Modul #07

TE3113 TE3113 SISTEM KOMUNIKASI 1SISTEM KOMUNIKASI 1

NOISEPADA SISKOM

TE-29-02TE-29-02Program Studi S1 Teknik Telekomunikasi

Departemen Teknik Elektro - Sekolah Tinggi Teknologi Telkomp gg gBandung 2007

Model Komunikasi Radio

Blah blah blah bl ah

)(trPEMANCAR (TX) PENERIMA (RX)

)(tsi)(thc

)(tr

)(tnSUMBER TUJUAN

2Modul 07 - Siskom I - Noise pada Siskom

Model Sinyal TerimaM d l th i d i l Model the received signal

)(thc)(tsi )(tr )()()()( tnthtstr i +=)(c)(i)(tn

)(

AWGN Additi Whit G i N i

)()()()( tnthtstr ci +

Si lif th d l

AWGN = Additive White Gausian Noise

Simplify the model:Received signal in AWGN

)(tn

)(tr)(tsiIdeal channels

)()( tthc = )()()( tntstr i +=)(tn

AWGN3Modul 07 - Siskom I - Noise pada Siskom

Klasifikasi Noise Noise/Derau sebagai unsur pengganggu yang hampir selalu Noise/Derau sebagai unsur pengganggu yang hampir selalu

terlibat dalam Siskom memerlukan pemodelan yangrepresentative untuk memudahkan keperluan analisis bagi

t k lit t ki j Si kpenentuan kualitas ataupun kinerja Siskom. Klasifikasi noise berdasarkan sumbernya :

Dari luar systemy Dari dalam system (umumnya paling dominan)

Klasifikasi noise berdasarkan equivalensi dengan suhu: Thermal-Noise Non Thermal-Noise

Klasifikasi noise berdasarkan model matematis/statistic : Klasifikasi noise berdasarkan model matematis/statistic : Gaussian Noise White noise White Gaussian Noise

Modul 07 - Siskom I - Noise pada Siskom 4

Gaussian Noisen1(t) [volt]

n3(t) [volt]

tn2(t) [volt]

t

f ngsi distrib si Ga ss

t

1 fungsi distribusi Gauss : 2n

607,022

v1 2n2n2

nNn e2

1)v(f)v(f ==

Modul 07 - Siskom I - Noise pada Siskom 5V0=n n+

Gaussian Noise dimana: n = standar deviasi, dan mean = 0

== 1)()( dvvfdvvf Nn

)]([ tNVARn = akar daya rata-rata = r m s/eff Tegangan r.m.s/eff. dapat diukur dengan TRUE-RMS

)]([n = r.m.s/eff.

VOLT-METER, yang dapat berupa sinyal apa saja, termasuk NOISE.

Tapi Voltmeter biasa hanya mengukur tegangan rata rata Tapi Voltmeter biasa hanya mengukur tegangan rata-rata sin/cos.

Modul 07 - Siskom I - Noise pada Siskom 6

White Noise

Its PSD is flat, hence, it is called white noise.

[ /H ][w/Hz]

Power spectral density

Autocorrelation

Probability density function

Autocorrelation function

7Modul 07 - Siskom I - Noise pada Siskom

AWGN: Additive White Gausian Noise Memiliki sifat gabungan antara Gaussian-noise dan white

noise Berupa noise dalam/thermal noise : Berupa noise dalam/thermal noise :

(f)NkT ==No (f)NkTNo ==222

D bl id d

Si l id d

R t d i i k i l i d th l

Double sided

KJk = /2310.38,1Boltzman konst.Single sided

Rapat daya noise mempunyai ekuivalensi dengan thermal. Sehingga secara praktis dapat juga noise dinyatakan dalam thermal (ekivalensinya).( y )

Modul 07 - Siskom I - Noise pada Siskom 8

Classification of signals

Deterministic and random signalsDeterministic signal: No uncertainty with

respect to the signal value at any time.Random signal: Some degree of uncertainty

in signal values before it actually occurs.Thermal noise in electronic circ its d e to the Thermal noise in electronic circuits due to the random movement of electrons

Reflection of radio waves from different layers of yionosphere

9Modul 07 - Siskom I - Noise pada Siskom

Classification of signals Periodic and non-periodic signals

A non-periodic signalA periodic signal

Analog and discrete signalsp g

A discrete signal

Analog signals10Modul 07 - Siskom I - Noise pada Siskom

Classification of signals ..

Energy and power signals A signal is an energy signal if, and only if, it has

nonzero but finite energy for all time:

A signal is a power signal if, and only if, it has finite but nonzero power for all time:

General rule: Periodic and random signals are power signals. Signals that are both deterministic and non-periodic are energy signals.

11Modul 07 - Siskom I - Noise pada Siskom

Random process

A random process is a collection of time functions, or signals, corresponding to various outcomes of a random experiment For each outcome there exists arandom experiment. For each outcome, there exists a deterministic function, which is called a sample function or a realization.

Random variables

m

b

e

r

Sample functionsor realizationsR

e

a

l

n

u

m

or realizations(deterministic

function)

time (t)time (t)

12Modul 07 - Siskom I - Noise pada Siskom

Random Sequences and Random Processes

13Modul 07 - Siskom I - Noise pada Siskom

Specifying a Random Process A random process is defined by all its joint CDFs

for all possible sets of sample times

t0 t1t2

tn

14Modul 07 - Siskom I - Noise pada Siskom

Stationarity If time-shifts (any value T) do not affect its joint CDF If time-shifts (any value T) do not affect its joint CDF

t tn+T

t0 t1t2

tnt0 + T

t1+T t2+T

n

15Modul 07 - Siskom I - Noise pada Siskom

Random process Strictly stationary: If none of the statistics of the Strictly stationary: If none of the statistics of the

random process are affected by a shift in the time origin.Wid t ti (WSS) If th d Wide sense stationary (WSS): If the mean and autocorrelation function do not change with a shift in the origin time.

Cyclostationary: If the mean and autocorrelation function are periodic in time.

Ergodic process: A random process is ergodic in Ergodic process: A random process is ergodic in mean and autocorrelation, if

dand

, respectively., respectively.

16Modul 07 - Siskom I - Noise pada Siskom

ErgodicityTi E bl Time averages = Ensemble averages

[i.e. ensemble averages like mean/autocorrelation can be computed as time-averages over a single realization of the random process]A d di i d t l ti (lik ) if A random process: ergodic in mean and autocorrelation (like w.s.s.) if

and

17Modul 07 - Siskom I - Noise pada Siskom

AutocorrelationA t l ti f i l Autocorrelation of an energy signal

Autocorrelation of a power signal

For a periodic signal:p g

Autocorrelation of a random signal Autocorrelation of a random signal

For a WSS process: p

18Modul 07 - Siskom I - Noise pada Siskom

Spectral density

Energy signals:

Energy spectral density (ESD):

Power signals:

Power spectral density (PSD):

Random process: Power spectral density (PSD): p y ( )

19Modul 07 - Siskom I - Noise pada Siskom

Properties of an autocorrelation functionfunction

For real-valued (and WSS in case of For real valued (and WSS in case of random signals):

1 Autocorrelation and spectral density form1. Autocorrelation and spectral density form a Fourier transform pair.

2 Autocorrelation is symmetric around zero2. Autocorrelation is symmetric around zero.3. Its maximum value occurs at the origin.4 Its value at the origin is equal to the4. Its value at the origin is equal to the

average power or energy.

20Modul 07 - Siskom I - Noise pada Siskom