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Spread Spectrum Ppt

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    Spread Spectrum

    The spread spectrum techniques was

    developed initially for military and intelligence

    requirements.

    The essential idea is to spread the information

    signal over a wider bandwidth to make

    jamming and interception more difficult.

    In this chapter, we will look some spread

    spectrum techniques and multiple access

    technique based on spread spectrum.

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    Outline

    5.1 Concept of Spread Spectrum

    5.2 Frequency-Hopping Spread Spectrum

    5.3 Direct Sequence Spread Spectrum

    5.4 Code Division Multiple Access5.5 Generation of Spreading Sequences

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    Concept of Spread Spectrum

    General model of spread spectrum digital

    communication system.

    Analog signal with

    a relatively narrow

    bandwidth

    To increase the

    bandwidth of the

    signal

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    Concept of Spread Spectrum

    Input is fed into a channel encoder

    Produce an analog signal with a relatively narrow bandwidth around

    some center frequency.

    Further modulated using a sequence of digits known as a

    spreading code or spreading sequence.

    The spreading code is generated by a pseudonoise, or pseudorandom

    number generator.

    The effect of this modulation is to increase significantly the bandwidth

    (spread the spectrum) of the signal to be transmitted. At the receiver, the same digit sequence is used to demodulate

    the spread spectrum signal.

    The signal is fed into a channel decoder to recover the data.

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    Concept of Spread Spectrum

    What can we gain from this apparent waste of

    spectrum?

    Gain immunity from various kinds of noise and

    multipath distortion

    Can be used for hiding and encrypting signals.

    Only a recipient who knows the spreading code

    can recover the encoded information.Several users can independently use the same

    higher bandwidth with very little interference

    (CDMA).

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    Outline

    5.1 Concept of Spread Spectrum

    5.2 Frequency-Hopping Spread Spectrum

    5.3 Direct Sequence Spread Spectrum

    5.4 Code Division Multiple Access5.5 Generation of Spreading Sequences

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    Frequency-Hopping Spread Spectrum

    Basic Approach

    FHSS Using MFSK

    FHSS Performance

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    Basic Approach

    Frequency-Hopping Spread Spectrum -- FHSS

    Signal is broadcast over a seemingly random series

    of radio frequencies, hopping from frequency to

    frequency at fixed intervals.

    A receiver, hopping between frequencies in

    synchronization with the transmitter, picks up the

    message.

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    Basic Approach

    Advantages

    Attempts to jam the signal on one frequency only

    knock out a few bits of it.

    Would-be eavesdroppers hear only unintelligible

    blips

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    Basic Approach

    An example of frequency-hopping signal

    A number of channels

    are allocated for the

    FH signal.

    Typically, there are 2k

    carrier frequencies

    forming 2k channels.

    The width of each

    channel corresponds to

    the bandwidth of the

    input signal.

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    Basic Approach

    The transmitter operates inone channel at a time for a

    fixed interval.

    During that interval, some

    number of bits are transmittedusing some encoding scheme.

    The sequence of channels

    used is dictated by a spreading

    code. Both transmitter and

    receiver use the same code to

    tune into a sequence of

    channels in synchronization.

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    Basic Approach

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    Basic Approach

    Typical block diagram for a FH system

    Generate

    spreading code

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    Basic Approach

    Binary data are fed into a modulator using some modulation

    scheme (FSK or BPSK)

    Spreading code (generate by PN sourse) serves as an index

    into a table of frequencies

    Each kbits of the spreading code specifies one of the 2kcarrier

    frequencies. At each k PN bits, a new carrier frequency is

    selected.

    The signal produced from the initial modulator is modulated

    by this frequency.

    Produce a new signal with the same shape but now centered on

    the selected carrier frequency.

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    [Example] An FHSS system employs a total

    bandwidth of Ws=400MHz and an individual

    channel bandwidth of 100Hz. What is the

    minimum number of PN bits required for each

    frequency hop?

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    Basic Approach

    The question is: How does the FH spreaderwork? (How it move the signal frequency to

    the selected frequency?)

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    Basic Approach

    Assuming we are using BFSK as the data

    modulation scheme.

    Then the output signal from modulator or the

    input signal to the FH spreader can be defined

    as:

    BFSKoffrequencycarrier,

    signalofamplitude

    0)2cos(

    1)2cos()(

    21

    2

    1

    ff

    A

    where

    binarytfA

    binarytfAtsd

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    Basic Approach

    The frequency synthesizer generates a constant-

    frequency tone.

    The frequency hops among a set of2kfrequencies.

    The hopping pattern determined by k bits from the PNsequence.

    Assume the duration of one hop is the same as

    the duration of one bit.

    Ignore phase differences between sd(t) and the

    spreading signal c(t), or chipping signal.

