Wireless systems – GSM
2015-05-04
Simon Sörman
Contents
1
Introduction ..................................................................................................................................... 1
2
Channels .......................................................................................................................................... 2
2.1
3
2.1.1
FDMA/TDMA ................................................................................................................... 2
2.1.2
Bursts ............................................................................................................................... 3
2.2
Logical channels....................................................................................................................... 3
2.3
Mapping of logical channels to physical channels .................................................................. 4
Radio path ....................................................................................................................................... 6
3.1
4
5
Physical channels ..................................................................................................................... 2
Synchronization ....................................................................................................................... 6
3.1.1
Time synchronization ...................................................................................................... 6
3.1.2
Frequency synchronization ............................................................................................. 6
3.2
Connection and random access .............................................................................................. 6
3.3
Power management ................................................................................................................ 7
3.4
Handoff .................................................................................................................................... 7
3.5
Equalization ............................................................................................................................. 7
Modulation ...................................................................................................................................... 9
4.1
GMSK ....................................................................................................................................... 9
4.2
Other modulations ................................................................................................................ 10
Coding ............................................................................................................................................ 11
5.1
Channel coding ...................................................................................................................... 11
5.1.1
Full rate TCH .................................................................................................................. 11
5.1.2
SACCH, SDCCH, FACCH, BCCH, PCH, AGCH, NCH and CBCH .......................................... 11
5.2
Source coding (Full Rate speech) .......................................................................................... 12
6
Summary........................................................................................................................................ 14
7
References ..................................................................................................................................... 15
Abstract
In the 1980s work started to develop the second generation mobile phone system, GSM. It was at
first commercialized in 1991 and has as of today spread world-wide. Even though the fourth
generation is currently deployed in some places, GSM still is in use in many of those areas.
In this paper we will delve into some basic wireless aspects of this cellular technology and present
the foundations of this cellular system.
Abbreviations
AB
AGCH
BCCH
BTS
DB
EFR
FACCH
FB
FCCH
FN
GMSK
MS
NB
NCH
PCH
RACH
RPE-LTP
SACCH
SB
SCH
SDCCH
SF
TCH
TN
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Access Burst
Access Grant Channel
Broadcast Control Channel
Base Transceiver Station
Dummy Burst
Enhanced Full Rate
Fast Associated Control Channel
Frequency Correction Burst
Frequency Control Channel
Frame number
Gaussian Minimum Shift Keying
Mobile Station
Normal Burst
Notification Channel
Paging Channel
Random Access Control Channel
Regular Pulse Excitation – Long Term Prediction
Slow Associated Control Channel
Synchronization Burst
Synchronization Channel
Stand-alone Dedicated Control Channel
Stealing flag
Transport Channel
Time slot Number
1 Introduction
This paper is part of the course TSKS03 Wireless Systems given at Linköping University during the
spring term of 2015. It is aimed at describing typical wireless telecommunications aspects, at the
lower layers of the OSI model, of the widespread GSM standard; such as modulation techniques,
channel coding, radio characteristics etc. The GSM standard is however quite broad and this paper
will only be able to go into details of a few parts of it. The interested reader is referred to the
specification 3GPP TS 41.101 for further information and reading about the GSM system.
When reading about GSM and comparing to other wireless systems, one should keep in mind that
GSM was designed for mobile telephony, i.e. it was heavily customized towards telephone calls and
only small amounts of other data. A larger support for other data (e.g. internet data) was added later
in the GSM development. Importantly, in terms of infrastructure GSM is a cell based system with a
Base Transceiver Station (BTS) in each cell handling all Mobile Stations (MS) committed to that
particular BTS.
1
2 Channels
In this chapter we present the different channels of the GSM system. The chapter begins with an
explanation of the physical channel partitioning, followed by a presentation of the numerous logical
channels and their function.
2.1 Physical channels
This section treats the physical channel arrangement with multiplexing both in the frequency domain
(FDMA) and the time domain (TDMA), and how the partitioning is used.
