichtensystemen/Funkschnittstelle#Die_verschiedenen_Arten_von_Bursts Arten von Bursts] (<i>Frequency Correction Burst</i>, <i>Synchronization Burst</i>, <i>Dummy Burst</i>, <i>Access Burst</i>) eine Rolle spielen. Alle haben eine einheitliche Länge von 156.25 Bitdauern. Hierauf wird in der Aufgabe A3.2 genauer eingegangen.
+
[[File:EN_Mob_T_3_3_S4.png|right|frame|Block diagram and signals with GMSK|class=fit]]
  
== Modulationsverfahren bei GSM (1) ==
+
*Starting from a Dirac shaped source signal&nbsp; $q_\delta(t)$&nbsp; at point&nbsp; $(1)$&nbsp; you pass through a filter with the rectangular impulse response&nbsp; $g_{\rm R}(t)$&nbsp; to the rectangular signal&nbsp; $q_{\rm R}(t)$&nbsp; at point&nbsp; $(2)$.
<br>
 
Bei GSM steht pro Frequenzkanal lediglich eine Bandbreite von <i>B</i> = 200 kHz zur Verfügung, worin eine Gesamtdatenrate (für 8 Nutzer) von <i>R</i><sub>ges</sub> &asymp; 270 kbit/s übertragen werden muss. Man benötigt deshalb ein Modulationsverfahren mit einer Bandbreiteneffizienz
 
  
:<math>\beta \ge \frac{R_{\rm ges}}{B} \approx 1.35 \,\,{\rm bit/s/Hz}.</math>
+
*If the Gaussian low-pass  with the impulse response&nbsp; $h_{\rm G}(t)$&nbsp; were to be omitted &nbsp; &#8658; &nbsp; $q_{\rm G}(t) = q_{\rm R}(t)$, a sectionwise linear phase function&nbsp; $\phi(t)$&nbsp; would result at point&nbsp; $(4)$.&nbsp; All phase values would be multiples of&nbsp; $&pi;/2$&nbsp; at multiples of the symbol duration&nbsp; $T$.
  
GSM verwendet das sehr bandbreiteneffiziente Modulationsverfahren [http://en.lntwww.de/Modulationsverfahren/Nichtlineare_Modulationsverfahren#GMSK_.E2.80.93_Gaussian_Minimum_Shift_Keying Gaussian Minimum Shift Keying] (GMSK). Es sei nochmals ausdrücklich erwähnt, dass sich dieses Modulationsverfahren ebenso wie der FDMA/TDMA&ndash;Vielfachzugriff ausschließlich auf die Funkschnittstelle zwischen der <i>Mobile Station</i> (MS) und der <i>Base Transceiver Station </i> (BTS) bezieht, die in der [http://en.lntwww.de/Mobile_Kommunikation/Die_Charakteristika_von_GSM#Systemarchitektur_und_Basiseinheiten_von_GSM Systemarchitektur&ndash;Grafik] zu Beginn des Kapitels durch gelbe Hinterlegung hervorgehoben ist.<br>
+
*After the phase modulator, a binary FSK signal&nbsp; $s(t)$&nbsp; would appear at point&nbsp; $(5)$&nbsp; with only two frequencies.&nbsp; This signal is at the same time a MSK signal due to the minimum modulation index&nbsp; $h = 0.5$&nbsp; in case of orthogonality.
  
GMSK wurde bereits im Kapitel 4.4 des Buches &bdquo;Modulationsverfahren&rdquo; beschrieben. Hier werden nur die wesentlichen Eigenschaften kurz zusammengefasst.
+
*Through the Gaussian low-pass&nbsp; $H_{\rm G}(f)$&nbsp; with the cutoff frequency&nbsp; $f_{\rm G}= 0.45/T$&nbsp; (valid for GSM) the frequency impulse&nbsp; $g(t)$&nbsp; is no longer rectangular but corresponds to the rectangular response of&nbsp; $H_{\rm G}(f)$.&nbsp; According to the Fourier transform,&nbsp; $g(t) = g_{\rm R}(t) \star h_{\rm G}(t)$ applies.
*GMSK ist eine Sonderform von binärem [http://en.lntwww.de/Modulationsverfahren/Nichtlineare_Modulationsverfahren#FSK_.E2.80.93_Frequency_Shift_Keying_.281.29 Frequency Shift Keying] (FSK). Voraussetzung für die Orthogonalität zwischen den beiden Signalformen ist, dass der Modulationsindex <i>h</i> ein Vielfaches von 0.5 ist. Für ganzzahlige Werte von <i>h</i> kann die Demodulation auch nichtkohärent erfolgen.<br>
 
