1strev main

7/27/2019 1strev Main

1/23

SEMIANALYTIC BER FOR PSK


2/23

ABSTRACT

The most commonly used method for valuating the BERof a Digital Communication system is the Semi-analytic biterror rate (BER) estimation. The main utility of the method isthe significant time savings in computation relative to MonteCarlo simulation. Despite this advantage, no known reference

defines the procedure for computing exact BER for M-aryphase shift keying (PSK) with ISI and AWGN using the semi-analytic method. This project defines an efficient procedure forcomputing exact semi-analytic BER for modulation formatswith circular constellations when the noise component of the

decision variable has a circularly symmetric Gaussiandistribution. The technique is demonstrated for 8PSK over theDigital Audio Broadcasting-Satellite-Second Generation(DVB-S2) channel. The project is carried out in MATLABsimulation.


3/23

BLOCK DIAGRAM

Modulator Output

Multiplexer

Traveling Wave

Tube Amplifier

Input

Multiplexer

Demodulator

Adder

Noise


4/23

Existing System

The bit error rate (BER) is computed using the

Monte Carlo (MC) simulation (Bit Error Counting). It

is shown that if we wish to have reliable results with

good precision, the total number of transmitted datamust be conversely proportional to the product of the

true BER by the relative error of estimate.

Consequently, computing time is reduced drastically.

Some theoretical results are also given to prove theconvergence of this new method in the sense of mean

square error (MSE) criterion.


5/23

Disadvantages

Long Computation time

Performance cannot be calculated Analytically

Requires the transmitted data to be conversely

proportional to true BER computed usingrelative error of estimate


6/23

Proposed System

Monte Carlo methods are often used when

simulating physical and mathematical systems.

Because of their reliance on repeated

computation and random or pseudo-random

numbers, Monte Carlo methods are mostsuited to calculation by a computer. Monte

Carlo methods tend to be used when it is

unfeasible or impossible to compute an exactresult with a deterministic algorithm.


7/23

MONTE CARLO SIMULATION

Monte Carlo methods are a class of computational algorithms that rely on

repeated random sampling to compute their results.

Monte Carlo methods are often used in simulating physical and

mathematical systems. Because of their reliance on repeated computation

of random or pseudo-random numbers, these methods are most suited to

calculation by a computer and tend to be used when it is infeasible orimpossible to compute an exact result with a deterministic algorithm

However, these approaches tend to follow a particular pattern:

Define a domain of possible inputs.

Generate inputs randomly from the domain using a certain specified

probability distribution. Perform a deterministic computation using the inputs.

Aggregate the results of the individual computations into the final result.


8/23

Advantages of MONTE CARLO

Often the only type of model possible for complex systems

Analytical models frequently infeasible

Process of building simulation can clarify understanding of real system

Sometimes more useful than actual application of final simulation

Allows for sensitivity analysis and optimization of real system without need

to operate real system Can maintain better control over experimental conditions than real

system

Time compression/expansion: Can evaluate system on slower or fastertime scale than real system


9/23

Disadvantages of MONTE

CARLO May be very expensive and time consuming to build

simulation

Easy to misuse simulationby stretching it beyond thelimits of credibility Problem especially apparent when using commercial simulation

packages due to ease of use and lack of familiarity withunderlying assumptions and restrictions

Slick graphics, animation, tables, etc. may tempt user to assignunwarranted credibility to output

Monte Carlo simulation usually requires several(perhaps many) runs at given input values Contrast: analytical solution provides exact values


10/23

WHEN TO USE THE

SEMIANALYTIC TECHNIQUE The semi analytic technique works well for certain types of communication

systems, but not for others. The semi analytic technique is applicable if asystem has all of these characteristics:

Any effects of multi path fading, quantization, and amplifier nonlinearitiesmust precede the effects of noise in the actual channel being modeled.

The receiver is perfectly synchronized with the carrier, and timing jitter is

negligible. Because phase noise and timing jitter are slow processes, theyreduce the applicability of the semi analytic technique to a communicationsystem.

The noiseless simulation has no errors in the received signal constellation.Distortions from sources other than noise should be mild enough to keepeach signal point in its correct decision region. If this is not the case, thenthe calculated BER will be too low. For instance, if the modeled system has

a phase rotation that places the received signal points outside their properdecision regions, then the semianalytic technique is not suitable to predictsystem performance.


11/23

PROCEDURE FOR THE

SEMIANALYTIC TECHNIQUE The procedure below describes how you would typically

implement the semi analytic technique using the semianalytic function:

Generate a message signal containing at least ML

symbols, where M is the alphabet size of the modulationand L is the length of the impulse response of thechannel, in symbols.

A common approach is to start with an augmentedbinary pseudo noise (PN) sequence of total length

(log2M)ML. An augmented PN sequence is a PNsequence with an extra zero appended, which makes thedistribution of ones and zeros equal.


