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# System prepended metadata

title: Daily Report day 3

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# Daily Report day 3
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22/07/2021
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## 1. Aspects : RF Engineering

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### A. Channel Modelling
#### 1. Channel model
Channel model is Characteristic modelling of the transmission media.
When a wireless signal propagates in the air from the transmitter to te receiver, it will change depending on various conditions, such as distance, trajectory, number of path, environmental condition an so on.

#### 2. Channel definition
The received signal y(t) can be defined as the result of the convolution between the transmitted signal x(t) and the channel response impulse h(t) plus the noise z(t).
<center>y(t) = h(t) * x(t) + z(t)</center>
In the freq domain:
<center>Y(n) = H(n) . X(n) + Z(n)</center>

#### 3. Additive White Gaussian Noise (AWGN)
Noise or AWGN interference is caused by various factors, such as thermal noise, shot noise, black body radiation from the earth and other warm objects, as well as the influence of space objects such as solar radiation. AWGN noise is also known as noise / thermal noise or Johnson-Nyquist noise.
The AWGN channel interference has additive, white noise character to the transmission signal and has Gaussian distribution with a probability density function:
![](https://i.ibb.co/8b6jG3M/2021-07-22-17h36-57.png)
this AWGN signal:
![](https://i.ibb.co/3W4JdfT/2021-07-22-17h38-30.png)
This is AWGN channel model, z(t) is noise:
![](https://i.ibb.co/brnXRj4/2021-07-22-17h39-59.png)

#### 4. Multipath Channel
There is Multipath propagation condition:
![](https://i.ibb.co/6mQLD4V/2021-07-22-17h42-09.png)
Multipath channels can be modeled into a delay line structure with N taps.
![](https://i.ibb.co/FHpwXrM/2021-07-22-17h54-16.png)

#### 5. Delay
- The delay spread is described in the form of a power and time pattern called the multipath power delay profile.
- The delay profile is the main signal, and the delayed signal is described by several pulse signals with different delays and power.

#### 6. Coherence Bandwidth
Coherence bandwidth states the maximum distance of two frequencies where the influence of the channel on the two frequencies is still highly correlated.
![](https://i.ibb.co/BPf5BR8/2021-07-22-17h47-20.png)
![](https://i.ibb.co/hLKK5Gy/2021-07-22-17h48-05.png)

#### 7. Channel Fading Effect
- The effects of delay spread and coherence bandwidth will also appear on channel fading.
- Fading is defined as the change in phase, polarization and amplitude of a signal to time.


#### 8. Rayleigh & Rician Distribution
![](https://i.ibb.co/VWpwKrK/2021-07-22-17h51-19.png)
- The Rayleigh distribution is used to describe the statistics of the super positioned signal from the overall reflection or diffraction signal due to the multipath path.
- The Rician distribution is used to describe conditions when the received signal contains a Line-of-Sight (LOS) signal component.

#### 9. Doppler Spread
Due to the movement of objects, the channel characteristics will change and can be represented in the Doppler power spectrum. The Doppler power spectrum is non-zero for(f - fD, f + fD), where fD is the Maximum Doppler Spread or Doppler Spread. Coherence time and Doppler spread inversely proportional to each other as in the following equation:
![](https://i.ibb.co/1z8ZvrD/2021-07-22-17h55-35.png)

#### 10. Frequency Offset
frequency shift is called frequency offset.

#### 11. Time Offset
The initial detection error of the frame is called time offset.

#### 12. IQ Imbalance
The IQ imbalance is caused by the difference in gain and phase on the I arm and the Q arm on the RF modulator or demodulator.
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:::info
### B. Rayleigh Multipath Channel Model

#### 1. Multipath Environment
Transmit bypass signal:
![](https://i.ibb.co/R7YS1sp/2021-07-22-17h58-48.png)
The received signal is:
![](https://i.ibb.co/8gc5xsF/2021-07-22-17h59-54.png)
Baseband equivalent of the received signal:
![](https://i.ibb.co/g6mFV96/2021-07-22-18h01-23.png)
Impulse response of the channel:
![](https://i.ibb.co/K6KD1YV/2021-07-22-18h02-28.png)

#### 2. Rayleigh Fading Model
When there are large number of paths, applying Central Limit Theorem, each path can be modelled as circularly symmetric complex Gaussian random variable with time as the variable.

#### 3. Probability Density Function Derivation
For a circularly symmetric complex random variable Z:
![](https://i.ibb.co/Fg4Xd7y/2021-07-22-18h09-53.png)
Variance:
![](https://i.ibb.co/R7vrzCX/2021-07-22-18h10-25.png)
Probability density of |Z| (Rayleigh random variable):
![](https://i.ibb.co/DgmT8Zf/2021-07-22-18h11-01.png)
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## 2. Summary
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### A. RF Engineering Summary

<iframe src="https://drive.google.com/file/d/110dsG0_x48E2gqSV1xGANTavY0wd6Crw/preview" width="100%" height="400"></iframe>

<center>RF Engineering Summary</center>
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## 3. Comment
Radio-frequency (RF) engineering is a subset of electronic engineering involving the application of transmission line, waveguide, antenna and electromagnetic field principles to the design and application of devices that produce or utilize signals within the radio band.

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# <center>Discussion with Team</center>

1. Discuss about Final Project and Choose Sub-Topic
2. Discuss about Course and Assignment
3. Discuss About Next Meeting