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    Basic Approach

    If the frequency of the signal generated by the

    frequency synthesizer during the ith hop is fi, the

    product signalp(t) during the ith hop is:

    Using the trigonometric identity:

    0)2cos()2cos(

    1)2cos()2cos()()()(i2

    i1

    binarytftfA

    binarytftfAtctstp d

    ))cos())(cos(21()cos()cos( yxyxyx

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    Basic Approach

    We can easily get

    The bandpass filter is used to block the difference

    frequency and pass the sum frequency, then the

    spread spectrum signal is

    0))(2cos())(2cos(5.0

    1))(2cos())(2cos(5.0)(

    i2i2

    i1i1

    binarytfftffA

    binarytfftffAtp

    0))(2cos(5.0

    1))(2cos(5.0)(

    i2

    i1

    binarytffA

    binarytffAts

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    Basic Approach

    Thus, during the ith bit interval, the frequency

    of the spread spectrum signal isf1+fi if the data

    bit is 1 and f2+fiif the data bit is 0.

    The central frequency is now moved tof2+fi or

    f1+fi.

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    Problems

    [Problems]1. How does the FH spreader work when we use

    BPSK modulation? (How it move the signal

    frequency to the selected frequency when BPSK is

    used?)

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    Basic Approach

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    Basic Approach

    On reception, a signal of the form s(t) just defined

    will be received.

    The spread spectrum signal is demodulated using the

    same sequence of PN-derived frequencies. Then demodulated to produce the output data.

    How does the receiver work?

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    Basic Approach

    Signal s(t) is multiplied by a replica of the spreading

    signal to yield a product signal of the form:

    Again using the trigonometric identity

    0)2cos())(2cos(5.01)2cos())(2cos(5.0)()()(

    i2

    i1'

    binarytftffAbinarytftffAtctstp

    i

    i

    0)2cos())2(2cos(25.0

    1)2cos())2(2cos(25.0)(

    2i2

    1i1'

    binarytftffA

    binarytftffAtp

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    Basic Approach

    At the receiver, the bandpass filter is used to

    block the sum frequency and pass the

    difference frequency, then a signal of the form

    of is yielded.

    0)2cos(25.0

    1)2cos(25.0)(

    2

    1'

    binarytfA

    binarytfAtsd

    )(' tsd

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    Problems

    [Problems]2. How does the FH despreader work when we use

    BPSK modulation? (How it move the signal

    frequency back to the carrier frequency when BPSK

    is used?)

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    Frequency-Hopping Spread Spectrum

    Basic Approach

    FHSS Using MFSK

    FHSS Performance

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    FHSS using MFSK

    MFSK is a common modulation technique used inconjunction with FHSS.

    Recall: MFSK uses M=2L different frequencies to

    encode the digital inputL bits at a time.

    elementsignalperbitsofnumber

    2elementssignaldifferentofnumber

    sfrequenciecarrierthe

    1)2cos()(MFSK i

    L

    M

    f

    where

    MitfAts

    L

    i

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    FHSS using MFSK

    If Tc is greater than or equal to Ts the

    spreading modulation is referred to as slow-

    frequency-hop spread spectrum

    Otherwise it is known as fast-frequency-hop

    spread spectrum.

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    FHSS using MFSK

    [Example 1] If we use the MFSK example from

    last chapter.

    M=4, which means that four different frequencies are

    used to encode the data input 2 bits at a time.

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    FHSS using MFSK

    Each signal element is a discrete frequency tone. The

    total MFSK bandwidth is Wd=Mfd.

    If we use an FHSS scheme with k=2, there are 4=2k

    different channels, each of width Wd. The total FHSSbandwidth is Ws=2

    kWd.

    Each 2 bits of the PN sequence is used to select one

    of the four channels. That channel is held for a

    duration of two signal elements, or four bits

    (Tc=2Ts=4T)

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    FHSS using MFSKPN sequence

    Input binary data

    Slow FHSS

    Frequency

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    [Example 2] Using the same MFSK example.

    M=4 and k=2. Wd=MfdandWs=2kWd.

    However in this case, each signal element is

    represented by two frequency tones. Then

    Ts=2Tc=2T.

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    Frequency

    PN sequence

    Input binary data

    Fast FHSS

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    Another two example

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    time

    Fr

    equency

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    time

    Frequency

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    Frequency-Hopping Spread Spectrum

    Basic Approach

    FHSS Using MFSK

    FHSS Performance

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    FHSS Performance

    Typically, a large number of frequencies are used in

    FHSS so that Ws is much larger than Wd.

