Need Help with Transition Probabilities from one state to another in Markov Chain

I have a constructed a Markov Chain with 5 States for CoMP-NOMA System Model, i need to find the transition probabilities from one state to another based the SNR below or above certain threshold. can anyone help me with that

States are 000 , 100, 101, 110 ,111

so from 000 to 000 the conditon is (SNR>= R0), where R0 is my threshold. likewise for all other states

Answer 1

[Yash]

Hi Syed,

I understand that you are interested in determining the transition probabilities between states based on the Signal-to-Noise Ratio (SNR). To accomplish this, it is important to have the knowledge of the SNR distribution. Once you have this information, calculating the probability P(SNR >= R0) becomes straightforward. where R0 is the threshold, as defined in the question.

For instance, consider the transition from state "000" to state "000". The transition probability in this case would be denoted as P(000 -> 000) and can be calculated as P(SNR > R0).

It is important to analyse the Probability Density Function (PDF) associated with this distribution. Suppose the SNR follows a uniform distribution from 0 to 2*R0. In this scenario, the probability would be 1/2.

You can implement PDF in MATLAB with the help of the "pdf()" function. To know more about it refer to the following link: https://www.mathworks.com/help/stats/prob.normaldistribution.pdf.html.

Further, to calculate the probability, you would need to integrate the pdf. For this, you can use the "trapz()" function. Refer to the below link for its documentation:

https://www.mathworks.com/help/matlab/ref/trapz.html.

I hope this helps in resolving the issue.