📻 FM RDS BPSK SDR Lab

Overview

Educational SDR laboratory for extracting and decoding Radio Data System (RDS) information from a commercial FM broadcast station. The RDS subcarrier is isolated from the FM multiplex, translated to baseband, synchronized, interpreted as a BPSK signal, and decoded into valid RDS groups.

This repository follows a technical and educational style: real IQ capture, FM demodulation, spectral analysis, FIR filtering, carrier recovery, BPSK visualization, bit extraction, RDS block validation, Program Identification (PI), Program Service name (PS), and RadioText (RT) reconstruction.

The figuras_rds_A/ folder name is intentionally preserved because the analysis script writes figures there by default. The included images are placeholders and should be replaced by the real plots generated after running Part A.

📂 Contents

• src → Python code for SDR capture, demodulation, and RDS decoding
• results → real capture logs and Part B summary figure

🧰 Hardware Setup

The measurements were performed using a low-cost RTL-SDR USB dongle connected to a standard FM broadcast antenna.

Device

• SDR Receiver: RTL-SDR (RTL2832U compatible)
• Frequency Band: FM broadcast band
• Interface: USB
• Antenna: Wideband FM antenna
• Local FM station with RDS transmission.

If an IQ capture is already available in .npz format, the RTL-SDR is not required.

The RTL-SDR is used exclusively for IQ data acquisition, while all signal processing is performed offline in Python.

🚀 Main Scripts

Script	Purpose
src/part_a_rds_analysis.py	Captures or loads IQ data, demodulates FM, analyzes the FM multiplex, extracts the RDS component, validates BPSK behavior, and generates didactic figures.
src/part_b_rds_decoding.py	Processes the IQ capture, searches for valid RDS groups, consolidates the dominant PI, reconstructs PS by segment voting, and extracts RadioText when enough segments are available.

🎯 Laboratory Goals

• Capture or load IQ samples from an FM broadcast station.
• Demodulate FM to obtain the composite multiplex signal.
• Identify the main spectral components of the FM multiplex:
  • mono audio band,
  • 19 kHz stereo pilot,
  • stereo difference region,
  • 57 kHz RDS subcarrier.
• Isolate the RDS band using FIR filtering.
• Translate the RDS subcarrier to baseband.
• Recover the BPSK-like symbol stream.
• Extract a binary RDS bitstream.
• Validate RDS blocks using syndrome checks.
• Decode and consolidate:
  • PI: Program Identification,
  • PS: Program Service name,
  • RT: RadioText.

📡 RDS in the FM Multiplex

In FM broadcasting, RDS is transmitted around the 57 kHz subcarrier inside the composite multiplex signal. This frequency is the third harmonic of the 19 kHz stereo pilot:

$$57\,\text{kHz} = 3 \cdot 19\,\text{kHz}$$

The RDS symbol rate is:

$$R_s = 1187.5\,\text{symbols/s}$$

In this implementation, the extracted RDS signal is resampled to:

$$F_s = 19\,\text{kHz}$$

which gives:

$$\frac{19000}{1187.5} = 16$$

samples per RDS bit/symbol interval.

🔄 Processing Pipeline

🧠 Key DSP Blocks

🔹 1. FM Demodulation

The FM multiplex is obtained from the phase difference between consecutive IQ samples:

$$x_{FM}[n] = \angle\left(x[n] \cdot x^*[n-1]\right)$$

where x[n] is the complex IQ signal.

🔹 2. RDS Band Extraction

The RDS component is isolated using a bandpass filter around the 57 kHz subcarrier:

$$54\,\text{kHz} \leq f \leq 60\,\text{kHz}$$

🔹 3. Baseband Translation

Two routes are implemented:

Route	Description
piloto_19k_al_cubo	Uses the 19 kHz stereo pilot raised to the third power to generate a 57 kHz reference.
oscilador_fijo_57k	Uses a fixed 57 kHz complex oscillator.

Using both routes improves robustness when different stations exhibit different RDS recovery behavior.