2.1.1 FDMA/TDMA
A GSM system uses 2 frequency bands of equal width, one for uplink and one for downlink. Since the
GSM standard has spread throughout the entire globe, different bands are allocated at different
places in the world. For the sake of this paper we will limit the discussion to P-GSM. This allocation
uses 890-915 MHz for uplink traffic and 935-960 MHz for downlink. This is split into radio channels of
200 kHz width, and placed such that the first and last 100 kHz of the bands are unused (this is for
protection). In GSM-900 this allows for 124 duplex channels. However, each base station is allocated
only a set of these, called the Cell Allocation (CA). (Eberspächer et al., 2009)
Apart from this frequency division multiplexing, GSM also uses time division multiplexing by splitting
each channel into 8 time slots of
3
5200
𝑠 ≈ 577 𝜇𝑠 each. These 8 slots together form what is called
the TDMA frame with duration of ≈ 4.62 𝑚𝑠. At the base transceiver station the timing of the uplink
frame is delayed by 3 time slots as compared to the downlink frame. At the mobile station (MS) this
delay is variable, which allows the MS to adjust for the signal propagation delay. The delay also
makes it possible to build a cheaper and more efficient MS since it doesn’t need a high-frequency
duplexing unit. The organization of the FDMA and the TDMA is presented graphically in figure 1.
(3GPP TS 45.002)
Figure 1: FDMA and TDMA in GSM (Eberspächer et al., 2009)
The TDMA frames are further grouped into multiframes, comprising either 26 or 51 normal frames. A
larger grouping, consisting of 26 ∗ 51 = 1350 frames is called a superframe, i.e. this contains 51 26multiframes and/or 51 26-multiframes. The duration of 2048 superframes is called a hyperframe and
2
each TDMA frame of a hyperframe has a unique frame number (FN) that is used for encryption
purposes. (3GPP TS 45.002)
2.1.2 Bursts
The physical use of a time slot is called a burst (i.e. modulated data), and for this discussion we will
present five types of bursts. The timeslot is divided into 156,25 symbol periods, and in this section
we will assume that the modulation used is GMSK (see Section 4) which results in one bit per symbol.
The structure of the bursts is visible in figure 2:
Figure 2: The structure of bursts in GSM (Eberspächer et al., 2009)
The 3 tail bits at the start and end of each burst are all set to 0, and these periods can be used to
ramp up/down power (the 8 tail bits at the start of the Access Burst are not all 0). Different bursts
are separated from each other by a guard period.
The Normal Burst (NB) is used for data transfer and its stealing flags signal what type of data it is. The
Frequency Correction Burst (FB) lets a MS correct its frequency since all bits are 0 which is equivalent
to an unmodulated carrier with a constant frequency offset. The Synchronization Burst (SB) is used
for time synchronization. The Dummy Burst (DB) is only transmitted by the BTS on the BCCH carrier
frequency and allows the MS to do signal power measurements. The Access Burst (AB) is used for
random access before the MS is time-synchronized to the BTS or it hasn’t got a connection yet.
(Eberspächer et al., 2009)
2.2 Logical channels
GSM defines several different channels for various uses. This paper won’t go much more into detail
than the absolute basics.
The BTS uses a set of Broadcast Channels (BCH) which all allows the BTS to broadcast information to
all MSs in the cell. The Broadcast Control Channel (BCCH) is transmitted on the first frequency of the
CA and broadcasts information about the cell (e.g. radio configuration) and its neighbours. The
Frequency Correction Channel (FCCH) is used to send FBs. And the Synchronization Channel (SCH) is
used to identify the BTS and for frame synchronization by transmitting SBs.
Traffic channels (TCH) are duplex channels used for circuit switched data transfer between a MS and
the BTS. There are several types, but most importantly a TCH can be split into two half-rate channels
to support more users.
