yu xiangyu - scut.edu.cn · figure below is an illustration of a typical tdma satellite...
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FDMA TDMA CDMA
Orthogonal code
PN Sequence
Spread Spectrum
SDMA OFDM
Haykin P214
Figure
Conceptual diagram of multiplexing-demultiplexing.
Taken at Communication Museum of Macau
Capacity of transmission medium usually exceeds capacity required for transmission of a single signal
Multiplexing - carrying multiple signals on a single medium
More efficient use of transmission medium
Beard P31
Cost per kbps of transmission facility declines with an increase in the data rate
Cost of transmission and receiving equipment declines with increased data rate
Most individual data communicating devices require relatively modest data rate support
Beard P31-32
Multiplexing in 4 dimensions
space (si)
time (t)
frequency (f)
code (c)
Goal: multiple use of a shared medium Important: guard spaces needed!
s2
s3
s1 f
t
c
k2 k3 k4 k5 k6 k1
f
t
c
f
t
c
channels ki
Schiller P42
Multiplexing
Purpose: to transmit multichannel independent signals on one link.
Basic principle: orthogonal division method
3 kinds of basic multiplexing methods: FDM, TDM, CDM
Tan P239
Multiple access techniques are based on orthogonalization of signals
A radio signal is a function of frequency, time, and code as
where s(f, t) is the function of frequency and time and c(t) is the function of code
s(f, t, c) = s(f, t)c(t)
Agrawal P101
Frequency-division multiplexing (FDM)
Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal
Time-division multiplexing (TDM)
Takes advantage of the fact that the achievable bit rate of the medium exceeds the required data rate of a digital signal
Beard P32
Multiple connection
▪ Purpose: combination and division of multichannel signals from several links.
▪ Key technologies － clock unification and timing of multichannel TDM signals from several links.
Multiple access
▪ Purpose: sharing the communication network, and dynamically distributing the network resources.
▪ Methods: FDMA, TDMA, CDMA, SDMA, PDMA, and others.
Fan P239-240
Use of different frequencies to transmit a signal: FDMA
Distinct time slot: TDMA Different codes CDMA Multiple simultaneous channels: OFDM Specially separable sectors: SDMA
Agrawal P101
Figure Illustrating the ideas behind multiple-access techniques. (a)
Frequency-division multiple access. (b) Time-division multiple
access. (c) Frequency-hop multiple access.
Haykin P514
Sklar P660
In the early days of telephony, a separate pair of wires was needed for each telephone trunk circuit (trunk circuits interconnect intercity switching centers). As illustrated in Figure, the skies of all the major cities in the world grew dark with overhead wires as the demand for telephone service grew. A major development in the early 1900s, frequency-division multiplex (FDM) telephony, made it possible to transmit several telephone signals simultaneously on a single wire, and thereby transformed the methods of telephone transmission.
Sklar P660-661
Separation of the whole spectrum into smaller frequency bands
A channel gets a certain band of the spectrum for the whole time
Schiller P43
Beard P33
The communications resource (CR) is illustrated in the figure below as the frequency-time plane. The channelized spectrum shown here is an example of FDM or FDMA.
Sklar P661
Orthogonality conditions of two signals in FDMA:
Single channel per carrier All first generation systems use FDMA
kjiji
jidftfstfs j
F
i ,...,2,1,,0
1),(),(
Agrawal P101-102
f1’
f2’
fn’
…
Reverse channels
(Uplink)
BS
f1
f2
fn
…
Forward channels
(Downlink)
MS1
MS2
MSn
…
Agrawal P102
…
f1’ f2’ fn’
…
f1 f2 fn
Reverse channels Forward channels
Guard Band
Wg
1 2 3 …
N
Frequency
Total Bandwidth W = NWc
4
Sub Band
Wc
Agrawal P102-103
Figure FDM system. Couch P353
Figure Block diagram of FDM system.
Haykin P106
Method: using SSB modulation to move the frequency spectrum for saving frequency band.
Example: 3 channel FDM telephone communication system
Fan P241
Figure below illustrates heterodyning (mixing).
Sklar P662
A simple FDM example with three translated voice channels is seen in Figure below.
Sklar P663
27
4 kHz 8 kHz 12 kHz Baseband
speech signal 300 – 3,400 Hz
4.3 – 7.4
kHz 8.3 – 11.4 kHz 12.3 – 15.4 kHz f 0
(a) Block diagram of transmitter
4.3 ~ 7.4 kHz
8.3 ~ 11.4 kHz
4 kHz
12 kHz
8 kHz
Multichannel signal output
Multiply bandpass Lowpass Speech input 1
f1
Multiply
bandpass
Lowpass
Speech input 2
f2
Multiply
bandpass
Lowpass
Speech input 3
f3
300 ~ 3400 Hz
300 ~ 3,400 Hz
300 ~ 3,400 Hz
Fan P242
Multichannel signal input
(b) Block diagram of receiver
Speech output 1
Speech output 2
Speech output 3
Multiply
Lowpass
bandpass
f1
Multiply
Lowpass
bandpass
f1
Multiply
Lowpass
bandpass
f1
4.3 ~ 7.4 kHz
8.3 ~ 11.4 kHz
12.3 ~ 15.4 kHz
3400 Hz
3400 Hz
3400 Hz
8 kHz
12 kHz
4 kHz
Fan P242
Basic group － 12 channels, occupies 48 kHz between 12 ～ 60 kHz
Super group － 60 channels composed of 5 basic groups, occupies 240 kHz of bandwidth
Master group － 600 channels composed of 10 super groups.
12 1 2 3 4 kHz f (kHz)
12 kHz 16 kHz 20 kHz 56 kHz
Fan P241 http://www.itu.int
Figure Illustrating the modulation steps
in an FDM system.
