reduced as compared to (pure) MSK. Gaussian shaping smoothes the phase diagram and
therefore realizes soft transitions between signal states, leading to a reduction in bandwidth.
The bandwidth time product of GSM is specified as BT ¼ 0.3. One drawback of GSM is that
this modulation mode is nonlinear. Fortunately a linearization method for GMSK exists, but
the physical price for this linearization is that the modulus of the complex signal envelope is
no longer constant. In [3] the linearization of GMSK is discussed in detail and it is shown that
the linearized GMSK meets all the requirements of the GSM standard.
As a channel access mode, GSM employs FDMA and TDMA with eight timeslots per
carrier. Uplink and downlink are separated by FDD and by TDD, which uses a time delay of
three slots. Therefore the terminal transmits and receives signals at different times. In GSM-
900 there are two transmission bands, each of 25 MHz bandwidth, that are used for FDD.
Thus GSM has 124 frequency channels in total. Since guard bands have to be introduced at
the beginning and at the end of the frequency intervals, 122 frequency channels remain for the
network providers. On each (duplex) frequency we have eight time slots, i.e. there are 976
speech channels available. Several different slot types are used – the normal burst, the
frequency correction burst, the synchronization burst, the dummy burst, and the access burst.
The normal burst, which is the carrier burst of the speech (or data) transmission, is shown
in Figure 8.1. At the beginning of the burst there are three tail bits followed by 57 information
bits. In the middle of the burst we see one (out of eight possible) training sequences of 26-bit
length, preceded and followed by one stealing flag bit, respectively. The training sequence is
used in the receiver as a reference signal for channel estimation and bit synchronization, the
stealing flag bits indicate whether the burst carries user or control data. The next bit block is
made up of the second 57 information bits, followed by three tail bits and a guard time that
corresponds to the duration of 8.25 bits. The guard time is necessary to avoid time slot overlap
caused by the switching of the transmitter’s amplifiers. In total, a burst is built up of 156.25
bits that are transmitted within 576.9 ms. The equalization of a slot is supported by the tail
Parametrization – a Technique for SDR Implementation 237
Figure 8.1 The GSM normal burst
bits. If the maximum likelihood sequence estimation (MLSE) method is used for equaliza-
tion, the tail bits serve for the termination of the sequence estimator in a predefined final state.
Equalization starts from the midamble in such a way that the first data bit block is equalized
from its end, while the second data bit block is equalized from its beginning. Eight bursts fit
into one TDMA frame.
As an example of channel coding in GSM we look at the full rate speech traffic channel
TCH FS. The speech encoder produces 260 bits within 20 ms, but there are differences
between the bits with respect to their importance. Some are more important for the recon-
struction of the speech signal than others. Therefore, the precoded bits are put into an order
according to their importance. In GSM there are two bit classes:
† class 1 and class 1a (with 182 bits in total)
† class 2 (with 78 bits)
The 50 most important bits are assigned to class 1a, encoded by a cyclic block code with three
check bits. The generator polynomial of this systematic cyclic block code is given by
gðxÞ¼x
3
1 x 1 1
All class 1 bits (i.e. also the class 1a bits) are error protected by a convolutional encoder of
rate 1/2. According to the GSM standard the generator polynomials used are
g
1
ðxÞ¼x
4
1 x
3
1 1
and
g
2
ðxÞ¼x
4
1 x
3
1 x 1 1
In total the encoding procedure transforms 182 class 1 data bits (plus three additional check
bits and four bits for the termination of the convolutional code) to 378 code bits. The class 2
bits are transmitted without coding. This results in a total of 456 bits, which corresponds to a
gross data rate of 22.8 kbit/s within a 20 ms speech frame. Besides convolutional and block
coding, interleaving of the traffic data is also performed, implemented via a rearranging
matrix.
8.3.2 Second Generation – IS-136 (DAMPS)
IS-136 is the North American equivalent of GSM. This system is also called digital AMPS
(DAMPS), which indicates that IS-136 is a derivative of the earlier analog advanced mobile
phone service (AMPS) standard. IS-136 specifies the air interface of a digital, terrestrial
cellular mobile radio standard. Table 8.2 shows the most important technical data of this
system. The access is done via FDMA/TDMA. Up- and downlink are separated by FDD. For
speech coding a vector sum excited linear predictive (VSELP) encoder is used.
