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ELEC0020: Photonics & Communication Systems > Class Notes > Flashcards

Class Notes Flashcards

1
Q

AWGN Channel Model

A

The most simple channel model, it is simply noised addition.

Commonly used in deep-space communication.

Most of the course is going to be based on this model.

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2
Q

Band-limited channel model examples.

A

Twisted Cable.

Coaxial Cable.

Optical fibre (large bandwidth, but still limited)

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3
Q

Band-limited Channel Model Stages

A

First, the input signal is going to be modeled by an impulse response or by a frequency response.

This is where the bandwidth limitation comes from, if the channel doesn’t respond or attenuates certain frequencies there must be a fundamental bandwidth limitation.

This could distort the input signal.

In addition to that distortion by the channel itself, there is also noise that adds to the signal.

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4
Q

What is a channel?

A

To send information from A to B we need a channel.

Depending on the media, we have different channel models.

Channel that only adds noise.

Channel that on top of noise can distort signal because of bandwidth limitations

There is also a wireless channel.

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5
Q

For Wireless Channels why does Dispersion In Frequency occur?

A

It happens because of the Doppler Effect.

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6
Q

If you multiply two signals in the time domain, what will happen in the frequency domain?

Vice-versa?

A

Convolution in the frequency domain.

If there is convolution in the time domain the signals multiply in the frequency domain.

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7
Q

What does a binary transmission scheme mean?

A

This is when we send 1 bit per each signal interval.

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8
Q

What does a M-ary transmission scheme mean?

A

M-ary is when we send more than 1 bit per signal interval.

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9
Q

What things do you need to consider when choosing a Baseband Digital Transmission Scheme

A

Energy efficiency, that is the Eb/N<strong>0</strong> ratio required to achieve a specific error probability.

Bandwidth efficiency, that is the data rate per unit of bandwidth.

Implementation cost and complexity.

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10
Q

Baseband Digital Transmission: What symbols are output from a mapper when a binary sequence is input?

A

1 for 1

-1 for 0

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11
Q

Why is it that you can encode 2 bits with 4 symbols?

What is the name of this mapping scheme?

What is the advantage of using this scheme over a Binary Polar Scheme?

A

There are four different values you can get with 2 bits when binary is used.

00, 01, 10, 11

Each of these values can have an associated symbol.

Thus 2 bits can be encoded in one signal interval.

Name: Quaternary Scheme

The advantage is that the Quaternary scheme can use less bandwidth to send the same signal, thus it has higher bandwidth efficiency.

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12
Q

What is the equation for symbol rate Rs ?

A

Rs = 1/Ts

Where Ts is the symbol interval (the duration of a symbol)

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13
Q

What is the equation for bit rate Rb ?

A

Rb = 1/Tb

Tb is the bit interval, i.e. the duration of a bit.

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14
Q

How are Rb and Rs related?

How are Tb and Ts related?

A

Rb = Rs*log2(M)

Tb = Ts/ log2(M)

The log2(M) converts the number of symbols to the number of bits. A Quaternary scheme would have M=4 and thus log2(4) would be equal to 2.

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15
Q

What is the Energy Efficiency defined as?

A

The amount of energy you need to sustain a certain error rate.

Where the error rate is the fraction of errors that I get out of the receiver, out of the total number of bits sent.

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16
Q

What does Xk refer to?

A

Refers to individual symbols one by one.

For example, in a binary polar scheme, X1 might refer to 1, X2 might be -1, X3 might be -1, etc.

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17
Q

Why does a Polar Binary Transmission scheme convery more energy per bit than in a Unipolar Binary Transmission?

A

Because polar has two amplitude levels, a positive and a negative amplitude level to encode 1 and 0.

On the other hand, unipolar has no amplitude level for 0, a null amplitude.

So unipolar uses have the energy per bit.

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18
Q

How do you calculate the average energy per symbol for an M-ary transmission scheme that has equal spacing between the levels?

A

Energy per symbol equation is in the middle.

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19
Q

What is the purpose of a constellation diagram?

A

It is a visual representation of the various symbols associated with a signaling scheme.

It is most importantly used for bandpass digital schemes.

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20
Q

What does an envelope detector do?

A

An envelope detector measures the amplitude of a signal.

Ak = |xk|2

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21
Q

Noise is generally assumed to be…

A

Gaussian

Following a Guassian distribution.

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22
Q

What is the setup of a Baseband Digital Reciever?

A
23
Q

How is thermal noise generated and what shape can it be modeled by?

A

Thermal noise is generated in electric devices by the vibration (thermal agitation) of electrons.

Thermal noise can be modelled by a zero-mean stationary white Gaussian process with spectral density

SN(f) = N0/2 = kT/2

24
Q

Baseband Digital Reciever: How is the signal component of a Matched Filter determined?

A
25
Q

Baseband Digital Reciever: How is the noise component of a Matched Filter determined?

A
26
Q

Baseband Digital Reciever: What does a Matched Filter do?

A

It maximizes the SNR when you sample its output at a certain instant of time.

27
Q

Baseband Digital Reciever: What is the maximum possible output signal-to-noise ratio of a Matched Filter ?