Haykin P107 Sklar P664
This figure illustrates the two lowest levels of the FDM multiplex hierarchy for telephone channels.
Advantages
no dynamic coordination necessary
works also for analog signals
Disadvantages
waste of bandwidth if the traffic is distributed unevenly
inflexible
Schiller P43
It requires very small nonlinear distortion of the system; otherwise, mutual interference between the signals of various channels will be generated due to nonlinear distortion.
The manufacturing technology of this kind of equipment is rather complex; especially the manufacture and debugging of the filters are difficult.
The cost is high.
Fan P241
A channel gets the whole spectrum for a certain amount of time
Advantages
only one carrier in the medium at any time
throughput high even for many users
Disadvantages
precise synchronization necessary
Schiller P44
Beard P33
Figure Two-channel bit-interleaved TDM
with pulse stuffing. Couch P227
Figure
Block diagram of TDM system.
Haykin P211
In the Figure below, CR is shared by assigning each of M signals or users the full spectral occupancy of the system for a short duration of time called a time slot. The unused time regions between slot assignments, called guard times, allow for some time uncertainty between signals in adjacent time slots, and thus act as buffer zones to reduce interference.
Sklar P665
Orthogonality conditions of two signals in TDMA:
Multiple channels per carrier Most of second generation systems use
TDMA
kjiji
jidttfstfs j
T
i ,...,2,1,,0
1),(),(
Agrawal P103
MS1
MS2
…
…
Reverse channels
(Uplink)
t
Frequency f ’ 1 … 1 …
Frame
Slot
Frame
…
t
2 … 2 …
…
t
n … n …
BS
Forward channels
(Downlink)
… 1 …
Frame
…
t
Frequency f
Frame
… 2 … 2 …
t
… n … n …
t
1
MSn
Agrawal P103
1 2 3 11 12 1 2 3 11 12
t downlink uplink
417 µs
Schiller P75
Figure below is an illustration of a typical TDMA satellite application. Time is segmented into intervals called frames. Each frame is further partitioned into assignable user time slots. The frame structure repeats, so that a fixed TDMA assignment constitutes one or more slots that periodically appear during each frame time. Each earth station transmits its data in bursts, timed so as to arrive at the satellite coincident with its designated time slot(s).
Sklar P665-666
When the bursts are received by the satellite transponder, they are retransmitted on the downlink, together with the bursts from other stations. A receiving station detects and demultiplexes the appropriate bursts and feeds the information to the intended user.
Sklar P665-666
… t
f 1
2
n
1
2
n
…
(a). Forward channel
… 1
2
n
Frame Frame Frame
… t
f ’
1
2
n
1
2
n
…
(b) Reverse channel
… 1
2
n
Frame Frame Frame
Agrawal P104
Frequency f = f ’
Frame Frame
… 1
2
n
1
2
n …
Forward
channel
Reverse
channel
… 1
2
n
Forward
channel
1
2
n …
Reverse
channel
Channels in TDMA/TDD
Agrawal P104
…
Time Fre
quen
cy
1
2
2
n
… … 1
2
n
Frame Frame Frame
Head Data Guard
time
n
1
Agrawal P104
Figure TDM with analog and digital inputs as described in Example 3-6. Couch P228
Figure North American digital TDM
hierarchy.
Couch P229
Figure CCITT digital TDM hierarchy.
Couch P232 https://en.wikipedia.org/wiki/ITU-T
Combination of both methods A channel gets a certain frequency band for a
certain amount of time Example: GSM, Bluetooth
Advantages
better protection against tapping
protection against frequency selective interference
but: precise coordination required
f
t
c
k2 k3 k4 k5 k6 k1
Schiller P44-45
Each channel has a unique code All channels use the same spectrum at the same
time Advantages
bandwidth efficient
no coordination and synchronization necessary
good protection against interference and tapping
Disadvantages
varying user data rates
more complex signal regeneration
Implemented using spread spectrum technology Schiller P45-46
Orthogonality conditions of two signals in CDMA:
kjiji
jidttsts j
C
i ,...,2,1,,0
1)()(
Frequency
• Users share bandwidth by using code sequences that are orthogonal to each other
• Some second generation systems use narrowband CDMA
• Most of third generation systems use wideband CDMA U
ser
1
Time
Use
r 2
Use
r n
Code
. . .
Agrawal P105
MS1
MS2
MSn
BS
C1’
C2’
Cn’
C1
C2
Cn
… …
…
Reverse channels (Uplink)
Forward channels (Downlink)
Frequency f ’
Ci’ x Cj’ = 0, i.e., Ci’ and Cj’ are orthogonal codes
Ci x Cj = 0, i.e., Ci and Cj are orthogonal codes
Frequency f
Agrawal P106
Basic Principles of CDMA
D = rate of data signal
Break each bit into k chips
▪ Chips are a user-specific fixed pattern
Chip data rate of new channel = kD
Beard P264
One might ask: Don’t the FDMA and TDMA options provide sufficient multiple access flexibility? FDMA and TDMA methods can surely be relied on to apportion the communications resource equitably. Of what use is this hybrid technique? CDMA offers some unique advantages, as follows:
1. Privacy. When the code for a particular user group is only distributed among authorized users, the CDMA process provides communications privacy, since the transmissions cannot easily be intercepted by unauthorized users without the code.
Sklar P673-674
2. Fading channels. If a particular portion of the spectrum is characterized by fading, signals in that frequency range are attenuated. In an FDMA scheme, a user who was unfortunate enough to be assigned to the fading position of the spectrum might experience highly degraded communications for as long as the fading persists. However, in a FH-CDMA scheme, only during the time a user hops into the affected portion of the spectrum will the user experience degradation. Therefore, with CDMA, such degradation is shared among all the users.
