Error probability of Recursive Least Square (RLS) algorithm

[abdulawal]

Dear All,

I have used RLS algorithm to predict channel SNR (lets define SNR as x).
SNR is received in frame by frame. The frame duration is 5ms.

Lets define the channel SNR in each frame is xi, for i = 1, 2, 3, ..., t

I used a window of size 4 in RLS algorithm. I want to predict the SNR 2 times in every 4 frame.

At any given frame t, the SNR vector will look like as below.
[xt-3 xt-2 xt-1 xt]

Now after predicting the SNR for next 2 frames, the SNR vector will look like

[xt-1 xt x't+1 x't+2]

Where x' is predicted SNR.

After prediction there could be some prediction error which I can write like below

et+1 = |xt+1 - x't+1|
and
et+2 = |xt+2 - x't+2|


Now my question is, can I derive any probability distribution or something else to quantify the amount of error (e)?

What is the probability of xt+1 in next frame conditioned that xt received in current frame?

I know the probability distribution of signal is Rayleigh.

Looking forward to hear from you please.

Thanks,
Awal.

 

[abdulawal]

Am I asking a very silly question that nobody is making any comment? I have little knowledge in this, thats why I am asking. Any comment would be nice please.