12/23

contd

Modulate a carrier with the message signal using base bandmodulation. Supported modulation types are listed on the referencepage for semi analytic. Shape the resultant signal with rectangularpulse shaping, using the oversampling factor that you will later useto filter the modulated signal. Store the result of this step as txsig forlater use.

Filter the modulated signal with a transmit filter. This filter is often asquare-root raised cosine filter, but you can also use a Butterworth,Bessel, Chebyshev type 1 or 2, elliptic, or more general FIR or IIRfilter. If you use a square-root raised cosine filter, use it on the non-oversampled modulated signal and specify the oversampling factorin the filtering function. If you use another filter type, you can apply it

to the rectangular pulse shaped signal.


13/23

.contd

Run the filtered signal through a noiseless channel. This channelcan include multipath fading effects, phase shifts, amplifiernonlinearities, quantization, and additional filtering, but it must notinclude noise. Store the result of this step as rxsig for later use.

Invoke the semi analytic function using the txsig and rxsig data fromearlier steps. Specify a receive filter as a pair of input arguments,

unless you want to use the function's default filter. The functionfilters rxsig and then determines the error probability of eachreceived signal point by analytically applying the Gaussian noisedistribution to each point. The function averages the errorprobabilities over the entire received signal to determine the overallerror probability. If the error probability calculated in this way is a

symbol error probability, then the function converts it to a bit errorrate, typically by assuming Gray coding. The function returns the biterror rate (or, in the case of DQPSK modulation, an upper bound onthe bit error rate).


14/23

PHASE-SHIFT KEYING

Phase-shift keying (PSK) is a digital modulation scheme thatconveys data by changing, or modulating, the phase of a referencesignal (the carrier wave).

Any digital modulation scheme uses a finite number of distinctsignals to represent digital data. PSK uses a finite number ofphases, each assigned a unique pattern of binary bits. Usually, each

phase encodes an equal number of bits. Each pattern of bits formsthe symbol that is represented by the particular phase.

The demodulator, which is designed specifically for the symbol-setused by the modulator, determines the phase of the received signaland maps it back to the symbol it represents, thus recovering theoriginal data. This requires the receiver to be able to compare the

phase of the received signal to a reference signal such a systemis termed coherent (and referred to as CPSK).


15/23

CONSTELLATION DIAGRAM

A constellation diagram is a representation of asignal modulated by a digital modulation schemesuch as quadrature amplitude modulation orphase-shift keying. It displays the signal as a

two-dimensional scatter diagram in the complexplane at symbol sampling instants.

In a more abstract sense, it represents thepossible symbols that may be selected by agiven modulation scheme as points in thecomplex plane. Measured constellationdiagrams can be used to recognize the type ofinterference and distortion in a signal.


16/23

PSK CONSTELLATION WITH ISI

AND AWGN


17/23

MODULE SEPERATION

Module 1: Psk Constellation with ISI and

Awgn

Module 2: Bit Error Rate Calculation

Module 3: Application Example


18/23

MODULE DESCRIPTION

Module 1:

The M signal waveforms for ideal M-ary PSK are represented As sm(t) = g(t)cos(ct

+ m). When distortions due to channel effects or modem imperfections are present.

The received decision variables will differ from the M ideal points, and their locations

will be data dependent due to ISI. In this context, ISI will refer to the effects of both

linear and non-linear time invariant distortions with memory.

Assuming equiprobable symbols, then in order to completely characterize the ISI of a

channel with L symbol periods of memory, it is sufficient to consider all possible

sequences of L symbols.

A maximal length pseudorandom ML symbol sequence will satisfy this property. ForM=2, linear feedback shift registers can be used to generate maximal length

pseudorandom bit sequences.


19/23

FUTURE ENHANCEMENT

In a similar way, the technique can also be

extended to frequency non-selective

slowly fading channels


20/23

Advantages The probability distributions within the model can be easily

and flexibly used, without the need to approximate them

Correlations and other relations and dependencies (such as 'if'statements) can be modeled without difficulty

The level of mathematics required is quite basic

Commercial Monte Carlo simulation packages can automatethe tasks involved in simulation

The behavior of and changes to the model can be investigatedwith great ease and speed.


21/23

APPLICATIONS

The technique is demonstrated for 8PSK

over the Digital Video Broadcasting-

Satellite-Second Generation (DVB-S2)

channel


22/23

DOMAIN-COMMUNICATION

Wireless communication is the transfer of information

over a distance without the use of electrical conductors or

"wires". The distances involved may be short (a few meters as

in television remote control) or long (thousands or millions ofkilometers for radio communications). When the context is

clear, the term is often shortened to "wireless". Wireless

communication is generally considered to be a branch of

telecommunications.


23/23

MATLAB SIMULATION

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1strev main

Documents