    Large value of k results in a system that is quite

    resistant to jamming. Suppose MFSK has bandwidth Wd and noise jammer

    has the same bandwidth. If the jammer has a fixed

    power Sj on the signal carrier frequency, then the ratio

    of signal energy per bit to noise power density is:

    j

    db

    dj

    b

    j

    b

    S

    WE

    WS

    E

    N

    E

    /

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    If frequency hopping is used, the jammer must jam all

    2kfrequencies.

    For fixed noise power, since Ws=2kWd, this reduces

    the jamming power density to Sj/(2kWd). Then

    The gain in signal-to-noise ratio (the processing gain)is

    j

    k

    db

    d

    k

    j

    b

    j

    b

    S

    WE

    WS

    E

    N

    E

    2)2/('

    k

    d

    sP

    W

    WG 2

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    [Example] An FHSS system using MFSK with

    M=4 employs 1000 different frequencies.

    What is the processing gain?

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    [Example] The following table illustrates the operationof an FHSS system for one complete period of thePN sequence.

    a. What is the period of the PN sequence?

    b. The system makes use of a form of FSK, what form of FSKis it?

    c. What is the number of bits per symbol?

    d. What is the number of FSK frequencies?

    e. What is the length of PN sequence per hop?

    f. Is this a slow or fast FH system?

    g. What is the total number of possible hops?

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    Time 12 13 14 15 16 17 18 19

    Input data0 1 1 1 1 0 1 0

    Frequency f1 f3 f2 f2

    PN sequence 001 001

    Time 0 1 2 3 4 5 6 7 8 9 10 11

    Input data 0 1 1 1 1 1 1 0 0 0 1 0

    Frequency f1 f3 f27 f26 f8 f10

    PN sequence 001 110 011

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    [Example] The following table illustrates the operationof an FHSS system for one complete period of thePN sequence.

    a. What is the period of the PN sequence?

    b. The system makes use of a form of FSK, what form of FSKis it?

    c. What is the number of bits per symbol?

    d. What is the number of FSK frequencies?

    e. What is the length of PN sequence per hop?

    f. Is this a slow or fast FH system?

    g. What is the total number of possible hops?

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    Time 12 13 14 15 16 17 18 19

    Input data 0 1 1 1 1 0 1 0

    Frequency f9 f1 f3 f3 f22 f11 f3 f3

    PN sequence 011 001 001 001 110 011 001 001

    Time 0 1 2 3 4 5 6 7 8 9 10 11

    Input data 0 1 1 1 1 1 1 0 0 0 1 0

    Frequency f1 f21 f11 f3 f3 f3 f22 f10 f0 f0 f1 f22

    PN sequence 001 110 011 001 001 001 110 011 001 001 001 110

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    Outline

    5.1 Concept of Spread Spectrum

    5.2 Frequency-Hopping Spread Spectrum

    5.3 Direct Sequence Spread Spectrum

    5.4 Code Division Multiple Access5.5 Generation of Spreading Sequences

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    Direct Sequence Spread Spectrum

    DSSS Using BPSK

    DSSS Performance

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    DSSS Using BPSK

    Direct Sequence Spread Spectrum DSSS

    Each bit in the original signal is represented by

    multiple bits in the transmitted signal, using a

    spreading code.The spreading code spreads the signal across a

    wider frequency band in direct proportion to the

    number of bits used.

    A 10-bit spreading code spreads the signal across a

    frequency band that is 10 times greater than a 1-bit

    spreading code.

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    DSSS Using BPSK

    One technique with DSSS is to combine the digital

    information stream with the spreading code bit stream

    using an exclusive-OR (XOR).

    The XOR obeys the following rules:

    101110011000

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    DSSS Using BPSK

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    DSSS Using BPSK

    This example shows that

    An information bit of one inverts the spreading

    code bits in the combination

    An information bit of zero causes the spreadingcode bits to be transmitted without inversion.

    The combination bit stream has the data rate of the

    original spreading code sequence, so it has a widerbandwidth than the information stream.

    In this example, the rate of spreading code bit

    stream is four times the information rate.

    DSSS U i BPSK

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    DSSS Using BPSK

    A BPSK signal can be expressed as:

    To produce the DSSS signal, we multiply the

    above by c(t), which is the PN sequence taking

    on values of +1 and -1.

    0binary1

    1binary1s(t)

    signalNRZbipolaris)(

    )2cos()(BPSK

    tswhere

    tfAtse cBPSK

    )2cos()()( tftctAse cDSSS

    DSSS U i BPSK

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    DSSS Using BPSK

    At the receiver, the incoming signal is

    multiplied by c(t). Because c(t)c(t)=1, the

    original signal is recovered:

    BPSKcDSSS etctftctAstce )()2cos()()()(

    DSSS U i BPSK

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    DSSS Using BPSK

    The DSSS signal expression can be interpreted

    in two ways, leading two different

    implementations.

