Spread Spectrum Introduction: A Direct Sequence Approach

8/14/2019 Spread Spectrum Introduction: A Direct Sequence Approach

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Abstract

Interest in wireless communications has increased dramatically in the past years. Thishas researchers and engineers focusing on the problems unique to the wireless environment.

This include capacity limits due to spectrum availability, propagation effects like multipath and

security concerns. One way to address all of these issues is to use spread spectrum

communication. For this projects we will analyze spread spectrum communication using direct

sequence. This technology of modulations main advantage lies in its ability to provide secure

communication between users. It was developed by the military and has the following

characteristics, which we will analyze in this paper.

Difficult to intercept.

Easily hidden, it is difficult to detect their presence. Resistance to jamming. This means that induced noise is not a factor at the receiver.

Immunity to distortion due to multipath propagation.

Provide multiple access capability without external synchronization (asynchronous).

Spread Spectrum is a kind of modulation scheme in which the modulated signal bandwidth is

much greater than the message (baseband) signal bandwidth. It may be seen as a wide-band

modulation. The spectral spreading is performed by a code that is independent of the message

signal, called the pseudonoise (PN) sequence. This code is known only to the user whom the

message is intended. This process increases the signal bandwidth of the message. By assigning

different codes to different signals, we can multiplex large numbers of users on the same band

of frequency. This is called Code Division Multiple Access (CDMA) and its one of the many

advantages of Spread Spectrum.

In this paper we will analyze such transmission modulation and provide the reader with an

understanding of the process, characteristics and advantages to other modulation schemes.


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Modulation/Demodulation Process

Modulator

The modulation is basically done by spreading the bandwidth of the bandpass signal,

that is, the modulated signal has much more bandwidth than the modulating signal. In Direct

Sequence SS the base-band signal is spread through the available bandwidth by multiplying the

signal with a code. The PN code or the pseudo-noise code is a periodic sequence of 1's and 0's

with a certain auto-correlation properties. These signals are pseudo-random, these means that

they are meant to look like random noise signal, but in fact they follow a predetermine

sequence. To an outsider they appear to be noise. This is what allows spread spectrum to

achieve secure communications.

The mathematical description to the modulation is:

y(t) = m(t)c(t); where y(t) is the DS/SS signal, m(t) is the baseband signal and c(t) is the PN

signal.

Each information bit is broken into small time increments called chips. Each chip is a binary state

of the PN sequence.

Each pulse in c(t) is called a chip, and the bit rate or chip rate of signal c(t) is chosen to be muchhigher than the bit rate of m(t), this allows us to achieve processing gain N = Bss/B. The

processing gain is a ratio used to determined how much the signal is spread. The bigger the PN

sequence, the more processing gain.

After the signal is modulated using Spread Spectrum, it is transmitted using a carrier frequency,

this allows wireless transmission. The most widely used method is BPSK (Binary Phase Shift

Keying).

Illustration 1: Simple block diagram of Spread Spectrum communication.Note that the key to success is using the same PN sequence at both ends

of transmission.


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The block diagram representation would be:

As illustrated in the block diagram, the baseband signal NRZ coded is multiplied with the PN

sequence, resulting in a processing gain depending on the chip rate. If the signal is to be

transmitted wirelessly then BPSK is used in the next stage. Here we take the DS-SS signal andmodulate it using BPSK or DSB modulation.

The phase has a value of 0 or representing binary 1 or 0.

The carrier would be:

2EbTb

cos w c t bin 0

2EbTb

cos w c t bin 1

Illustration 2: Using a spectrum analyzer we can see the resultingDSSS signal.


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The illustration above presents a simplified explanation of the Direct Sequence SpreadSpectrum. The polar Non Return to Zero Level signal b(t) is multiplied by the PN code c(t)

resulting in signal m(t), which is modulated using BPSK for wireless transmission.


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Demodulation

The process of receiving the signal is divided in two parts. First we must convert the

bandpass BPSK signal into baseband. This is done using a coherent detector and multiplying by

the local carrier, then the signal is passed through a Low Pass Filter to remove unwanted signals.The second part of demodulation involves despreading the signal by using the same process

done to transmit. The signal is multiplied by the PN sequence to obtain the original signal.

