## Acquisition and wipeoff for JT9A

Lately, I have been playing around with the concept of doing acquisition and wipeoff of JT9A signals, using a locally generated replica when the transmitted message is known. These are concepts and terminologies that come from GNSS signal processing, but they can applied to many other cases.

In GNSS, most of the systems transmit a known spreading sequence using BPSK. When the signal arrives to the receiver, the frequency offset (given by Doppler and clock error) and delay are unknown. The receiver runs a search correlating against a locally generated replica signal which uses the same spreading sequence. The correlation will peak for the correct values of frequency offset and delay. The receiver then mixes the incoming signal with the replica to remove the DSSS modulation, so that only the data bits that carry the navigation message remain. This process can be understood as a matched filter that removes a lot of noise bandwidth. The procedure is called code wipeoff.

The same ideas can be applied to almost any kind of signal. A JT9A signal is a 9-FSK signal, so when trying to do an FFT to visually detect the signal in a spectrum display, the energy of the signal spreads over several bins and we lose SNR. We can generate a replica JT9A signal carrying the same message and at the same temporal delay than the signal we want to detect. Then we mix the signal with the complex conjugate of the replica. The result is a CW tone at the difference of frequencies of both signals, which we call wiped signal. This is much easier to detect in an FFT, because all the energy is concentrated in a single bin. Here I look at the procedure in detail and show an application with real world signals. Recordings and a Python script are included.

## WSJT-X and linear satellites: part I

Several weeks ago, in an AMSAT EA informal meeting, Eduardo EA3GHS wondered about the possibility of using WSJT-X modes through linear transponder satellites in low Earth orbit. Of course, computer Doppler correction is a must, but even under the best circumstances we cannot assume a perfect Doppler correction. First, there are errors in the Doppler computation because the TLEs used are always measured at an earlier time and do not reflect exactly the current state of the satellite. This was the aspect that Eduardo was studying. Second, there are also errors because the computer clock is not perfect. Even a 10ms error in the computer clock can produce a noticeable error in the Doppler computation. Also, usually there is a delay between the time that the RF signal reaches the antenna and the time that the Doppler correction is computed for and applied to the signal, especially if using SDR hardware, which can have large buffers for the signal. This delay can be measured and compensated in the Doppler calculation, but this is usually not done.

Here we look at errors of the second kind. We denote by $D(t)$ the function describing the Doppler frequency, where $t$ is the time when the signal arrives at the antenna. We assume that the correction is not done using $D(t)$, but rather $D(t - \delta)$, where $\delta$ is a small constant. Thus, a residual Doppler $D(t)-D(t-\delta)$ is still present in the received signal. We will study this residual Doppler and how tolerant to it are several WSJT-X modes, depending on the value of $\delta$.

The dependence of Doppler on the age of the TLEs will be studied in a later post, but it is worthy to note that the largest error made by using old TLEs is in the along-track position of the satellite, and that this effect is well modelled by offsetting the Doppler curve in time. This justifies the study of the residual Doppler $D(t)-D(t-\delta)$.

## Simulating JT modes: how low can they get?

In this post I'll show how one can use the signal generation tools in WSJT-X to do decoding simulations. This is nothing new, since the performance of the modes that WSJT-X offers has being thoroughly studied both with simulations and real off-air signals. However, these tools seem not very widely known amongst WSJT-X operators. Here I'll give some examples of simulations for several JT modes. These can give the operators a hands-on experience of what the different modes can and cannot achieve.

Please note that when doing any sort of experiments, you should be careful before jumping to conclusions hastily. You should make sure that the tools you're using are working as they should and also as you intend to (did you enter correctly all the parameters and settings?). Also, you should check that your results are reproducible and agree with the theory and other experiments.

Another warning: some of the software that I'll be showing here, in particular the Franke-Taylor soft decoder for JT65 and the QRA64 mode, is still under development. The results that I show here may not reflect the optimal performance that the WSJT-X team aims to achieve in the final release version.

After all these warnings, let's jump to study the modes. We'll be considering the following modes: WSPR, JT9A, JT65A, JT65B and QRA64B. To give our tests some purpose, we want to find the decoding threshold for these different modes. This is the signal to noise ratio (SNR) below which the probability of a successful decode is too small to be useful (say, lower than 20%). For each mode, we will generate 100 test files containing a single signal with a fixed SNR. We will then see how many files can be successfully decoded for each SNR.