Posted on 15 January 2023
Tags: linkpost

Sunday linkpost

Here’s some interesting papers and webpages that I have hanging around in open browser tabs. Better to have them here than languishing in browser tabs/history/bookmarks!

signal processing stuff #

array and spatial processing #

spicy signal processing: beyond circularity and linearity #

  • “Cyclic Wiener filtering: Theory and Model” by Gardner

    • normal filters add up multiple copies of the same signal, but time-offset
    • array processing adds up multiple copies of the same signal, but space-offset
    • FRESH (FREquency SHift) filters add up multiple copies of the same signal, but frequency-offset
    • this is useful because many signals (like communication/radar RF signals) have redundancy/correlation in their frequency domain (a property called cyclostationarity)

  • “Noncircularity exploitation in Signal Processing Overview and Application to Radar” by F. Barbaresco, Pascal Chevalier; about widely linear processing/filtering/estimation

    • a lot of time it’s justified to assume that complex-valued signals through complex-valued systems behave the same as real valued signals and systems (and using the same sort of filters / estimators you’d use for real-valued everythings)
    • pretending that complex signals work just like real signals depends on an assumption called “second-order circularity”
    • second-order circularity doesn’t always hold!
    • for instance if the signal (prior to passing through the channel) only takes a real value (like -1 or 1, like with a BPSK), then there’s a fundamental asymmetry between the inphase and quadrature channels, and that violates the second-order circularity assumption.
    • note: a symmetric QAM signal (modulated with random data, as always) is itself not circularly symmetric (add a phase offset and the little square lattice gets tilted) but it is second-order circular
    • if second-order circularity doesn’t hold and you process the received signal in a way that can’t tease apart the asymmetry then you are leaving signal on the table.
    • in the case where the modulated signal is only real-valued (or can be transformed to be only real-valued) that special signal structure morally lets you get a sort of processing gain because you know that any variation in the complex axis is noise/interference/etc: processing gain
    • a linear filter looks like \(y = h\cdot x\) (\(y\) output, \(h\) coefficients, \(x\) input), the widely-linear model looks like \(y = g \cdot x + h \cdot x^*\) (\(y\) output, \(h\) and \(g\) coefficients, \(x\) input, and \(x^*\) the complex conjugate of \(x\)) – so it’s linear in both \(x\) and its complex conjugate \(x^*\)
    • as i understand it, this lets the system do stuff like “take only the real part of the signal” (because the noise all lives in the imaginary axis) but in a principled way

  • “Widely Linear Estimation with Complex Data”, by Bernard Picinbono, Pascal Chevalier, also about widely linear processing

  • “Receivers with widely linear processing for frequency-selective channels” by H. Gerstacker; R. Schober; A. Lampe: more about widely linear processing

  • Widely linear filtering isn’t new: “Conjugate linear filtering” by W. Brown; R. Crane is from 1969!

  • “Enhanced widely linear filtering to make quasi-rectilinear signals almost equivalent to rectilinear ones for SAIC/MAIC” by Pascal Chevalier, Rémi Chauvat, Jean-Pierre Delmas

    • we saw earlier that if a signal (as transmitted) has a special form and only lives in the reals (like BPSK or a PAM), this allows for a form of processing gain at the receiver
    • even more interestingly, this allows for signal separation / interference cancellation (if both the desired and interfering signal are of this form): the receiver can adjust the phase of the received signal until the desired signal lives only on the reals (this is a linear operation), and trash the imaginary component of the signal altogether
    • the real-world realization is more complex since there are two channels (desired signal channel, interferer signal channel) that need to be taken into account, but this actually works: it’s called “single antenna interference cancellation” (SAIC)
    • some papers about SAIC:
    • the titles of those papers implies that this is deployed for GSM networks, which notably uses GMSK, which is definitely not BPSK nor a PAM
    • however, it turns out we can use this “single antenna interference cancellation” for certain modulations that aren’t BPSK or a PAM, with an additional step: the infamous “derotation”, which converts an MSK into BPSK, and converts GMSK into an almost-BPSK (“almost” because of the second Laurent pulse)
    • this paper goes well beyond the standard SAIC; looking into both widely-linear filtering and FRESH filtering, in order to exploit the spectral structure of the signal of interest

  • two books i found that might be useful later

hardware #

software engineering stuff #

parsing #

random stuff #

other people’s websites i liked (it’s nice seeing what other people get up to with static site generators) #