The mathematical process is the following:

the received signal y(t) I multiplied by the PN code c(t) which yields desired signal m(t) because

y(t)*c(t) = m(t)c2(t) = m(t) because c2(t) = 1.

The process of detection (despreading) is identical to the process of spectral spreading.

Since we are using BPSK, we need a coherent detector to detect the incoming signal. This means

we use a carrier of the same frequency used to modulate the signal at the BPSK stage.

Illustration 3: Block diagram of receiver.

Illustration 4: Since we use coherent detection we need to use a LPF toeliminate the unwanted frequencies that were shifted to 2wo.


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PN sequence generation

The pseudo-noise (PN) sequence is a periodic binary sequence with a noise like

waveform that is usually generated by a bank of feedback registers. The feedback registersconsists of ordinary shift register made up ofm flip flops, which are two state memory devices,

and a logic circuit that provides the feedback; commonly used is a XOR.

A good PN sequence is characterized by an auto correlation similar to white noise. This means it

is high at = 0 and low elsewhere. To reduce interference the cross correlation among different

PN sequences is supposed to be small. The PN sequence is created by a shift register network

with feedback, which can be flip flops, or any type of memory device. This registers contain an

initial state which changes with each clock pulse and outputs a binary state depending on the

previous state.

The longer we make the PN sequence, the larger will be the processing gain. This means that as

we increase the chip number and the chip time TC, the more we will spread the signal in the

spectrum, the more secure our data is and less susceptible to jamming.

For our given example we will design the PN sequence for 31 chip, 31 Processing Gain. This is

the gain achieved by processing a SS signal over an unspread signal.

For N=31 we need must find how many shift registers we will use.

N=2m 1; where m the number of shift registers required for N chip PN sequence.

31 = 2m 1

m = 5

Using the reference table provided by S. Haybin Comm. Systems 4th Ed.

For length m = 5 we can use feedback taps [5,2], [5,4,3,2], [5,4,2,1]

Illustration 5: auto correlation function of the PN sequence.


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we will use taps at [5,2]

Our shift register network will look something like this:

Our initial state will be 0 0 0 0 1. All states except all zeros are allowed. The code generation

scheme would be:


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The output PN sequence will be: 1000010101110110001111100110100

This is the PN sequence. Notice that it contains 31 chips, this will increase the baseband

bandwidth by 31 times. We can also say it has a processing gain of 31.

Feedback symbol State of Shift Registers Output symbol

0 0 0 0 1

1 1 0 0 0 0 1

0 0 1 0 0 0 0

1 1 0 1 0 0 0

0 0 1 0 1 0 01 1 0 1 0 1 0

1 1 1 0 1 0 1

1 1 1 1 0 1 0

0 0 1 1 1 0 1

1 1 0 1 1 1 0

1 1 1 0 1 1 0

0 0 1 1 0 1 1

0 0 0 1 1 0 1

0 0 0 0 1 1 0

1 1 0 0 0 1 1

1 1 1 0 0 0 1

1 1 1 1 0 0 0

1 1 1 1 1 0 0

1 1 1 1 1 1 0

0 0 1 1 1 1 1

0 0 0 1 1 1 1

1 1 0 0 1 1 1

1 1 1 0 0 1 1

0 0 1 1 0 0 1

1 1 0 1 1 0 0

0 0 1 0 1 1 0

0 0 0 1 0 1 1

1 1 0 0 1 0 1

0 0 1 0 0 1 0

0 0 0 1 0 0 1

0 0 0 0 1 0 0

0 0 0 0 0 1 0


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Transmitted Bandwidth

Because of the processing gain, the transmitted bandwidth of the Spread Spectrum

signal if much larger than the minimum required bandwidth. This is what allows DS-SStransmission to have many advantages over all other transmission schemes like PSK, ASK, FSK,

QAM and their M-ary counterparts. The advantages include secure communication and

jamming resistance, multiple access of several users on the same frequency band and resistance

to multipath fading.

To analyze the transmitted bandwidth of the spread spectrum signal we must look at its

signal spectrum. We know that the minimum theoretical bandwidth of a binary signal at a rate

Rb (bits/s) is Rb/2 (two pieces of information per second per hertz); and that the bandwidth of

practical binary schemes is proportional to the bit rate. The bit rate of the spread spectrum

signal y(t) is the same as the chip rate RC

. The bandwidth of y(t) is RC/R

btimes the bandwidth of

m(t).