🔹 4. BPSK Carrier Recovery

A BPSK Costas loop is used to stabilize the recovered baseband phase. A PCA-based rotation is then applied to align the BPSK symbol cloud with the in-phase axis.

🔹 5. Biphase Bit Metric

The RDS bit decision metric compares the first and second halves of each bit interval:

$$m_k = \frac{1}{N_1}\sum_{n \in \text{first half}} x[n] - \frac{1}{N_2}\sum_{n \in \text{second half}} x[n]$$

The sign of this metric is used to estimate the corresponding bit state.

🔹 6. RDS Group Validation

Each RDS block has:

16 information bits + 10 check bits = 26 bits

A complete RDS group contains four blocks:

A | B | C/C' | D

Therefore, one full RDS group contains:

$$4 \cdot 26 = 104\,\text{bits}$$

The decoder searches for valid A, B, C/C', and D blocks, filters by the dominant PI, removes duplicates, and consolidates the final information.

---

🖼️ Main Figures

The most relevant figures are reserved in figuras_rds_A/. Replace the placeholder images with the real figures generated by the script.

📊 FM Multiplex Spectrum and RDS Zoom

FM Multiplex Spectrogram

🧩 RDS Extraction Stages

🔢 RDS Bitstream Extraction

🟣 BPSK Time Signal and Validated Constellation

🧾 Validated 104-bit RDS Group

✅ Real Capture Results: Radio Carolina 98.9 MHz

A real off-air FM capture was performed using an RTL-SDR receiver tuned to Radio Carolina 98.9 MHz.
This result is included as the main experimental validation case of the repository.

The capture demonstrates a realistic scenario: the RDS Program Service name was fully recovered, and the RadioText message was reconstructed almost completely from received RDS groups.

📡 Capture Setup

Item	Value
FM station	Radio Carolina
Frequency	98.9 MHz
RF sample rate	2.048 MS/s
Capture duration	65 s
RTL-SDR gain	30 dB
IQ samples	133,120,000
Tuner detected	Rafael Micro R828D

🧪 Part A: RDS Extraction and BPSK Validation

Item	Result
MPX sample rate	228 kHz
MPX duration	65.00 s
Main RDS route	19 kHz pilot cubed
Estimated residual RDS offset	-0.86 Hz
Raw RDS groups found	104
Consolidated RDS groups	13
Dominant PI	0xCB1A
Program Service	CAROLINA
PS segments	4/4
Part A total time	80.36 s

Part A confirms that the RDS component around 57 kHz was successfully extracted, translated to baseband, synchronized, and interpreted as a valid BPSK-like signal.

🧬 Part B: Generic AUTO RDS Decoding

Item	Result
Search mode	Generic AUTO
Main route used	piloto_19k_al_cubo
Estimated residual offset	-0.86 Hz
Useful RDS duration	64.74 s
Raw detected groups	272
PI count	0xCB1A: 272
Consolidated groups	20
Program Service	CAROLINA
PS segments	4/4
RT segments received	12/16
Part B total time	115.87 s

Recovered Program Service:

CAROLINA

Recovered RadioText:

Escribenos un Whatsapp 569 61246007 ????arolina 98.9

The missing ???? characters correspond to incomplete RadioText segment coverage during the capture. This is expected in a real broadcast scenario when the receiver stops before all RadioText segments are repeated. Even so, the message is reconstructed almost entirely, which validates that the processing chain is working with real RDS data rather than a synthetic example.