    First multiply s(t) and c(t) together and thenperform the BPSK modulation.

    Alternatively, we can first perform the BPSK

    modulation on the data stream s(t) to generate thedata signal eBPSK. This signal can then be multiplied

    by c(t).

    DSSS U i BPSK

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    DSSS Using BPSK

    Transmitter using the second interpretation:

    DSSS U i BPSK

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    DSSS Using BPSK

    Receiver using the second interpretation:

    DSSS U i BPSK

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    DSSS Using BPSK

    [Example]

    DSSS U i BPSK

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    DSSS Using BPSK

    Di t S S d S t

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    Direct Sequence Spread Spectrum

    DSSS Using BPSK

    DSSS Performance

    DSSS P f

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    DSSS Performance

    The information signal has a bit width of T,

    which is equivalent to a data rate of 1/T. the

    spectrum of the signal depending on the

    encoding technique, is roughly 2/T.

    Similarly, the spectrum of the PN signal is

    2/Tc.

    The amount of spreading that is achieved is adirect result of the data rate of the PN stream.

    DSSS P f

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    DSSS Performance

    DSSS P f

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    DSSS Performance

    Effectiveness against jammingAssume a simple jamming signal at the center

    frequency of the DSSS system. The jamming

    signal is:

    The received signal is

    )2cos(2)( tfSts cjj

    noisewhiteadditive)(

    signalreceived)(

    powersignaljammer

    )()()()(

    tn

    te

    Swhere

    tntstete

    r

    j

    jDSSSr

    DSSS Performance

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    DSSS Performance

    The despreader at the receiver multiplies er(t) by c(t), so the

    signal component due to the jamming signal is:

    This is simply a BPSK modulation of the carrier tone. Thus

    the carrier power Sj is spread over a bandwidth of

    approximately 2/Tc.

    The BPSK demodulator following the DSSS despreader

    includes a bandpass filter matched to the BPSK with

    bandwidth of2/T.

    Most of the jamming power is filtered.

    )2cos()(2)( tftcSty cji

    DSSS Performance

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    DSSS Performance

    As an approximation, the jamming power passed by

    the filter is

    The jamming power has been reduced by a factor of(Tc/T) through the use of spread sprectrum.

    The gain in signal-to-noise ratio is:

    )/()/2/()/2( TTSTTSFS cjcjj

    bandwidthsignalspectrumspread

    bandwidthsignal

    ratebitspreadingratedata

    c

    d

    c

    d

    cc

    c

    P

    W

    W

    RRwhere

    W

    W

    R

    R

    T

    TG

    Outline

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    Outline

    5.1 Concept of Spread Spectrum

    5.2 Frequency-Hopping Spread Spectrum

    5.3 Direct Sequence Spread Spectrum

    5.4 Code Division Multiple Access5.5 Generation of Spreading Sequences

    Code Division Multiple Access

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    Code Division Multiple Access

    Basic Principles

    CDMA for DSSS

    Code Division Multiple Access

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    Code Division Multiple Access

    CDMA is a multiplexing technique used with

    spread spectrum.

    Assuming data signal with rate D, break each bit

    into k chips according to a fixed pattern that isspecific to each user, called the users code.

    The new channel has a chip data rate of kD chips

    per second.

    Code Division Multiple Access

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    Code Division Multiple Access

    A simple example with k=6. It is simplest tocharacterize a code as a sequence of 1s and -1s.

    Code Division Multiple Access

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    Code Division Multiple Access

    Three users A, B and C, each of which is

    communicating with the same base station

    receiverR. The code for each user:

    CA= < 1 -1 -1 1 -1 1>

    CB= < 1 1 -1 -1 1 1>

    CC= < 1 1 -1 1 1 -1>

    The base station receiver is assumed to knowuserA B Cs code.

    Code Division Multiple Access

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    Code Division Multiple Access

    At the receiver

    If the receiver receives a chip pattern d=

    The receiver has user us code Cu=< c1 c2 c3 c4 c5c6>

    The receiver performs electronically the following

    decoding function

    665544332211)( cdcdcdcdcdcddSu

    Code Division Multiple Access

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    Code Division Multiple Access

    User A:

    If A wants to send a 1 bit, A transmits its code as

    a chip pattern d=< 1 -1 -1 1 -1 1>.

    If A wants to send a 0 bit, A transmits thecomplement of its code (1s and -1s reversed) as a

    chip pattern d=.

    The code for user A is c=CA

    = < 1 -1 -1 1 -1 1>

    Code Division Multiple Access

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    Code Division Multiple Access

    User A:

    If A sends a 1 bit,

    If A sends a 0 bit

    Note that it is always the case that -6SA(d)6no

    matter what dis.