Sklar P674
3. Jam resistance. During a given CDMA hop, the signal bandwidth is identical to the bandwidth of conventional MFSK, which is typically equal to the minimum bandwidth necessary to transmit the MFSK symbol. However, over a duration of many time slots, the system will hop over a frequency band which is much wider than the data bandwidth. We refer to this utilization of bandwidth as spread spectrum.
Sklar P674
4. Flexibility. The most important advantage of CDMA schemes, compared to TDMA, is that there need be no precise time coordination among the various simultaneous transmitters. The orthogonality between user transmissions on different codes is not affected by transmission-time variations.
Sklar P674
Orthogonal codes All pairwise cross correlations are zero
Fixed- and variable-length codes used in CDMA systems
For CDMA application, each mobile user uses one sequence in the set as a spreading code ▪ Provides zero cross correlation among all users
Types Walsh codes
Variable-Length Orthogonal codes
Stallings P184-185
If k=6 and code is a sequence of 1s and -1s For a ‘1’ bit, A sends code as chip pattern
▪ <c1, c2, c3, c4, c5, c6>
For a ‘0’ bit, A sends complement of code ▪ <-c1, -c2, -c3, -c4, -c5, -c6>
Receiver knows sender’s code and performs electronic decode function
▪ <d1, d2, d3, d4, d5, d6> = received chip pattern
▪ <c1, c2, c3, c4, c5, c6> = sender’s code
665544332211 cdcdcdcdcdcddSu
Beard P264
Slot 1 Slot 0
d1 = -1
1 1 1 1
1 - 1 - 1 - 1 -
d0 = 1
1 1 1 1
1 - 1 - 1 - 1 -
1 1 1 1
1 - 1 - 1 - 1 -
1 1 1 1
1 - 1 - 1 - 1 -
slot 0
Channel
output
slot 1
Channel
output
Channel output Zi,m
Sender
Code
Data
bits
Zi,m= di.cm
Slot 1 Slot 0
d1 = -1
d0 = 1
1 1 1 1
1 - 1 - 1 - 1 -
1 1 1 1
1 - 1 - 1 - 1 -
1 1 1 1
1 - 1 - 1 - 1 -
1 1 1 1
1 - 1 - 1 - 1 -
Slot 0
channel
output
Slot 1
channel
output Receiver
Code
Received
input
Di = S Zi,m.cm m=1
M
M
User A code = <1, –1, –1, 1, –1, 1> To send a 1 bit = <1, –1, –1, 1, –1, 1>
To send a 0 bit = <–1, 1, 1, –1, 1, –1> User B code = <1, 1, –1, – 1, 1, 1>
To send a 1 bit = <1, 1, –1, –1, 1, 1> Receiver receiving with A’s code
(A’s code) x (received chip pattern) ▪ User A ‘1’ bit: 6 -> 1
▪ User A ‘0’ bit: -6 -> 0
▪ User B ‘1’ bit: 0 -> unwanted signal ignored
Beard P264-265
Correlation The concept of determining how much similarity one set
of data has with another
Range between –1 and 1 ▪ 1 The second sequence matches the first sequence
▪ 0 There is no relation at all between the two sequences
▪ -1 The two sequences are mirror images
Cross correlation The comparison between two sequences from different
sources rather than a shifted copy of a sequence with itself
Stallings P181-182
Concept of codeword orthogonality: Assume x and y are two codewords:
Where i = 1, 2, …, N
Definition of cross-correlation coefficient:
The necessary and sufficient condition of
orthogonality of two codewords:
),,,,,( 21 Ni xxxxx ),,,,,( 21 Ni yyyyy
)1,1(, ii yx
N
i
ii yxN
yx1
1),(
0),( yx
Fan P252
Example:
)1,1,1,1(
)1,1,1,1(
)1,1,1,1(
)1,1,1,1(
4
3
2
1
s
s
s
s
0
0
0
0
-1
+1
+1
+1
+1
-1
-1
-1
s3
s1
s2
s4
Orthogonal codewords
t
t
t
t
Fan P252
Using 1 and 0 to express binary symbol: “1” “-1”
“0” “+1”
Definition of cross-correlation coefficient:
where A － the number of symbols in x, which are identical with the corresponding symbols in y. D － the number of symbols in x, which are different from the corresponding symbols in y.
DA
DAyx
),(
Fan P252
Example:
▪ Advantage:
Mapping:
“” “”
)1,0,1,0(
)0,1,1,0(
)1,1,0,0(
)0,0,0,0(
4
3
2
1
s
s
s
s
)1,1,1,1(
)1,1,1,1(
)1,1,1,1(
)1,1,1,1(
4
3
2
1
s
s
s
s
0 1
0 0 1
1 1 0
+1 -1
+1 +1 -1
-1 -1 +1
Fan P252
Definition of autocorrelation coefficient of codeword:
Assume the value of xi takes +1 or -1, then
where the subscript i + j of x should be operated according to mod N, i.e., xN+i xi .
N
i
jiix NjxxN
j1
)1(,,1,01
)(
Fan P252
Example: assume x = (x1, x2, x3, x4) = (+1, -1, -1, +1), then its autocorrelation coefficients are
14
1)0(
4
1
2 i
ix x
0)1111(4
1
)(4
1
4
1)1( 14433221
4
1
1
xxxxxxxxxxi
iix
1)1111(4
1
)(4
1
4
1)2( 2434231
4
1
2
xxxxxxxxxxi
iix
0)1111(4
1
)(4
1
4
1)3( 34231241
4
1
3
xxxxxxxxxxi
iix
Fan P253
If the value of xi takes 0 or 1, then we have
where A is the number of symbols in xi , which are identical with the corresponding symbols in xi+j .