The modulation mode of IS-136 is
p
/4-DQPSK, i.e. two data bits are transmitted by each
symbol. Therefore a symbol duration of 41.14 ms results, i.e. IS-136 is a system that is in
the border area between broadband and narrowband systems. Unlike GSM, equalization is
not absolutely necessary. In contrast to GMSK, the modulation mode
p
/4-DQPSK is linear.
The envelope of a
p
/4-DQPSK signal is not constant, but due to the phase offset of at least
l
¼
p
/4 for two consecutive symbols the complex envelope avoids zero crossings.
Within one TDMA frame three user signals may be transmitted. A user’s downlink burst is
Software Defined Radio: Enabling Technologies238
shown in Figure 8.2. Data for clock synchronization as well as for channel estimation are
located at the beginning of the burst. In front of the first half of the user data, control data are
inserted. The user data are followed by the colour code, which identifies the base station.
Afterwards, the second half of the data, as well as the attached guard bits for the burst’s
transmission time synchronization, is transmitted.
The VSELP speech encoder provides a data rate of 159 bits every 20 ms. These bits are, as
in GSM, arranged into two classes. There are 77 class 1 and 82 class 2 bits. Class 2 bits are
transmitted without error protection. The 12 most important class 1 bits (class 1a) are
protected by seven bits of a cyclic block code. The corresponding generator polynomial is
gðxÞ¼x
7
1 x
5
1 x
4
1 x
2
1 x 1 1
The class 1 bits as well as the check bits are fed into a terminated convolutional encoder of
rate 1/2 with generator polynomials
Parametrization – a Technique for SDR Implementation 239
Table 8.2 Key air interace parameters of the IS-136 system
Uplink 824–849 MHz
Downlink 869–894 MHz
Channel width 30 kHz
Channel access FDMA/TDMA
Duplex mode FDD/TDD
Users per carrier frequency 3
Speech encoder VSELP
Net speech rate 7.95 kbit/s
Modulation
p
/4-DQPSK
Error correction coding CRC, convolutional
Number of carrier frequencies 832
Bit duration 20.57 ms
Burst duration 6.67 ms
Channel bit rate 48.6 kbit/s
Maximum cell radius 20 km
Figure 8.2 IS-136 downlink burst
g
1
ðxÞ¼x
5
1 x
3
1 x 1 1
and
g
2
ðxÞ¼x
5
1 x
4
1 x
3
1 x
2
1 1
The 77 class 1 bits, seven check bits, and five tail bits (for the termination of the convolutional
encoder) produce 178 code bits at the channel coder’s output. Moreover, there are 82 uncoded
class 2 bits. Related to the speech frame of 20 ms duration, this leads to a gross data rate of
13 kbit/s.
8.3.3 Third Generation – Universal Mobile Telecommunication System (UMTS)
The universal mobile telecommunication system (UMTS), the European version of IMT-
2000, provides two air interfaces, UTRA-FDD and UTRA-TDD. Within the spectral interval
allocated to UMTS there are 12 (duplex) bands for UTRA-FDD and seven bands for UTRA-
TDD. Two out of the seven UTRA-TDD bands are for self-provided applications (similar to
the cordless phone system DECT). The two air interfaces share several similarities: for
example, the bandwidth of 5 MHz, the chip rate of 3.840 Mchip/s, the QPSK-modulation,
as well as the root raised cosine roll-off impulse shaping filter g
s
ðtÞ that employs a roll-off
factor of 0.22. On the other hand, the two air interfaces use different access modes for the
frequency resource. The TDMA component of UTRA-TDD requires synchronization of the
users in the down- as well as in the uplink. Therefore, multiuser detectors [4] that are able to
eliminate multiple access interference (MAI) (which occurs because of nonideal cross-corre-
lation properties of the spreading codes) can be implemented in the base stations. Moreover,
asymmetric data traffic can flow efficiently with TDD. The UTRA-FDD air interface uses
different frequency bands for up- and downlink as well as higher spreading factors. The cell
radii of UTRA-FDD are bigger and the users can move at higher velocities compared with
UTRA-TDD.
