ROACH2 packetised correlator sizing
ROACH-II was primarily specified for the packetised correlator, which was considered to be the most demanding application. This page explains the reasoning behind choosing the memory interfaces and capacities, as well as IO bandwidth for ROACH2.
Executive Summary
To enable MeerKAT, PAPER and ATA correlator requirements, ROACH2 should be upgraded over ROACH1 as follows:
- A Virtex-6 SX475 main FPGA.
- Four 36bit QDR parts of 36Mibit each (144Mibit for MeerKAT2 upgrade path).
- A 72-bit DRAM DIMM slot, capable of housing at least a 256MiB DIMM running at or faster than 250MHz DDR.
- At least four 10GbE ports (more will be needed for beamforming).
Additionally, it would be convenient to have:
- Increased PPC-FPGA datarates (32bit bus?).
F engine coarse delay compensation
Simple delay compensation implementation requires dual-ported memory. Likely to put in on-FPGA BRAM.
Delay = baseline / speed of signal. Speed of signal ~ 300 000km/s.
For each polarisation, we then need:
Longest delay | Sample rate | Samples | Mem req'd at 8b/sample |
---|---|---|---|
1 km | 1Gsps | 3K | 26Kb |
8 km | 2Gsps | 53K | 417Kb |
20 km | 1Gsps | 66K | 520Kb |
20 km | 2Gsps | 133K | 1017Kb |
60 km | 1Gsps | 198K | 1562Kb |
60 km | 2Gsps | 396K | 3125Kb |
60 km | 4Gsps | 792K | 6250Kb |
MeerKAT will see each F board processing two polarisations, so the numbers in the table above need to be doubled.
Conclusion: MeerKAT-1 will require at least 2Mb of BRAM for delay processing. Any of the Virtex-6 devices will be sufficient if ignoring FFT, PFB and fine delay requirements.
F engine logic requirements
Not yet thoroughly checked, but as a guideline: FFT scales linearly with bandwidth and NlogN for Nchans. ROACH1 runs out of logic at 8k chans at 500MHz.
PAPER's processing requirements are small.
MeerKAT will need at least four times the logic to do 16k chans at 1GHz. SX95 * 4 = SX380.
F engine corner-turn bandwidth
There is a small matrix transpose that happens inside the F engines in order to have each packet contain data for a single antenna, single frequency channel.
For reference, ROACH has two 18bit-wide dual-ported DDR SRAMs (QDR) and a single 72bit wide DDR DRAM which are each presented as SDR 36 bit and 144 bit interfaces in application space.
On each FPGA clock cycle, we need to be able to read and write:
bus_width = n_pols * n_parallel_stream * n_bits * complex
PAPER is processing 100MHz on a 200MHz FPGA.
PAPER-64: 8 * 0.5 * 4 * 2 = 32 bit PAPER-128: 8 * 0.5 * 4 * 2 = 32 bit
ATA is processing two 1GHz dual pol antennas on a 250MHz FPGA.
ATA-42: 4 * 8 * 4 * 2 = 256 bit
MeerKAT1 is processing 1GHz on a 250MHz FPGA.
MeerKAT1: 2 * 4 * 4 * 2 = 64 bit
MeerKAT2 is processing 4GHz on a 250MHz FPGA.
MeerKAT2: 2 * 16 * 4 * 2 = 256 bit
We're double buffering this CT at the moment and need to read from one memory while writing to the other.
Conclusion: two 64 bit memory interfaces will suffice for naive implementation up to MeerKAT1, however, ATA and MeerKAT2 require wider bitwidths of 256bit. These are probably best implemented in 4x QDR 36 bit parts which appear as 4x 72bit SDR interfaces.
F engine corner-turn space
For reference, ROACH1 has 2x 36Mib QDRs and 1x 1GiB DRAM.
Calculation is as follows: req'd_mem = double_buffer * pkt_len * n_chans * n_parallel_streams * n_bits * complex.
We assume 4 bit quantisation (4b real + 4b imaginary).
PAPER-64: 2 * 128 * 2048 * 8 * 4 * 2 = 32 Mibit PAPER-128: 2 * 256 * 2048 * 8 * 4 * 2 = 128Mibit MeerKAT1: 2 * 256 * 16384 * 2 * 4 * 2 = 128Mibit MeerKAT3: 2 * 256 * 65536 * 2 * 4 * 2 = 512Mibit
Conclusion: ROACH2 should have at least 128Mbit of QDR memory to support the matrix transpose operation for MeerKAT phase-1. Should we want to use ROACH2 for future MeerKAT phases, we will need at least 512 Mib (4x 144Mib parts) for the F engine.
X engine VACC data rates
The X engine cores output data in windows. You need to be able to output all baselines, all stokes complex values within one window to avoid overflows. Each window is length n_ants*pkt_size. The Xengine must produce n_baselines*n_stokes*complex during this time.
The vector accumulator needs to be able to read and write once per incomming value. On QDR, this is a single-clock operation (since it's dual ported), but on DRAM, this requires two clocks.
The choice of pkt size has implications for minimum integration period.
For reference, ROACH has 2x 36bit QDR interfaces and 1x 144bit DRAM interface.