🖼️ Part B Summary Figure

The full console logs are included in:

results/radio_carolina_98_9_part_a_console_output.txt
results/radio_carolina_98_9_part_b_console_output.txt

📦 Python Dependencies

Install the main dependencies:

pip install numpy scipy matplotlib

For direct RTL-SDR capture:

pip install pyrtlsdr

On Linux, RTL-SDR system libraries may also be required:

sudo apt install rtl-sdr librtlsdr-dev

🧪 Running Part A: Analysis and Figure Generation

Part A performs IQ capture or IQ loading, FM demodulation, multiplex analysis, RDS extraction, BPSK visualization, and figure generation.

python src/part_a_rds_analysis.py

Before running, review the configuration section at the beginning of the script:

STATION_MHZ = 98.9
CAPTURE_SECONDS = 65.0
GAIN_DB = 30.0
CAPTURE_NEW = False
SAVEFIGS = True

Relevant parameters:

Parameter	Description
STATION_MHZ	Selected FM station frequency.
CAPTURE_SECONDS	IQ capture duration.
GAIN_DB	RTL-SDR gain.
CAPTURE_NEW	If True, captures from RTL-SDR. If False, loads an existing capture.
SAVEFIGS	Saves the generated figures.
AUTO_IQ_FILENAME	Automatically names captures based on station frequency.
STRICT_STATION_MATCH	Verifies that the IQ capture matches the configured station.

---

🧬 Running Part B: RDS Decoding

Part B processes the same IQ capture and attempts to recover valid RDS groups.

python src/part_b_rds_decoding.py

This stage reports:

• raw detected RDS groups,
• dominant PI,
• consolidated groups,
• PS segments,
• PS by voting,
• RadioText segments,
• reconstructed RadioText when enough segments are available.

🔍 Search Modes

The scripts include automatic synchronization search options so the lab is not tied to a single radio station.

SEARCH_MODE = "AUTO"

For general laboratory use, AUTO is recommended.

💾 IQ Capture Naming

When AUTO_IQ_FILENAME = True, the IQ capture name is generated from the selected frequency.

Example:

STATION_MHZ = 98.9

produces:

fm_rds_iq_98_9MHz.npz

This avoids accidentally analyzing an old capture from a different station.

✅ Expected Output

A successful decoding run may produce a console summary similar to:

============================================================
GLOBAL RESULT
============================================================

Raw detected groups: XX

Detected PI count:
  0xXXXX: XX

Dominant PI: 0xXXXX
Consolidated groups: XX

PS by voting:
  segment 0: 'XX' votes=X
  segment 1: 'XX' votes=X
  segment 2: 'XX' votes=X
  segment 3: 'XX' votes=X

Consolidated PS: 'XXXXXXXX'
PS segments: [True, True, True, True]

RadioText:
  group 2A segment 0: '....'
  group 2A segment 1: '....'

Consolidated RT: 'Recovered text from the FM station'

🧑‍🏫 Educational Use

This project can be used in courses or workshops related to:

• analog communications,
• digital communications,
• software-defined radio,
• FM demodulation,
• stereo FM multiplexing,
• FIR filtering,
• spectral analysis,
• BPSK modulation,
• carrier recovery,
• symbol synchronization,
• digital frame decoding,
• error detection and block validation.

🧰 Suggested Future Improvements

• Refactor the processing chain into reusable Python modules.
• Add command-line arguments with argparse.
• Export decoded PI, PS, and RT results to JSON or CSV.
• Add a Jupyter notebook for teaching demonstrations.
• Include a LaTeX laboratory guide.
• Compare multiple FM stations in a single report.
• Add unit tests for the RDS syndrome and block validation functions.
• Add an optional graphical interface for selecting frequency and capture settings.

📚 References

• GNU Radio – Official Documentation: GNU Radio
• Frequency Modulation (FM) – Wikipedia: Wikipedia Frequency Modulation
• FM broadcasting – Wikipedia: FM broadcasting
• RDS – Wikipedia: RDS

⚠️ Disclaimer

This project is intended for educational and experimental purposes only.

It is provided to demonstrate signal processing concepts related to FM broadcast reception and spectrum analysis.
The author does not encourage or endorse any unauthorized or improper use of radio equipment.

Users are responsible for ensuring compliance with local laws and regulations regarding radio reception and spectrum usage.

🤝 Support projects

Support me on Patreon https://www.patreon.com/c/CrissCCL

📜 License

MIT License