3
For signalling between single MSs and the BTS there are four simplex Common Control Channels
(CCCH). The Paging Channel (PCH) is used by the BTS to page a specific MS. The MS uses the Random
Access Channel (RACH) to request the assignment of a SDCCH or TCH with a random access burst,
using the principle of slotted Aloha. This principle basically means that the MS sends in a slot of the
RACH as soon as possible. If no acknowledgement is received in an expected time, a random back-of
time is used and then the transmission is resent. The BTS uses the Access Grant Channel (AGCH) to
assign a SDCCH or a TCH to a MS (this constitutes the acknowledgement). And at last, the BTS also
uses the Notification Channel (NCH) to notify MSs of group and broadcast calls.
Another type of channel is the Dedicated Control Channels (DCCH) which are duplex signalling
channels between a single MS and the BTS, and there are three main types of them. The Stand-alone
Dedicated Control Channel (SDCCH) is used when there is no active connection (e.g. a call). The Slow
Associated Control Channel (SACCH) is always used together with a TCH or SDCCH to signal
synchronization commands and power control. Transmission of SACCH data is also taken as proof of
the connection. The last channel is the Fast Associated Control Channel (FACCH) which only can be
used when using a TCH. When transmitting NBs on a TCH, setting the stealing flags (SF) signals that
the data is not user data but FACCH data, i.e. the FACCH allows to send signals immediately but at
the expense of the user data rate.
Lastly, there is a Cell Broadcast Channel (CBCH) used by the BTS to send Short Message Service Cell
Broadcast messages at the same physical channel as the SDCCH.
When a mobile phone gets a call the following occurs: The MS gets paged on the PCH and uses the
RACH to request a SDCCH. This is granted through the AGCH, and the SDCCH is then used to respond
to the page, setup authentication and encryption, and to confirm the call. The BTS then uses the
SDCCH to assign a TCH to the MS, which in turn uses the FACCH of the TCH to acknowledge this and
finish the call setup. After this, voice data can be transferred on the TCH, see figure 3. (3GPP TS
45.002) (Eberspächer et al., 2009)
Figure 3: GSM call setup (Eberspächer et al., 2009)
2.3 Mapping of logical channels to physical channels
A full rate TCH occupies one specific time slot of each frame on one uplink and one downlink
frequency. This is however multiplexed together with the SACCH using the 26-multiframe. In one
4
such multiframe 1 frame is for the SACCH, 24 for the TCH and one frame is idle in this configuration.
This means that the resulting data rate (before encryption and channel coding) for a full rate TCH is
57∗2 24
8∗3/5200 26
𝑏𝑝𝑠 = 22.8 𝑘𝑏𝑝𝑠.
Other channels (i.e. broadcast and control channels, SDCCH and SACCH) are all using only the BCCH
carrier frequency (except CBCH, SDCCH and SACCH which also can be put on other frequencies).
Most of these channels are only allowed to use timeslot 0 of a frame, but BCCH, PCH, AGCH and
RACH can also use timeslots 2, 4 and 6. The channels are mapped in time on this frequency using the
51-multiframe, and the mapping is dependent of the current channel usage. This means that only
part of the BCCH carrier frequency is reserved for signalling in the system and the rest of the time
and spectrum can be used for TCHs (with associated SACCH and FACCH) and SDCCHs. (3GPP TS
45.002)
5
3 Radio path
This chapter deals with the physical procedures that are done to ensure successful communication
on the radio path for all units.
3.1 Synchronization
3.1.1 Time synchronization
There are two reasons to why it is very important for a MS to be synchronized in time to the BTS. The
first is the TDMA structure with slots and numbered frames; the MS needs to know which frame and
time slot is which to be able to interpret received communication and know when to transmit. The
second reason is that inside a GSM cell, MSs are mobile and can be at different distances from the
BTS. But at the BTS the bursts from different MSs must not overlap by more than the guard period.
To resolve the first problem, the BTS uses the SCH with SBs to transmit the current FN, so the MS
knows the current frame.