A

maximum possible SNR is equal to 2*Ɛp/N0

28
Q

Correlation and Dump Filter Setup

A
29
Q

Baseband Digital Reciever: What is the signal component output of a correlation and dump filter?

A
30
Q

Baseband Digital Reciever: What is the noise component output of a correlation and dump filter?

A

Note how the noise component of a Correlation and Dump filter is equivalent to a Matched Filter

31
Q

What is the essence behind filters in Baseband Digital Recievers?

A

Each pulse creates an impulse response, this impulse response is sampled periodically to reconstruct the signal without noise.

32
Q

What is the probability density function of Noise Nk ?

A
33
Q

What is the probability density function of Yk given Xk ?

What is it useful for?

A

You can determine the distribution of Yk for all the values of Xk .

34
Q

MAP Detector/Decision Rule

What is it ‘optimal’ and what are its equations?

A

MAP decision rule is optimal in the sense that it minimizes the (symbol) error probability.

35
Q

MAP Decision Rule: What does the function mean and how does it work?

A

The argmax() function is going to select the symbol (taken from the available symbols) that maximises the specific function it is acting on. In this case, the argmax() is applied to conditional distribution of Xk occurring given Yk .

Each possible transmitted symbol needs to be substituted in the function, and whatever outputs the largest value is to be chosen.

For example, in the binary case, for Xk = -1 you evaluate the result, for Xk = 1 you evaluate, and then you select the one which maximises the function.

In essence, we are looking at whether the value is due to noise or not. Seeking to maximise the probability that a value might be correct, reduces the probability of an error.

36
Q

ML Decision Rule: What is it and what is its function?

A

You use ML when you do not know the individual probabilities of the symbols being transmitted.

It is not optimal as it does not minimise the error probability in general.

When all the symbols are equally likely using MAP, the values obtained are equal to ML and means the ML decision rule is optimal in this case.

37
Q

What is the decision region?

A

The decision region partitions the output space into M regions. Whenever the output is in region M, the estimate of the device is going to be DM .

38
Q

Given an alphabet A = {-A,A} how do you determine the decision regions/thresholds associated with these symbols?

In other words, under what conditions does the Decision Device declare that symbol A has been transmitted?

A

It produces the estimate Xk = A.

Whenever the output of the matched filter Yk is greater than the RHS it declares that the symbol A has been transmitted.

The equation for Yk is determined by equating the argmax of A and -A with a greater than or equal to symbol.

39
Q

What is the probability density function of a conditional

A
40
Q

How do you determine the probability of error when the symbol Xk = A is transmitted?

A

It involves taking the integral of the probability density over the range of the Gaussian distribution which does not lie in the decision region. This is the equivalent to finding the area under the distribution.

41
Q

Error Probability: What does this graph show us?

A

This is a graph of the signal-to-noise ratio vs the probability of an error.

It shows that the unipolar scheme needs roughly 3db more to maintain the same error probability.

Similarly, the quaternary scheme needs a larger signal-to-noise ratio to get the same error probability as the unipolar.

42
Q

Error Probability: What is the issue regarding the number of levels?

A

The more levels to the scheme the more it will be affected by noise, so the scheme will require more energy to maintain the same error probability.

However, the advantage of more levels is a better bandwidth efficiency.

So there needs to be a compromise between energy efficiency (related to error probability) and bandwidth efficiency.

43
Q

Baseband vs Passband: What is the difference.

A

Baseband sends the signal as it is without frequency shifting (i.e. modulation). On the other hand, Passband transmission shifts the frequency of the signal to a higher frequency and then transmits it, the transmitted signal is then shifted back at the receiver.

44
Q

What is the generic setup of a Passband Digital Transmission?

A
45
Q

What happens to the frequency spectrum of a signal when you multiply the time domain by a sine wave?

A

The frequency domain is shifted.

It gets shifted to the frequency of the sine wave that was multiplied.

46
Q

How do you determine that ej*π/2 = j ?

A

Through Eulers Formula which states that:

ex*j = cos(x) +jsin(x)

47
Q

Passband Transmission: What do we achieve by making the symbols complex?

A

It allows for more phase differences in the passband digital signal.

48
Q

Passband Digital Transmission: What is the phase shift for each of these symbols?

A

These are complex symbols, the phase shift for each of the symbol is determined by π and its associated coefficient values.

So in this case, eπ*j leads to a phase shift of pi or 180º.

e3π*j/2 leads to a phase shift of 3π/2 or 270º, etc.

49
Q

LEFT OFF AT MIDDLE OF LECTURE 6

A

LEFT OFF AT MIDDLE OF LECTURE 6

50
Q

Passband Digital Reciever Setup

A

The down-converters converts the passband back to baseband equivalent.

51
Q

What are the associated expressions for each of these product of sine waves?

A
52
Q

Passband Digital Recievers: What is the probability density function of the real and imaginary Noise Nk ?

A
53
Q

Baseband Transmission: What is the average energy per symbol for a M-ary transmission scheme?

A

ELEC0020: Photonics & Communication Systems (15 decks)

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