    611)1()1(11

    )1()1()1()1(11)1,1,1,1,1,1( AS

    61)1()1(11)1(

    )1(1)1(111-)1,1,1,1,1,1( AS

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    Code Division Multiple Access

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    Code Division Multiple Access

    User A:

    The only ds resulting in the extreme values of

    6 and -6 are As code and its complement

    respectively.

    If SA produces a +6, received a 1 bit from A

    If SA produces a -6, received a 0 bit from A

    Otherwise we assume that someone else is sendinginformation or there is an error.

    Code Division Multiple Access

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    Code Division Multiple Access

    If userB is sending and we try to received it with SA,that means we are decoding the received chip pattern

    with the wrong code (CA).

    If B sends a 1 bit, then d= < 1 1 -1 -1 1 1>, c=CA= < 1 -

    1 -1 1 -1 1>

    Since SA=0, we know that someone else apart from A is

    sending information (in this case is user B).

    If B had sent a 0 bit, the decoder would produce a value of

    0 for SA again.

    01)1()1()1(11

    )1(1)1()1(1)1()1,1,1-,1,1,1( AS

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    Transmit (data bit = 0) -1 -1 1 1 -1 -1

    Receiver codeword 1 -1 -1 1 -1 1

    Multiplication -1 1 -1 1 1 -1 = 0

    Code Division Multiple Access

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    Code Division Multiple Access

    If the decoder is linear and if A and B transmit

    signals dA and dB respectively, at the same

    time, then since

    equal to 0 when it is decoded by As code.

    The code of A and B that have the property

    that are called orthogonal

    code.

    )()()()( AABAAABAA dSdSdSddS )( BA dS

    0)()( ABBA CSCS

    Code Division Multiple Access

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    Code Division Multiple Access

    Combined signal 2 0 -2 0 0 2

    Receiver codeword 1 1 -1 -1 1 1

    Multiplication 2 0 2 0 0 2 = 6

    Transmission from A and B, receiver attempts to recover As transmissionA (data bit = 1) 1 -1 -1 1 -1 1

    B (data bit = 1) 1 1 -1 -1 1 1

    Combined signal 2 0 -2 0 0 2

    Receiver codeword 1 -1 -1 1 -1 1

    Multiplication 2 0 2 0 0 2 = 6

    Transmission from A and B, receiver attempts to recover Bs transmission

    Code Division Multiple Access

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    Code Division Multiple Access

    Combined signal 0 -2 0 2 -2 0

    Receiver codeword 1 1 -1 -1 1 1

    Multiplication 0 -2 0 -2 -2 0 = -6

    Transmission from A and B, receiver attempts to recover As transmissionA (data bit = 1) 1 -1 -1 1 -1 1

    B (data bit = 0) -1 -1 1 1 -1 -1

    Combined signal 0 -2 0 2 -2 0

    Receiver codeword 1 -1 -1 1 -1 1

    Multiplication 0 2 0 2 2 0 = 6

    Transmission from A and B, receiver attempts to recover Bs transmission

    Code Division Multiple Access

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    Code Division Multiple Access

    Such code are very nice but there are not many

    of them. More common is the case that is

    small in absolute value when XY.

    Then it is easy to distinguish between the twocases when X=Y and when XY.

    In our example, but

    , in the latter case the C

    signal would make a small contribution to the

    decoded signal.

    )( YX CS

    0)()( ACCA CSCS

    2)()( BCCB CSCS

    Code Division Multiple Access

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    Code Division Multiple Access

    Transmit (data bit = 0) -1 -1 1 -1 -1 1

    Receiver codeword 1 1 -1 -1 1 1

    Multiplication -1 -1 -1 1 -1 1 = -2

    Code Division Multiple Access

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    Code Division Multiple Access

    Combined signal 2 2 -2 0 2 0

    Receiver codeword 1 1 -1 1 1 -1

    Multiplication 2 2 2 0 2 0 = 8

    Transmission from B and C, receiver attempts to recover Cs transmission

    Code Division Multiple Access

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    Code Division Multiple Access

    B (data bit = 1) 1 1 -1 -1 1 1

    C (data bit = 0) -1 -1 1 -1 -1 1

    Combined signal 0 0 0 -2 0 2

    Receiver codeword 1 1 -1 1 1 -1

    Multiplication 0 0 0 -2 0 -2 = -4

    (f) Transmission from B and C, receiver attempts to recover Bs transmissionB (data bit = 1) 1 1 -1 -1 1 1

    C (data bit = 0) -1 -1 1 -1 -1 1

    Combined signal 0 0 0 -2 0 2

    Receiver codeword 1 1 -1 -1 1 1

    Multiplication 0 0 0 2 0 2 = 4

    Transmission from B and C, receiver attempts to recover Cs transmission

    Code Division Multiple Access

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    Code Division Multiple Access

    Using the decoder Su, the receiver can sort outtransmission from u even when there may be other

    users broadcasting in the same cell.

