Channel Capacity (Unfinished with simulation )

According to the concepts, we know that in the presence of noise, if the number of signal levels M increases, the ability of the receiever to distinguish between symbols decreaes. Hence, we should try to find an appropriate channel to achieve the mitigation of the noise.

There are some channels which are normal to be used in the communication system. AWGN channel and Rayleigh Fading Channel. When we are doing some calculations, the Shannon's Theorem is strongly recommended.

In this experiment, we should find the lower and upper AWGN channel capacity bound and the approximate capacity, then find the numerically computed shannon capacity.

Shannon capacity upper and lower bound are shown in the following formulas, respectively 

At the end of the today's experiment, we havn't simulated all results, so the final figure will be posted in the next blog.

 

The Rayleigh Flat Fading Channel

The Rayleigh Flat Fading Channel can be expressed as following

Shannon capacity equation: 

The AWGN Channel

The AWGN Channel, the model can be expressed as following Figure.

 Vt=Ut+Nt

   Vt:  the channel output

   Ut:  the channel input

   Nt: AWGN random variable with mean zero and variance N0

The Shannon capacity equation:        C=B log2(1+S/N)

Three simulations as the project goes so far.

As we mentioned before, we've already make the Unipolar NRZ in AWGN channel, the figure below is the Bioplar NRZ in AWGN channel;

SUMMARY: As these two figures shows, we can know that the BER of binary bipolar NRZ signal is smaller than the unipolar both in AWGN channel.

Additionally, we make a graph to compare the fading channel and AWGN channel which shown below,

SUMMARY: As the figure shows, the capacity of the AWGN channel is higer than the Fading channel and it is always at the top of the Fading channel.

Some concepts in the project------A SUMMARY

Summary:
1.Channel capacity is limited by the combined effects of channel bandwidth and noise.
2. Hartley' s law (for noiseless channel) 

3.Shannon capacity (for AWNG channel)
 
The reliable communication: R≤C, E_b/N₀≥-1.6dB

Simulate the numerical BER of Unipolar NRZ in AWGN channels

After reading the sheets given from the supervisor, we clearly understand some concepts of the noise systems and some parameters such as unipolar, bipolar and bits error rate(BER) etc. In matlab, the simulation of the unipolar NRZ is shown below,

As the project required, we should simulate another AWGN channel which relate to Bipolar. The latest result will come out at next blog. 

BER of Unipolar and Bipolar

The BER of unipolar (only have nonnegative voltage levels) can be expressed in terms of Eb

The BER of bipolar (both positive and negative voltage levels) can beexpressed in terms of Eb

Try to use MATLAB to show the equations

Understanding the project

Today,we have finished two tasks.

1. Make a plan for this project
   This project has four parts:
   a. Understanding what noise is and how use MATLAB to analyse and simulate from materials.
   b. Simulate the noise in wireless communication system.
   c. Find the solution on how to mitigate the noise in high speed wireless communication.
   d. Finish the project and correct the mistake to be shown.
   (Each part will be finished with two partner meetings in each week.)
2. Prepare the materials
   a. Read the project sheets: Noise and Signal in Digital Communication Systems [Dr. Xu(Judy)Zhu]
   b. Read the report: Rayleigh Flat Fading Channels' Capacity.