Possible teaser talk content ideas.

doc/erko_teaser_talks.txt

+Teaser talk topic ideas
+
+1) Teaser talk: Quantization in LOFAR2.0 Station Firmware
+2) Teaser talk: Subbands, beamlets and channels
+3) Teaser talk: Signal statistics, correlation and beamforming
+
+
+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)
+  . 2**+127 -------------------------- 1. ------------------ 2**-127
+                              <n bit int>
+                                        .   <n bit fxp>           fraction only
+                                    <n bit fxp>                   with fraction
+                     <n bit fxp>        .                         scaled
+  . format:
+    - unsigned : u(w, p)
+    - signed : s(w, p)
+
+* Operations (*, +) cause bit growth
+  - rounding (to remove LSbits)
+    . truncation: int(x), //  (-7 // 6 = -2, 7 // 6 = 1)
+    . half away: python2, matlab
+    . half up
+    . half to even: python3, SDPFW
+  - clipping or wrapping (to remove MSbits)
+    . intermediate beamlet sum in BF uses wrapping
+    . final subband output and beamlet output use clipping
+
+* SDP signal path
+  - Task: Preserve sensitivity of the ADC input and maintain sufficient dynamic range
+  - Figure of SDP data path block diagram with:
+    . ADC samples
+    . subbands (FFT processing gain)
+    . beamlets (BF processing gain)
+      - BST
+      - beamlet output (8 bit samples to CEP)
+  - Figure of internal signal levels
+    . 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)
+
+* Implementation details
+  - Use separate function to do DFT for two real ADC inputs with complex FFT
+  - Spectral inversion to have incrementing subband indexes and frequencies in all Nyquist zones
+  - FFT switch / unswitch to decorrelate the quantisation noise crosstalk between the two real
+    signal input of the complex FFT in the PFB
+  - Go in and out via the MSbits, use backoff to avoid FIR and first stage FFT overflow
+  - 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.
+
+* References:
+  [] SDP FW design, https://support.astron.nl/confluence/display/L2M/L4+SDP+Firmware+Design+Document
+  [] SDP FW quantization, https://support.astron.nl/confluence/pages/viewpage.action?spaceKey=L2M&title=L4+SDPFW+Decision%3A+LOFAR2.0+SDP+Firmware+Quantization+Model
+  [] Fixed point numbers, https://support.astron.nl/confluence/display/L2M/L3+SDP+Decision%3A+Definition+of+fixed+point+numbers
+  [] Resizing and rounding, https://support.astron.nl/confluence/display/L2M/L4+SDPFW+Decision%3A+Number+representation%2C+resizing+and+rounding
+  [] Understanding DSP, 3rd edition, R. Lyons
+
+
+2) Teaser talk: Subbands, beamlets and channels
+
+* Implement delays by phase rotation
+  - sinus --> phase exactly reprensent delay
+  - narrow band --> phase is only exact at center of band, approximate towards the edges
+* f_sub
+  - coherence bandwidth T_sub >> B diameter of a Station antenna field
+  - 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)
+  - 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
+* 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
+    . 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).
+* CEP correlator and beamformer
+  - operate on channels that are narrow band frequency signals within a beamlet, so from a PFB at CEP.
+  -
+
+* References:
+  [] https://support.astron.nl/confluence/pages/viewpage.action?spaceKey=L2M&title=Temporary+storage+of+documents+and+papers
+     4b LOFAR doc
+     apertif fringe stopping doc
+  [] https://support.astron.nl/confluence/pages/viewpage.action?pageId=35165733 section 8.4
+  [] BF weights update scheme, https://support.astron.nl/confluence/display/L2M/L2+STAT+Decision%3A+Update+scheme+for+beamlet+weights
+  [] beamlet sum wrapping, https://support.astron.nl/confluence/display/L2M/L3+SDP+Decision%3A+Beamformer+sum+overflow+handling
+  [] beamlet output width 8 bit, https://support.astron.nl/confluence/display/L2M/L2+STAT+Decision%3A+Beamlet+output+width
+
+
+3) Teaser talk: Signal statistics, correlation and beamforming
+  - coherent, incoherent
+  - summation
+  - correlation
+  - XST --> u,v plane
+
+
+* References:
+  [] Signal statistics, https://git.astron.nl/desp/hdl/-/blob/master/applications/lofar2/model/signal_statistics.ipynb