    In practice, the CDMA receiver can filter out the

    contribution from unwanted users or they appear aslow-level noise.

    However the system breaks down:

    if there are many users competing for the channel with theuser the receiver is trying to listen to

    if the signal power of one or more competing signals is too

    high (perhaps because it is very near the receiver)

    Code Division Multiple Access

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    Code Division Multiple Access

    Basic Principles

    CDMA for DSSS

    CDMA for DSSS

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    CDMA for DSSS

    Look at CDMA from the viewpoint of a DSSS system usingBPSK.

    CDMA for DSSS

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    CDMA for DSSS

    There are n users, each transmitting using a differentorthogonal PN sequence.

    For each user, the data stream di(t) is BPSK

    modulated to produce a signal with a bandwidth ofWsand then multiplied by the spreading code ci(t) for

    that user.

    All of the signals, plus noise, are received at the

    receivers antenna.

    CDMA for DSSS

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    C o SSS

    Suppose that the receiver is attempting to recover thedata of user 1. The incoming signal is multiplied by

    the spreading code of user 1 and them demodulated.

    The effect of this is to narrow the bandwidth of thatportion of the incoming signal corresponding to user

    1 to the original bandwidth of unspread signal, which

    is proportional to the data rate.

    Because the remainder of the incoming signal isorthogonal to the spreading code of user 1, that

    remainder still has the bandwidth Ws.

    CDMA for DSSS

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    Thus the unwanted signal energy remainsspread over a large bandwidth and the wanted

    signal is concentrated in a narrow bandwidth.

    The bandpass filter at the demodulator cantherefore recover the desired signal.

    Outline

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    5.1 Concept of Spread Spectrum

    5.2 Frequency-Hopping Spread Spectrum

    5.3 Direct Sequence Spread Spectrum

    5.4 Code Division Multiple Access5.5 Generation of Spreading Sequences

    Generation of Spreading Sequences

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    p g q

    Spreading consists of multiplying the inputdata by the spreading sequence, where the bit

    rate of the spreading sequence is higher than

    that of the input data. When the signal is received, the spreading is

    removed by multiplying with the same

    spreading code, exactly synchronized with thereceived signal.

    Generation of Spreading Sequences

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    p g q

    Spreading code:There should be an approximately equal number of

    ones and zeros in the spreading code.

    Few or no repeated patterns In CDMA application, further requirement of lack

    of correlation

    Two general categories of spreading

    sequences:

    PN sequences

    Orthogonal codes

    Generation of Spreading Sequences

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    p g q

    PN Sequences

    Orthogonal Code

    Multiple Spreading

    Generation of Spreading Sequences

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    p g q

    PN Sequences

    PN Properties

    LFSR implementation

    M-Sequences Properties

    PN Sequences

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    q

    Ideal spreading sequence would be a randomsequence of binary ones and zeros.

    It is required that transmitter and receiver must

    have a copy of the random bit stream.

    A predictable way is needed to generate the

    same bit stream at the transmitter and receiver

    and also retain the desirable properties of arandom bit stream.

    A PN generatorcan meet this requirement.

    PN Sequences

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    q

    A PN generator will produce a periodic sequence thateventually repeats but that appears to be random.

    PN sequences are generated by an algorithm using

    some initial value called the seed.

    The algorithm is deterministic and therefore producessequences of numbers that are not statistically random.

    But if the algorithm is good, the resulting sequences will

    pass many reasonable tests of randomness.

    Such numbers are often referred to as pseudorandomnumbers, orpseudorandom sequences.

    Unless you know the algorithm and the seed, it is

    impractival to predict the sequence.

    PN Sequences

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    q

    PN properties:

    Randomness

    Unpredictability

    Two criteria are used to validate that a

    sequence of numbers is random

    Uniform distribution

    Independence

    PN Sequences

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    q

    Uniform distribution:The distribution of numbers in the sequence should

    be uniform

    The frequency of occurrence of each of the

    numbers should be approximately the same.

    For a stream of binary digits, we need to expand

    on this definition.

    PN Sequences

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    For a stream of binary digits, two properties aredesired:

    Balance property: in a long sequence the fraction of

    binary ones should approach .

    Run property: a run is defined as a sequence of all 1s or

    a sequence of all 0s. The appearance of the alternate

    digit is the beginning of a new run. About of the runs

    should be of length 1, of length 2, 1/8 of length3, and

    so on.

    000100110101111

    PN Sequences

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    Independence:

    No one value in the sequence can be inferred from

    the others.