  
*Bei GSM verwendet man den kleinstmöglichen Modulationsindex <i>h</i> = 0.5. Ein größerer Wert würde eine deutlich größere Bandbreite beanspruchen. Eine solche FSK mit <i>h</i> = 0.5 nennt man auch [http://en.lntwww.de/Modulationsverfahren/Nichtlineare_Modulationsverfahren#MSK_.E2.80.93_Minimum_Shift_Keying Minimum Shift Keying] (MSK). Allerdings ist dann eine kohärente Demodulation erforderlich.<br>
+
*Thus, the phase function&nbsp; $\phi(t)$&nbsp; is no longer linear in sections but the corners are rounded, as can be seen from the phase function at point&nbsp; $(4)$.&nbsp; The violet&ndash;dotted curve applies to the data sequence assumed at point&nbsp; $(1)$.
  
*Ein sehr schmales Spektrum ergibt sich allerdings erst dann, wenn die Phasenwerte  an den Symbolgrenzen aneinander angepasst und dadurch Phasensprünge vermieden werden, was bei  MSK gegeben ist. Man bezeichnet solche Verfahren als [http://en.lntwww.de/Modulationsverfahren/Nichtlineare_Modulationsverfahren#Allgemeing.C3.BCltige_Beschreibung_der_CPMContinuous Phase Frequency Shift Keying] (CP&ndash;FSK).<br>
+
*The signal&nbsp; $s(t)$&nbsp; at point&nbsp; $(5)$&nbsp; of the block diagram is the GMSK signal.
  
*Bei GSM wird vor dem Frequenzmodulator noch ein Tiefpass mit Gauß&ndash;Charakteristik eingefügt &#8658; <i>Gaussian Minimum Shift Keying</i> (GMSK), wodurch die Bandbreite weiter verringert und die Bandbreiteneffizienz verbessert wird.<br><br>
 
  
Hinsichtlich der hier behandelten Thematik (kohärente bzw. nichtkohärente Demodulation von FSK) verweisen wir auf folgende Aufgaben im Buch &bdquo;Digitalsignalübertragung&rdquo;:
+
Note: &nbsp; The GMSK signal contains much more than just two discrete frequencies.&nbsp; Its power-spectral density decreases very fast, see&nbsp; [[Examples_of_Communication_Systems/Radio_Interface#Advantages_and_disadvantages_of_GMSK|$\text{diagram}$]]&nbsp; in the book "Examples of communication systems".&nbsp; From the above time representation at point&nbsp; $(5)$&nbsp; of the block diagram this fact is difficult to recognize.
*Aufgabe A4.16: Binary Frequency Shift Keying (Kapitel 4.4),<br>
+
<br clear=all>}}
*Aufgabe Z4.18: FSK kohärent/nichtkohärent (Kapitel 4.5).<br><br>
 
  
== Modulationsverfahren bei GSM (2) ==
+
== GSM extensions ==
 
<br>
 
<br>
[[File:P ID2206 Mob T 3 3 S4 v1.png|Blockschaltbild und Signale bei GMSK|class=fit]]<br>
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GSM was designed and developed as a European mobile radio system for telephone calls with the additional option of data transmission, but only at a low data rate&nbsp; $(9.6 \ \rm kbit/s)$.&nbsp; The standardization of the&nbsp; $\text{GSM-Phase 2}$&nbsp; however, from 1995 on, already included first further developments and some new additional services, already known from ISDN and appreciated by the users.<br>
  
