Software-defined radio and digital communications
A 20 MHz band centered at 70 MHz can be digitized with a 56 MS/s converter, less than its highest frequency. The converter, well chosen, acts as a mixer.
01Software-defined radio
In a classic receiver, each function is a circuit: the channel filter, the demodulator, the carrier recovery. In a software-defined radio (SDR), the analog front end is reduced to amplifying, sometimes translating, and digitizing; everything else is done by a processor, an FPGA or a computer. Changing the standard, the bandwidth or the modulation is changing the program. The same blocks of receivers and transmitters are still there, but on the digital side of the converter:
| Digital block | Function |
|---|---|
| Numerically controlled oscillator and digital mixer | Bring the channel down to baseband, with perfectly balanced I and Q |
| Decimating filters (CIC and FIR) | Select the channel and reduce the sampling rate |
| Synchronization | Recover the carrier, the symbol clock and the frame |
| Equalizer and demodulator | Correct the channel and decide the symbols |
| Channel decoder | Correct errors using the code |
The processing relies on the hardware of digital signal processing, and the modulations and their error rates are those of noise in digital modulations.
02Bandpass sampling
The sampling theorem calls for sampling at twice the maximum frequency, but for a bandpass signal, which occupies only from \( f_L \) to \( f_H \), twice the bandwidth is enough, if the sampling frequency is chosen well: the alias of the band falls cleanly in the first Nyquist zone, without overlapping itself. This is undersampling, which replaces a mixer with the converter itself:
A band of width B centered at fc. Above, where it appears after sampling, in the first Nyquist zone, from 0 to fs/2; below, the valid sampling frequencies in green and the chosen one in yellow.
03Current digital systems
Mobile communications, Wi-Fi and digital television combine everything seen: adaptive QAM modulations, OFDM with hundreds of subcarriers that turn a channel with echoes into many flat channels, LDPC or turbo codes close to the Shannon limit, multiple antennas (MIMO) that multiply the capacity by exploiting the different propagation paths, and an RF front end that is, in large part, a software-defined radio.
04In the lab
With a low-cost SDR receiver and GNU Radio, receive a commercial FM station, filter the channel, demodulate and listen to the audio. Identify each block of the diagram.
Sample a 10.7 MHz signal with a 4 MS/s converter and find where it appears in the digital spectrum.
Transmit and receive a QPSK between two SDRs and observe the constellation before and after carrier recovery.
05Common mistakes
- Sampling a bandpass signal at any frequency greater than 2B. Only the valid intervals work.
- Forgetting the bandpass filter before the converter. Noise and signals from all the Nyquist zones fold onto the band.
- Using a noisy clock to undersample. Jitter degrades the signal-to-noise ratio in proportion to the signal frequency.
- Forgetting the spectrum inversion in even zones. The frequency has to be inverted in the processing.
06Self-assessment
What sampling frequencies work for a 60 to 80 MHz band with n = 2?
From 80 to 120 MHz.
With fs = 100 MHz, where does that band appear and how?
Between 20 and 40 MHz, inverted.
What is the theoretical minimum sampling frequency for a 20 MHz band?
40 MHz, if the band is located at an integer position relative to its width.
What advantage does the digital mixer have over an analog one?
Its I and Q branches are exactly equal: there is no imbalance or carrier leakage.
07Further reading
- Travis F. Collins, Robin Getz, Di Pu and Alexander M. Wyglinski. Software-Defined Radio for Engineers. Artech House, 2018. Software-defined radio with exercises on real hardware, freely available.
- Richard G. Lyons. Understanding Digital Signal Processing. 3rd ed., Prentice Hall, 2010. Bandpass sampling and digital frequency conversion.
- Jeffrey H. Reed. Software Radio: A Modern Approach to Radio Engineering. Prentice Hall, 2002. The architecture of software-defined radios.