    No such test to prove independenceA number of tests can be applied to demonstrate

    that a sequence does not exhibit independence.

    General strategy is to apply a number of such testsuntil confidence that independence exists is

    sufficiently strong.

    PN Sequences

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    In applications such as spread spectrum,Correlation property is required.

    If a period of the sequence is compared term by

    term with any cycle shift of itself, the number ofterms that are the same differs from those that are

    different by at most 1.

    Generation of Spreading Sequences

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    PN Sequences

    PN Properties

    LFSR implementation

    M-Sequences Properties

    LFSR implementation

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    Linear Feedback Shift Register Implementation: acircuit consisting of XOR gates and a shift register

    implementing the PN generator for spread spectrum

    A string of 1-bit storage devices.

    Each device has an output line, which indicates the value

    currently stored, and an input line.

    At discrete time instants, known as clock times, the value in

    the storage device is replaced by the value indicated by its

    input line.

    The entire LFSR is clocked simultaneously, causing a 1-bit

    shift along the entire register.

    LFSR implementation

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    The circuit is implemented as follows:

    The LFSR contains n bits.

    There are from 1 to (n-1) XOR gates.

    The presence or absence of a gate corresponds tothe presence or absence of a term in the generator

    polynomial (explained subsequently), P(X),

    excluding theXn term.

    LFSR implementation

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    Two equivalent ways of characterizing the PNLFSR:

    A sum of XOR terms

    Generator polynomial

    11221100 nnn BABABABAB

    nn

    n XXAXAXAXAXP1

    1

    2

    2

    1

    1

    0

    0)(

    LFSR implementation

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    Fig: Binary Linear Feedback Shift Register Sequence Generator

    LFSR implementation

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    An actual implementation would not have themultiple circuits; instead, forAi=0, the corresponding

    XOR circuit is eliminated.

    [Example] A 4-bit LFSR:

    103 BBB

    LFSR implementation

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    Advantages of shift register technique:The sequences generated can be nearly random

    with long periods

    LFSRs are easy to implement in hardware and canrun at high speeds (this is important because the

    spreading rate is higher than the data rate)

    LFSR implementation

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    Output ofn-bit LFSR: Is periodic with maximum periodN=2n-1.

    All-zeros sequence occurs

    if the initial contents of the LFSR are all zero or the coefficients ofBn are all zero (no feedback)

    When a period of N is given, a feedback

    configuration can always be found, the resulting

    sequence are called maximal-length sequences, or

    m-sequences.

    LFSR implementation

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    Step-by-step operation ofthe 4-bit LFSR with an

    initial state of 1000

    (B3=1, B2=0, B1=0,

    B1=0).

    The values currently

    stored in the four shift

    register elements

    The values that

    appear at the output

    of the XOR circuit

    The value of the

    output bit, which is B0

    in this example.

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    LFSR implementation

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    The period of the sequence, or the length of them-sequence: 24-1=15. the output repeats after

    15 bits.

    The same periodic m-sequence is generatedregardless of the initial state of the LFSR

    (except for 0000).

    With each different initial state, the m-sequence begins at a different point in its

    cycle.

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    LFSR implementation

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    For any given size of LFSR, a number ofdifferent unique m-sequences can be generated

    by using different values for the Ai.

    The table next page shows the sequence lengthand number of unique m-sequences that can be

    generated for LFSRs of various sizes, also an

    example generating polynomial.

    LFSR implementation

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    Bn for

    LFSR implementation

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    One useful attribute of the generatorpolynomial is that it can be used to find

    sequence generated by the corresponding

    LFSR, by taking the reciprocal of thepolynomial.

    [Example] A three bit LSFR with

    P(X)=1+X+X3

    , we perform the division1/(1+X+X3).

    LFSR implementation

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    Watch out: The

    subtractions are done

    modulo 2, or using

    the XOR function, in

    this case, subtraction

    produces the same

    result as addition.

    LFSR implementation

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    So the result of 1/(1+X+X3) is

    1+X+X2 +(0X3)+X4+(0X5) +(0X6)

    after which the pattern repeats.

    This means that the shift register output is

    1110100

    Because the period of this sequence is 7=23-1,

    this is an m-sequence.

    Generation of Spreading Sequences

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    PN Sequences

    PN Properties

    LFSR implementation

    M-Sequences Properties

    M-Sequences

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    M-sequences have several properties that makethem attractive for spread spectrum

    applications:

    Property 1. m-sequence has 2n-1 ones and 2n-1-1zeros.

    Property 2. If we slide a window of length n along

    the output sequence for N shifts (where N=2n-1),

    each n-tuple appears exactly once.

