• LTE downlink: reference signals and transmit diversity

In this post I continue with the analysis of an LTE downlink recording, which I started by looking at the primary and secondary synchronization signals. This recording is a one second excerpt of a 10 MHz cell in the B20 band that I recorded close to the base station, with a line-of-sight channel.

Now we will handle the reference signals to perform channel estimation. This will be used to equalize the received data transmissions. We will also handle the transmit diversity used by the base station, and show how to locate and demodulate some of the physical channels. All the calculations and plots are done in a Jupyter notebook.

The cell-specific reference signals (CRS) are transmitted in every subframe across all the cell bandwidth. They can be transmitted on either one, two or four antenna ports. In LTE, the concept of an antenna port does not necessarily correspond to a physical antenna. Signals are said to use the same antenna port if they have the same propagation channel to the user. Therefore, different beamforming combinations of the same physical antennas constitute different antenna ports.

The figure below shows the resource elements that are used for the reference signals in each of the ports. The resource elements allocated to reference signals for the antenna ports that are active are only used for this purpose, and only one of the ports transmits the reference signal in each of these resource elements. For instance, say that the cell uses two antenna ports. Then the elements marked as $$R_0$$ and $$R_1$$ below will only be used for the CRS, while the elements marked as $$R_2$$ and $$R_3$$ are free and can be used for other purposes.

To the pattern shown above, a frequency offset that consists of the PCI (physical cell ID) modulo 6 subcarriers is applied. This is done so that the reference signals of cells having different PCIs use different subcarriers, so as to prevent interference (especially those cells in the same group, since their PCI modulo 3 is different).

In the waterfall of our recording, we can clearly see the CRS transmissions. They last one symbol and occupy the whole bandwidth of the cell. We can also see the PSS, SSS and PBCH, as we remarked in the previous post. These indicate us where the subframes start. Thus, we can see that the first and fifth symbol of each slot are used for transmission of the CRS. This means that the cell does not use four antenna ports, since their corresponding CRS would be transmitted on the second symbol of each slot.

I have been posting about analysing LTE signals, with a focus on the structure of the pilot signals. I my two previous posts on this topic, I looked at the uplink using an IQ recording of my phone. Now I turn my attention to the downlink. I have done a short recording of the B20 band carrier of my local base station and I will be analysing it in this and future posts.

In this post, we will look at the primary synchronization signal (PSS) and secondary synchronization signal (SSS). These are the first signals in the downlink that a UE (phone) will attempt to detect and measure to estimate the carrier frequency offset, symbol time offset, start of the radio frames, cell identity, etc.

In an FDD system such as the one we are looking at here, the PSS is transmitted in the last symbol of slots 0 and 10 in each radio frame (Recall that LTE FDD signals are organized in 0.5 ms slots each containing 7 OFDM symbols. A radio frame lasts 10 ms and contains 20 slots). The SSS is transmitted on the symbol before the PSS.

The figure below shows the waterfall of the first 20 ms of the recording. I have marked the locations of the PSS and SSS with a red tick. These signals only occupy the 6 central resource blocks (1.08 MHz), so that they are compatible with all the possible cell bandwidths (LTE supports cell bandwidths of 1.4, 3, 5, 10, 15 and 20 MHz) and can be received by a UE which doesn’t know the cell bandwidth yet. In this case, we are looking at a 10 MHz cell, and we can see the neighbouring 10 MHz cells in the top and bottom of the waterfall.

We can see that every other PSS and SSS transmission there is another 1.08 MHz transmission following it. This corresponds to the PBCH (physical broadcast channel), which is transmitted on the first 4 symbols of slot 1 in each radio frame. The keen reader will have noticed that the PBCH is slightly wider than the PSS and SSS. This is because the PSS and SSS only use the central 62 out of 72 subcarriers in the 6 resource blocks they occupy, leaving 5 subcarriers at each edge as a guardband. This helps UEs having a large carrier frequency offset to detect these signals. On the other hand, the PBCH occupies all the 72 subcarriers.

• Timing SDR recordings with GPS

Following a discussion on Twitter about how to use satellite signals to check that distributed receivers are properly synchronized, I have decided to write a post about how to use GPS signals to timestamp an SDR recording. The idea is simple: we do a short IQ recording of GPS signals, and then process those signals to find the GPS time corresponding to the start of the recording. This can be applied in many contexts, such as:

• Checking if the 1PPS synchronization in an SDR receiver is working correctly.
• Timestamping an SDR recording without the need of a GPS receiver or 1PPS input, by first recording GPS signals for some seconds and then moving to the signals of interest (this only works if you’re able to change frequency without stopping the sample stream).
• Measuring hardware delays between the 1PPS input and the ADC of an SDR (for this you need to know the hardware delay between the antenna connector and 1PPS output of your GPSDO).
• Checking if synchronization is repetitive across restarts or power cycles.

We will do things in a fairly manual way, using a couple of open source tools and a Jupyter notebook. The procedure could certainly be automated more (but if you do so, at some point you might end up building a full fledged GPS receiver!). The post is written with a walk-through approach in mind, and besides the usefulness of timestamping recordings, it is also interesting to see hands-on how GPS works.

• A Rust implementation of Galileo OSNMA

Galileo OSNMA (Open Service Navigation Message Authentication) is a protocol that will allow Galileo GNSS receivers to authenticate cryptographically the navigation data that is broadcast by Galileo satellites. The system is currently in a public test phase and according to the roadmap it will begin the initial service in 2023.

This month I have spent some time working in a new Rust library that implements the receiver-side processing of OSNMA. The library is called galileo-osnma. Although there are still some features that are not implemented, and some other future ideas that I have for this library, it has already reached a point where I feel it can be released and used by others. In its present state it is already able to perform all the steps that are needed to check all the OSNMA authentication data that is currently being transmitted by the satellites during the test phase. The library is licensed under a permissive open source license (Apache + MIT, which is common in the Rust ecosystem).

• Demodulation of LTE PUCCH

In a previous post I showed how to demodulate the LTE physical uplink shared channel (PUSCH) by using a recording of my phone and some Python code. This is a continuation of that post. Here we will look at the physical uplink control channel (PUCCH) transmissions in that recording, and use a similar approach to demodulate them. All the work is done in a Jupyter notebook, which is linked at the end of the post.

The PUCCH carries control information from the UE to the eNodeB, such as scheduling requests, ACK/NACK for HARQ, and the CQI (channel quality indicator). A PUCCH transmission lasts for one subframe (1 ms) and typically occupies a single 12-subcarrier resource block in each of the two 0.5 ms slots in the subframe (there are more recently introduced PUCCH formats which use more subcarriers).

PUCCH transmissions are allocated to the edges of the uplink bandwidth, so as to leave the centre clear as a contiguous segment to be used for PUSCH. On its first slot, the PUCCH transmission uses some particular resource block. On its second slot it uses the symmetric resource block with respect to the centre frequency. This gives some frequency diversity to the transmissions.

The figure below shows a portion of the waterfall of the LTE uplink recording that we will be using (the link to the recording is included in the previous post). It corresponds to a 10MHz-wide cell in the B20 band. The PUCCH transmissions are the narrow bursts. The wider stronger bursts are PUSCH.

This illustrates that the PUCCH subframes are allocated to the edges of the cell, and how each subframe jumps to the symmetric resource block on its second slot.