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ANALYSIS OF DIFFERENT PSEUDO-RANDOM AND ORTHOGONAL SPREADING SEQUENCES IN DS-CDMA

Mr.Praveen PN Safareena KKLecturer CEAKEEC101ECE Department S8 EC2

Spread code

Informationsignal

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Demodulatedsignal

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Spread code

Spread signalEach user is below the noise deeply

CDMA – Transmission and Reception

Direct Sequence Spread Spectrum Example

Each user is assigned a unique code which is acts as a carrier

Spreading Signal

f

C(f)

Data Signal

f

D(f)Frequency Domain

Transmitted Signal

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S(f)

T ime Domain

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Data Signal

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d(t)

Spreading Signalc(t)

Transmitted Signals(t)

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INTRODUCTION

• A device in WCDMA system can access several services simultaneously

• Spread spectrum is a radio communications system in which the baseband signal bandwidth is spread over a larger bandwidth by a higher-frequency signal.

• CDMA (DS-CDMA) uses direct sequence spread spectrum (DSSS) technology to spread the spectrum

• spreading is carried out using a PN sequence

PSEUDO-NOISE SEQUENCE

• A pseudo-noise (PN) sequence is a sequence of 1’s and 0’s and it is periodic.

• The PN sequences have the following three properties; Balance, run and auto-Correlation Properties.

MAXIMAL LENGTH SEQUENCES

The general structure of a m-sequence generator

Gold Sequences

• Gold sequences can be constructed by the modulo-2 operation of two different preferred pair of m-sequences of length N=2n.

• The set of Gold sequences generated with the two preferred pair of m-sequences f and h is defined as

The auto correlation and cross correlation is given by

GOLD-LIKE SEQUENCES

• These are similar to Gold sequence and have good correlation properties.

• Gold-like sequence set contains 2n sequences and each sequence has a period of N = 2n-1.

• Gold-like sequences can be defined as

BARKER SEQUENCES

• Barker sequences are short length codes that offer good correlation properties.

• A Barker code is a binary {-1, +1} sequence, {ci}, of some finite length N such that the discrete auto-correlation function r (τ), can be defined as:

satisfies

• It has very low cross correlation• The degree n of the primitive polynomial used

to generate Kasami sequences. • These sequences are defined for even values

of n . • There are two types of kasami sequences a) small set of kasami sequences b) large set of kasami sequences

KASAMI SEQUENCES

Kasami sequence generator

ORTHOGONAL SEQUENCE

• when the inner product between two sequences is zero then the signals are orthogonal ..ie

•There are two types of orthogonal codes 1 Fixed length Orthogonal Codes 2 Variable length Orthogonal Codes

Fixed length orthogonal code

• Fixed length orthogonal codes include Walsh Hadamard (WH) and modified WH (MWH) codes.

• The WH sequences of length N are defined with a class of orthogonal matrices HN called Hadamard matrices.

• MWH codes are generated by multiplying the Hadamard matrix HN by a diagonal matrix DN of same order .

Variable length orthogonal codes

• Orthogonal codes with different length are called variable orthogonal code.

• It also known as Orthogonal Variable Spreading Factor (OVSF).

• The codes can be generated using the tree structure instead of Hadmard matrix.

ORTHOGONAL GOLD CODES

• Orthogonal gold code can be constructed by simply padding zero to the gold codes.

• Cross correlation value is zero

• Length of orthogonal gold code is 2n

• Auto correlation value is similar to that of gold sequence

MEAN SQUARE CORRELATION

• The Mean Square Aperiodic Auto-Correlation (MSAAC) and Mean Square Aperiodic Cross-Correlation (MSACC) measures are accepted performance measures for correlation properties of sequences applied in DS-CDMA.

• The mean square aperiodic auto-correlation (MSAAC) value RAC for a given code set containing M sequences is defined as:

• Measure for the mean square aperiodic cross-correlation (MSACC) value RCC is given by:

• Auto-correlation refers to the degree of correspondence between a sequence.

• Cross-correlation is the measure of agreement between two different codes.

MERIT FACTOR• It is a criterion which quantitatively

determine how significant the auto correlation degradation for a given set of sequences.

• Sequences with low MF has narrow flat spectrum and they are neither suitable for CDMA

• The Merit Factor for a sequence, ci(n), of length N having the auto-correlation function rij(τ ) is defined as:

• This is nothing more than the inverse of the MSAAC value for a given sequence.

RESULTS AND DISCUSSION

• Performance of Gold code is good as compared to m-sequence.

• The Barker sequences have many advantages over other PN sequences, but they are very limited in number of sequences

• The autocorrelation and cross-correlation functions of Kasami sequences provide excellent properties, as good or better, than Gold Codes. Also, the possible numbers of large Kasami sequences are more compared to all other PN Sequences

Histograms comparing aperiodic correlation measures and Merit Factor for Pseudo-noise and orthogonal sequences

• The correlation values of orthogonal codes are high compared to that of PN sequences. But, compared to WH codes, the MWH codes have less correlation values making the cross-correlation values of these codes high.

• The orthogonal Gold codes have the correlation values similar to that of original Gold codes.

• OVSF codes have the correlation functions, the MSAAC and MSACC values almost same as that of MWH codes

CONCLUSION

• Large Kasami sequence has both good correlation values and high MF, which make these sequences to have wide flat spectrum that is better suited to be used in the WCDMA uplink transmission.

• In the downlink of WCDMA, variable data rate is supported by using orthogonal variable spreading factor (OVSF) codes.

• We have reviewed different PN as well as fixed- and variable-length orthogonal sequences that can be used in many applications including spreading codes for CDMA cellular networks.

REFERENCES• D.Torrieri, “Principles Of Spread-Spectrum Communication Systems“, Springer, 2nd edition, 2011

•Valery P. Ipatov, “Spread Spectrum and CDMA Principles and Applications” Jhon Wiley & Sons Ltd, 2005.

• K. Fazel and S. Kaiser, “Multi-carrier spread-spectrum: for future generation wireless systems”

Couch. L.W,“Digital and Analog Communication Systems”, 7th Ed, Prentice Hall, Inc., 2007,

T.S. Rappaport, “Wireless Communication, principles & practice”, PHI, 2001.

E. STRO¨M, T. OTTOSSON, A.SVENSSON, “An Introduction to Spread Spectrum Systems”, Department of Signals and systems chalmers university of technology G¨oteborg, Sweden, 2002.

THANKS