The PSD of a polar NRZ binary signal with pulse p(t) = rect(t/Tb) and P() = Tbsinc(Tb/2)

then Sm() = Tbsinc2( Tb/2) and Sy() = Tcsinc

2( Tc/2)

The interesting part is that the power remains the same. This is because the PSD (Power

Spectral Density) function of the bandwidth is directly proportional to the bit rate; the PSD of

y(t), the SS signal, is wider than the PSD of m(t), the baseband signal, by a factor N (the

processing gain).

For our given assignment we will find the transmitted bandwidth BT for a DS-SS modulator.

Our baseband signal bit rate RB = 100, B = 100MHz

For a roll off factor r=1 raised cosine shaping filter BT = (1 + r)Rb/2

Illustration 6: PSDs of the input and output signals of a DS-SS system. Notice

that the spread spectrum signal PSDs is N times wider than the message signal.


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1st stage: NRZL to baseband shaping filter

BT1 = (1 + 1)100Mbps/2 = 100Mbps

2nd stage: DS-SS modulation

BSS = NB = 31(100Mbps) = 3.1 GHz

3rd stage: BPSK modulation to apply wireless carrier

BPSK doubles the bandwidth so we have:

BT = 6.2 GHz final transmission bandwidth.


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Performance of Direct Sequence Spread Spectrum

To analyze the performance characteristics of any modulation scheme, we need to have

some sort of criterion. This would be the probability of error at the receiver, relative to thetransmitted power. One of the advantages of digital communications is this trade off. One can

increase power (higher signal to noise ration SNR) to achieve less error rate. We refer to the

probability of error at the receiver as BER, or Bit Error Rate. An acceptable BER is in the order of

10-3. This means that for every 1000 bit transmitted we have one error.

In DS-SS the BER rate increases as we have more users using the same frequency band.

This is one of the main advantages to DS-SS, through the use of CDMA, we assign a different PN

sequence to each user and are able to take advantage of the same large transmitted bandwidth

that provides secure communications to multiplex multiple users. The tradeoff is that as we

increase the number of users in channel, we increase the BER.

Pb=Q1

K1

3N

N0

2Eb

The equation above calculates the probability of bit error for Knumber of users and N chip

code. This is a Gaussian distribution, thus it makes use of the Q function. You can find the Q

function values in table 10.2 of P.B. Lathi Modern Digital and Analog Communication Systems 4th

Ed.

For our design system of 31 chip code (N=31) we will find the required SNR to transmit with a

BER of 10-4. Assuming a worst case scenario of full users, that means K=30, the maximum

number of users for 31 chip code; since we have increased the minimum transmitted bandwidth

31 times, we can transmit N-1 users.

Substituting in the above formula we obtain that for 10-4 BER the Q function corresponding is:

3.72=1

301

331

N0

2Eb

this yields a SNR as ratio of 22.5, which is about 13.5dB. Please refer to Appendix for

calculations. As the number of user increases the SNR required to maintain the same BER

increases.


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The following graph demonstrates this characteristic of DS-SS modulations

This depends on the number of PN sequence N.


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Conclusion

Through this assignment project we demonstrated the advantages that Direct SequenceSpread Spectrum has over the non-wideband modulation schemes that only use a digital carrier

for transmission. DSSS provides the user with a secure way to transmit information and most

importantly a more efficient way, since we can take advantage of this large bandwidth to

multiplex multiple users using different PN sequences.

The cellular telephony industry has benefited greatly by this advantage. The use of CDMA allows

improved frequency reuse, and is less vulnerable to multipath fading.

Another use of DSSS technology lies in the GPS (Global Positioning System) satellites. These

satellites are used by the military and civilians and allow a user to determine its exact position

on Earth and its speed. The use of DSSS allows only those with a receiver capable of producing

the PN sequence required to use them. More importantly since the power required is less due

to the processing gain, the satellites can be made smaller and cheaper; also they can use the

same frequency band without interference.

The performance of DSSS was analyzed and we demonstrated that the Bit Error Rate

depends on the number of users using the frequency band and the chip length. In all, DSSS

modulation is a very efficient modulation scheme when it comes to providing secure

communications to a large number of users at the same time, wirelessly.

Spread Spectrum Introduction: A Direct Sequence Approach

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