Modulation Methods/Tasks and Classification

1. Modulation Methods
2. Multiple Access Methods
3. Tasks and Classification

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# OVERVIEW OF THE FIFTH MAIN CHAPTER #

In the last chapter of the book  "Modulation Methods",  two examples of modern digital modulation methods are discussed,  namely   »CDM«   and  »OFDM«   which are also frequently used as multiple access methods under the names  »CDMA«  and  »OFDMA«. 

•   In  $\rm CDMA$  $($"Code Division Multiple Access"$)$,  a specific spreading sequence is provided for each subscriber.  Such spreading sequences – and thus also the overall signal – are high-frequency compared to the useful signal,  so this method is also known as  "Band Spreading".   It is used in particular in third-generation cellular networks such as  $\rm UMTS$. 

•   $\rm OFDM$  $($"Orthogonal Frequency Division Multiplex"$)$  is a multicarrier modulation method based on the orthogonality of the carriers used,  which are usually very many.  Due to its advantageous properties,  it is frequently used in wired systems  $($example:   $\rm xDSL)$  and since 2010 also in mobile systems.  In particular, it is used in fourth-generation  $\rm (4G)$  cellular networks as a multiple access method  $\rm (OFDMA)$.   More detailed information can be found in the chapter  $\rm LTE$  of the book  "Mobile Communications".

This chapter deals in detail with

1. the  »tasks of multiple access methods«  in general,
2. a general description of  »band spreading techniques and CDMA«,
3. some  »realization aspects and applications of CDMA«,
4. a  »general description of OFDM« ,
5. some  »realization aspects and applications of OFDM«.

Multiplexer and demultiplexer

So far, we have always assumed a single message source that transmits information

• to a single sink  (»point-to-point connection«),  or
• supplies several participants at the same time  (»point-to-multipoint connection«,  "broadcast").

However,  this rarely corresponds to the situations that occur in practice.  Rather,  a communication system - at least one that is economically viable - serves many subscribers who want to send information while acting as a message sink for the other subscribers.

For each class of application,  there is usually only a limited amount of frequency bandwidth available.  In radio systems in particular,  bandwidth - since it cannot be increased at will - is an important resource. 

The  "World Administrative Radio Conference"  (WARC)  coordinates the use of the frequencies available today and in the future worldwide.  Engineers have the task of using the frequency band made available for an application as effectively as possible and thus supplying as many subscribers as possible.

Schematic diagram for multiplexing

The graphic shows the procedure:

• The  $K$  source signals  $q_1(t)$, ... , $q_K(t)$  are each suitably modulated,  combined by the multiplexer  $\rm (MUX)$  to form the transmitted signal  $s(t)$  and then transmitted via the common physical channel.

• The demultiplexer  $\rm (DEMUX)$  has the task of extracting the information for the  $K$  subscribers  (sinks)  from the received signal  $r(t)$  and forwarding it to the desired subscriber.

FDMA, TDMA, and CDMA

Diagram of FDMA, TDMA and CDMA multiple access methods

The diagram with the three axes, namely  "time",  "frequency"  and  "power"  illustrates three widely used  »Multiple Access Methods«, namely

1.   Frequency Division Multiple Access  $\rm (FDMA)$,
2.   Time Division Multiple Access  $\rm (TDMA)$, and
3.   Code Division Multiple Access  $\rm (CDMA)$.

"Multiple Access Method"  indicates that there are several transmitter-receiver pairs that independently share a transmission medium.

• In mobile communications,  this transmission medium is the radio interface,  in simplified terms the  "air”  in the environment of a base station.
• The allocation is done either with a central instance in the base station or the subscribers work with collision detection.

»Multiplexing«,  on the other hand,  is when a multiplexer bundles several signals at the beginning of a transmission path  (as shown in the  $\text{previous diagram}$)  and a demultiplexer splits this common signal again at the end.  In this case, the abbreviations FDM, TDM and CDM are used instead of FDMA, TDMA and CDMA:

1.   Frequency Division Multiplexing  $\rm (FDM)$,
2.   Time Division Multiplexing  $\rm (TDM)$, and
3.   Code Division Multiplexing  $\rm (CDM)$.

The processes shown in the diagram can be characterized as follows:

• In  "Frequency Division Multiple Access",  each of the  $K$  users is allocated only a portion of the total bandwidth  $B$  and can transmit continuously (analog or digital) within it.  As already described in detail in the introductory chapter  "Objectives of Modulation and Demodulation",  all users can transmit simultaneously at different carrier frequencies without any deterioration in transmission quality.  The prerequisite is that no user occupies more than the currently permissible bandwidth  $B/K$  and that filters with arbitrarily steep edges are also available for channel separation.  Otherwise,  protective distances between the individual frequency bands must be observed.