D is the number of symbols in xi , which are different from the corresponding symbols in xi+j .
DA
DAxx jii
),(
Fan P253
The range of :
According to different value of ,
When = 0, the codeword is called orthogonal code
When 0, the codeword is called quasi-orthogonal code
When < 0, the codeword is called transorthogonal code
11
Fan P253
The orthogonal code and its inverse code construct a bi-orthogonal code. Example:
(0, 0, 0, 0) (1, 1, 1, 1)
(0, 0, 1, 1) (1, 1, 0, 0)
(0, 1, 1, 0) (1, 0, 0, 1)
(0, 1, 0, 1) (1, 0, 1, 0)
Fan P253
Hadamard matrix: it is a square matrix, and is composed of only +1 and -1. It is also called H matrix for short.
The Hadamard matrix with the lowest order is of the order of 2:
For simplicity, the above equation can be written as
11
112H
H
Fan P254-255
The Hadamard matrix with the order of power of 2 can be derived by the following recursive equation:
where － Kronecker product. Algorithm of Kronecker product: to use the matrix H2 instead
of each element in the matrix HN/2 . For example,
2HHH 2 / NN
22
22
224HH
HHHHH
Fan P255
▪ Normal Hadamard matrix: The matrix constructed by the above method is a symmetric matrix, and the elements of its first row and first column are all + .
44
44248
HH
HHHHH
Fan P255
Walsh matrix: If the rows in an H matrix are arranged according to the ascending order of the number of the sign changes, then the Walsh matrix will be obtained. For example,
Walsh matrix is still kept the orthogonality.
8W
Fan P256
Set of Walsh codes of length n consists of the n rows of an n ´ n Walsh matrix:
W1 = (0)
▪ n = dimension of the matrix
Every row is orthogonal to every other row
Requires tight synchronization ▪ Cross correlation between different shifts of Walsh
sequences is not zero
nn
nnn
WW
WWW2
Stallings P184-185
Wal (0, t) t
Wal (1, t) t
Wal (2, t) t
Wal (3, t) t
Wal (4, t) t
Wal (5, t) t
Wal (6, t) t
Wal (7, t) t Agrawal P108
The spread-spectrum approach called transmitted reference (TR) can utilize a truly random code signal for spreading and despreading, since the code signal and the data-modulated code signal are simultaneously transmitted over different regions of the spectrum. The stored reference(SR) approach cannot use a truly random code signal since the code needs to be stored or generated at the receiver. For the SR system a pseudonoise or pseudorandom code signal must be used.
Sklar P728
How does a pseudorandom signal differ from a random one? A random signal cannot be predicted; its future variations can only be described in a statistical sense.
However, a pseudorandom signal is not random at all; it is a deterministic, periodic signal that is known to both the transmitter and receiver. Why the name “pseudonoise” or “pseudorandom”? Even though the signal is deterministic, it appears to have the statistical properties of sampled white noise. It appears, to an unauthorized listener, to be a truly random signal. Sklar P729
PN generator produces periodic sequence that appears to be random
PN Sequences Generated by an algorithm using initial seed
Sequence isn’t statistically random but will pass many test of randomness
Sequences referred to as pseudorandom numbers or pseudonoise sequences
Unless algorithm and seed are known, the sequence is impractical to predict
Stallings P175?
Pseudo-random code is also called pseudo-random sequence.
It has the random characteristics like the white noise, but can be repeatedly generated
It has fine correlation characteristic, and can be used in code division multiplexing, multiple access, telemetering, ciphering, spread spectrum communication, and the separation of multipath signals.
There are many kinds of pseudo-random sequences. Among them the m sequence is most important.
Fan P256
What are these randomness properties that make a pseudorandom signal appear truly random? There are three basic properties that can be applied to any periodic binary sequence as a test for the appearance of randomness.
The properties, called balance, run, and correlation, are described for binary signals as follows:
Sklar P729
1. Balance property. Good balance requires that
in each period of the sequence, the number of binary ones differs from the number of binary zeros by at most one digit.
Sklar P729
2. Run property. A run is defined as a sequence of a single type of binary digit(s). The appearance of the alternate digit in a sequence starts a new run. The length of the run is the number of digits in the run. Among the runs of ones and zeros in each period, it is desirable that about one-half the runs of each type are of length 1, about one-fourth are of length 2, one-eighth are of length 3, and so on.
Sklar P729
3. Correlation property. If a period of the sequence is compared term by term with any cyclic shift of itself, it is best if the number of agreements differs from the number of disagreements by not more than one count.
Sklar P729
m sequence － is the sequence with longest period generated by a liner feedback shift register.
Fan P256-257
Figure Feedback shift register.
Haykin P480
Rappaport P331
Stallings P176
Consider the linear feedback shift register illustrated in the Figure below. It is made up of a four-stage register for storage and shifting, a modulo-2 adder, and a feedback path from the adder to the input of the register. The shift register operation is controlled by a sequence of clock pulses (not shown).
Sklar P729-730
At each clock pulse the contents of each state in the register is shifted one stage to the right. Also, at each clock pulse the contents of stages X3 and X4 are modulo-2 added (a linear operation), and the result is fed back to stage X1. The shift register sequence is defined to be the output of the last stage—stage X4 in this example.
Sklar P729
Assume that stage X1 is initially filled with a one and the remaining stages are filled with zeros, that is, the initial state of the register is 1 0 0 0. From the Figure we can see that the succession of register states will be as follows:
Sklar P729-730
Since the last state, 1 0 0 0, corresponds to the initial state, we see that the register repeats the foregoing sequence after 15 clock pulses. The output sequence is obtained by noting the contents of stage X4 at each clock pulse. The output sequence is seen to be
0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 where the leftmost bit is the earliest bit. Let us test
the sequence above for the randomness properties outlined in the preceding section.
