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: QPSKReceiverWithADALMPLUTORadioExample.
Simulink implementation using blocks: QPSKReceiverWithADALMPLUTORadioSimulinkExample.
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 QPSKTransmitterAndReceiverExample.
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 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 re-sampling 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'
prmQPSKReceiver = struct with fields: Rsym: 200000 ModulationOrder: 4 Interpolation: 2 Decimation: 1 Tsym: 5.0000e-06 Fs: 400000 BarkerCode: [1 1 1 1 1 -1 -1 1 1 -1 1 -1 1] BarkerLength: 13 HeaderLength: 26 Message: 'Hello world' MessageLength: 16 NumberOfMessage: 100 PayloadLength: 11200 FrameSize: 5613 FrameTime: 0.0281 RolloffFactor: 0.5000 ScramblerBase: 2 ScramblerPolynomial: [1 1 1 0 1] ScramblerInitialConditions: [0 0 0 0] RaisedCosineFilterSpan: 10 DesiredPower: 2 AveragingLength: 50 MaxPowerGain: 60 MaximumFrequencyOffset: 6000 PhaseRecoveryLoopBandwidth: 0.0100 PhaseRecoveryDampingFactor: 1 TimingRecoveryLoopBandwidth: 0.0100 TimingRecoveryDampingFactor: 1 TimingErrorDetectorGain: 5.4000 PreambleDetectorThreshold: 0.8000 MessageBits: [11200×1 double] BerMask: [7700×1 double] PlutoCenterFrequency: 915000000 PlutoGain: 30 PlutoFrontEndSampleRate: 400000 PlutoFrameLength: 11226 PlutoFrameTime: 0.0281 StopTime: 10 Address: 'usb:0'
The function runPlutoradioQPSKReceiver implements the QPSK receiver using the QPSK receiver System object, QPSKReceiver, and ADALM-PLUTO radio System object, comm.SDRRxPluto.
This example communicates with the ADALM-PLUTO radio using the ADALM-PLUTO Receiver System object. The parameter structure prmQPSKReceiver sets the CenterFrequency, Gain, and InterpolationFactor etc.
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 power to a level ensuring 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 two. This process improves the accuracy of the estimate.
2) Coarse frequency compensation: Uses a correlation-based algorithm to roughly estimate the frequency offset and then compensate for it. The estimated coarse frequency offset is averaged so that fine frequency compensation is allowed to lock/converge. Hence, the coarse frequency offset is estimated using a "comm.CoarseFrequencyCompensator" System object and an averaging formula; the compensation is performed using a "comm.PhaseFrequencyOffset" System object.
3) Timing recovery: Performs timing recovery with closed-loop scalar processing to overcome the effects of mismatched sample rate between the transmitter and the receiver due to inaccuracies of crystal oscillators used in sampling clock generation, we employ a comm.SymbolSynchronizer System object. The object implements a PLL to correct the symbol timing error in the received signal. The rotationally-invariant Gardner timing error detector is chosen for the object in this example; thus, timing recovery can precede fine frequency compensation. The input to the object is a fixed-length frame of samples. The output of the object is a frame of symbols whose length can vary due to bit stuffing and stripping, depending on actual channel delays.
4) Fine frequency compensation: Performs closed-loop scalar processing and compensates for the frequency offset accurately, using a comm.CarrierSynchronizer System object. The object implements a phase-locked loop (PLL) to track the residual frequency offset and the phase offset in the input signal.
5) Preamble Detection: Detects the location of the known Barker code in the input using a comm.PreambleDetector System object. The object implements a cross-correlation based algorithm to detect a known sequence of symbols in the input.
6) Frame Synchronization: Performs frame synchronization and, also, converts the variable-length symbol inputs into fixed-length outputs, using a FrameSynchronizer System object. The object has a secondary output that is a boolean scalar indicating if the first frame output is valid.
7) Data decoder: Performs phase ambiguity resolution and demodulation. Also, the data decoder compares the regenerated message with the transmitted one 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.
printReceivedData = false; % true if the received data is to be printed BER = runPlutoradioQPSKReceiver(prmQPSKReceiver, printReceivedData); 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));
## Establishing connection to hardware. This process can take several seconds. Error rate is = 0.332508. Number of detected errors = 911472. Total number of compared samples = 2741200.
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.