From 47a6483bdb2ce8846fba65961a66225aad16abee Mon Sep 17 00:00:00 2001
From: Eric Kooistra <kooistra@astron.nl>
Date: Wed, 25 Jan 2023 17:27:55 +0100
Subject: [PATCH] Add more ideas.
---
doc/erko_teaser_talks.txt | 89 +++++++++++++++++++++++++++++----------
1 file changed, 66 insertions(+), 23 deletions(-)
diff --git a/doc/erko_teaser_talks.txt b/doc/erko_teaser_talks.txt
index dc3ce9d905..c6c183887b 100644
--- a/doc/erko_teaser_talks.txt
+++ b/doc/erko_teaser_talks.txt
@@ -1,18 +1,39 @@
Teaser talk topic ideas
+0) Teaser talk: Introduction to Geometric Algebra (18 Jan 2022)
1) Teaser talk: Quantization in LOFAR2.0 Station Firmware
2) Teaser talk: Subbands, beamlets and channels
3) Teaser talk: Signal statistics, correlation and beamforming
+0) Introduction to Geometric Algebra (18 Jan 2022)
+
+Abstract:
+
+For my hobby I wanted to calculate the positioning of a robot arm. I did that using rotation
+matrices, like I learned from Linear Algebra. Instead of using matrices I wanted to use
+quarternions. In short quarternions are in 3-D what complex numbers are in 2-D, so they
+represent rotations. Therefore I started googling to learn more about it and that is how I came
+across Geometric Algebra, which is the topic of this talk. For me Geometric Algebra is the most
+interesting topic that I have ever studied. I enjoy it very much, because it generalizes Linear
+Algebra, complex numbers, quarternions, Pauli matrices, and much more in a coherent way.
+Geometric Algebra can also be applied with Calculus and then it appears that for example
+Maxwell's 4 equations for electromagnetism can be written as one equation. I will present an
+introduction to Geometric Algebra and also explain why we did not learn about it at school and
+at university.
+
+
+
1) Teaser talk: Quantization in LOFAR2.0 Station Firmware
-* floating point - fixed point - integer (two complement, so range e.g. -8 to +7 for 4 bit value)
+* floating point - fixed point - integer
. 2**+127 -------------------------- 1. ------------------ 2**-127
<n bit int>
. <n bit fxp> fraction only
<n bit fxp> with fraction
<n bit fxp> . scaled
+
+ . two complement, so range e.g. -8 to +7 for 4 bit value
. format:
- unsigned : u(w, p)
- signed : s(w, p)
@@ -39,7 +60,8 @@ Teaser talk topic ideas
. dBFS
. SNR, P_quant
. processing gain log2(sqrt(N_fft)) = 5b, log2(sqrt(N_ant)) = 3.3b for N_ant = 96
- . coherent input (sine), incoherent input (sky noise, weak astronomical signal burried in noise)
+ . coherent input (sine), incoherent input (sky noise, weak astronomical signal burried in
+ noise)
* Implementation details
- Use separate function to do DFT for two real ADC inputs with complex FFT
@@ -50,8 +72,9 @@ Teaser talk topic ideas
- Interally extra LSbit inside PFB and before applying the weights, see try_round_weight.py
* Conclusion:
- - Fixed point arithmetic uses less FPGA resources (multipliers, RAM, logic) than floating point,
- but requires carefull bookkeeping or the fixed point position in the FW implementation.
+ - Fixed point arithmetic uses less FPGA resources (multipliers, RAM, logic) than floating
+ point, but requires carefull bookkeeping or the fixed point position in the FW
+ implementation.
* References:
[] SDP FW design, https://support.astron.nl/confluence/display/L2M/L4+SDP+Firmware+Design+Document
@@ -63,41 +86,61 @@ Teaser talk topic ideas
2) Teaser talk: Subbands, beamlets and channels
-* Implement delays by phase rotation
+* Implement delays by phase rotation:
- sinus --> phase exactly reprensent delay
- - narrow band --> phase is only exact at center of band, approximate towards the edges
+ - narrow band --> phase is only exact at one frequency (typically the center frequency) in the
+ band, approximate towards the band edges
* f_sub
- - coherence bandwidth T_sub >> B diameter of a Station antenna field
+ - coherence bandwidth of a staion requires T_sub >> B / c, where B is the diameter of a Station
+ antenna field and c = 3e8 m/s the speed of light in free space.