Sklar P730
a1 a0
+
a2 a3
Fan P257
m sequence generator: 4 stage m sequence generator
4 stage shift register has totally 24 =16 possible statuses, the longest period equals 15.
a1 a0
+
a2 a3
a3 a2 a1 a0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 --------------------------------------
1 0 0 0
Initial status
period＝24 – 1 = 15
Fan P257
Randomness
Uniform distribution
▪ Balance property
▪ Run property
Independence
Correlation property
Unpredictability
Stallings P175
Property 1:
For a window of length n slid along output for N (=2n-1) shifts, each n-tuple appears once, except for the all zeros sequence
Property 2(Balance): In a period of an m sequence, the numbers of 0s
and 1s are approximately equal. Accurately speaking, the number of 1s is one more than the number of 0s.
Has 2n-1 ones and 2n-1-1 zeros
Stallings P180 Fan P259-260
Property 3(Run): Sequence contains one run of ones, length n
One run of zeros, length n-1
One run of ones and one run of zeros, length n-2
Two runs of ones and two runs of zeros, length n-3
2n-3 runs of ones and 2n-3 runs of zeros, length 1
Stallings P180
▪ Distribution of the runs: The run is referred to a piece of elements which
have the same (unchanged) value. And the number of the elements in this piece is called the length of the rum. For example,
In the above one period, there are 8 runs, and there is one run with the
length of 4 among them, i.e., 1111; there is one run with the length of 3,
i.e., 000; there are two runs with the length of 2, i.e., 11 and 00; there are 4
runs with the length of 1, i.e., two 1s and two 0s.
m = 15 …1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1
0 … Run Run
Fan P259-260
Generally speaking, in an m sequence, the number of runs with the length of 1 occupies 1/2 of the total number; the number of runs with the length of 2 occupies 1/4 of the total number; the number of runs with the length of 3 occupies 1/8; …. In other words, the number of runs with the length of k occupies 2-k of the total number, where 1 k (n – 1), and the number of runs with the continuous 1s is the same as the number of runs with the continuous 0s.
Fan P260
0 0 0 1 0 0 1 1 0 1 0 1 1 1 1
First, the balance property; there are seven zeros and eight ones in the sequence—therefore, the sequence meets the balance condition.
Next, the run property; consider the zero runs—there are four of them. One-half are of length 1, and one-fourth are of length 2. The same is true for the one runs. The sequence is too short to go further, but we can see that the run condition is met.
Sklar P730
Property 4:
The periodic autocorrelation of a ±1 m-sequence is
otherwise
... 2N, N,0,
11
τ
N
R
Stallings P180
The cross correlation between an m-sequence and noise is low
This property is useful to the receiver in filtering out noise
The cross correlation between two different m-sequences is low
This property is useful for CDMA applications
Enables a receiver to discriminate among spread spectrum signals generated by different m-sequences
Stallings P182
Figure Autocorrelation and PSD for an m-
sequence PN waveform. Couch P393 Haykin P480
Sklar P731
Figure (a) Autocorrelation function Rc(), and
(b) cross-correlation function R12() of the two PN sequences [7, 1] and [7, 6, 5, 4].
Haykin P506
Figure Maximal-length sequence
generator for m 3.
Haykin P481
Figure Two different configurations of
feedback shift register of length m 5. (a)
Feedback connections [5, 2]. (b) Feedback
connections [5, 4, 2, 1]. Haykin P485
Gold sequences constructed by the XOR of two m-sequences with the same clocking
Codes have well-defined cross correlation properties
Only simple circuitry needed to generate large number of unique codes
In following example (Figure next page) two shift registers generate the two m-sequences and these are then bitwise XORed
Stallings P182
Stallings P182
Figure
Generator for a Gold sequence of period 27
1 127.
Haykin P507
Figure Cross-correlation function R12() of a pair
of Gold sequences based on the two PN
sequences [7, 4] and [7, 6, 5, 4].
Haykin P507
Problem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interference
Solution: spread the narrow band signal into a broad band signal using a special code
protection against narrow band interference
Side effects:
coexistence of several signals without dynamic coordination
tap-proof
Alternatives: Direct Sequence, Frequency Hopping Schiller P54
11.6
What is spread spectrum modulation?
Any modulation where the bandwidth of the modulated signal is much larger than the bandwidth of the modulating signal.
Purpose of SS modulation: ▪ To increase the anti-interference ability of narrow band interference.
▪ To conceal the transmitted signals in the background noise for the prevention of interception.
▪ To increase the ability of anti-multipath transmission effect.
▪ To provide the possibility of sharing the same frequency band by multiple users.
▪ To provide the ability of distance telemetering.
Fan P333
What can be gained from apparent waste of spectrum?
Immunity from various kinds of noise and multipath distortion
Can be used for hiding and encrypting signals
Several users can independently use the same higher bandwidth with very little interference
Stallings P160-161
Spread-spectrum (SS) technology has only emerged since the 1950s. Yet, this novel approach to applications, such as multiple access, ranging, and interference rejection, has rendered SS techniques extremely important to most current NASA and military communication systems.
The initial application of spread-spectrum (SS) techniques was in the development of military guidance and communication systems. By the end of World War II, spectrum spreading for jamming resistance was already a familiar concept to radar engineers, and during subsequent years, SS investigation was motivated primarily by the desire to achieve highly jam-resistant communication systems.
Sklar P719
As a result of this research, there emerged an assortment of other applications in such areas as energy density reduction, high-resolution ranging, and multiple access, which will be discussed in later sections. The techniques considered in this chapter are called spread spectrum because the transmission bandwidth employed is much greater than the minimum bandwidth required to transmit the information.