The solution to the second problem is to let the BTS detect if the MS needs to transmit earlier or later
and send commands about this on the SACCH. The MS can at most advance the transmission of burst
by 63 symbol times, which then is supposed to adjust for the round trip-time delay. This means that
the maximum distance between the MS and the BTS that is supported corresponds to 31.5 symbol
periods which equals approximately 113.3 𝜇𝑠 or in actual distance 35 km. This is therefore the
maximum radii of a GSM cell. (Eberspächer et al., 2009)
3.1.2 Frequency synchronization
GSM allows for cheap MSs to be produced that can utilize cheap oscillators which aren’t very stable.
It is thus important to continuously synchronize the frequency of the MS to the BTS to assure that
the MS does not drift too much. The BTS provides this synchronization by frequently sending FBs on
the FCCH. The FB is a burst with only 0s, which due to GMSK modulation (see section 4.1) renders in
an unmodulated carrier of frequency
1625
24
≈ 67.7 kHz more than the frequency that should be set.
(Eberspächer et al., 2009)
3.2 Connection and random access
Before a MS is synchronized at all to a BTS it may be that it does not have any information about the
BTS at all (e.g. BCCH carrier, BTS identification, FN). Still it should be able to synchronize to it. The
first thing the MS needs to do is to find the BCCH carrier to be able to discern information needed for
registration with that particular BTS. Specification 3GPP TS 45.008 specifies that the MS should
monitor all GSM frequencies during a period of 3-5 s, but not how to determine the BCCH carrier
with this information. However this could be done by realizing that the BCCH carrier is most probably
the frequency with the most energy since the BTS is required to send a DB during any unused time
slot, while other frequencies can remain silent. The MS will probably find several BCCH frequencies
from different close cells, and have to choose the one where it will have the highest probability of
being able to communicate. When the MS is synchronized to a BTS (called camping) it can start
communicate with the BTS (registration with the network, receiving pages for calls etc.).
Before a MS can transmit any information to the BTS, it must request a SDCCH (as in the call setup in
figure 3). This is requested with the use of the RACH, sending an AB, which is much shorter than a
6
regular burst. This is because at this time, the MS maybe hasn’t transmitted anything yet, and so the
BTS haven’t sent any time synchronization data yet. The shortened AB ensures that there is no
overlap at the BTS to the next burst even if the MS is at the edge of the cell (35 km from the BTS).
(Eberspächer et al., 2009)
3.3 Power management
Another important part of the GSM system is power management. This function has two benefits; a
MS can save battery, and it decreases the interference between adjacent channels.
The MS always measures the signal level (RXLEV) and the signal quality (RXQUAL, which is related to
the received bit error rate) received from the BTS. Whenever the MS has a SACCH it will continuously
send these values to the BTS including the currently used power level. The BTS can use these values
to adjust its own power level for bursts to that particular MS, although it never changes the power of
the BCCH carrier which always shall be constant so that a MS can compare the received signal from
different BTSs. However, the BTS always sends commands to the MS about changes that should be
made to the MSs power level, which can be adjusted in steps of 2 dB. Before any power level
commands have been received, or when transmitting on RACH, the MS uses a maximum allowed
power level that is broadcast by the BTS. (3GPP TS 45.008)
3.4 Handoff
When not in an active connection (i.e. a SDCCH or a TCH) the MS itself monitors other BCCH carriers
from nearby BTSs and chooses if it should synchronize to another one. But during an ongoing
connection this is not as easily done.
During a connection the MS shall the entire time measure RXLEV and RXQUAL for the connected BTS
and for surrounding BTSs and send all these values on the SACCH. To know which BTSs these values
come from, the MS needs to read an identification value from each BTS which is broadcast on the
SCH. This is the reason to the idle frame in the 26-multiframe for full rate TCH. During the idle frame
the MS should perform measurements on other BCCH carriers. The control channels uses the 51multiframe which means that the position of this multiframe always shifts as compared to the 26multiframe, and at some point there will be a SCH burst from a neighbouring cell in the idle frame.