    1 1 1 0 1 0 0 1 1 1 0 1 0

    111, 110, 101, 010, 100, 001, 011

    M-Sequences

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    Property 3. There is one run of ones of length n;one run of zeros of length n-1; one run of ones and

    one run of zeros of length n-2; two runs of ones

    and two runs of zeros of length n-3; and in general,

    2n-3 runs of ones and 2n-3 runs of zeros of length 1.

    When n=4,N=15, 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1

    1 run of1s of length 4

    1 run of0s of length 3 1 run of1s and 1 run of0s of length 2

    2 runs of1s and 2 runs of0s of length 1 (2n-3 =2)

    M-Sequences

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    Correlation is the concept of determining how muchsimilarity one set of data has with another.

    Correlation is defined with a range between -1 and 1

    with the following meanings:

    Value 1, the second sequence matches the first sequenceexactly

    Value 0, there is no relation at all

    Value -1, the two sequences are mirror images of each

    other.

    Other value indicate a partial degree of correlation.

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    Autocorrelation is the correlation of a sequence withall phase shifts of itself.

    Cross correlation function: the comparison is made

    between two sequences from different sources ranther

    than a shifted copy of a sequence with itself. It is

    defined as: N

    k

    kkBAN

    R1

    1)(

    N

    k

    kkBB

    N

    R1

    1)(

    M-Sequences

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    Property 4. For many applications, the 0,1sequence is changed to a 1 sequence. Tthe

    periodic autocorrelation of the resulting sequence

    is:

    The periodic autocorrelation of a 1 m-sequence

    is:

    N

    k

    kkBBN

    R1

    1)(

    otherwise

    ...2N,N,0,

    11

    N

    R

    M-Sequences

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    M-Sequences

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    The cross correlation between an m-sequence andnoise 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

    Generation of Spreading Sequences

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    PN Sequences

    Orthogonal Code

    Multiple Spreading

    Orthogonal Code

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    Orthogonal Code: a ser of sequences in which all

    pairwise cross correlations are zero.

    An orthogonal set of sequences is characterized by

    the following equality:

    For CDMA, each user uses one of the sequences in

    the set as a spreading code, providing zero cross

    correlation among all users.

    durationbit

    settheofmembersthandththeare,

    settheinsequenceeachoflengththe

    01

    0

    ji

    Mwhere

    jikk

    ji

    M

    k

    ji

    Generation of Spreading Sequences

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    Orthogonal Code

    Walsh Codes

    Variable-length Orthogonal code

    Walsh Codes

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    Walsh codes: the most common orthogonalcodes used in CDMA applications.

    A set of Walsh codes of length n consists of the nrows of an nn Walsh matrix.

    The matrix is defined recursively as:

    Where n is the dimension of the matrix and theoverscore denotes the logical NOT of the bits inthe matrix.

    nn

    nn

    n

    WW

    WWW0W 21

    Walsh Codes

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    The Walsh matrix has the property that everyrow is orthogonal to every other row and to the

    logical NOT of every other row.

    The next figure shows the Walsh matrices ofdimensions 2, 4 and 8. Recall that to compute

    the cross correlation, we replace 1 with +1 and

    0 with -1.

    Walsh Codes

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    Generation of Spreading Sequences

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    Orthogonal Code

    Walsh Codes

    Variable-length Orthogonal code

    Variable-length Orthogonal code

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    3G mobile CDMA systems are designed tosupport users at a number of different datarates.

    Effective support can be provided by usingspreading codes at different rates whilemaintaining orthogonality.

    Suppose that the minimum data rate to be

    supported is Rmin and that all other data rate arerelated by power of 2.

    Variable-length Orthogonal code

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    If a spreading sequence of lengthNis used for theRmin data rate, such that each bit of data is spread byN=2nbits of the spreading sequence, then thetransmitted data rate isNRmin.

    For a data rate of2Rmin

    , a spreading sequence oflengthN/2=2n-1 will produce the same output rate of

    NRmin.

    In general, a code length of2n-kis needed for a bitrate of2kR

    min.

    E.H. Dinan and B. Jabbari, Spreading codes for directsequence CDMA and wideband CDMA cellular networks,

    IEEE Comm. Mag. 36 (September 1998)

    Generation of Spreading Sequences

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    PN Sequences

    Orthogonal Code

    Multiple Spreading

    Multiple Spreading

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    When sufficient bandwidth is available, a multiplespreading techniques can prove highly effective. A

    typical approach is:

    Spread the data rate by an orthogonal code to provide

    mutual orthogonality among all users in the same cell

    To further spread the result by a PN sequence to provide

    mutual randomness between users in different cells.

    In such a two-stage spreading, the orthogonal codes are

    referred to as channelization codes, and the PN codes arereferred to as scrambling codes.

    Stallings W. Wireless Communications and Networkschapter 10.

    Review Questions

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    [Review Questions]


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