analog noice part 2

Analog

analogCommunicatio

n6/13/2015Analog Communication - NOISE

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Noise

Parameters SIGNAL TO NOISE RATIO

NOISE FACTOR

EFFECTIVE NOISE TEMPERATURE

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Signal to Noise Ratio (SNR)

where: PS is the signal power in wattsPN is the noise power in watts

Hartley-Shannon Theorem (also calledShannons Limit) states that the maximum datarate for a communications channel isdetermined by a channels bandwidth and SNR.

A SNR of zero dB means that noise power equalsthe signal power.

6/13/2015Analog Communication - NOISE

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N

S10

P

P log 10 dB SNR

Noise Figure / Factor (NF or F or

Fn) Electrical noise is defined as electrical energy of random amplitude, phase,

and frequency.

It is present in the output of every radio receiver.

The noise is generated primarily within the input stages of the receiver

system itself.

Noise generated at the input and amplified by the receiver's full gain

greatly exceeds the noise generated further along the receiver chain.


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Noise Figure / Factor (NF or F or

Fn) The noise performance of a receiver is described by a figure of merit called

the noise figure (NF).

where G = Antenna Gain


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Effective noise temperature

T = environmental temperature (Kelvin)

N = noise power (watts)

K = Boltzmanns constant (1.38 10 -23 J/K)

B = total noise factor (hertz)

Te = equivalent noise temperature

F = noise factor (unitless)6/13/2015Analog Communication - NOISE

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NT

KB

1eT T F 1 eT

FT

Narrowband

Noise

INTRODUCTION TO NARROWBAND NOISE

REPRESENTATION OF NARROWBAND NOISE IN TERMS OF

IN PHASE AND QUADRATURE COMPONENTS

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Narrow band noise Preprocessing of received signals

Preprocessing done by a Narrowband Filter

Narrowband Filter Bandwidth large enough to pass the modulated signal.

Noise also pass through this filter.

The noise appearing at the output of this NB filter is called NARROWBAND

NOISE.


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Narrow band noise

Fig (a) spectral components of NB Noise concentrates about +fc

Fig (b) shows that a sample function n(t) of such process appearssomewhat similar to a sinusoidal wave of frequency fc


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Narrow band noise We need a mathematical representation to

analyze the effect of this NB Noise.

There are 2 specific representation of NB Noise

(depending on the application)


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Representation of narrowband noise

in terms of In

phase and Quadrature Components

Let n(t) is the Narrowband Noise with Bandwidth 2B centered at fc

We can represent n(t) in canonical (standard) form as:

We can extract nI(t) (In Phase Component) and nQ(t) (Quadrature

Component) from n(t).


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Extraction of nI(t) and nQ(t) from n(t)

Each LPF have bandwidth B

This is known as NARROWBAND NOISE ANALYSER 6/13/2015Analog Communication - NOISE

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Generation of n(t) from nI(t) and nQ(t)

This is known as NARROWBAND NOISE SYNTHESISER


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Important properties of nI(t) and nQ(t)


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Important properties of nI(t) and nQ(t)


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Noise in CW

modulation Systems

NOISE IN LINEAR RECEIVERS USING COHERENT DETECTION

NOISE IN AM RECEIVERS USING ENVELOPE DETECTION

NOISE IN FM RECEIVERS

6/13/2015 Analog Communication - NOISE 17

Gaussian process

Let X(t) denote a random process for an intervalthat starts at time t = 0 and lasts until t = T.

The random variable Y is a linear functional of therandom process X(t) if:

where g(t) is an arbitrary function

By definition:

The random process X(t) is a Gaussian process if every linear functional of X(t) is a Gaussian random

variable.


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Main virtues of the Gaussian process:

Gaussian process has many properties thatmake results possible in analytic form

Random processes produced by physicalphenomena (see thermal noise as an example)are often such that they may be modeled bythe Gaussian process

If the input to a linear time invariant (LTI) systemis Gaussian then its output is also Gaussian


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Thermal noise

Is generated by each resistor.

Used to model channel noise in analysis the of

communication systems.

It is an ergodic, Gaussian process with the mean of

zero.


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Gaussian distribution

Main virtue of the Gaussian process:

Two parameters, the mean and variance are enough to fully characterize a

Gaussian distribution.


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Power spectral density (PSD) of a

random process

By definition, the power spectral density SX(t) andautocorrelation function RX() of an ergodic random processX(t) form a Fourier transform pair with and f as the variablesof interest.

The power of an ergodic random process X(t) is equal to the

total area under the graph of power spectral density.

The power spectral density is that characteristic of a random

process which is easy to measure and which is used in

communication engineering to characterize noise. 6/13/2015Analog Communication - NOISE

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White Gaussian Noise

Gaussian means Gaussian process.

A measurable consequence: Measured instantaneous

values of a thermal noise give a Gaussian distribution.

White means that the autocorrelation function consists of

a delta function weighted by the factor N0=2 andoccurring a = 0.

Power spectral density of white noise is:


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Thermal noise is a white Gaussian noise.

It is an ergodic Gaussian process with mean of zero, itspower is given by the variance 2.

Its power spectral density is:

where k is the Boltzmanns constant and Te is theequivalent noise temperature.

Note:

Power of white noise is infinite. Only the bandlimitedwhite noise has a finite power!


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Noisy Receiver Model

where the receiver noise is included in N0 given by:

the bandwidth and center frequency of ideal band-passchannel filter are identical to the transmission bandwidth BTand the center frequency of modulated waveform,respectively.


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Noisy Receiver Model

The filtered noisy received signal x(t) available for

demodulation is defined by:

Note: Noise n(t) is the band-pass filtered version of w(t)6/13/2015Analog Communication - NOISE

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Power spectral density (PSD) of

band-pass filtered noise

The average noise power may be calculated from the

power spectral density.

The average power N of filtered Gaussian white noise is:


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Signal to Noise Ratio (SNR) A measure of the degree to which a signal is contaminated with additive

noise is the signal-to-noise ratio (SNR)


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Figure of Merit Of CW Modulation

Schemes Goal: Compare the performance of different CW

modulation schemes.

Signal-to-noise ratio (SNR) is a measure of the degree to

which a signal is contaminated by noise.

Assume that the only source of degradation in message

signal quality is the additive noise w(t).

Noisy receiver model:


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Schemes

The signal-to-noise ratio at the demodulator input:

The signal-to-noise ratio at the demodulator output:


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Schemes (SNR)O is well defined only if the recovered

message signal and noise appear additively at

demodulator output. This condition is:

Always valid for coherent demodulators

But is valid for noncoherent demodulators only if the

input signal to- noise ratio (SNR)I is high enough

Output signal-to-noise ratio (SNR)O depends on:

Modulation scheme

Type of demodulator6/13/2015Analog Communication - NOISE

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SchemesConditions of comparison

To get a fair comparison of CW modulation schemes

and receiver configurations, it must be made on an

equal basis.

Modulated signal s(t) transmitted by each modulation schemehas the same average power

Channel and receiver noise w(t) has the same average power

measured in the message bandwidth W

According to the equal basis, the channel signal-to-

noise ratio is defined as:


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Schemes Noise performance of a given CW modulation scheme

and a given type of demodulator is characterized bythe figure of merit.

By definition, the figure of merit is:

The higher the value of the figure of merit, the better thenoise performance


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SNRs & Figure of Merit


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