Moreover, the BTS also measures RXLEV and RXQUAL, and the current interference on its idle
channels.
With all this information, the BTS can (optionally supported by the Mobile Switching Center) decide if
a handover should be done and signal this to the MS. A handover can be made both in the current
BTS to another channel, or to a different BTS. The criteria for a handover to be made and the entire
handover process are not specified by the GSM standard but are left to the network operator. The
specification only provides a default algorithm for decision and handover procedure that could be
used. This allows operators to configure their network more freely, and perhaps also use handover to
try to level out traffic distribution. (3GPP TS 45.008)
3.5 Equalization
Since GSM is a narrowband system used all over the world with different environments and moving
MSs, it is absolutely vital for adaptive equalizers as to “undo” the effect of the filtering of the signal
between sender and receiver.
7
GSM does not specify anything about equalizers but provides means that are to be used by them.
Each and every burst contains a training sequence that is known by the receiver, moreover the tail
bits in the beginning and end of each burst is also known. These two properties of the bursts makes it
possible for all receivers to adaptively perform equalization of received signals.
As an example of how adaptive equalization can be performed we can look at an example developed
by Agilent Technologies (2008). In their library an equalizer is available that consists of an adjustable
matched filter and a modified Viterbi processor. The matched filter tries to provide an optimum
signal-to-noise ratio either by help of a channel estimator or by adjusting the filter using a gradient
algorithm. The output of the filter is fed into the modified Viterbi processor. A Viterbi decoder is used
to get a Maximum Likelihood Sequence Estimate (MLSE) of a received signal. Together the two parts
provide an adaptive equalization of the received GSM signals.
8
4 Modulation
In GSM there are many different modulation schemes allowed: APQSK, QPSK, 16-QAM, 32-QAM, 8PSK and GMSK. In this section we will mostly focus on GMSK since this technique is characteristic for
1
GSM. For the discussion in this chapter we denote the symbol time as 𝑇 =
1625
6
𝑘𝑠𝑦𝑚𝑏𝑜𝑙𝑠/𝑠 ≈
270.833 𝑘𝑠𝑦𝑚𝑏𝑜𝑙𝑠/𝑠, in accordance with section 2.1.
4.1 GMSK
GMSK stands for Gaussian Mean Shift Keying which comes from that this modulation is a variation of
Mean Shift Keying combined with a Gaussian filter as explained further in this section.
The internal state of the modulator both before and after the burst (which is to be modulated) is as if
continuous ones enter the modulator right before and right after the actual bits of the burst. We call
the input bit sequence 𝑑𝑖 ∈ {0, 1}, and thus for bits outside the burst we have 𝑑𝑖 = 1.
The first step of the modulation is to encode this differentially: 𝑑̂𝑖 = 𝑑𝑖 ⊕ 𝑑𝑖−1 where ⊕ is the XOR
operation. This sequence generates another sequence according to 𝛼𝑖 = 2𝑑̂𝑖 − 1 which implies
that 𝛼𝑖 ∈ {−1, +1}, and it is this sequence as Dirac pulses that is actually modulated.
