## BER simulation in GNU Radio

David Rowe always insists that you should simulate the bit error rate for any modem you build. I’ve been intending to do some simulations of the decoders in gr-satellites since a while ago, and I’ve finally had some time to do so. I have simulated the performance of the LilacSat-1 decoder, both for uncoded BPSK and for the Viterbi decoder. This is just the beginning of the story, as the code can be adapted to simulate other modems. Here I describe some generalities about BER simulation in GNU Radio, the simulations I have done for LilacSat-1, and the results.

## Testing a simple pulse generator for Linrad calibration

Lately, I’ve being talking with Juan Antonio EA4CYQ and Pedro EA4ADJ about performing Linrad calibration to enable the use of the smart noise blanker. They pointed me to the SIGP-1 by Alex HB9DRI, which is a 144MHz pulse generator with which I was already familiar, and a simpler pulse generator by Leif SM5BSZ which I hadn’t seen before.

Leif’s generator is very simple. It uses a 555 timer to generate a square wave, a 74AC74 flip-flop to divide the frequency of the square wave by 2 and obtain a precise 50% duty cycle, a 74AC04 inverter as a driver, and capacitive coupling to turn the edges of the square wave into RF pulses. Alex’s SIGP-1 is an improvement over Leif’s design. It generates the square wave in the same manner, but then it uses a helical bandpass filter for 144MHz with around 5MHz bandwidth to convert the square wave into 144MHz pulses, and a PGA-103+ MMIC RF amplifier and a BFR91 RF NPN transistor as a class A amplifier to increase the output level. The SIGP-1 has two main advantages over Leif design. The output is stronger, so the S/N of the pulses is higher, and the filtering helps prevent saturation in the receiver. However, Leif’s design uses only simple components and it’s adequate in many cases.

I have built and tested Leif’s generator and used it to calibrate my FUNcube Dongle Pro+ at 144MHz. I’ve also tried doing the calibration at other frequencies and it also works well, but the pulses are not very strong at 432MHz and above.

## Testing Opera sensitivity with GNU Radio

Some fellow Spanish Amateur Operators were talking about the use of the Opera mode as a weak signal mode for the VHF and higher bands. I have little experience with this mode, but I asked them what is the advantage of this mode and how it compares in sensitivity with the JT modes available in WSJT-X. I haven’t found many serious tests of what is the sensitivity of Opera over AWGN, so I’ve done some tests using GNU Radio to generate signals with a known SNR. Here I’ll talk about how to use GNU Radio for this purpose and the results I’ve obtained with Opera. Probably the most interesting part of the post is how to use GNU Radio, because it turns out that Opera is much less sensitive than comparable JT modes.

## Calibrating the S-meter in Linrad

In a previous post, I talked about the GALI-39 amplifier kit from Minikits. Here I will describe the procedure to calibrate the S-meter in Linrad (or another SDR) using this amplifier or any other amplifier with a known NF and an uncalibrated signal source. Leif Åsbrink has a youtube video where he speaks about the calibration of the S-meter in Linrad. However, he doesn’t use an amplifier, so I will be following a slightly different procedure.

## Estimation of the contribution of the frontend to the total noise figure

In a radio receiver composed of two stages, the total noise factor $$F$$ can be computed using Friis’s formula as$F = F_1 + \frac{F_2 – 1}{G_1},$where $$F_1$$ is the noise factor of the first block, $$G_1$$ is the gain of the first stage and $$F_2$$ is the noise factor of the second stage. If $$G_1$$ is large enough, then the contribution of the second factor is small and the total noise factor of the whole system is essentially the same as the noise factor of the first stage. This is the reason why a low noise amplifier is useful as a frontend, because it has a low noise factor $$F_1$$ and high gain $$G_1$$.

If $$F_2$$ and $$G_1$$ are known (perhaps only approximately), then it is easy to check if the contribution of the frontend to the total noise figure is large enough so that the total noise figure is determined by the noise figure such frontend alone. However, it may happen that one or both of $$F_2$$ and $$G_1$$ are not known. In email communication, Leif Åsbrink mentioned that there is an easy way of checking the contribution of the frontend without knowing these parameters. The method is to switch off the frontend and note the drop in the noise floor. He gave the following estimates: if the noise floor drops by more than 10dB, then the total noise figure is the same as the noise figure of the frontend up to 1dB; if the noise floor drops by more than 17dB, then the total noise figure is the same as the noise figure of the frontend up to 0.1dB. Here I present the maths behind these kind of estimates.