Part A: Spread Spectrum Systemsswedishcr.weebly.com/uploads/1/5/2/2/15223984/lec_6.pdf · Dr. ir....

Telecommunication Systems and Applications (TL - 424)

Part A: Spread Spectrum Systems

Dr. ir. Muhammad Nasir KHAN

Department of Electrical EngineeringSwedish College of Engineering and Technology

March 6, 2014

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IntroductionSpectrum is a general term used to encompass the spatial and temporalproperties of any medium, including fiber optic cable, coaxial cable, andambient air. From the view of a strict constructionist, spectrum is a type ofdivision based on frequency or wavelength. Generally, we think of signals inthe real-world setting as being functions of time.

T

0 2 4 6 8 10 12 14-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

sin(t)

Dr. ir. Muhammad Nasir KHAN (SCET) Part A: Spread Spectrum Systems March 6, 2014 2 / 1

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Introduction (Cont’d)

It is an interesting exercise to discover how frequency is related to the timedomain.

In the time domain, it becomes evident that the sine wave in las slide hassimilar characteristics after the time T. In fact, the function repeats itself afterthis point.

The point labeled T is a special point in that it marks the periodicity of thefunction (i.e., the shortest length of time after which the function repeatsitself). The frequency, f , of the function is defined as the reciprocal of theperiod T, i.e., f = 1/T.

From this expression, it is demonstrated that the frequency domain is theinverse of the time domain. This is seemingly at odds with the originalexplanation of spectrum.


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Narrowband Systems

Traditionally spectrum efficiency (measured in bits per seconds per Hz) indigital communication system is obtained by transmitting as much informationas possible using a narrow frequency bands.

Narrowband Systems: Bandwidth is close to the minimum necessaryrequired to transmit the information.

In contrast to NB, wideband systems or spread spectrum (SS) systems use abandwidth much wider than minimum necessary for the application

MotivationMotivations for the SS initially from the military context


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Narrowband Systems (Cont’d)

In general, signal transmission is enabled through some means ofmodulation.

In the past, systems have relied primarily on narrow-band modulationschemes. In these systems, all of the power in a transmitted signal isconfined to a very narrow portion of the frequency bandwidth.

As a result of these narrow frequencies, an interfering frequency at ornear the transmitting frequency can cause interference,⇒ render the signal unrecoverable.


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Narrowband Systems Examples

Amplitude Modulation is one example of a narrow-band modulation schemein which the amplitude of the carrier signal is made stronger or weaker basedon the information in the signal to be transmitted.

The large amounts of power that are associated with Amplitude Modulationallow the signal to travel large distances before it attenuates to anundetectable level.

A second popular form of modulation is Frequency Modulation, in which thephase of the carrier frequency is adjusted in accordance with the signal beingtransmitted.


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Narrowband Systems (Cont’d)Narrow-band modulation schemes are not the only implementations availableto broadcasters.

Broadcasting entities may take advantage of the fact that a defined spectralpower density may be achieved not only through high power over a verynarrow frequency range, but also through lower powers spread over muchlarger frequency ranges.

Narrow Band Signal

Wide Band Signal

Power Spectral Density Frequency


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Spread Spectrum

A transmission technique in which a pseudo-noise code, independent of theinformation data, is employed as a modulation waveform, to spread the signalenergy over a bandwidth much greater than the information signal bandwidth.

At the receiver the signal is de-spread using a synchronised replica of thepseudo-noise code.

Most commercial spread spectrum systems transmit an RF signal bandwidthin the neighbourhood of one to two orders of magnitude greater than thebandwidth of the information that is being sent.

Transmitted bandwidth can be as large as three orders of magnitude abovethe bandwidth of the information.


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Principles of SS Communications

The SS system is the one in which the transmitted signal is spread over awide frequency band, much wider than the minimum bandwidth required totransmit the information being sent.

A system is said to be a SS system, if it fulfils the following requirements;

The signal occupies a bandwidth much larger than the minimumrequired bandwidth.

Spreading is accomplished by means of a code which is independent ofthe data.

Spreading code is pseudo-random, thus the spreading signal resemblesnoise.

A synchronised reception with the code at the receiver is used forde-spreading the information before data recovery.


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Principles of SS Communications Block Diagram


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Principles of SS Communications Block Diagram


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Why Spread Spectrum

In general the motivations for the use of SS can be categorized as follow,

Anti-jamming/Anti-interference capability

Spread Spectrum makes use of spreading code which is known only bythe intended receiver.

Signal de-spreading can then reject strong undesired signals.

Low Probability of Intercept (LPI)

Signals spread uniformly in the frequency domain.

Masks the transmitted signal in the background noise, making thedetection very difficult.


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Why Spread Spectrum (Cont’d)

Multiple Access

Multiple SS links can share the same band with minimal co-channelinterference.

Spread spectrum methods can be used a multiple access technique, inorder to multiplex (share) a communication resource among numeroususers.