At this point we need to define a couple of functions:
1
𝑡
𝑟𝑒𝑐𝑡 ( ) = {𝑇 ,
𝑇
0,
ℎ(𝑡) =
1
√2𝜋𝛿𝑇
𝑇
2
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑓𝑜𝑟 |𝑡| <
exp (
−𝑡 2
)
2𝛿 2 𝑇 2
with
𝛿=
√ln(2)
,
2𝜋𝐵𝑇
𝐵𝑇 = 0.3
This implies that 𝐵 is the 3 dB bandwidth of a linear filter with ℎ(𝑡) as impulse response. The Dirac
𝑡
sequence 𝛼𝑖 now excites the filter with impulse response 𝑔(𝑡) = 𝑟𝑒𝑐𝑡 (𝑇) ∗ ℎ(𝑡). The output of this
filter is then used to produce the phase of the modulation signal according to:
𝑡−𝑖𝑇
𝜙(𝑡) = ∑ 𝑎𝑖 𝜋ℎ ∫ 𝑔(𝑠)𝑑𝑠
𝑖
−∞
1
Here ℎ is called the modulation index and has a constant value of 2, which means that the maximum
𝜋
phase change is 2 per data interval. And the final transmitted signal is then
2𝐸𝑐
𝑥(𝑡) = √
cos(2𝜋𝑓0 𝑡 + 𝜙(𝑡) + 𝜙0 )
𝑇
9
Where 𝐸𝑐 denotes the energy per bit, 𝑓0 the carrier frequency and 𝜙0 a random phase that is
constant for the entire burst. The transmitter filter impulse response 𝑔(𝑡) is presented in figure 4.
(3GPP TS 45.004)
Figure 4: Impulse response of the transmitter filter
This entire procedure produces Mean Shift Keyed modulation with an extra Gaussian lowpass filter in
the process. The Mean Shift Keying results in a constant amplitude envelope of the signal which
makes receivers cheaper, since the amplifiers don’t have much demand on linearity. The Gaussian
filter makes the spectrum of the signal more narrow, but at the cost of increasing the inter-symbol
interference (see figure 4, where the impulse response lasts more than one symbol interval). The
benefit is that interference from adjacent channels is reduced. (Eberspächer et al., 2009)
4.2 Other modulations
The other allowed modulation techniques are the standard AQPSK, 8-PSK, QPSK, 16-QAM and 32QAM with some small modifications.
For a symbols sequence 𝑠𝑖 that is to be modulated, GSM creates a new sequence before modulation
which is a continuous rotation of the input sequence: 𝑠̂𝑖 = 𝑠𝑖 𝑒 𝑗𝑖𝜙 , where 𝜙 is a constant that
depends on the modulation scheme.
The rotated sequence is then pulse shaped with a linear filter with impulse response 𝑐0 (𝑡):
𝑦(𝑡) = ∑ 𝑠̂𝑖 𝑐0 (𝑡 − 𝑖𝑇 + 2𝑇)
𝑖
𝑐𝑜 (𝑡) is a linearized GSMK pulse. The expression for this is quite complicated and will not be
presented here, but can be found in the specification 3GPP TS 45.004, section 3.5.
The transmitted signal is then as usual:
2𝐸𝑠
𝑥(𝑡) = √
𝑅𝑒[𝑦(𝑡)𝑒 𝑗(2𝜋𝑓0 𝑡+𝜙0 ) ]
𝑇
Where 𝐸𝑠 is the energy per symbol. (3GPP TS 45.004)
10
5 Coding
In this chapter coding schemes that are used in GSM are presented. In the first section methods for
error correction and detection are explained, and in the second we will discuss compression methods
used when transmitting voice.
5.1 Channel coding
Since there are numerous types of channels there are also many channel codes, each channel has its
own. In this document we will only present two of the most important ones. However, the general
structure is the same for all channels. The first step is to create some parity bits using a block code on
a block of data mostly used for error detection. This is followed by encoding both information and
parity bits with a convolutional code or a turbo code for error correction. Finally, these bits are
reordered and interleaved before they are sent over the channel. These techniques can reduce a very
high bit error probability of order 10−1 to 10−3 down to error probabilities in the range of 10−5 to
10−6 (Eberspächer et al., 2009).
5.1.1 Full rate TCH
The input to the channel coder for full rate TCH is either blocks of 260 bits from a Full Rate speech
coder, or blocks of 244 bits from an Enhanced Full Rate (EFR) speech coder. If EFR is used an extra
step is done at first to produce a block of 260 bits.
This extra step is to first use an 8-bit CRC code on the most important 65 bits, these parity bits are
placed last in the block. The generator polynomial of this code is 𝑔(𝐷) = 𝐷 8 + 𝐷 4 + 𝐷 3 + 𝐷 2 + 1.