Sklar P719
A system is defined to be a spread-spectrum system if it fulfills the following requirements:
1. The signal bandwidth much > the minimum bandwidth necessary to send the information.
2. Spreading is accomplished by means of a spreading signal, often called a code signal, which is independent of the data.
3. At the receiver, despreading (recovering the original data) is accomplished by the correlation of the received spread signal.
Sklar P719
Standard modulation schemes such as frequency modulation and pulse code modulation also spread the spectrum of an information signal, but they do not qualify as spread-spectrum systems since they do not satisfy all the conditions outlined above.
Sklar P720
Input is fed into a channel encoder
Produces analog signal with narrow bandwidth
Signal is further modulated using sequence of digits
Spreading code or spreading sequence
Generated by pseudonoise, or pseudo-random number generator
Effect of modulation is to increase bandwidth of signal to be transmitted
On receiving end, digit sequence is used to demodulate the spread spectrum signal
Signal is fed into a channel decoder to recover data Stallings P160
Figure
Illustrating the waveforms in the transmitter.
Haykin P480
Spreading of data signal s(t) by the code signal c(t) to result in message signal m(t) as )()()( tctstm
Digital
signal
s(t)
Code c(t)
Spreading
signal
m(t)
Spreading
Frequency
Power
Frequency
Power
Agrawal P106
Frequency
Baseband signal
0
Interference signals
Frequency
Despread signal
f
Frequency
Interference
baseband signals
Spectrum spreading signal
f
Rappaport P333
narrowband channels
spread spectrum channels
Schiller P55-56
Kinds of SS modulation:
Direct-sequence SS (DSSS)
Frequency hopping (FH)
Linear frequency modulation (LFM)
Fan P334
Figure below highlights the popular techniques for spreading the information signal over a large number of signal coordinates or dimensions.
Sklar P724-725
Sklar P725
For signals of bandwidth W and duration T, the dimensionality of the signaling space is approximately 2WT. To increase the dimensionality, we can either increase W by spectrum spreading, or increase T by time spreading or time hopping (TH). With spectrum spreading the signal is spread in the frequency domain.
With time hopping, a message with data rate R is allocated a longer transmission-time duration than would be used with a conventional modulation scheme. During this longer time the data are sent in bursts according to the dictates of a code. We can say that with time hopping the signal is spread in the time domain. For both cases, frequency spreading and time spreading, a jammer will be uncertain regarding the signaling subset that is currently in use.
Sklar P724
In Figure 12.4, the first two items listed under the category of spreading, direct sequencing (DS) and frequency direct sequencing (DS) and frequency hopping (FH), are the most commonly used techniques for spectrum spreading. As a jamming-rejection technique, time hopping (TH), the third item in the list, is similar to spread spectrum in that the location of the signal coordinates is hidden from potential adversaries.
Sklar P724
Also, there are hybrid combinations of the spreading techniques, for example, DS/FH, FH/TH, and DS/FH/TH; Here we focus only on the two major spread-spectrum techniques: DS and FH .
Sklar P724
Spreading Sequence Categories PN sequences
Orthogonal codes For FHSS systems
PN sequences most common For DSSS systems not employing CDMA
PN sequences most common For DSSS CDMA systems
PN sequences
Orthogonal codes
Stallings P173-184
Spread data rate by an orthogonal code (channelization code)
Provides mutual orthogonality among all users in the same cell
Further spread result by a PN sequence (scrambling code)
Provides mutual randomness (low cross correlation) between users in different cells
Stallings P185
Code
c(t)
Spreading
signal m(t)
Spreading
Transmitter
Code
c(t)
Digital signal
s(t)
Despread
Receiver
Power
Digital
signal s(t)
Frequency Frequency
Power
Frequency
Power
Agrawal P107
DSSS system
DSSS system
Input pseudo-random code
Threshold value
‘ Search
control
Local pseudo-code
generator
Clock
Bandpass
filter
Envelop
detector Threshold
Synchronization indication ‘
Fan P337
XOR of the signal with pseudo-random number (chipping sequence)
many chips per bit (e.g., 128) result in higher bandwidth of the signal
user data
chipping
sequence
resulting
signal
0 1
0 1 1 0 1 0 1 0 1 0 0 1 1 1
XOR
0 1 1 0 0 1 0 1 1 0 1 0 0 1
=
tb
tc
tb: bit period
tc: chip period
Schiller P57
Figure Direct-sequence spread coherent phase-
shift keying.
(a) Transmitter. (b) Receiver. Haykin P491
Schiller P57-58
user data
spread
spectrum
signal transmit
signal
correlator
▪ Symbol duration = T
▪ SS code c(t) usually uses m sequence.
▪ The symbol of SS code is called chip.