If we assume the use of QDR for the VACC, which allows simultaneous reads and writes, the following table results...
n_ants | pkt_size | clk_avil | n_bls | demux | clk_req'd |
---|---|---|---|---|---|
32 | 128 | 4096 | 528 | 8 (32bit VACC) | 4224 |
32 | 128 | 4096 | 528 | 4 (64bit VACC) | 2112 |
64 | 128 | 8192 | 2080 | 8 (32bit VACC) | 16640 |
64 | 256 | 16384 | 2080 | 8 (34bit VACC) | 16640 |
64 | 128 | 8192 | 2080 | 4 (64bit VACC) | 8320 |
64 | 256 | 16384 | 2080 | 4 (68bit VACC) | 8320 |
64 | 128 | 8192 | 2080 | 2 (128bit VACC) | 4160 |
128 | 128 | 16384 | 8256 | 2 (128bit VACC) | 16512 |
128 | 256 | 32768 | 8256 | 2 (136bit VACC) | 16512 |
128 | 512 | 65536 | 8256 | 2 (144bit VACC) | 16512 |
Conclusion: We will need a single 128-bit interface for larger numbers of antennas (128). For smaller numbers of antennas (<=64), we would like multiple 64-bit interfaces. QDR is more convenient for these VACCs as implementation is easier. Multiple QDR parts would give additional flexibility in terms of how the memory is arranged (single large databus vs multiple smaller busses). Thus, there should be at least four 32-bit interfaces, which can be configured for use as four stand-alone VACCs, or combined in parallel to use as two 64-bit VACCs or as a single 128-bit interface. Four 36-bit QDR parts are appropriate, and match Feng corner-turn bandwidth requirements (see above section).
X engine VACC capacities
Each X engine processes a subset of frequency channels. The number of X engines required scale with the bandwidth you're processing. If your FPGAs are running at the same speed as the bandwidth you're processing, then you need one X engine for every F engine. However, if you're processing a wideband design (eg 1GHz with FPGAs running 250MHz) then you need X:Y times more X engines than F engines where X is the bandwidth you're processing and Y is the FPGA clock rate of your X engine.
For PAPER, 100MHz is processed on FPGAs running at 200MHz. Thus there are twice as many F engines than X engines.
MeerKAT-1 will likely process 1GHz of bandwidth on FGPAs at 250MHz (four times as many X engines as F engines).
MeerKAT-2 will likely process 4GHz of bandwidth on FPGAs at 250MHz (16 times as many X engines as F engines).
Each baseline has 4 stokes, 32 bit complex numbers (=256bits per baseline).
Data must be double-buffered, so that previous accumulation can be read out slowly while capturing next accumulation.
n_ants | n_chan | n_xeng | n_bls | mem_per_xeng | n_xeng_per_roach2 | total_double_buff_mem_per_roach2 |
---|---|---|---|---|---|---|
32 | 2048 | 64 | 2080 | 4.125Mb | 4 | 33Mb |
64 | 2048 | 32 | 2080 | 32.5Mb | 2 | 130Mb |
64 | 4096 | 256 | 2080 | 8.13Mb | 2 | 33Mb |
128 | 2048 | 64 | 8256 | 64.5Mb | 1 | 130Mb |
128 | 16384 | 512 | 8256 | 64.5Mb | 1 | 130Mb |
128 | 65536 | 512 | 8256 | 258Mb | 1 | 512Mb |
Conclusion: ROACH2 should have at least 130Mb of QDR memory for MeerKAT1. MeerKAT-2/3/4 can switch to DRAM VACC at the expense of minimum dump times (see section above on VACC bandwidth).
Minimum integration period
This is affected linearly by number of freq channels and packet size.
Ignoring VACC output datarates, yields the following possible example:
Processing 2GHz bandwidth, 16384 chans, minimum integration as follows: 1/2GHz: 0.5ns 16384 chans: *16384 pkt size: * 256 ========= min dump time: ~2.048ms
However, this ignores the fact that with the current design, the VACC uses spare FPGA cycles to retrieve the previous accumulation while storing the current one. If the data is forwarded through the VACC, how quickly you can retrieve the previous accumulation (even if only integrating a single spectrum) thus depends on your board clock rate and the ratio of number of valid clocks to idle clocks. Realistically, this will be another factor of ~4, increasing the minimum dump time in afore-mentioned example to ~8ms. Alternatively, you can bypass the VACC entirely and output at a fixed ~2ms period.
Switch and 10GbE requirements
Calculating maximum analogue bandwidth transportable over a 10GbE link...
Digital link: 156.25MHz*4*20, but 8/10 encoding -> 10Gbps.
Channel utilisation:
Bits | %pkt | |
---|---|---|
Layer1 overhead | 160 | 6% |
Ethernet header and footer | 160 | 6% |
IPv4 header | 160 | 6% |
UDP header | 64 | 2% |
Application header | 64 | 2% |
Data payload | 2048 | 77% |
77/100 * 10Gbps = 7.7Gbps max application usable per 10GbE link.
Assuming 4 bit complex data: 7.7/8b = 962.5MHz total. With 2 pols (single antenna/F engine per board) gives max 481MHz bandwidth per link.
- This does NOT account for any out of band signalling (currently used for heartbeat signals and legacy data synchronisation).
- This does NOT conform to SPEAD packet formats. It is the maximum efficiency we can get away with.
- Not recommended to run links near 100%.
Conclusion: MeerKAT1 will thus require at least four ports per board (X engines need two to switch and two to F engines to carry 1GHz bandwidth).