The technique, termed code division multiple access (CDMA), sinceeach simultaneous user employ a unique spread spectrum signallingcode. One of the by products of this type of multiple access is the abilityto provide communication privacy between users with differentspreading signals. An un-authorized user cannot easily monitor thecommunications of the authorised users.


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Why Spread Spectrum (Cont’d)

Low Probability of Detection (LPD)

Since in SS System, the signal is spread over many more signallingcomponents than conventional modulation schemes,

⇒ the resulting signal power is spread uniformly in the spread domain.

Thus the received signal is small, very difficult to detect by anyoneexcept the desired receiver (or intended receiver) systems designed forthis special task are known as low probability of detection (LPD) or lowprobability of intercept (LPI).


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Basis of SS Technology

The basis of SS technology is expressed by Shannon theorem in the form ofchannel capacity as,

C = B log2 (1 + γ)

where

C is the capacity in bps, γ = SN is the signal to noise ratio and B is the

bandwidth in Hz.

The above equation shows the relationship between the ability of a channel totransfer error-free information, compared with the signal to noise ratio existingin the channel and the bandwidth used to transmit the information.


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Basis of SS Technology (Cont’d)

Letting C be the desired system information rate and by changing bases ofEq. in above slide, we find

CB = 1.44 loge (1 + γ)

For very small SNR, loge (1 + γ) ≈ γ, then we get B = NC1.44S

This shows that for any given noise to signal ratio, we can have a lowinformation error rate by increasing the bandwidth used to transfer theinformation.

Example

If we want a system to operate in a link in which the interfering noise is 100times greater than the signal and if C = 3kbps, then, B = 2MHz.


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Spread Spectrum Techniques

The following techniques are used in SS systems

Direct Sequence (DS)

Frequency Hopping (FH)

Time Hopping (TH)

Pulse frequency modulation (chirp)

Hybrid forms [DS/FH, FH/TH and DS/FH/TH]


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DS Spread Spectrum (DS-SS

Each bit in the original signal is represented by multiple bits in thetransmitted signal

Spreading code spreads signal across a wider frequency band

Spread is in direct proportion to the number of bits used

One technique combines digital information steam with the spreadingcode bit stream using exclusive-OR


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Spread Spectrum (Cont’d)

DS-SS modulation was originally developed for military communicationsystems between 1950 - 1980 to ensure robust and covered communications.

In DS-SS modulation, the information signal is spread over a much widerbandwidth that required based on the symbol rate.

A narrowband signal is made wideband !

How?

Signal spreading over a much wider bandwidth is achieved by multiplying thesignal at the transmitter by a wideband code signal.

Why?

To create robustness against: multi-path fading and dispersion, interference,detection, eavesdropping.Because of the low PSD, its presence is difficult to detect.


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How?Signal spreading over a much wider bandwidth is achieved by multiplying thesignal at the transmitter by a wideband code signal.

Why?

To create robustness against: multi-path fading and dispersion, interference,detection, eavesdropping.Because of the low PSD, its presence is difficult to detect.


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How?Signal spreading over a much wider bandwidth is achieved by multiplying thesignal at the transmitter by a wideband code signal.

Why?To create robustness against: multi-path fading and dispersion, interference,detection, eavesdropping.Because of the low PSD, its presence is difficult to detect.


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DS-SS Transmitter

In DS-SS spreading of the signal over a much wider bandwidth is achieved bymultiplying the signal at the transmitter by a code sequence c(t) ∈ {−1,+1}consisting of code chips.

The transmitted signal is:xc(t) = Acd(t)c(t) cosωct


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DS-SS Transmitter (Cont’d)

Signals in a DS-SS transmitter for a BPSK data modulation signal.


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2Rs

f

data signal

The chip rate Rc =1Tc� symbol rate Rs =

1Ts

The ratio Gp = BWDS−SSBWdata

= RcRs

= TsTc

is called the processing gain or spreadingfactor.


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2Rc

f

c(t)

d(t) d(t)c(t)

PN-code signal

2Rsf

data signal


1Ts


= RcRs

= TsTc



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DS-SS signal

2Rc

f

The PSD of the spread signal is 1/Gp

less than the PSD of the un-spread

signal

2Rc

f

c(t)

d(t) d(t)c(t)

PN-code signal

2Rsf

data signal


1Ts


= RcRs

= TsTc



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DS-SS Reception

At the DS-SS receiver, thereverse operation is performed

We can recover the signal only if:c(t)c′(t)d(t) = d(t)⇒

The code is known

Perfect synchronization

2Rc

f

2Rc

f

c′(t)

d(t)d(t)c(t)

PN-code signal

2Rsf

data signal

DS-SS signal


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DS-SS Reception (Cont’d)DS-SS is very robust against interference. When de-spreading the desiredsignal, the interference is spread.

Only a fraction 1/Gp of the spread interference overlaps with the de-spreaddata signal spectrum.