Also four important bits that are not otherwise protected by the channel coding are repeated two
times each. This adds the extra 16 bits needed to get a block of the same length as with full rate
speech encoding, and concludes the extra coding step needed for EFR.
The block is divided into two classes; 182 bits for class 1, and 78 bits for class 2. Only the bits in class
1 are protected by the channel coding, the bits of class 2 are not equally important and are left
unprotected.
The block code used to create the parity bits in the first step is a degenerate cyclic block code with
parameters (53, 50, 2) which is used on the first 50 bits of class 1, and produces 3 parity bits. Then
the information bits of class 1 and the parity bits are reordered and appended with four tail bits, all
0, making a total of 189 new class 1 bits.
The bits of class 1 are then encoded by a rate ½ convolutional code with memory of order 𝑚 = 4 and
free distance of 𝑑𝑓𝑟𝑒𝑒 = 7. The coded bits followed by the bits of class 2 now constitute a block of
456 bits.
Each coded block of 456 bits are then interleaved over 8 bursts, with 57 bits in each. This means that
every 4th TCH burst a new block starts, which is spread over 8 bursts. (3GPP TS 45.003)
5.1.2 SACCH, SDCCH, FACCH, BCCH, PCH, AGCH, NCH and CBCH
For these channels, the information blocks that are to be sent are 184 bits long. Apart from the first
block code which for these channels is a shortened cyclic block code generating 40 parity bits, the
11
channel coding is the same as for a full rate TCH. I.e. the same rate ½ convolutional code is used, and
the interleaving procedure is the same.
The special case is for the full rate FACCH which steals bits from the TCH which, due to the same
interleaving scheme used, all belong to the same block. The stealing of bits in bursts is indicated by
the SFs in the NB. For the first four bursts the first SF is set, and for the last four the last SF is set.
(3GPP TS 45.003)
5.2 Source coding (Full Rate speech)
The standard full rate speech encoding used in GSM is called Regular Pulse Excitation – Long Term
Prediction (RPE-LTP). The speech is sampled at 8 kHz with 13 bits uniform quantization and is
grouped into frames of 160 samples (20 ms). These frames are also divided into 4 sub-frames of 40
samples each. The general structure of the algorithm is presented in figure 5.
Figure 5: The structure of the RPE-LTP algorithm (3GPP TS 46.010)
The pre-processing step is to remove offset of the signal and to filter it with a pre-emphasis FIR filter.
In the short term Linear Prediction Speech (LPC) analysis block, reflection coefficients are calculated
from the frame. These are a model of the human speech. The coefficients are transformed into Log
Area Ratios (LAR) according to a bijective mapping. These are quantized and coded with different
amounts of bits depending of their importance, and totals in 36 bits.
The short term analysis filter uses the LPC coefficients to calculate residuals for the frame and
forwards on a sub-frame basis (i.e. the rest of the system operates on sub-frames).
The long term analysis filter and LTP analysis produces a long term correlation lag (using history from
previous sub-frames) and an associated gain factor. These are coded with 7 and 2 bits respectively,
making a total of 36 bits per frame.
The RPE part of the coding first filters each residual sub-frame with a weighting filter. Then it does an
adaptive sample rate decimation which is also called RPE grid selection, since it finds the optimal
decimation grid out of four candidates. The samples of the selected sequence are then quantized.
The information that is transmitted is the RPE grid selection and the quantization of the samples
which totals in 47 bits per sub-frame, or 188 bits per frame.