UTRA can usually provide several transport channels per user. These transport channels
are separated by time multiplex or physically. A physical channel in UTRA-FDD is defined
by a spreading code, in UTRA-TDD by a spreading code and a time slot on a specific
frequency band. One particular property of UTRA is that many individual data rates are
possible. The different transport channels may employ different data rates and their data may
be transmitted with different error protections. Speech coding (adaptive multirate (AMR)) is
very flexible and leads to data rates between 12.2 and 4.75 kbit/s. For each transport channel,
data can be channel coded, rearranged, and transmitted in sets of transports blocks within
transmission time intervals (TTIs) of 10, 20, 40, or 80 ms (Figure 8.3). The channel data are
adapted to one of the data rates permitted by flexible channel coding and rate adaptation.
First, a systematic block coding for transmission quality control is employed, i.e. to each
transport block a number of CRC bits (between 0 and 24) is appended.
For error correction coding we find the following options:
† convolutional coding with a rate of 1/2 or 1/3, constraint length 8, and maximum code
block length Z ¼ 504 (for example with speech transmission);
† turbo coding with rate 1/3 and maximum code block length Z ¼ 5114 for BERs of at most
10
26
;or
Software Defined Radio: Enabling Technologies240
† no channel coding, if the data to be transmitted are already channel coded by the user, or if
the transmission conditions are ideal.
The number of bits to be transmitted (user data plus CRC) within a TTI is set to the coding
block length N, if it is less than Z; otherwise, the bits have to be divided into several coding
blocks. For termination of the convolutional coding eight zeros are appended at the end of
each coding block. Then a variable block interleaving with column re-arrangement over the
total TTI duration is performed followed by a rate adaptation which depends heavily on the
transmission conditions and upon the cell occupancy. The rate adaptation punctures or
repeats specific bits to achieve the nearest data rate of a physical channel. In the UTRA-
FDD downlink the rate adaptation is applied first, followed by the first interleaving. Then all
transport channels of the user are divided into 10-ms blocks and multiplexed into one single
data stream (coded composite transport channel (CCTrCH)). This data stream is then distrib-
Parametrization – a Technique for SDR Implementation 241
Figure 8.3 UTRA transport channel data
uted to one or several physical channels (dedicated physical channels (DPCHs)), again in
blocks of 10 ms in length, and afterwards rearranged once more by a second block interleaver
with column rearrangement. This means that for UTRA-FDD a CCTrCH of one user is
transformed on to physical channels of an equal transmission rate or spreading factor, respec-
tively. For UTRA-TDD, different physical channels (characterized by time slot and spreading
factor) can contain different numbers of data bits. With the exception of UTRA-FDD uplink
several such CCTrCHs may be built per user and transmitted. The simultaneous transmission
of several physical channels, by using different codes, leads to increased amplitude variations
of the mobile station’s transmission signal in the uplink.
Each physical channel (DPCH) consists of information data (dedicated physical data
channel (DPDCH)) and connection specific control data (dedicated physical control channel
(DPCCH)). The control data contain:
† pilot sequences (with a length of 2, 4, 8, or 16 bits) used for channel estimation and for the
estimation of the carrier to interference ratio C/I for power control;
† feedback information (FBI) bits which are used for transmission of mobile station infor-
mation to the base station and therefore are sent in the uplink only;
† transmit power control (TPC) bits that carry instructions for power control (2, 4, or 8 bits)
† transport format combination indicator (TFCI) bits that give information about the compo-
sition of the data stream (0, 2, or 8 bits).
Pilot sequences are separately sent within each connection. This results in the benefit that
the pilots can be employed for channel estimation even if adaptive antennas are used. More-
over, power control in the downlink and phase control in the uplink become possible too. In
UTRA the transmit power is controlled very quickly, so that even fast fading can be accom-
modated. The distribution of control and data bits for the signals I- and Q-components is
different for the UTRA-FDD up- and downlink. Therefore, we have to discuss them sepa-
rately. Pure control channels like the random access channel (RACH) or the broadcast
channel (BCH) are not further discussed within this text.
