QPSK Receiver with ADALM-PLUTO Radio
This example shows how to use the ADALM-PLUTO Radio System objects to implement a QPSK receiver. The receiver addresses practical issues in wireless communications, such as carrier frequency and phase offset, timing offset and frame synchronization. This system receives the signal sent by the QPSK Transmitter with ADALM-PLUTO Radio example. The receiver demodulates the received symbols and prints a simple message to the MATLAB® command line.
This example describes the MATLAB implementation of a QPSK receiver with ADALM-PLUTO Radio. There is another implementation of this example that uses Simulink®.
MATLAB script using System objects: plutoradioQPSKReceiverExample.m.
Simulink implementation using blocks: plutoradioQPSKReceiverSimulinkExample.slx.
You can also explore a no-radio QPSK Transmitter and Receiver example that models a general wireless communication system using an AWGN channel and simulated channel impairments at commQPSKTransmitterReceiver.m.
This example has the following motivation:
- To implement a real QPSK-based transmission-reception environment in MATLAB using ADALM-PLUTO System objects.
- To illustrate the use of key Communications System Toolbox™ System objects for QPSK system design, including coarse and fine carrier frequency compensation, closed-loop timing recovery with bit stuffing and stripping, frame synchronization, carrier phase ambiguity resolution, and message decoding.
In this example, the ADALM-PLUTO System object receives data corrupted by the transmission over the air and outputs complex baseband signals which are processed by the QPSK Receiver System object. This example provides a reference design of a practical digital receiver that can cope with wireless channel impairments. The receiver includes FFT-based coarse frequency compensation, PLL-based fine frequency compensation, timing recovery with fixed-rate resampling and bit stuffing/skipping, frame synchronization, and phase ambiguity resolution.
The plutoradioqpskreceiver_init.m script initializes the simulation parameters and generates the structure prmQPSKReceiver.
% Receiver parameter structure prmQPSKReceiver = plutoradioqpskreceiver_init; % Specify Radio ID prmQPSKReceiver.Address = 'usb:0'
The function runPlutoradioQPSKReceiver implements the QPSK receiver using two System objects, QPSKReceiver and comm.SDRRxPluto.
This example communicates with the ADALM-PLUTO Radio using the ADALM-PLUTO Receiver System object. The parameter structure prmQPSKReceiver sets the CenterFrequency, and Gain arguments.
This component regenerates the original transmitted message. It is divided into five subcomponents, modeled using System objects. Each subcomponent is modeled by other subcomponents using System objects.
1) Automatic Gain Control: Sets its output amplitude to 1/sqrt(Upsampling Factor) (0.5), so that the equivalent gains of the phase and timing error detectors keep constant over time. The AGC is placed before the Raised Cosine Receive Filter so that the signal amplitude can be measured with an oversampling factor of four. This process improves the accuracy of the estimate.
2) Coarse frequency compensation: Uses nonlinearity and a Fast Fourier Transform (FFT) to roughly estimate the frequency offset and then compensate for it. The object raises the input signal to the power of four to obtain a signal that is not a function of the QPSK modulation. Then it performs an FFT on the modulation-independent signal to estimate the tone at four times the frequency offset. After dividing the estimate by four, the Phase/Frequency Offset System object corrects the frequency offset.
3) Fine frequency compensation: Performs closed-loop scalar processing and compensates for the frequency offset accurately. The Fine Frequency Compensation object implements a phase-locked loop (PLL) to track the residual frequency offset and the phase offset in the input signal. For more information, see Chapter 7 of [ 1 ]. The PLL uses a Direct Digital Synthesizer (DDS) to generate the compensating phase that offsets the residual frequency and phase offsets. The phase offset estimate from DDS is the integral of the phase error output of the Loop Filter. To obtain details of PLL design, refer to Appendix C.2 of [ 1 ].
4) Timing recovery: Performs timing recovery with closed-loop scalar processing to overcome the effects of delay introduced by the channel. The Timing Recovery object implements a PLL, described in Chapter 8 of [ 1 ], to correct the timing error in the received signal. The NCO Control object implements a decrementing modulo-1 counter described in Chapter 8.4.3 of [ 1 ] to generate the control signal for the Modified Buffer to select the interpolants of the Interpolation Filter. This control signal also enables the Timing Error Detector (TED), so that it calculates the timing errors at the correct timing instants. The NCO Control object updates the timing difference for the Interpolation Filter, generating interpolants at optimum sampling instants. The Interpolation Filter is a Farrow parabolic filter with alpha set to 0.5 as described in Chapter 8.4.2 of [ 1 ]. Based on the interpolants, timing errors are generated by a zero-crossing Timing Error Detector as described in Chapter 8.4.1 of [ 1 ], filtered by a tunable proportional-plus-integral Loop Filter as described in Appendix C.2 of [ 1 ], and fed into the NCO Control for a timing difference update. The Loop Bandwidth (normalized by the sample rate) and Loop Damping Factor are tunable for the Loop Filter. The default normalized loop bandwidth is set to 0.01 and the default damping factor is set to 1 for critical damping. These settings ensure that the PLL quickly locks to the correct timing while introducing little phase noise.
5) Data decoder: Uses a Barker code to perform frame synchronization, phase ambiguity resolution, and demodulation. Also, the data decoder compares the regenerated message with the transmitted message and calculates the BER.
For more information about the system components, refer to the QPSK Receiver with ADALM-PLUTO Radio example using Simulink.
Execution and Results
Connect two ADALM-PLUTO Radios to the computer. Start the QPSK Transmitter with ADALM-PLUTO Radio example in one MATLAB session and then start the receiver script in another MATLAB session.
BER = runPlutoradioQPSKReceiver(prmQPSKReceiver); fprintf('Error rate is = %f.\n',BER(1)); fprintf('Number of detected errors = %d.\n',BER(2)); fprintf('Total number of compared samples = %d.\n',BER(3));
When you run the simulations, the received messages are decoded and printed out in the MATLAB command window while the simulation is running. BER information is also shown at the end of the script execution. The calculation of the BER value includes the first received frames, when some of the adaptive components in the QPSK receiver still have not converged. During this period, the BER is quite high. Once the transient period is over, the receiver is able to estimate the transmitted frame and the BER dramatically improves. In this example, to guarantee a reasonable execution time of the system in simulation mode, the simulation duration is fairly short. As such, the overall BER results are significantly affected by the high BER values at the beginning of the simulation. To increase the simulation duration and obtain lower BER values, you can change the SimParams.StopTime variable in the receiver initialization file.
If the message is not properly decoded by the receiver system, you can vary the gain of the source signals in the ADALM-PLUTO Transmitter and ADALM-PLUTO Receiver System objects by changing the SimParams.PlutoGain value in the transmitter initialization file and in the receiver initialization file.
Finally, a large relative frequency offset between the transmit and receive devices can prevent the receiver functions from properly decoding the message. If that happens, you can determine the offset by running the Frequency Offset Calibration (Tx) with ADALM-PLUTO Radio and the Frequency Offset Calibration (Rx) with ADALM-PLUTO Radio models, then applying that offset to the center frequency of the ADALM-PLUTO Receiver System object.
This example uses the following script and helper functions:
1. Rice, Michael. Digital Communications - A Discrete-Time Approach. 1st ed. New York, NY: Prentice Hall, 2008.