Dear  Imtiyaz,

Would you please define rho? what is its range?

Best wishes

From the way you framed your question it seems that rho is the correlation between two different channel samples, correct? Which channel model are you using?  Also what performance metric are you evaluating? It's hard to tell how the outdated channel might affect the performance without knowing the metric you're evaluating.

@Zekry @Victor

\rho is the correlation coefficient between the current and outdated channel and the value of \rho lies from 0 to 1. 

My performance metric is Outage Probability of a system. 

With this model, the channel distribution is the same all the time, so that might explain why you get the same distribution all the time. There is nothing wrong with the model. What you need to consider is that h^* is what the receiver knows and utilizes for receiver processing, while h is what the true channel is. You need an expression for your performance that utilizes this mismatch.

By the way, I am unsure if outage probability is an appropriate metric for your application. The outage probability assumes that you send a large data block over just one realization of the channel, so it is unclear how this can be combined with having a varying channel.

@Emil

Thanks for your reply. I wanted to tell you most of the papers I read deals with Outdated CSI or FeedBack Delay represent their performance on the basis of Outage Probability.

For example, I am trying to implement this paper "Effect of Feedback Delay on Amplify-and-Forward Relay Networks With Beamforming" (Matlab Script Attached). I am sure that there is almost no error in the theoretical part but something wrong with the Montecarlo. 

Dear Imtiyaz,

I could not open your file. However i would like shed some light about the solution of the problem that may help trouble shooting it. 

Assuming that your transmitted signal is S(t) and the added noise at the receiver is n(t), the received signal r(t) = h * S + n 

Given S, h and n, one can calculate r. Then one can get the received signal power r^2 and compare it to the noise power sigma noise^2. This value must be greater than certain threshold for successful signal detection and decoding. If it is smaller than the threshold there will be an outage which means the x can nor be reproduced.

This may be an outline of the problem solution. 

According to the equation given above as long as the channel and the noise and the transmit signal level is above the threshold for successful detection, there will be no outage. You have to adjust the parameters to see such interruption instants.

Best wishes 

Dear Imtiyaz

Please try to give idea how to write matlab program for spectrum sensing using matched filter.

my mail id is [email protected]

You need to make sure that you are using h* in the transmission. Then, you need to use h in detecting the symbols (i.e., in the receiver). In this case, if we have \rho = 1 (i.e., h and h* are typically similar), then based on the equation, h = h* which returns the perfect CSI and you will have the best performance. On the other hand, if we have \rho = 0 (i.e., h and h* are totally different), then h = v (i.e., in your detection you are using some random numbers that far away from the actual channel) and you will have the worst performance. Consequently, any value of \rho between 0 and 1 provides a performance between the worst and best performances, respectively.

So, if you change the value of \rho without affecting the performance, I think you were mistakenly using the same channel for both transmission and detection.