▪ Duration of chip = Tc, usually Tc << T
Fan P334
Advantages
reduces frequency selective fading
in cellular networks
▪ base stations can use the same frequency range
▪ several base stations can detect and recover the signal
▪ soft handover
Disadvantages
precise power control necessary
Schiller P57
Each bit in original signal is represented by multiple bits in the transmitted signal
Spreading code spreads signal across a wider frequency band
Spread is in direct proportion to number of bits used
One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure next page)
Beard P259-260
Signal is broadcast over seemingly random series of radio frequencies A number of channels allocated for the FH signal
Width of each channel corresponds to bandwidth of input signal
Signal hops from frequency to frequency at fixed intervals Transmitter operates in one channel at a time
Bits are transmitted using some encoding scheme
At each successive interval, a new carrier frequency is selected
Beard P254
Channel sequence dictated by spreading code Receiver, hopping between frequencies in
synchronization with transmitter, picks up message Advantages
Eavesdroppers hear only unintelligible blips
Attempts to jam signal on one frequency succeed only at knocking out a few bits
Beard P254
https://en.wikipedia.org/wiki/Hedy_Lamarr
https://en.wikipedia.org/wiki/Frequency-
hopping_spread_spectrum
http://www.hedylamarr.com/
Hopping
pattern
Spreading signal
Spreading
Transmitter
Frequency
Power
Digital signal
s(t)
Despread
Receiver
Hopping
pattern
Frequency
Power Power
Digital signal
Frequency
Agrawal P107
Figure Frequency-hopped spread spectrum system (FH-SS). Couch P398
Haykin P501
Rappaport P335 Schiller P61
Frequency
Time Agrawal P108
Discrete changes of carrier frequency sequence of frequency changes determined via pseudo random
number sequence Two versions
Fast Hopping: several frequencies per user bit(there is only 1 bit or less than 1 bit in one hop)
Slow Hopping: several user bits per frequency(there are several bits in one hop)
Advantages frequency selective fading and interference limited to short period simple implementation uses only small portion of spectrum at any time
Disadvantages not as robust as DSSS simpler to detect
Schiller P59-61 Fan P336
user data
slow
hopping
(3 bits/hop)
fast
hopping
(3 hops/bit)
0 1
tb
0 1 1 t
f
f1
f2
f3
t
td
f
f1
f2
f3
t
td
tb: bit period td: dwell time
Schiller P59
Large number of frequencies used Results in a system that is quite resistant to
jamming
Jammer must jam all frequencies
With fixed power, this reduces the jamming power in any one frequency band
Stallings P165
Space divided into spatially separate sectors
Beam n Beam 1
Beam 2
Beam 3
Beam i
s(f,t,c) s(f,t,c)
s(f,t,c)
s(f,t,c)
s(f,t,c) Omni-directional
transmission
The concept of
SDMA
Agrawal P112
The basic structure of a SDMA system.
MS1
MS2 MS3 BS
Beam 1 Beam 2 Beam 3
Agrawal P113
Technique FDMA TDMA CDMA SDMA
Concept
Divide the frequency
band into disjoint
subbands
Divide the time into
non-overlapping time
slots
Spread the signal
with orthogonal
codes
Divide the space in to
sectors
Active terminals
All terminals active
on their specified
frequencies
Terminals are active
in their specified slot
on same frequency
All terminals active
on same frequency
Number of terminals
per beam depends on
FDMA/ TDMA/CDMA
Signal separation
Filtering in frequency Synchronization in
time
Code separation Spatial separation using
smart antennas
Handoff Hard handoff Hard handoff Soft handoff Hard and soft handoffs
Advantages Simple and robust Flexible Flexible Very simple, increases
system capacity
Disadvantages
Inflexible, available
frequencies are fixed,
requires guard bands
Requires guard space,
synchronization
problem
Complex receivers,
requires power
control to avoid
near-far problem
Inflexible, requires
network monitoring to
avoid intracell handoffs
Current applications Radio, TV and analog
cellular
GSM and PDC 2.5G and 3G Satellite systems, other
being explored Agrawal P113
Approach SDMA TDMA FDMA CDMA
Idea segment space into cells/sectors
segment sending time into disjoint time-slots, demand driven or fixed patterns
segment the frequency band into disjoint sub-bands
spread the spectrum using orthogonal codes
Terminals only one terminal can be active in one cell/one sector
all terminals are active for short periods of time on the same frequency
every terminal has its own frequency, uninterrupted
all terminals can be active at the same place at the same moment, uninterrupted
Signal separation
cell structure, directed antennas
synchronization in the time domain
filtering in the frequency domain
code plus special receivers
Advantages very simple, increases capacity per km²
established, fully digital, flexible
simple, established, robust
flexible, less frequency planning needed, soft handover
Disadvantages inflexible, antennas typically fixed
guard space needed (multipath propagation), synchronization difficult
inflexible, frequencies are a scarce resource
complex receivers, needs more complicated power control for senders
Comment only in combination with TDMA, FDMA or CDMA useful
standard in fixed networks, together with FDMA/SDMA used in many mobile networks
typically combined with TDMA (frequency hopping patterns) and SDMA (frequency reuse)
higher complexity, lowered expectations; integrated with TDMA/FDMA
Schiller P90
OFDM is a kind of multi-carrier parallel modulation system.
Application: ADSL, HDTV, DVB, WLAN, etc.. It has started to be used in WWAN, and is being researched for application in the next generation of cellular networks.
OFDM created great expansion in wireless networks
Greater efficiency in bps/Hz
Main air interface in the change from 3G to 4G
Also expanded 802.11 rates
Critical technology for broadband wireless access
WiMAX
Beard P237
Features:
To improve frequency utilization and increase transmission rate, frequency spectra of modulated subcarriers are partially overlapped;
Modulated signals are strictly orthogonal to each other in order to be completely separated in the receiver;
The modulation of each subcarrier is M-ary modulation;
The modulation system of each subcarrier can be different and adaptive to the variation of the channel.
Fan P324
Also called multicarrier modulation Start with a data stream of R bps
Could be sent with bandwidth Nfb
With bit duration 1/R
OFDM splits into N parallel data streams
Called subcarriers
Each with bandwidth fb
And data rate R/N (bit time N/R)
Conceptual Understanding of Orthogonal
Frequency Division Multiplexing Beard P238
Divide a channels in to multiple sub-channels and do parallel transmission
Orthogonality of two signals in OFDM can be given by a complex conjugate
relation indicated by *:
kjiji
jidttfstfs j
F
,....,2,1,,,0
,1),(),( *
Spectrun of an
OFDM signal with
multiple subchannels
Spectrum of a single
OFDM subchannel
Agrawal P111
The spacing of the fb frequencies allows tight packing of signals Actually with overlap between the signals
Signals at spacing of fb ,2fb, 3fb ,etc.
