Hi all, I'm working on a direction finding project and I'm asking for help on the phase alignment step. My configurations are: 4 * N200+XCVR2450 as the receiver array 1 * N200 + SBX as the reference TX 1 * N200 + SBX as the target transmiter GnuRadio and Matlab code of MUSIC algorithm The reference TX are connect to receivers' RF2 using SMA splitter 4 receivers have been time and frequency synchronized. I'm not familiar with signal processing. I've read a lot of posts in the mailing list and really didn't get how to do phase alignment. Can anybody give me a hint on how to set the reference TX parameters and how to do "post-processing phase alignment based on the offsets and gains observed from the known reference signal"? Thank you! -- Best regards! Charlie

Hi Charlie, I know I've already answered you in private, but it seemed better to share this answer: this really sounds like an interesting project! > I'm not familiar with signal processing. The GNU Radio project has a list of literature it recommends, [1]. I'd especially like to point you at Lapidoth's book, which is available for free [2], if you don't have access to e.g. a university library of signal processing/signal theory books. MIT actually has an online course in digital signal processing [3], which I find quite nice, if a bit short on a few details, but that's just my personal preferences. > post-processing phase alignment based on the offsets and gains observed from the known reference signal So, ok, there's multiple aspects to these instructions: 1. phase 2. observation 3. reference signal So, first of all, we'll have to define */phase/*. It's a property of a periodic process, in this case the oscillator that is used to mix down the radio frequency signal to complex baseband. (You really need to understand complex baseband; if you don't understand it yet, [4] might be a good and easy start). We can define the periodic process to be represented by a complex sinusoid, ie.: $s(t) = A e^{j2\pi f_\text{LO}t + \phi}$, we say: The signal $s$ at time $t$ has the amplitude $A$, oscillates with the frequency $f_\text{LO}$ and has the phase $\phi$. Now, from /*observing* /the four different RX signals from your XCVR2450s, you will need to determine the individual $A_1, A_2, A_3, A_4$, $f_{\text{LO}1}, f_{\text{LO}2}, f_{\text{LO}3}, f_{\text{LO}4}$ and $\phi_1, \phi_2, \phi_3, \phi_4$. That problem is typically not trivial, because by short-term observation, you typically can't tell the difference of an effect of $f_\text{LO}$ and $\phi$. Hence, it's really useful if $f_{\text{LO}1}\equiv f_{\text{LO}2}\equiv f_{\text{LO}3}\equiv f_{\text{LO}4}$. The USRPs help with that by offering an external 10MHz reference input. You will need to use an externel 10MHz clock source and clock distributor, to feed all four RX USRPs the same clock. Otherwise, your phase calibration will need to first consist of frequency estimation, and then of a phase offset calibration. It's definitively not impossible to do that, but it's both more complicated, and also requires that you calibrate regularly. Observing $A$ is relatively simple; you could just compare the digital power (ie. energy $|s[n]|$ per sample) to that of a sinusoid with $A=1$, or (see below), by measuring the maximum of the autocorrelation or cross-correlation with the known TX signal. The thing you want to observe and later correct are $\phi_1, \phi_2, \phi_3, \phi_4$. There's a lot of ways to do that. You can, for example, take $N$ samples from each of the four USRPs, do four N-point /Discrete Fourier Transforms/, and evaluate and compare the arguments of the complex numbers representing the frequency DFT bin where you expect a reference TX sinusoid in. That has a few downsides, so the typical approach here is to use /correlation/ with a known /*reference **signal*./ I hence strongly recommend understanding correlation, too. It's very important for the signal model that's behind MUSIC, too, so if you need to present what MUSIC does, correlation is the analytic tool behind it. The rest is "just" some estimation theory and linear algebra. So you'd profit twice from understanding it. After you obtained $\phi_1, \phi_2, \phi_3, \phi_4$, you will want to use these to bring all your receive signals to the same phase; luckily, exponential math allows us to just correct by multiplying with $e^{-\phi}$, so that the corrected signals look like, including an amplitude correction term (I use the tilde to identify things that are based on an estimation based on observation) \documentclass{article} \usepackage[utf8x]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{trfsigns} \DeclareMathOperator*{\argmin}{arg\,min} \usepackage{tikz} \usepackage{circuitikz} \usepackage[binary-units=true]{siunitx} \sisetup{exponent-product = \cdot} \DeclareSIUnit{\dBm}{dBm} \newcommand{\imp}{\SI{50}{\ohm}} \newcommand{\wrongimp}{\SI{75}{\ohm}} \pagestyle{empty} \begin{document} \begin{align*} \tilde s_n(t) &= A_n e^{j2\pi f_\text{LO}t + \phi_n} \cdot \left(\frac{1}{\tilde A_n} e^{-\phi}\right),\quad n=1,2,3,4\\ &= A_n \frac{1}{\tilde A_n} e^{j2\pi f_\text{LO}t + \phi_n - \tilde \phi_n} \intertext{assuming $\tilde A_n = A_n$ and $\tilde \phi_n = \phi_n$} &= e^{j2\pi f_\text{LO}}\text{.} \end{align*} \end{document} Now, the reference signal should have specific properties to allow for exact observation of phase; the property most important in a correlation based approach is that the correlation with itself is as low as possible everywhere but for the point where it's multiplied with itself without shift (the correlation with itself is called autocorrelation). I hope I've explained the signal processing problem you need to solve well enough, and was a little helpful. Best regards, Marcus Müller [1] https://gnuradio.org/redmine/projects/gnuradio/wiki/SuggestedReading [2] http://www.afidc.ethz.ch/A_Foundation_in_Digital_Communication/Getting_The_Book.html [3] http://ocw.mit.edu/resources/res-6-008-digital-sgnal-processing-spring-2011/ [4] http://greatscottgadgets.com/sdr/ On 29.07.2015 17:42, Changlai Du via USRP-users wrote: > Hi all, > > I'm working on a direction finding project and I'm asking for help on > the phase alignment step. > My configurations are: > 4 * N200+XCVR2450 as the receiver array > 1 * N200 + SBX as the reference TX > 1 * N200 + SBX as the target transmiter > GnuRadio and Matlab code of MUSIC algorithm > > The reference TX are connect to receivers' RF2 using SMA splitter > 4 receivers have been time and frequency synchronized. > > I'm not familiar with signal processing. I've read a lot of posts in > the mailing list and really didn't get how to do phase alignment. > Can anybody give me a hint on how to set the reference TX parameters > and how to do "post-processing phase alignment based on the offsets > and gains observed from the known reference signal"? > Thank you! > > > -- > Best regards! > Charlie > > > _______________________________________________ > USRP-users mailing list > USRP-users@lists.ettus.com > http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com

On 06/08/15 22:04, Marcus Müller via USRP-users wrote: > MIT actually has an online course in digital signal processing [3], > which I find quite nice, if a bit short on a few details, but that's > just my personal preferences. [snip] > [3] > http://ocw.mit.edu/resources/res-6-008-digital-sgnal-processing-spring-2011/ There is a hard to spot typo in the URL, the correct one is: http://ocw.mit.edu/resources/res-6-008-digital-signal-processing-spring-2011/ Thanks Marcus for the interesting pointer. Cheers, Daniele