Effective Interference power: Ieff = PIBWdata

BWspread−interference= PI

2Rs2Rc

= PIGp

c′(t)

d(t)d(t)c(t)

DS-SS code signal

de-spread data signal

DS-SS data signal

Narrowband Interference

Spread Interference


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DS-SS Reception (Cont’d)

DS-SS is also robust against other DS-SS interference signals. When theSS-code or code phase is different, the signal remains spread.

Also in this situation, only a fraction 1/Gp of the interference spectrumoverlaps with the de-spread data signal spectrum.

c′1(t)

d1(t) + c′1(t)c2(t)d2(t)d1(t)c1(t) + d2(t)c2(t)

DS-SS code signal


DS-SS data signal 1 and 2 Spread data signal 2


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Pseudo-noise code generators

A DS-SS code is a ”pseudo random” sequence of {−1, 1}. There are severalways to generate DS-SS codes depending on the required properties. Oneway is to use ”Maximum length sequences” which are also calledPseudo-Noise (PN) codes because of their noise like spectral properties.

Maximum Length (ML) sequences can be digitally generated in a simple wayusing a shift register with a feedback.

A ML-code generator using a five stage shift register with code length 31.


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Desired Properties of PN codes

Auto-correlationLow auto-correlation of a PN-code outside the main peak is required:

to achieve reliable synchronisation

to lock on the main resolvable path and reduce interference from otherpaths.

cross correlationLow cross correlation between PN-codes is required:

to be able to separate signals of different users.

to obtain good detection performance because of low interference fromother users


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Spectral Efficiency of DS-SS

For DS-SS, withM-level modulation, the spectral efficiency is given by:

η , RbBT

= lRsBT

= lRs2Rc

= l2Gp

[bit/s/Hz]

The price, we pay for the increased robustness against interference andmulti-path fading (large Gp) is very low spectral effaciency.

This can be improved by letting multiple users share the same bandwidth!


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Spectral Efficiency of DS-SS

For DS-SS, withM-level modulation, the spectral efficiency is given by:

η , RbBT

= lRsBT

= lRs2Rc

= l2Gp

[bit/s/Hz]

The price, we pay for the increased robustness against interference andmulti-path fading (large Gp) is very low spectral effaciency.

This can be improved by letting multiple users share the same bandwidth!


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Code Division Multiple Access (CDMA)

In code division multiple access (CDMA) the spectral responses are sharedamong multiple users based on different DS-SS code.

Each user is defined by its code. The cross-correlation between the codeshas to be low (ideally zero⇒ orthogonal codes).

c′1(t)

d1(t) +5∑

j=2c′1(t)cj(t)dj(t)

5∑j=1

cj(t)dj(t)

DS-SS code signal


DS-SS data signal 1 and 5 Spread DS-SS signals 2 to 5


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Pseudo-Noise Code Generator

Only a few combinations of feedback taps result in an ML-code:the number of ML-codes is limited.

When a large number of codes is required, i.e., to assign to different users ina multiple access communication system, other techniques for codegeneration are applied.

Gold codes are generated beaded on two ML-codes:

pro: many different codes.

con: worse auto-correlation and cross correlation properties among thecodes.


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Bit Error Rate in DS-SS systems

The BER in DS-SS systems is deteriorated by interference produced by otherusers due to non-orthogonal codes.

For BPSK: Pe = Q(√

2EbN′o

)with N′

o = No + NI

In case of many users, the interference can be assumed to be Gaussiandistributed. The power spectral density for single interfere is:

NI =PI

2Rcwhen synchronised and NI =

PI3Rc

when not synchronised.

For K equal-power DS-SS users:

Pe = Q

(1√

K−13N + No

2Eb

)


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DS-SS (Cont’d)

In DS-SS modulation the bandwidth of the signal is increased by multiplyingthe data with a code known to the receiver.


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DS-SS (Cont’d)

To retrieve the data at the receiver, the DS-SS signal is de-spread:

requires the same code.

requires perfect synchronisation.

The system is robust against interference and multiple paths, since:

signals with a different code remain spread.

narrowband signals are spread in the frequency domain.

multi-path signals can be separated if the delay difference > Tc

The robustness is determined by the processing gain.

Gp = BWDS−SSBWdata

= TsTc


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DS-SS (Cont’d)

To retrieve the data at the receiver, the DS-SS signal is de-spread:

requires the same code.

requires perfect synchronisation.

The system is robust against interference and multiple paths, since:

signals with a different code remain spread.

narrowband signals are spread in the frequency domain.

multi-path signals can be separated if the delay difference > Tc

The robustness is determined by the processing gain.

Gp = BWDS−SSBWdata

= TsTc


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Employing DS-SS

By applying DS-SS, spectral efficiency is traded for increased robustness dueto the introduced processing gain. Different trade-offs can be made, e.g., thespectral efficiency can be increased by:

1 Increasing the symbol rate at the same chip rate.

the processing gain is decreased.less robust.

2 Increasing the modulation level at the same symbol and chip rate.

robustness is maintained: same processing gain.increase of signal power may be required.

3 Allow multiple users to share the same bandwidth: CDMA


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Exercise


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