Further elaboration of LOW station model simulations

Timeboxed activity to continue work done for SP-1203 (described in the demo found here: https://confluence.skatelescope.org/display/SE/2020-11-11+DP+ART+System+Demo+8.5) 

This is an Exploration Enabler to further improve our understanding of LOW Calibration and stability requirements. This is an interaction between array-level calibration and station level calibration required for two different operating modes: 

1. Imaging
2. Tied-array beamforming

Also, see discussion at https://confluence.skatelescope.org/display/TDT/Questions+to+address+using+signal+chain+model

Notes (from Daniel Hayden, slightly edited by Ben Mort):

We need to know how big the gain variations at station level can be before it results in:

• Unacceptable imaging performance and,
• Unacceptable tied array beam performance.

We're interested in the effect of both

• the variation of the mean complex gain itself and,
• the variation of complex gains of individual receive paths with respect to the mean.

Although AAVS results seem to suggest we don't need direct delay measurement for every signal chain in a station, we should confirm this intuition quantitatively. 

There are two steps:

1. Complete development of Stefan's model for a single station. Remaining steps here are input realistic values for production tolerances and temperature data. The model should be able to show the effect of both variations within a station and variation between stations.
2. To feed this model's output as input to an array level simulation.

The first step at minimum is a good candidate for a PI9 Feature.

Possible stretch goals:

• Produce a Python version of the model.
• Do we want to model with a full set of individual EEPs in OSKAR?

Notes from meeting 3 Dec 2020 to scope Feature

1: validate model using INAF production data compared to (e.g. AAVS) behaviour.

2: using model with realistic temperature curves determine expected variability due to temperature.

We want to understand variation 'between' stations as well, and what the big contributors to this are. 

Prove that can be put into the array model, but analysis not needed.

Prioritised list of test cases to answer specific questions, as input for next PI.

Dependency with Curtin (Marcin?) and INAF? to help with validation of model?

Acceptance criteria

• Model parameters loaded with production data
• Set of predicted complex gain curves for a limited set of frequency and temperature (realistic) conditions.
• Comparison of predicted delay over frequency with measured delay over frequency (from AAVS data).
• Short report that summarises finding with regards to temperature stability - what are the dominant contributors (both intra-station and inter-station).
• Prioritised list of test cases to answer specific design questions, for future work.