Exploration of Channel Producing Power of Baseline Board Pairs

Abstract: The purpose of this document is to assist the developers of the software that observers will use to configure the WIDAR correlator. Its focus is on the number of channels that a baseline board pair (BLBP) can produce for a single subband, and for the polarization products (PPs) thereof.

Maximum Channels for a Subband with RQ=4, RF=256:
Variation by Number of
Polarization Products & Baseline Board Pairs
(hover over blue text for allocation of products to BLBPs)

PPs\BLBPs	1	2	3	4
1	pp1 = 64K total = 64K	pp1 = 128K total = 128K	pp1 = 192K total = 192K	pp1 = 256K total = 256K
2	pp1 = 16K pp2 = 16K total = 32K	pp1 = 64K pp2 = 64K total = 128K	pp1 = 128K pp2 = 64K total = 192K	pp1 = 128K pp2 = 128K total = 256K
3	pp1 = 16K pp2 = 16K pp3 = 16K total = 48K	pp1 = 64K pp2 = 16K pp3 = 16K total = 96K	pp1 = 64K pp2 = 64K pp3 = 64K total = 192K	pp1 = 128K pp2 = 64K pp3 = 64K total = 256K
4	pp1 = 16K pp2 = 16K pp3 = 16K pp4 = 16K total = 64K	pp1 = 16K pp2 = 16K pp3 = 16K pp4 = 16K total = 64K	pp1 = 64K pp2 = 64K pp3 = 16K pp4 = 16K total = 160K	pp1 = 64K pp2 = 64K pp3 = 64K pp4 = 64K total = 256K

In the above table, wherever you see "16K" for a polarization product, it means that that product is on a BLBP that is producing more than one product. If multiple products are produced on a single board, there is an absolute maximum number of channels per product of 16,384.

Note that 256K (262,144) is the absolute maximum number of channels that may be obtained for a single subband. Look at the first row of the above table; adding more BLBPs in this situation will not get us more channels. In the situation where we want 2, 3, or 4 PPs, we could make use of more BLBPs, not to get more total channels, but to give us more flexibility in distributing those channels across products. For example,... (before writing example, make sure statement is true!).

In the above table the maximum recirculation factor of 256 was used. What is the situation if we use the next largest RF of 128? The table below illustrates.

Note that for many of the cells in the above table there are a number of possible distributions of channels among products. For example, in the PP=2, BLBP=8 cell, pp1 could have any multiple of 32K from 32K through 224K, with the remainder of the 256K channels going to pp2. This document is not interested in detailing all the combinations. The combinations illustrated tend to be those that spread the channels as evenly as possible over the polarization products.

Highlighted Cells
A single correlator chip cell (CCC) produces 64 * RF channels. Here RF=128, so a CCC produces 8,192 channels. In highlighted cells PP=2 / BLBP=1 and PP=3 / BLBP=1 we have assumed that we can concatenate CCCs within a single CCQ (correlator chip quad) to produce channels for a single PP, up to the 16K limit. Is this permitted? Note that in the previous table (see same PP=2 / BLBP=1 and PP=3 / BLBP=1 cells) we had to leave some CCCs unused. This was because a single CCC gave us the 16K limit for a single PP when doing multiple PPs per BLBP. With RF=128 (and lower) we might be permitted to concatenate CCCs for a single product to get more channels for that product.

VCI
If the numbers in the tables are correct, at least in spirit, then the SSS code will have to at least nominally assign BLBPs not just to subbands, but to the individual polarization products thereof. If that is the case, one wonders whether the VCI should allow its clients to specify BLBPs at the product level or, alternatively, specify the products to be produced on particular BLBPs.