- distributed processing of N_pn processing nodes f_sub = RF_BW / N_pn / N_sub_per_pn
* PFB to separate ADC sampled signal into frequency bands
- FFT bin has sync bandpass, PFB has narrow band bandpass --> bins are called subbands
- Repeat FFT per N_fft samples in time yields bin coefficients per T_sub
- Bin is complex value, because it has to represent phase and gain of the bin
- . complex /= difficult --> complex = aggregate number of two parts: re and im or gain and phase A*exp(phi)
+ . complex /= difficult --> complex = aggregate number of two parts: re and im or gain and
+ phase A*exp(phi)
- For CW in center of bin the subband the subband value is a constant phase
- For CW left or right of center the phasor rotates left or right
- - Narrow band noise in subband is a noisy CW at RF_sub = n * f_sub, so can be delayed using phase rotation
- . plot fft(noise) --> keep only subband bin n, make other bins zero --> ifft() --> noisy CW at RF_sub
- - subband = Narrow band frequency signal from PFB output. Also called coarse channel in other radio telescopes
+ - Narrow band noise in subband is a noisy CW at RF_sub = n * f_sub, so can be delayed using
+ phase rotation
+ . plot fft(noise) --> keep only subband bin n, make other bins zero --> ifft() --> noisy CW
+ at RF_sub
+ - subband = Narrow band frequency signal from PFB output. Also called coarse channel in other
+ radio telescopes.
* BF
- weight and summate subbands from all antenna signal inputs that are part of the beam
- - BF weights are complex values, the phase points the beam by compensating for the geometrical delay and the gain shapes the beam
- . Jones matrix, cross pol weights are not used (kept 0), because the dual pol antenna are all aligned in the field
- - Update rate
+ - BF weights are complex values, the phase points the beam by compensating for the geometrical
+ delay and the gain shapes the beam
+ . Jones matrix, cross pol weights are not used (kept 0), because the dual pol antenna are all
+ aligned in the field
+ - BF weights update rate:
. depends of f_RF and B
. applied when written (no need for double buffer like in LOFAR1)
- beamlet = beamformed subband. A station beam of one subband.
* Subband equalizer
- - weights the subbands to fine adjust for cable delays and fine adjust for frontend gain differences
- . coarse delays are compensated by a sample input delay buffer in the SDPFW at the ADC input
- . coarse gains are compensated by an attenuator in the RCU2 in steps of 1 dB = factor 1.26 in power
- - in LOFAR1 subband weights were incoporated into the BF weights, in LOFAR2 they are separate CP
- - the subband weights can also be used to compensate for the bandpass shape of the RCU2 and antenna, to
- keep the dynamic range of the subbands signals within the lowest bits. This then can be used to
- have beamlets of 4 bits instead of 8 bit (default).
+ - Weights the subbands to fine adjust for cable delays and fine adjust for frontend gain
+ differences between receiver inputs:
+ . coarse delays are compensated by a sample input delay buffer in the SDPFW at the ADC
+ input
+ . coarse gains are compensated by an attenuator in the RCU2 in steps of 1 dB = factor
+ 1.26 in power
+ - In LOFAR1 subband weights were incoporated into the BF weights, in LOFAR2 they are separate CP
+ - The subband weights can also be used to compensate for the bandpass shape of the RCU2 and
+ antenna, to keep the dynamic range of the subbands signals within the lowest bits. This then
+ can be used to have beamlets of 4 bits instead of 8 bit (default).
* CEP correlator and beamformer
- - operate on channels that are narrow band frequency signals within a beamlet, so from a PFB at CEP.
- -
+ - Operate on channels that are narrow band frequency signals within a beamlet, so from a PFB at
+ CEP.
+ - Also called fine channels in other radio telescopes.
+ - Coarse geometrical delay differences between stations can be compensated by beamlet sample
+ delays of T_sub, so in steps of T_sub * c = 5.12us * 3e8 m/s = 1536 m. So for stations that
+ are 1000 km apart this implies coarse delays of ~1000 beamlet samples.
+ - The remaining fine geometrical delay differences within ~1500 m can be compensated using
+ phase rotation of the fine channels. The coherence bandwidth of whole LOFAR requires
+ T_chan >> T_sub, so typically more than 10 channels per beamlet. In fact CEP uses N_chan =
+ 64 - 512 for for coirrealtor pipeline and N_chan = 256 for tied array BF pipeline.
+
* References:
[] https://support.astron.nl/confluence/pages/viewpage.action?spaceKey=L2M&title=Temporary+storage+of+documents+and+papers
--
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