The choice of fb is related to the bit rate to make the signals orthogonal Average over bit time of s1(t) × s2(t) = 0
Receiver is able to extract only the s1(t) signal
▪ If there is no corruption in the frequency spacing
Traditional FDM makes signals completely avoid frequency overlap OFDM allows overlap which greatly increases capacity
Beard P237-238
Since the frequency spacings of various adjacent subcarriers equal f = 1/T, the spectral density curves of combined subcarriers are as
Fan P326
Bandwidth
Advantages:
There is no need of guard space between subcarriers in frequency domain, so the frequency band can be sufficiently utilized.
Modulation systems of various subcarriers can be different, so OFDM has considerable flexibility.
Fan P326
Frequency selective fading only affects some subcarriers Can easily be handled with a forward error-correcting code
More importantly, OFDM overcomes intersymbol interference (ISI) ISI is a caused by multipath signals arriving in later bits
OFDM bit times are much, much longer (by a factor of N)
▪ ISI is dramatically reduced
N is chosen so the root-mean-square delay spread is significantly smaller than the OFDM bit time
It may not be necessary to deploy equalizers to overcome ISI
▪ Eliminates the use of these complex and expensive devices.
Beard P240
Principle of implementation：Since the form of OFDM signal expression is similar to that of inverse discrete Fourier transform (IDFT), the calculation methods used for IDFT and DFT can be used for OFDM modulation and demodulation.
Fan P327
Inverse Fast Fourier Transform (IFFT)
The OFDM concept (Figure 8.1) would use N oscillators for N different subcarrier frequencies ▪ Expensive for transmitter and receiver
Discrete Fourier Transform (DFT) processes digital signals ▪ If N is a power of two, the computational speed dramatically
improves by using the fast version of the DFT (FFT).
Transmitter takes a symbol from each subcarrier ▪ Makes an OFDM symbol
▪ Uses the Inverse FFT to compute the data stream to be transmitted
▪ OFDM symbol provides the weights for each subcarrier
▪ Then it is sent on the carrier using only one oscillator
Beard P241
Assume: s(k) － sampling function of a time signal s(t), where k = 0, 1, 2, … , K– 1， then the definition of DFT of s(k) is
and the IDFT of S(n) is:
1
0
)/2()(1
)(K
n
nkKjenSK
ks )1,,2,1,0( Kk
1
0
)/2()(1
)(K
k
nkKjeksK
nS
)1,,2,1,0( Kn
Fan P327
Orthogonality of OFDM system Assume there are N subchannels in an OFDM
system, each subchannel uses a subcarrier: where Bk － amplitude of the k-th subcarrier,
decided by the input symbols fk － subcarrier frequency of the k-th subchannel k － initial phase of the carrier of the k-th
subchannel
1,,1,0)2cos()( NktfBtx kkkk
Fan P324
then the sum of the N sub-signals in the system can be expressed as
The above equation can be rewritten as the complex form as follows:
where Bk is the complex input data of the k-th subchannel.
1
0
)2cos()(N
k
kkk tfBts
1
0
2)(
N
k
tfj
kkkeBts
Fan P324-325
Let OFDM signal expression be
and k＝0，then the above equation becomes
and the expression of IDFT is
1
0
2)(
N
k
tfj
kkkeBts
1
0
2)(
N
k
tfj
kkeBts
1
0
)/2()(1
)(K
n
nkKjenSK
ks )1,,2,1,0( Kk
Fan P327
Block diagram of OFDM modulation
Framing
Grouping Serial/ parallel
converter
Coding
Mapping
.
.
.
.
.
.
IDFT
. . .
Serial/ parallel
converter
D/A
converter
Upward
frequency
converter OFDM
signal Binary
input signal
Fan P329
Couch P388
Modulation operation at the OFDM transmitter
High speed
data stream
Serial to parallel
conversion
IDFT Guard interval
insertion
Low speed bit stream
N2 ….
Nn
Transmission
of OFDM
signal
Guard interval
removal DFT
N1
N2
….
Nn
Parallel to serial
conversion
High speed
data stream
N1
Demodulation steps at the OFDM receiver
Received
OFDM signal
Agrawal P111-112
Figure PSD for the complex envelope of OFDM with N = 32. Couch P389
Orthogonal Frequency Division Multiple Access (OFDMA) uses OFDM to share the wireless channel Different users can have different slices of time and different groups
of subcarriers
Subcarriers are allocated in groups
▪ Called subchannels or resource blocks
▪ Too much computation to allocate every subcarrier separately
Subchannel allocation Adjacent subcarriers – similar SINR
▪ Must measure to find the best subchannel
Regularly spaced subcarriers – diverse SINR
Randomly space subcarriers – diverse SINR and reduced adjacent-cell interference
Beard P246
FDMA TDMA CDMA
Orthogonal code
PN Sequence
Spread Spectrum
SDMA OFDM
Beard’s book P36 Review Questions 2.14 2.15 2.14 Why is multiplexing so cost- effective? 2.15 How is interference avoided by using frequency division
multiplexing? P270-271 Review Questions 9.3 9.5 9.7 9.3 What is frequency hopping spread spectrum? 9.5 What is direct sequence spread spectrum? 9.7 What is CDMA? P271 Problems 9.2 9.2 An FHSS system employs a total bandwidth of Ws = 400
MHz and an individual channel bandwidth of 100 Hz. What is the minimum number of PN bits required for each frequency hop?