Die obige Grafik soll die Aussagen der letzten Seite verdeutlichen.
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In the years from 1997 to 2000 new data services with higher bit rates were developed, which are attributed to the&nbsp; $\text{GSM-Phase 2+}$&nbsp; $($or&nbsp; $\text{GSM-Phase 2.5)}$:
*Ausgehend von einem diracförmigen Quellensignal <i>q<sub>&delta;</sub></i>(<i>t</i>) am Punkt (1) kommt man durch ein Filter mit der rechteckförmigen Impulsantwort <i>g</i><sub>R</sub>(<i>t</i>) zum Rechtecksignal <i>q</i><sub>R</sub>(<i>t</i>) am Punkt (2).
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*[[Examples_of_Communication_Systems/Weiterentwicklungen_des_GSM#High_Speed_Circuit.E2.80.93Switched_Data_.28HSCSD.29| $\text{High&ndash;Speed Circuit&ndash;Switched Data}$]]&nbsp; $\rm (HSCSD)$&nbsp; offers a line-oriented transmission with&nbsp; $14.4 \ \rm kbit/s$&nbsp; $($against $9.6 \ \rm kbit/s)$, if the channel is sufficiently good due to a higher code rate&nbsp; (dotting of the convolutional code).&nbsp; It also enables channel bundling by combining several time slots &nbsp; &#8658; &nbsp; "Multislot Capability".&nbsp; With a bundling of four time slots, this results in a maximum transmission rate of&nbsp; $57.6 \ \rm kbit/s$.<br>
  
*Würde man auf den Gaußtiefpass mit der Impulsantwort <i>h</i><sub>G</sub>(<i>t</i>) verzichten &#8658; <i>q</i><sub>G</sub>(<i>t</i>) = <i>q</i><sub>R</sub>(<i>t</i>), so ergäbe sich am Punkt (4) eine abschnittsweise lineare Phasenfunktion <i>&#981;</i>(<i>t</i>). Bei allen Vielfachen der Symboldauer <i>T</i> wären damit alle Phasenwerte Vielfache von &pi;/2.
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*[[Examples_of_Communication_Systems/Weiterentwicklungen_des_GSM#General_Packet_Radio_Service_.28GPRS.29|$\text{General Packet Radio Service}$]]&nbsp; $\rm  (GPRS)$&nbsp; enables communication with other networks such as the Internet or company intranets.&nbsp; It is packet-oriented&nbsp; (instead of line-oriented)&nbsp; and supports many data transfer protocols, for example the Internet Protocol (IP), X.25 and Datex&ndash;P.&nbsp; The charges for GPRS are not based on the connection duration, but on the amount of data transmitted.&nbsp; A GPRS user benefits from the shorter access times and the higher data rate up to&nbsp; $21.4 \ \rm kbit/s$.&nbsp; By the bundling of six time slots one reaches so maximally&nbsp; $128.4 \ \rm kbit/s$.<br>
  
*Nach dem Phasenmodulator würde dann am Punkt (5) ein binäres FSK&ndash;Signal <i>s</i>(<i>t</i>) mit nur zwei Frequenzen auftreten. Aufgrund des bei Orthogonalität minimalen Modulationsindex <nobr><i>h</i> = 0.5</nobr> ist <i>s</i>(<i>t</i>) gleichzeitig ein MSK&ndash;Signal.
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*[[Examples_of_Communication_Systems/Weiterentwicklungen_des_GSM#Enhanced_Data_Rates_for_GSM_Evolution|$\text{Enhanced Data Rates for GSM Evolution}$]]&nbsp; $\rm  (EDGE)$&nbsp; used in addition to GSM standard "GMSK" as a further modulation method&nbsp; [[Modulation_Methods/Quadrature_Amplitude_Modulation#Other_signal_space_constellations|$\text{8-PSK}$]], so that with each symbol three data bits are transmitted and in this way the data rate can (theoretically) be tripled. <br><br>
  
