# Interference Distribution Assumption in NOMA IoT Scenario

I am assuming a NOMA IoT Uplink scenario, which is interference marred. I have to ascertain the SINR at the Access Point (AP) for the NOMA users. A sub-channel is allocated to various users and interference is considered at each sub-channel. What is the realistic and best assumption for Interference Distribution at each sub-channel?

The interference intensity is different at each sub-channel but varies with same distribution.

• hey, you haven't accepted or commented on your previous question's answer, so that's something you might want to fix. – Marcus Müller Mar 7 at 13:43

interference intensity is different at each sub-channel but varies with same distribution

You're already using the term intensity, so this sounds like you're most likely implicitly using a Poisson Process, which is a stochastic typical model for "arrival processes", e.g. packets appearing in a network. It's based on the idea that the probability of an event occurring within a time period is simply proportional to the length of that period, and does not depend on the start time of the period.

Really check your literature thrice for them indications of where the term "intensity" came from. It's totally possible that something in there confirms the above (i.e. they say that the intensity $$\lambda$$ defines the factor between expected number $$N$$ of occurences and the duration of observation $$T$$, $$\mathbb E[N(T)] = \lambda T$$); it's also totally possible that other assumptions make this model impossible ("we assume interference to happen in bursts/clusters…").

Notice how careful I am about proposing this: it is a mathematically very convenient model, and it's pretty accurate to model a lot of naturally occurring behaviours, but it can badly jump in your face if you forget it's likely a simplifying behaviour.

Take this example (which I made up right now, but I think it's realistic enough to make my point):

Our packets are 0.1 s long. Interference emissions are much shorter, 0.001 s; they either appear within a packet (leading to a broken packet), or they don't. We model the occurrence of the interference to be a Poisson process.

This works well if the interferers are, for example, independent sensors that send a short packet when someone enters a room. In essence, your model represents the reality of when interference bursts happen accurately.

Even when the interferers are actually doing ALOHA for medium access, due to the packets being so short, the chance that you'll see them clustering is so low that you can still assume disjoint time periods (i.e. your packet transmissions) have independent interference arrival probabilities.

Now, if you happen to make your packets shorter, e.g. 0.008 s, you'll start "seeing" that ALOHA of the interferers mean that if there is indeed a correlation between interference occurrence during a packet and during a following packet.

If you made assumptions for your NOMA system based on the Poisson-ness of the process (like, you're doing CSMA/CD with deterministic backoff, you don't use an overly long spreader to distribute your info,…), you will run into a real congestion problem although your channel isn't actually heavily occupied.

So, treat your model assumptions with care. If in doubt, back them up with a quick simulation of what happens if they aren't fully met; if you can show that your overall system is robust about small model deviations, that greatly increases the credibility of whatever you're writing/designing.

• Thankyou very much for the prompt reply. I really appreciate. Let me elaborate my requirement please. I meant to portray a scenario, wherein there is an external or internal interference caused by unknown interferers in a dense IoT environment. Since allocation of sub-channel is involved, hence an optimization problem. My question is about the PDF associated with interference. Is there any popular model being followed ? – Khurram Mar 7 at 16:18
• The interference is the spectrum crowding of the sub-channel. But due to unknown interferers. – Khurram Mar 7 at 16:23