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I am a newbie to AWGN.

My professor has given me a task of taking 4 different AWGN (0 mean and SD of 1) channels (Lets say each channel has 100 samples). Then I recombine these noise samples by adding all the noise samples together. Now I divide the AWGN channel by the square root of the channel count. In this case, I have 4 samples so I divide the newly generated channel by 2. Now as I understand this new channel has same mean and SD as each of the channels that were recombined to generate this new channel. I now use this new AWGN and combine it with my signal and study a Decoders performance using signal+newly created AWGN. I will be adding the noise to a BIAWGN channel. So my signal will be +1 or -1 and noise will be added on top of that

My questions are as follows: 1. What could be the motivation of doing this. Will this help me in any way? 2. Does anyone know of any research papers that employ this method when studying a decoders performance?

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My guess is your professor is trying to teach you about how noise in a dual-pol QAM system affects decoder performance. In such a system, there are 4 uncorrelated AWGN noise channels (XI,XQ,YI,YQ). It could also be that your professor is trying to teach you about linear impairments and their properties.

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  • $\begingroup$ I will be adding the noise to a BIAWGN channel. So my signal will be +1 or -1 and noise will be added on top of that. Do you know of any research papers that has this kind of analysis. If not what can I use to search terms to obtain literature similar to what I have described $\endgroup$ – Rejoy Mathews Mar 14 at 17:48
  • $\begingroup$ The signaling your describing is a specific case of Pulse Amplitude Modulation (PAM) (may also be refered to as Amplitude Shift Keying or Binary Antipodal Signaling). Any introductory book on digital communications should have a section describing the analysis of the theoretical ideal decoding of PAM signal in an AWGN channel. For instance, "Digital Communications 5th edition" by Proakis has an analysis on the subject on page 173. $\endgroup$ – ytgsyk4h Mar 14 at 18:19
  • $\begingroup$ Thanks. I meant the analysis of recombining multiple uncorrelated AWGN noise channels to obtain a single noise channel. $\endgroup$ – Rejoy Mathews Mar 14 at 18:24
  • $\begingroup$ The analysis of the combining sampled AWGN channels can be done using the properties of discrete Gaussian random variables. The variance of the sum of independent gaussian random variables is the sum of the variance. Check out en.wikipedia.org/wiki/… $\endgroup$ – ytgsyk4h Mar 14 at 18:35

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