*Durch den Gaußtiefpass <i>H</i><sub>G</sub>(<i>f</i>) mit der Grenzfrequenz <i>f</i><sub>G</sub>  = 0.45/<i>T</i> (gültig für GSM) ist der Frequenzimpuls <i>g</i>(<i>t</i>) nicht mehr rechteckförmig, sondern entspricht der Rechteckantwort von <i>H</i><sub>G</sub>(<i>f</i>). Nach den Gesetzen der Fouriertransformation gilt <i>g</i>(<i>t</i>) = <i>g</i><sub>R</sub>(<i>t</i>) &#8727; <i>h</i><sub>G</sub>(<i>t</i>).
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With the combination of GPRS and EDGE &ndash; one speaks then of&nbsp; $\text{E-GPRS}$&nbsp; &ndash; there are nine different&nbsp; [[Examples_of_Communication_Systems/Weiterentwicklungen_des_GSM#Enhanced_Data_Rates_for_GSM_Evolution|$\text{Modulation and Coding Schemes}$]]&nbsp; $\rm (MCS)$, between which the operator can choose:
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*with GMSK or with 8&ndash;PSK modulation,<br>
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*resulting code rates between&nbsp; $0.37$&nbsp; and&nbsp; $1.00$, and<br>
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*data rates between&nbsp; $8.8 \ \rm kbit/s$&nbsp; (for MCS&ndash;1) and&nbsp; $59.2 \ \ \rm kbit/s$&nbsp; (for MCS&ndash;9).<br><br>
  
*Somit steigt die Phasenfunktion <i>&#981;</i>(<i>t</i>) nicht mehr abschnittsweise linear an oder fällt linear ab, sondern die Ecken sind abgerundet, wie aus dem Signalverlauf am Punkt (4) zu ersehen ist. Die violett&ndash;gepunktete Kurve gilt für die am Punkt (1) angenommene Datenfolge.
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In practice, however, MCS&ndash;8&nbsp; $(54.4 \ \rm kbit/s)$&nbsp; and seven time slots are the maximum applicable.&nbsp; With this, one reaches&nbsp; $380.8 \ \rm kbit/s$&nbsp; and thus the order of magnitude of UMTS&nbsp; $(384 \ \rm kbit/s)$.<br>
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We should also mention the&nbsp; [[Mobile_Communications/General_Information_on_the_LTE_Mobile_Communications_Standard#Development_of_the_UMTS_mobile_phone_standards_towards_LTE|$\text{EDGE Evolution}$]]&nbsp; or "Evolved EDGE", i.e. the further development of the evolution of GSM in Release 7 (December 2007). For this, the developers specify data rates up to&nbsp; $1 \ \rm Mbit/s$&nbsp; and halved latency times&nbsp; $(10 \ \rm ms$ instead of $20 \ \rm ms)$&nbsp;. These values can be achieved among other things
 +
*by&nbsp; 32&ndash;QAM or &nbsp;16&ndash;QAM Modulation instead of 8&ndash;PSK,
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* an improved error correction through the use of&nbsp; [[Channel_Coding/Grundlegendes_zu_den_Turbocodes| $\text{Turbo codes}$]], and
 +
* an increase of the symbol rate of&nbsp; $20\%$&nbsp; from&nbsp; $270.833 \ \rm ksymbol/s$&nbsp; to&nbsp; $325\ \rm ksymbol/s$.<br>
 +
 
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==Exercises for the chapter==
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<br>
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[[Aufgaben:Exercise 3.5: GMSK Modulation]]
  
*Das GMSK&ndash;Signal <i>s</i>(<i>t</i>) beinhaltet nun deutlich mehr als nur zwei diskrete Frequenzen und das Leistungsdichtespektrum fällt schneller ab, wie das [http://en.lntwww.de/Beispiele_von_Nachrichtensystemen/Funkschnittstelle#Vor.E2.80.93_und_Nachteile_von_GMSK Diagramm] im Buch &bdquo;Beispiele von Nachrichtensystemen&rdquo; zeigt. Aus der obigen Zeitdarstellung des Sendesignals <i>s</i>(<i>t</i>) am Punkt (5) des Blockschaltbildes ist dieser Sachverhalt allerdings nur schwer zu erkennen.
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[[Aufgaben:Exercise 3.5Z: GSM Network Components]]
  
 
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Latest revision as of 18:41, 20 February 2023

System architecture and basic units of GSM


$\rm GSM$  $\rm (G$lobal  $\rm S$ystem  for  $\rm M$obile Communication$)$  is a strongly hierarchically structured system of different network components.  You can see from the graphic:

