poster

                       
                                Today we complete our poster. o(∩_∩)o  !!

Fading ber analysis

 Generally for a good communication system, BER should be less than 10^-5, in order to achieve this level ,fading channel system requires more transmit energy , in another word it will consume more energy.

Result of BER in fading channel

       The error rate of PSK is much better than FSK in fading channel.

The performance of AWGN channel is much better than the Fading channel in the BER

Error probability of fading channel

Rayleigh Fading channel
 For a fixed attenuation α, the error rate of binary PSK as a fuction of the received SNR γb is  
                           
                               Pb(γb)=Q(sqrt(2*γb))

The expression for the error rate of binary  FSK is given by equation as

                              Pb(γb)=Q(sqrt(γb))
where γb=α^2*Eb/No

When α is Rayleigh-distributed, we must average Pb(γb) , therefore the probability density function of γb must be evaluated by the integral function

The result of this integration for binary PSK is

and the probability of error for binary FSK in the form  that shown in below

   

channel capacity

The top curve descirbe the AWGN capacity and the bottom is the Shannon capacity lower bands. From this figure, it shows  the fading channel capacity is located between the AWGN capacty and the Shannon capacity lower bound .

Shannon capacity upper and lower  bound computed by the following formulas, respectively.

So far, we got three simulation results:
Comparison between AWGN channel and fading channel

As can be seen form this figure, the capacity of the AWGN channel is better than the Rayleigh fading channel , as the value of singal noise ratio increases, the channel capacity is higher and higher. 

Bipolar NRZ in AWGN channel

Unipolar NRZ in AWGN channel

Compare the bit error ratio in AWGN channel with different model, BER of binary bipolar NRZ signal is smaller than the unipolar, in addition  the error rate decrease inversely with the SNR.

Monte Carlo Simulation

This project mainly uses Monte Carlo method, which is a numerical method of solving mathematical problems by the simulation of random variables.

In Monte Carlo simulations of digital communication systems
Numerical BER = Total nubmer of errors generated in simulation / Total number of bits simulated

Summary

AWGN channel model

The additive white Gaussian noise (AWGN) channel model is a channel whose sole effect is additon of whiter Gaussian noise process to the transmitted signal.

r(t) = Sm(t) + n(t)

Source from: Digital Communications by J. G. Proakis & M. Salehi



Shannon Capacity

 •Given a source transmitting data at data rate R bps and a channel with capacity C.

If R≤C, then we can encode the source in such a way that it can be transmitted through the channel with no error.

–If R>C, then we are certain to make errors no matter what we do.

Source from: Dr. Xu Zhu, Lecture notes, The university of Liverpool

Shannon's Theorem

Shannon's theorem atates the combined effects of finite bandwidth B and finite receive SNR S/N on channel capacity C.

Source from: Dr. Xu Zhu, Lecture notes, The university of Liverpool

Bandwidth Efficiency

Bandwidth Efficiency: a measure of how well a particular modulation format (and coding scheme) is making use of the avaiable bandwidth.


Bandwidth Efficiency = data rate / bandwidth (bits / sec/ Hz)

Source from: Dr. Xu Zhu, Lecture notes, The university of Liverpool