NON-PERIODIC SEQUENCES DESIGN WITH GOOD CORRELATION PROPERTIES

S. Srinivasa RaoAssociate professor

ECE DepartmentMGIT

OBJECTIVE

The objective of the research work is to design coded sequence sets with good correlation properties using a global optimization algorithm that can significantly improve spread spectrum communication performance.

INTRODUCTION

• Spread spectrum is a means of transmission in which the signal occupies a bandwidth in excess of the minimum necessary to send the information.

• The band spread is accomplished by means of a code which is independent of the data.

• The same code is also used at the receiver to despread the received signal in order to recover the message signal.

ADVANTAGES

• The reasons for spreading the spectrum areSecure communicationsIncreasing resistance to interference

and jamming Multiple-access capabilityRadar Communication

CRITERIA OF GOODNESS FOR CODED SEQUENCES

For a multiple access communication system it is desirable to have a set of sequences such that

a) each sequence has a peaky on auto-correlation as possible and

b) each pair of sequence has a negligible cross-correlation as possible.

The autocorrelation and cross-correlation properties of

orthogonal codes should satisfy or nearly satisfy the following

Shift-Register sequences or m-sequence (maximum length sequences )

These sequences can be created using a shift-register with feedback taps

GOLD SEQUENCES

• Combining two m-sequences creates Gold codes

• Shift-Register sequences are not orthogonal, but they do have a

narrow autocorrelation peak

KASAMI CODES

Kasami codes are similar to Gold codes in that they are produced by Exclusive-ORing two distinct sequences. The twist in the case of Kasami codes is that both these sequences are produced by a single linear feedback shift register. One sequence is the output of the LFSR, whereas the other is derived from the first by decimating it by a factor of N, and then repeating it N times

WALSH CODE

The matrix contain one row of all zeros and the other rows each have equal number of ones and zeros.

These codes are orthogonal to each other and thus have zero cross-correlation between any pair.

The codes do not have a single, narrow autocorrelation peak.

The spreading is not over the whole bandwidth, but over a number of discrete frequency components

OPTIMIZATION

Optimization is the task of finding the absolute best set of parameters to optimize an objective function.

A object function measures the degree to which a specific result meets the design requirements .

The most typical approach to binary code optimization is the iterative improvement algorithm.

For the design of orthogonal code sets, the cost function is based on the sum of the square of maximum autocorrelation sidelobe peaks and the square of maximum cross-correlation peaks

L

1

1- L

1 p

L

1 p q

2q p

k

2

0 k ) | k) , s , s( | (max ) | k) , s( A| (max E

llC

HAMMING SCAN ALGORITHM

• Random Search Process• Fast convergence but

gets stuck at local minimum

The Hamming scan algorithm mutates all the elements in a given sequence one by one and looks at all the first order Hamming neighbours of the given sequence. Mutation is a term metaphorically used for a change in an element in the sequence. For example, in the case of binary sequence, a mutation of binary element implies +1-1 or -1+1. Thus, a single mutation in a sequence results in Hamming distance of one from the original sequence.

Thus, Hamming scan performs recursively local search among all the Hamming-1 neighbours of the sequence and selects the one whose objective function value is minimum.

Flow Chart

SIMULATED ANNEALING ALGORITHM

Advantage of the SA algorithm over the Hamming SCAN algorithm is the ability to avoid becoming trapped in local optima during the search process. The algorithm employs a random variable search that not only accepts the changes that decrease the cost function but some changes that increase it with a probability of

 

 

as well, where ΔE is the cost change due to a random research, and Ti

is the control parameter. Normally, the temperature Ti slowly decreases

from a large value to a very small one during the annealing process

DESIGN ALGORITHM

WORKING OF HYBRID ALGORITHM

• Hybrid Algorithm is a combination of both Hamming Scan algorithm and Simulated Annealing.

• It uses the good methodologies of these algorithms like fast

convergence rate of Hamming Scan algorithm and Global

minima trapping capability of Simulated Annealing algorithm to

increase the probability of convergence to the global minimum

point.

• The new Hybrid Algorithm overcomes these drawbacks as it

makes use of Simulated Annealing to randomly generate a sequence and then it invokes the Hamming scan to converge to

the local minima corresponding to that point. Thus the selection of Simulated Annealing and mutations of Hamming scan work well for this algorithm.

References

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