The UTRA-FDD downlink’s slot and frame structures are presented in Figure 8.4. A slot is
built up of 2560 chips and therefore its duration is 0.667 ms. Within a slot the DPDCH and the
DPCCH bits are sent successively. The number of bits transmitted by a slot depends on the
spreading factor N
s
, which can take values N
s
¼ 2
k
with k [ {2; 3; …; 9}. Therefore a slot
contains, because of the QPSK modulation, 2 (2560/4) ¼ 1280 control and data bits if the
spreading factor N
s
equals 4. For N
s
¼ 512 the number of control and data bits is 2 (2560/
512) ¼ 10. Because of this concept of variable spreading factors, different data rates can be
transmitted within the same bandwidth of 5 MHz. Accordingly, low data rates are transmitted
with a high spreading factor due to the advantageous properties of the spreading code’s cross
correlation functions (CCFs) and autocorrelation functions (ACFs). The signals are then
resistant against multipath and MAI. For high data rates, low spreading factors apply and
the resistance against multipath and MAI is diminished.
An UTRA frame consists of 15 slots or 38,400 chips and has a duration of 10 ms. A
superframe is composed of 72 UTRA frames. If a single user occupies several DPCHs, the
corresponding DPCCH bits are transmitted only once and the control data are suppressed in
all the other DPCHs.
From Figure 8.5 we see how the modulated and spread transmitter signal sðtÞ is constructed
from the bit stream.
Software Defined Radio: Enabling Technologies242
First, the DPCH bits are distributed on to the I- and Q-branches by serial to parallel
transformation. Afterwards, the data are spread at the chip rate of 3.840 Mchip/s, applying
the same orthogonal variable spreading factor (OVSF) code to the I- and the Q-branch.
Finally, the chip sequence is scrambled a second time by a cell specific spreading sequence.
This procedure is necessary for cell identification and improves the signal’s CCF and ACF
properties. The complex scrambling sequences of a length of 38,400 chips are formed from
sections of Gold sequences. In UMTS the base stations are not synchronized, but each cell has
its own scrambling sequence allocated to it. The cost for the missing base station synchro-
nization is an increased effort at the connection setup, because the cell search can be time
consuming for the mobile, since in total 262,144 scrambling sequences, which are divided
into 512 groups, can be applied for cell identification. The scrambling sequences are deduced
from Gold sequences of length 2
18
2 1, whose generator polynomials are given by
g
1
ðxÞ¼1 1 x
7
1 x
18
and
g
2
ðxÞ¼1 1 x
5
1 x
7
1 x
10
1 x
18
Parametrization – a Technique for SDR Implementation 243
Figure 8.4 The UTRA-FDD downlink structure
Figure 8.5 Construction of the UTRA-FDD transmission signal
The generation of the different Gold sequences is controlled by the initial state of the linear
feedback shift register defined by g
1
ðxÞ. The initial state chosen corresponds to the index of
the generated Gold sequence and can take values between 0 and 262,143. As indicated in
Figure 8.5 the scrambling sequences are complex. If {a
n
; n ¼ 0; …; 2
18
2 1} is a Gold
sequence with index # 262,143, the corresponding complex scrambling sequence of period
38,400 is given by
{c
scr;n
} ¼ {a
n
} 1 j{a
n1131072
}
0 # n # 38; 399
On the downlink the same scrambling sequence is applied for all users, only their separa-
tion is done by the OVSF codes. It can be shown that the family of OVSF codes can be
transformed into the family of Walsh codes by applying bit reversal. All OVSF codes of the
same spreading factor N
s
are mutually orthogonal. For different spreading codes orthogon-
ality is not always guaranteed. Therefore the selection of the OVSF codes, applied in a single
cell, in which user signals of different spreading factors are transmitted, is done by using the
code tree shown in Figure 8.6. Only those codes may be chosen which are not located on the
same path from the root to the outermost branches of the tree. If the codes are chosen by this
procedure, orthogonality is preserved for different spreading factors too.