• In  "Time Division Multiple Access",  on the other hand,  all $K$  subscribers use the entire frequency band  $B$, but only for a fraction  $(1/K)$  of the time.  In the case of time-continuous symbols,  time division multiplexing requires intermediate storage at the transmitter,  blockwise transmission at a data rate that is higher by a factor of  $K$,  and a facility at the receiver,  which reassembles the blocks in the individual time slots to form a continuous data stream.

• In  "Code Division Multiple Access",  the same frequency band of width  $B$  is shared by all subscribers at all times;  they are virtually on top of each other in terms of power.  In order to be able to separate the subscriber signals at the receiver, they are multiplied at the transmitter by a periodic binary sequence with a higher frequency than the useful bandwidth by a factor of  $J ≥ K$,  which corresponds spectrally to a band spreading by this factor  $J$.  
• This is referred to as  »PN modulation«  or  "Direct Sequence Spread Spectrum".  If  $J$  mutually orthogonal spread sequences are found,  then under ideal conditions,  up to  $J$  users can occupy the common channel simultaneously without mutual interference,  but each only with the useful bandwidth  $B/J$  (based on the data rate).  Due to the band spreading,  however,  each user occupies the entire frequency band  $B$  at all times.

For the sake of completeness,  another multiple access method should be mentioned:  Space Division Multiple Access  $\rm (SDMA)$. 

• Here,  the use of group antennas  (also called antenna arrays)  at the transmitter enables selective spatial propagation of the signal components. 
• The individual users are separated at the receiver by the spatial position of the respective end devices.

Application examples

(1)  $\text{Time Division Multiplexing}$  $\rm (TDM)$  has been used for a very long time,  for example in the  "Plesiochronous Digital Hierarchy"  $\rm (PDH)$  standardized in 1972.

• Starting from a data rate of  $\text{2.048 Mbit/s}$,  the higher bit rates  $\text{8.448, 34.368, 139.264}$  and  $\text{564.992 Mbit/s}$  are obtained,  in each case by quadrupling,  taking into account a certain overhead.  
• Since 1988,  there is still the  "Synchronous Digital Hierarchy"  $\rm (SDH)$  with the data rates  $\text{155.52, 622.08, 2488.32, 9953.28, 39813.12 Mbit/s ≈ 40 Gbit/s}$  $($in each case exactly the factor $4)$,  which is used in the newer optical systems.

(2)  The oldest multiplexing method is  $\text{Frequency Division Multiplexing}$  $\rm (FDM)$,  which has been used since the early days of analog broadcasting technology in the 1930s. 

• For example,  the "VHF II" range – in Germany better known as "UKW" – covers the frequency range from  $\text{87.5}$  to  $\text{108 MHz}$, i.e. a bandwidth of  $\text{20.5 MHz}$. 
• With the original frequency grid of  $\text{300 kHz}$,  $K = 68$  channels could be provided.  Nowadays,  the channel spacing is usually narrower,  with  $\text{150 kHz}$  intervals.

(3)  The European mobile communications standard  $\rm GSM$  ("Global System for Mobile Communications")  introduced in the early 1990s also uses an FDMA component in addition to a TDMA component  (eight time slots per frequency channel). 

• For the connection from the mobile station to the base station   ⇒   "uplink",  the frequency range  $890.1$ ...  $914.9 \ \rm MHz$  is used and in the opposite direction  ⇒   "downlink"  the range  $935.1$ ...  $959.9 \ \rm MHz$.
• The entire bandwidth  $B\text{ = 24.8 MHz}$  available in the so-called  "D band"  for uplink and downlink is divided by  "Frequency Division Multiplexing"  $\rm (FDMA)$  into  $124$  bands, each  $\text{200 kHz}$  wide. 
• The maximum possible number of channels is thus  (theoretically)  $\text{8 · 124 = 992}$.  However,  since neighboring cells must not use the same frequencies,  as this would result in a considerable loss of quality at the cell boundaries,  the maximum possible number of channels for the GSM system is  $\text{330}$  $($reuse factor $3)$.

(4)   "Orthogonal Frequency Division Multiplex"  $\rm (OFDM)$,  which is described in detail in the  "second part of this chapter",  is of great importance.

• Both the wired  $\rm DSL$  ("Digital Subscriber Line")  and the 4G mobile communications system  $\rm LTE$  ("Long Term Evolution")  are based on this.
• These are multi-carrier systems in which the individual spectral functions overlap but do not interfere with each other due to orthogonality.

(5)  Before that, we will look at different variants of band spreading methods and  "Code Division Multiple Access"  $\rm (CDMA)$ in the three following chapters.  This is used,  for example,  in the 3G mobile communications standard  $\rm UMTS$  ("Universal Mobile Telecommunications System"). 

Exercises for the chapter

Exercise 5.1: FDMA, TDMA and CDMA

Exercise 5.1Z: GSM System/E–Band