Application of bio-inspired techniques to

telecommunication

Overview:Source of inspirationDifferent types of adaptive algorithmsApplications in field of telecommunication

Channel equalizer model

LMS Principles, Usage, Advantages & Disadvantages

PSO Basic ideas, Advantages over LMS Brief comparision

Why bio-inspired?

Types of Adaptive algorithms:

LMS

Least Mean Square

Recursive Least Square

Particle Swarm Optimization

Differential Evolution

Genetic Algorithm

Use of adaptive algorithms in telecommunication:

Channel equalizer

Prediction filters

Echo cancellation

Channel equalizer using LMS & PSO algorithms

kr

Data Source Encoder Modulator

Decision Device

EqualizerDemodulator

Decoder

Physical ChannelAWGN

Receiver

Transmitter

ks

k-d's

Figure: Block Diagram of a Digital Communication System

Overview of a Digital Communication System:-

kr

Data Source

Decision Device

Equalizer Decoder

Physical Channel ks

k-d's

Figure: Baseband Model of a Digital Communication System

AWGN

Overview of a Digital Communication System:-

Located in the front end of the receivers ( in series with the channel )

Inverse system of the channel model (Transfer function of the equalizer is inverse to the transfer function of the channel)

Use to reduce : - Inter-Symbol Interference (ISI) Inter User Interference in the form of Co-channel

Interference(CCI)Adjacent Channel Interference(ACI) in the presence of Additive

White Gaussian Noise (AWGN)

Digital Channel Equalizers:-

Digital Channel H (z)

Channel Noise

++

Random Binary Input

x (k) ChannelEqualizer

Delay z-m

+_

d (k)y (k)

AdaptiveAlgorithm

Figure: Block Diagram For Channel Equalization

e (k)

∑ ∑

Standard LMS Algorithm for updating channel weights, uses a gradient descent to estimate a time varying signal, finds a minimum, if it exists, by taking steps in the direction negative of the gradient.

An adaptive channel equalizer is basically an adaptive tap-delay digital filter.

Equalization problem can be viewed as an optimization problem i.e. it can be viewed as a squared error minimization problem.

The LMS algorithm approaches the minimum of a function to minimize error by taking the negative gradient of the function.

The LMS Algorithm:

Weight Update Rule

LMS equation to compute the FIR coefficients:

c(n+1) = c(n) + μ * e(n) * x(n)μ= step size d(n) =desired signale(n)= error signalc(n+1)= updated coefficient

LMS Implementation Using FIR Filter:-

Random BinaryInput( +1, -1 )

e (k)

x(k) a0

Z-1

Z-1

a1

a2

Z-1

Z-1

Z-1

Z-1

Z-1

Z-1

Z-1

∑_

+

LMS Algorithm

d (k)

y (k)

Delay z-m

h0(k)

h1(k)

h2(k)

h3(k)

h4(k)

h5(k)

h6(k)

h7(k)

∑

∑

Noise Equalizerx(k)

x(k-1)

x(k-2)

Channel

Standard LMS Algorithm For Channel Equalization

The weights of the equalizer is suitably adjusted such that the transmitted message is reconstructed.

The order of the Channel equalizer is higher than that of channel filter (almost twice of the latter).

Plot of mean square error

No. of iterations

Erro

r squ

are

Derivative based algorithm, so there are chances that the parameters may fall to local minima during training.

Does not perform satisfactorily under high noise condition. Does not perform satisfactorily if the order of the channel

increases. Once close to optimal solution they normally rattle around it

rather than converging. Does not perform satisfactorily for nonlinear Channels. Above mentioned disadvantages motivated us to go for

another adaptive algorithm using PSO Algorithm.

Disadvantages of LMS Algorithm:-

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Optimization heuristic inspired by social behavior of bird flocking or swarming of bees, proposed by Eberhart and Kennedy in 1995

Based on attraction of particle to best found solutions Each candidate solution is called PARTICLE and represents one

individual of a population The population is set of vectors and is called SWARM The particles change their components and move (fly) in a

space They can evaluate their actual position using the function to

be optimized. The function is called FITNESS FUNCTION. Particles also compare themselves to their neighbors and

imitate the best of their neighbors.

Particle Swarm Optimization:-

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PSO continue…..

• Swarm of particles is flying through the parameter space and searching for optimum

• Each particle is characterized by• Position vector….. xi(t)• Velocity vector…...vi(t)

• Search space D-Dimensional:Xi = [xi1, …, xiD]T = ith particle of Swarm

Vi = [vi1, …, viD]T = Velocity of ith particle

Pi = [pi1, …, piD]T = Best previous position of the ith particle

Particle Swarm Optimization:-

xi(t)

vi(t)

Particle i

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• Each particle has – Individual knowledge pbest

– its own best-so-far position– Social knowledge gbest

– pbest of its best neighbor• Velocity update: vi(t+1)=w vi(t) +c1*rand *(pbest(t) - xi(t))

+c2*rand*(gbest(t) - xi(t)) • Position update:

• xi(t+1)=xi(t) + vi(t+1)

PSO Algorithm:-

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Start

Initialize particles with random position and velocity vectors.

For each particle’s position (x) evaluate fitness

If fitness(x) better than fitness(pBest) then pBest= x

Loo

p u

nti

l all

p

arti

cles

exh

aust

Set best of pBests as gBest

Update particles velocity and position

Loop

unti

l max

iter

ation

Stop: giving gBest, optimal solution.

Flow chart depicting the General PSO Algorithm:-

• Simple and fast• Can be coded in few lines• Requires minimal storage.• PSO has memory, i.e., every particle remembers

its best solution (local best) as well as the group’s best solution (global best).

• Its initial population is maintained fixed throughout the execution of the algorithm, and so, there is no need for applying operators to the population

Advantages of PSO over LMS:-

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• C. A. Belfoior & J. H. Park, Jr. “Decision Feedback Equalization”, Proc. IEEE, vol. 67, pp. 1143-1156, Aug. 1979.

• B. Widrow and S. D. Sterns, “Adaptive Signal Processing”, Pearson Education, pp. 22, Inc. 1985.

• J. C. Patra, R. N. Pal, R. Baliarsingh and G. Panda, “Nonlinear channel equalization for QAM signal constellation using Artificial Neural Network, IEEE Trans. On Systems, Man and Cybernetics – Part B: vol. 29, No. 2, pp.262-272, April 1999.

• Faten BEN ARFIA, Mohamed BEN MESSAOUD: ”Nonlinear adaptive filters based on Particle Swarm Optimization” Leonardo Journal of Sciences, ISSN 1583-0233, Issue 14, January-June 2009

• Ali T. Al-Awami, Azzedine Zerguine, Lahouari Cheded, Abdelmalek Zidouri, Waleed Saif: “A new modified particle swarm optimization algorithm for adaptive equalization”

References:-