GSM system architecture
  • The mobile station  $\rm (MS)$  communicates via the radio interface with the nearest  base transceiver station  $\rm (BTS$, transmit and receive base station).
  • Several such BTS's are grouped together area by area and are jointly subordinate to a  base station controller  $\rm (BSC$, control station$)$.
  • The  base station sub–system  $\rm(BSS)$  consists of a multitude of BTS's and several BSC's.  In the graphic such a  BSS  is framed in blue.
  • Each BSC is connected to a mobile switching center  $\rm (MSC$, switching computer$)$, whose function is comparable to a switching node in the fixed network.
  • The gateway mobile switching center  $\rm (GMSC)$  is responsible for the connection between the fixed and mobile networks.  For example, if a mobile subscriber is called from the fixed network, the GMSC determines the responsible MSC and transfers the call.
  • The operation and maintenance center  $\rm (OMC)$  monitors a part of the mobile network.  It also takes on organizational tasks such as traffic flow control, charging, security management, etc.


More detailed information on GSM system architecture and the individual network components can be found in the chapter  "General Description of GSM"  of the book "Examples of Communication Systems".

Multiple access with GSM


Realization of FDMA and TDMA with "GSM 900"

GSM uses two multiple access methods in parallel:

  • $\text{Frequency Division Multiple Access}$   $\rm (FDMA)$,
  • $\text{Time Division Multiple Access}$   $\rm (TDMA)$.


The graphic and the following description is valid for the original system "GSM 900" (in the following:  "GSM–D"). 

For "GSM/DCS 1800"  ⇒   "GSM–E" comparable statements apply.

  • With "GSM–D", a bandwidth of  $25\ \rm MHz$  is provided for uplink and downlink respectively  $($duplex spacing:  $45\ \rm MHz)$.  This is called  "Frequency Division Duplex"  $\rm (FDD)$.  For "GSM–E", the bandwidth is  $75\ \rm MHz$  and the duplex spacing is  $95\ \rm MHz$.
  • Uplink and downlink bands are divided into frequency bands of width  $200\ \rm kHz$.  Taking into account the protection areas at the respective edges, there are  $N_{\rm F} = 124$  (GSM–D) or  $N_{\rm F} = 374$  (GSM–E) frequency channels.
  • Each cell is assigned a subset of the frequencies   ⇒   "Cell Allocation".  Neighboring cells usually work at different frequencies, for example with the reuse–factor  $3$, as in section  "Cellular architecture" indicated by the colors white, yellow, and blue.
  • The  $124$  GSM frequency channels are further divided by time division multiplexing  $\rm (TDMA)$.  Each FDMA channel is divided into TDMA frames, which each comprise  $N_{\rm T} = 8$  time slots.
  • The slots are periodically assigned to the individual GSM users and each contain a so-called  $\text{Burst}$.  Each user has a time slot available in each TDMA frame.  A bundling (maximum six per user) is only possible with GPRS/EDGE.
  • The TDMA frames of the uplink are sent delayed by three slots compared to the downlink:   "Time Division Duplex"  $\rm (TDD)$.  The hardware of the mobile station can thus be used for sending and receiving a message simultaneously.


Data and frame structure for GSM


The mapping of logical to physical channels is done using the GSM frame structure.  Here we only look to traffic channels and to the mapping in time.  In this case, each multi–frame of   $120 \ \rm ms$  duration is divided into  $26$  TDMA frames (two of them for control channels) of  $4.615\ \rm ms$  duration.  Thus, the duration of a time slot is approximately  $T_{\rm Z} = 576.9\ \rm µ s$.

Data and frame structure for GSM

You can see from this graphic:

  • In each time slot one "burst" is transmitted, whose duration corresponds to  $156.25$  bits.  The bit duration is  $T_{\rm B} = 576.9\ \rm µ s/156.25 \approx 3.692 \ \rm µs$  and for the total gross data rate:
\[R_{\rm total} = {1}/{T_{\rm B}}= 270.833\,{\rm kbit/s}\hspace{0.05cm}.\]
  • The  »gross data rate«  of each user is  $R_{\rm gross} = 33.854 \ \rm kbit/s$.  But since in every normal burst only  $2 · 57 = 114$  data bits (highlighted blue in the graphic) are transmitted, it results in the lower  »net data rate«  $R_{\rm net} = 22.8 \ \rm kbit/s$.
  • This net data rate also takes the channel coding into account.  In the case of a speech signal, for every  $20\ \rm kbit/s$  speech frame  $456$  bits are transmitted, which results in exactly the rate  $R_{\rm net} = 22.8 \ \rm kbit/s$.   Without channel coding, the data rate would be only  $13 \ \rm kbit/s$.
  • In addition to the traffic data, a  »normal burst«  also contains
–   twice three tailbits (red, during this time the channel is remeasured),
–   two signaling bits (green),
–   the "Guard Period"  $\rm (GP)$  with  $8.25$  bit duration $($grey, ca.  $30.5 \ \rm µ s)$,
–   $26$  bit for a training sequence (for channel estimation and synchronization).