The UTRA-FDD uplink’s slot and frame structures are presented in Figure 8.7. Here the
control bits (DPCCH) are transmitted in the Q-branch, while the data (DPDCH) bits are sent
in the I-branch (Figure 8.8).
Usually the data rates of the two branches are different in the uplink. To achieve the same
chip rate, the spreading factor 256 is always used in the Q-branch, and for the I-branch
spreading factors N
s
¼ 2
k
; k [ {2; 3; …; 8} are applied, similarly to the downlink. This
means that between 10 and 640 data bits can be transmitted per slot. The assignment of
control and data bits to the Q- and I-branches, respectively, was introduced with regard to the
increased electromagnetic compatibility (EMC). Since the control data have to be transmitted
in every slot, a continuous signal is guaranteed in spite of discontinuous transmission (DTx).
Transmission breaks, which would lead to an on and off switching of the power amplifier, are
Software Defined Radio: Enabling Technologies244
Figure 8.6 The OVSF spreading code tree
avoided. On the downlink, some signals (e.g. the BCCH) are continuously sent. Therefore, no
transmission breaks occur in this case.
Since in the uplink the users are not only separated by the OVSF codes but also by the
scrambling sequences, the same OVSF code may be assigned to several users within the same
cell.
For the uplink the complex scrambling sequences can be chosen from two families: the first
family is constructed of quarternary sequences, 256 chips long, that are generated from the
following polynomials:
g
1
ðxÞ¼1 1 2x 1 x
2
1 3x
3
1 x
5
1 x
8
mod 4
g
2
ðxÞ¼1 1 x 1 x
5
1 x
7
1 x
8
mod 2
and
g
3
ðxÞ¼1 1 x
4
1 x
5
1 x
7
1 x
8
mod 2
Parametrization – a Technique for SDR Implementation 245
Figure 8.7 The UTRA-FDD uplink structure
Figure 8.8 The UTRA-FDD uplink I- and Q-branch
Subsequently, the symbols
a
n,j
ðj ¼ 1; 2; 3Þ, generated by the three polynomials, are
combined:
z
n
¼ð
a
n;1
1 2
a
n; 2
1 2
a
n; 3
Þ mod 4
From the last equation a number z
n
[ {0; 1; 2; 3} results, leading to the complex scram-
bling symbols a
n
, via Table 8.3. These short scrambling sequences are intended to reduce the
computational load in the base station if multiuser detection is applied.
The second family consists of sections of length 38,400, out of Gold sequences {a
n
}of
length 2
25
2 1 and generator polynomials
g
1
ðxÞ¼1 1 x
3
1 x
25
and
g
2
ðxÞ¼1 1 x 1 x
2
1 x
3
1 x
25
The complex scrambling sequences are constructed from the sequence {a
n
}by
{c
scr;n
} ¼ {a
n
ð1 1 jð21Þ
n
a
2½n=211677232
Þ}
0 # n # N 2 1
By using this compound procedure for constructing the scrambling sequence for the uplink,
variations of the modulus of the signal’s complex envelope are avoided. The design of the
scrambling sequences guarantees that within N
s
chips, i.e. within one code period, maximal
one-phase rotation of 1808 can occur; furthermore only phase rotations of 908 and maximal
one 08 rotation appear. Since every user within the network is assigned its own scrambling
sequence, the number of scrambling codes is extremely large; there are 2
24
long as well as 2
24
short scrambling sequences. The most important technical data of the UTRA-FDD air inter-
face are summarized in Table 8.4.
8.4 Parametrization Example
In Section 8.3 we described the air interfaces of the standards GSM, IS-136, and UMTS-FDD
in some detail. Of course, there are substantial differences between the second-generation
(TDMA) standards and the third-generation (CDMA) standard: GSM and IS-136 are on one
side while UMTS-FDD is on the other. Here, spreading in the transmitter and despreading in
the receiver have to be additionally realized.
Software Defined Radio: Enabling Technologies246
Table 8.3 Complex scrambling symbols
z
n
a
n
011 j
1 21 1 j
2 21 2 j
312 j
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