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In total this gives 260 bits per frame to be sent to the channel coding procedure. The original frame
size was 160 ∗ 13 = 2080 bits, which means that this is a compression of factor
2080
260
= 8 (the
compressed stream takes up only 12.5 % of the original data size). The uncompressed data stream
that is transmitted with some distortion by the GSM has a rate of 13 ∗ 8000 = 104 kbps. (3GPP TS
46.010)
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6 Summary
In this paper we have described and discussed some basic parts of the widespread cellular mobile
telephony standard GSM. The division of time and frequency to create several channels and the
structure of logical channels was presented. We have explained some procedures that are used to
ensure the quality of the communication in an efficient manner. Also the characterizing modulation
for GSM, GMSK was thoroughly described and lastly an overview of the compression of voice data
that is employed was made. Together this is aimed at giving the reader a fundamental understanding
of the wireless aspect of GSM, and if interest arises there is much more to read and learn in the
references of this report.
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7 References
Internet
ETSI TS 141 101 V11.1.0 (2014-07) “Digital cellular telecommunications system (Phase 2+); Technical
Specifications and Technical Reports for a GERAN-based 3GPP system (3GPP TS 41.101 version 11.1.0
Release 11)”. Available at:
http://www.etsi.org/deliver/etsi_ts/141100_141199/141101/11.01.00_60/ts_141101v110100p.pdf
[PDF]
ETSI TS 123 002 V12.6.0 (2015-01) “Digital cellular telecommunications system (Phase 2+); Universal
Mobile Telecommunications System (UMTS); LTE; Network architecture (3GPP TS 23.002 version
12.6.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/123000_123099/123002/12.06.00_60/ts_123002v120600p.pdf
[PDF]
ETSI TS 145 005 V12.4.0 (2015-01) “Digital cellular telecommunications system (Phase 2+); Radio
transmission and reception (3GPP TS 45.005 version 12.4.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145005/12.04.00_60/ts_145005v120400p.pdf
[PDF]
ETSI TS 145 002 V12.3.0 (2015-01) “Digital cellular telecommunications system (Phase 2+);
Multiplexing and multiple access on the radio path (3GPP TS 45.002 version 12.3.0 Release 12)”.
Available at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145002/12.03.00_60/ts_145002v120300p.pdf
[PDF]
ETSI TS 145 001 V12.1.0 (2015-01) “Digital cellular telecommunications system (Phase 2+); Physical
layer on the radio path; General description (3GPP TS 45.001 version 12.1.0 Release 12)”. Available
at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145001/12.01.00_60/ts_145001v120100p.pdf
[PDF]
ETSI TS 146 010 V12.0.0 (2014-10) “Digital cellular telecommunications system (Phase 2+); Full rate
speech; Transcoding (3GPP TS 46.010 version 12.0.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/146000_146099/146010/12.00.00_60/ts_146010v120000p.pdf
[PDF]
ETSI TS 145 003 V12.1.0 (2014-10) “Digital cellular telecommunications system (Phase 2+); Channel
coding (3GPP TS 45.003 version 12.1.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145003/12.01.00_60/ts_145003v120100p.pdf
[PDF]
ETSI TS 145 004 V12.0.0 (2014-10) “Digital cellular telecommunications system (Phase 2+);
Modulation (3GPP TS 45.004 version 12.0.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145004/12.00.00_60/ts_145004v120000p.pdf
[PDF]
15
ETSI TS 145 008 V12.4.0 (2015-01) “Digital cellular telecommunications system (Phase 2+); Radio
subsystem link control (3GPP TS 45.008 version 12.4.0 Release 12)”. Available at:
http://www.etsi.org/deliver/etsi_ts/145000_145099/145008/12.04.00_60/ts_145008v120400p.pdf
[PDF]
Agilent Technologies, Advanced Design System 2008 Documentation (2008) “GSM Equalizer”.
Available at:
http://cp.literature.agilent.com/litweb/pdf/ads2008/gsm/ads2008/GSM_Equalizer.html#GSMEqualiz
er-GSMEqualizer [WWW]
Books
J. Eberspächer, C. Bettstetter, H. Vögel, C. Hartmann ”GSM – Architecture, Protocols and Services”
(2009). John Wiley & Sons, New Jersey.
S. M. Redl, M. K. Weber, M. W. Oliphant “An introduction to GSM” (1995). Artech House, Boston.
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