These bits increase the data rate from  $22.8$  to  $33.854 \ \rm kbit/s$.

Note:

  • In GSM, besides the "Normal Burst" there are some other  $\text{types of bursts}$:  Frequency Correction Burst,  Synchronization Burst,  Dummy Burst,  Access Burst, ... .
  • All these bursts have a uniform length of  $156.25$  bit durations.  This is discussed in more detail in the  "Excercise 3.2".

Modulation method for GSM


With GSM, only a bandwidth of  $B = 200 \ \rm kHz$  is available per frequency channel, in which a total data rate (for eight users) of  $R_{\rm total} = 270.833 \ \rm kbit/s$  must be transmitted.  Required is therefore a modulation method with a bandwidth efficiency of at least

\[\beta \ge {R_{\rm total}}/{B} \approx 1.35 \,\,{\rm bit/s/Hz}.\]

GSM uses the very bandwidth-efficient modulation method  $\text{Gaussian Minimum Shift Keying}$  $\rm (GMSK)$.  It should again be expressly mentioned that this modulation method, just like the FDMA/TDMA multiple access, is exclusively based on the air interface between the mobile station  $\rm (MS)$  and the base transceiver station   $\rm (BTS)$, which is highlighted in yellow in the  $\text{system architecture graphic}$  at the beginning of the chapter.

GMSK has already been described in chapter  "Properties of nonlinear modulation methods"  of the book "Modulation Methods".  The most important properties are briefly summarized here.

  • GMSK is a special form of binary  $\text{Frequency Shift Keying}$  $\rm (FSK)$.  A prerequisite for the orthogonality between the two waveforms is that the modulation index  $h$  is a multiple of  $0.5$ . For integer values of  $h$  the demodulation can also be performed non-coherently.
  • For GSM you use the smallest possible modulation index  $h = 0.5$.  A higher value would require a much larger bandwidth.  Such an FSK with  $h = 0.5$  is also called $\text{Minimum Shift Keying}$   $\rm (MSK)$.  However, a coherent demodulation is then required.
  • A very narrow spectrum, however, is only obtained if the phase values at the symbol boundaries are matched to each other, thus avoiding phase jumps, which is given with MSK.  Such methods are referred to as  $\text{Continuous Phase Frequency Shift Keying}$  $\rm (CP–FSK)$. 
  • For GSM, a low-pass filter with Gaussian characteristic is inserted before the frequency modulator   ⇒   $\text{Gaussian Minimum Shift Keying}$  $\rm (GMSK)$, which further reduces the bandwidth and improves bandwidth efficiency.

Regarding the topic treated here  (coherent or non-coherent demodulation of FSK)  we refer to two exercises in the book "Digital Signal Transmission":


$\text{Example 1:}$  The following graphic is to clarify the previous statements:

Block diagram and signals with GMSK
  • Starting from a Dirac shaped source signal  $q_\delta(t)$  at point  $(1)$  you pass through a filter with the rectangular impulse response  $g_{\rm R}(t)$  to the rectangular signal  $q_{\rm R}(t)$  at point  $(2)$.
  • If the Gaussian low-pass with the impulse response  $h_{\rm G}(t)$  were to be omitted   ⇒   $q_{\rm G}(t) = q_{\rm R}(t)$, a sectionwise linear phase function  $\phi(t)$  would result at point  $(4)$.  All phase values would be multiples of  $π/2$  at multiples of the symbol duration  $T$.
  • After the phase modulator, a binary FSK signal  $s(t)$  would appear at point  $(5)$  with only two frequencies.  This signal is at the same time a MSK signal due to the minimum modulation index  $h = 0.5$  in case of orthogonality.
  • Through the Gaussian low-pass  $H_{\rm G}(f)$  with the cutoff frequency  $f_{\rm G}= 0.45/T$  (valid for GSM) the frequency impulse  $g(t)$  is no longer rectangular but corresponds to the rectangular response of  $H_{\rm G}(f)$.  According to the Fourier transform,  $g(t) = g_{\rm R}(t) \star h_{\rm G}(t)$ applies.
  • Thus, the phase function  $\phi(t)$  is no longer linear in sections but the corners are rounded, as can be seen from the phase function at point  $(4)$.  The violet–dotted curve applies to the data sequence assumed at point  $(1)$.
  • The signal  $s(t)$  at point  $(5)$  of the block diagram is the GMSK signal.


Note:   The GMSK signal contains much more than just two discrete frequencies.  Its power-spectral density decreases very fast, see  $\text{diagram}$  in the book "Examples of communication systems".  From the above time representation at point  $(5)$  of the block diagram this fact is difficult to recognize.

GSM extensions


GSM was designed and developed as a European mobile radio system for telephone calls with the additional option of data transmission, but only at a low data rate  $(9.6 \ \rm kbit/s)$.  The standardization of the  $\text{GSM-Phase 2}$  however, from 1995 on, already included first further developments and some new additional services, already known from ISDN and appreciated by the users.

In the years from 1997 to 2000 new data services with higher bit rates were developed, which are attributed to the  $\text{GSM-Phase 2+}$  $($or  $\text{GSM-Phase 2.5)}$:

  • $\text{High–Speed Circuit–Switched Data}$  $\rm (HSCSD)$  offers a line-oriented transmission with  $14.4 \ \rm kbit/s$  $($against $9.6 \ \rm kbit/s)$, if the channel is sufficiently good due to a higher code rate  (dotting of the convolutional code).  It also enables channel bundling by combining several time slots   ⇒   "Multislot Capability".  With a bundling of four time slots, this results in a maximum transmission rate of  $57.6 \ \rm kbit/s$.
  • $\text{General Packet Radio Service}$  $\rm (GPRS)$  enables communication with other networks such as the Internet or company intranets.  It is packet-oriented  (instead of line-oriented)  and supports many data transfer protocols, for example the Internet Protocol (IP), X.25 and Datex–P.  The charges for GPRS are not based on the connection duration, but on the amount of data transmitted.  A GPRS user benefits from the shorter access times and the higher data rate up to  $21.4 \ \rm kbit/s$.  By the bundling of six time slots one reaches so maximally  $128.4 \ \rm kbit/s$.

With the combination of GPRS and EDGE – one speaks then of  $\text{E-GPRS}$  – there are nine different  $\text{Modulation and Coding Schemes}$  $\rm (MCS)$, between which the operator can choose:

  • with GMSK or with 8–PSK modulation,
  • resulting code rates between  $0.37$  and  $1.00$, and
  • data rates between  $8.8 \ \rm kbit/s$  (for MCS–1) and  $59.2 \ \ \rm kbit/s$  (for MCS–9).

In practice, however, MCS–8  $(54.4 \ \rm kbit/s)$  and seven time slots are the maximum applicable.  With this, one reaches  $380.8 \ \rm kbit/s$  and thus the order of magnitude of UMTS  $(384 \ \rm kbit/s)$.

We should also mention the  $\text{EDGE Evolution}$  or "Evolved EDGE", i.e. the further development of the evolution of GSM in Release 7 (December 2007). For this, the developers specify data rates up to  $1 \ \rm Mbit/s$  and halved latency times  $(10 \ \rm ms$ instead of $20 \ \rm ms)$ . These values can be achieved among other things

  • by  32–QAM or  16–QAM Modulation instead of 8–PSK,
  • an improved error correction through the use of  $\text{Turbo codes}$, and
  • an increase of the symbol rate of  $20\%$  from  $270.833 \ \rm ksymbol/s$  to  $325\ \rm ksymbol/s$.

Exercises for the chapter


Exercise 3.5: GMSK Modulation

Exercise 3.5Z: GSM Network Components