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Reception of a QPSK Waveform Using USRP E3xx

This example shows how to use the USRP™ Embedded Series Radio Support Package and Communications Toolbox™ software to implement a QPSK receiver in Simulink®. The receiver addresses practical issues in wireless communications, such as carrier frequency and phase offset, timing offset and frame synchronization. This model receives the signal sent by the Transmission of a QPSK Waveform Using USRP E3xx model. The receiver demodulates the received symbols and outputs a simple message to the MATLAB® command line.

Refer to the Guided Host-Radio Hardware Setup documentation for details on configuring your host computer to work with the Support Package for USRP Embedded Series Radio.


This example receives a QPSK signal over the air using SDR hardware. It has two main objectives:

  • Implement a prototype QPSK-based receiver in Simulink using the USRP Embedded Series Radio Support Package.

  • Illustrate the use of key Communications Toolbox System objects for QPSK system design.

In this example, the E3xx Receiver block receives a signal impaired by the over-the-air transmission and outputs complex baseband signals that are processed in Simulink. This example provides a sample 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

  • Bit stuffing/skipping

  • Frame synchronization

  • Phase ambiguity correction


Before running the example, ensure you have performed the following steps:

1. Configure your host computer to work with the Support Package for USRP Embedded Series Radio. See Guided Host-Radio Hardware Setup for help.

2. Ensure that a suitable signal is available for reception. This example is designed to work in conjunction with the following signal source:

Running the Example

Start the transmitter before running the model. When you run the model, the received messages are decoded and printed out in the Diagnostic Viewer. To open the Diagnostic Viewer select Debug->Diagnostics->Diagnostic Viewer from the menu bar. If the received signal is decoded correctly, you should see 'Hello world 0##' messages in the Diagnostic Viewer similar to those shown below.

Hello world 031
Hello world 032
Hello world 033
Hello world 034
Hello world 035
Hello world 036
Hello world 037
Hello world 038
Hello world 039
Hello world 040

You can configure various receiver algorithm parameters using the Model Parameters block.

Receiver Design: System Architecture

The top-level structure of the model is shown in the following figure.

The Signal Specification block is used to impart a sample rate on the receiver block data output.

The detailed structures of the QPSK Receiver subsystem are illustrated in the following figure.

The components are further described in the following sections:

  • Automatic Gain Control - Applies a variable gain to try to keep the signal amplitude at 1/Upsampling Factor

  • Raised Cosine Receive Filter - Uses a roll-off factor of 0.5, and downsamples the input signal by two

  • Coarse Frequency Compensation - Estimates an approximate frequency offset of the received signal and corrects it

  • Fine Frequency Compensation - Compensates for the residual frequency offset and the phase offset

  • Timing Recovery - Resamples the input signal according to a recovered timing strobe so that symbol decisions are made at the optimum sampling instants

  • Data Decoding - Aligns the frame boundaries, resolves the phase ambiguity caused by the Fine Frequency Compensation subsystem, demodulates the signal, and decodes the text message

Automatic Gain Control AGC

The phase error detector gain $K_p$ of the phase and timing error detectors is proportional to the received signal amplitude and the average symbol energy. To ensure an optimum loop design, the signal amplitude at the inputs of the carrier recovery and timing recovery loops must be stable. The AGC sets its output power to 1/Upsampling Factor (0.25), so that the equivalent gains of the phase and timing error detectors remain 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, thus improving the accuracy of the estimate. The AGC subsystem updates its compensation gain after each block of ten QPSK symbols in order to smooth out variations in signal amplitude. You can refer to Chapter 7.2.2 and Chapter 8.4.1 of [ 1 ] for details on how to design the phase detector gain $K_p$.

Raised Cosine Receive Filter

The Raised Cosine Receive Filter downsamples the input signal by a factor of two, with a roll-off factor of 0.5. It provides matched filtering for the transmitted waveform.

Coarse Frequency Compensation

The Coarse Frequency Compensation subsystem corrects the input signal with a rough estimate of the frequency offset. The following diagram shows the Find Frequency Offset subsystem in the Coarse Frequency Compensation subsystem. This subsystem uses a baseband QPSK signal with a designated phase index $n$, frequency offset $\Delta f$ and phase offset $\Delta \phi$ expressed as $e^{(j(n\pi/2+\Delta ft+\Delta \phi))}$, $n=0,1,2,3$. First, the subsystem raises the input signal to the power of four to obtain $e^{(j(4\Delta ft+4\Delta \phi))}$, which 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 library block corrects the frequency offset. There is usually a residual frequency offset even after the coarse frequency compensation, which would cause a slow rotation of the constellation. The Fine Frequency Compensation subsystem compensates for this residual frequency.

Fine Frequency Compensation

The Fine Frequency Compensation subsystem implements a phase-locked loop (PLL), described in Chapter 7 of [ 1 ], to track the residual frequency offset and the phase offset in the input signal, as shown in the following figure. 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.

A maximum likelihood Phase Error Detector (PED) , described in Chapter 7.2.2 of [ 1 ], generates the phase error. A tunable proportional-plus-integral Loop Filter , described in Appendix C.2 of [ 1 ] filters the error signal and then feeds it into the DDS. The Loop Bandwidth (normalized by the sample rate) and the Loop Damping Factor are tunable for the Loop Filter. The default normalized loop bandwidth is set to 0.06 and the default damping factor is set to 2.5 (over damping) so that the PLL quickly locks to the intended phase while introducing minimal phase noise.

Timing Recovery

The Timing Recovery subsystem implements a PLL, described in Chapter 8 of [ 1 ], to correct the timing error in the received signal. The input of the Timing Recovery subsystem is oversampled by two. On average the Timing Recovery subsystem generates one output sample for every two input samples. The NCO Control subsystem implements a decrementing modulo-1 counter, described in Chapter 8.4.3 of [ 1 ], to generate the control signal for the Modified Buffer, that selects 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 subsystem updates the timing difference for the Interpolation Filter , generating interpolants at optimum sampling instants. The Interpolation Filter is a Farrow parabolic filter with $\alpha=0.5$ as described in Chapter 8.4.2 of [ 1 ]. The filter uses an $\alpha$ of 0.5 so that all the filter coefficients become only 1, -1/2 and 3/2, which significantly simplifies the interpolator structure. Based on the interpolants, timing errors are generated by a zero-crossing Timing Error Detector, described in Chapter 8.4.1 of [ 1 ], filtered by a tunable proportional-plus-integral Loop Filter, 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 unity (critical damping) so that the PLL quickly locks to the correct timing while introducing little phase noise.

When the timing error (delay) reaches symbol boundaries, there will be one extra or missing interpolant in the output. The TED implements bit stuffing/skipping to handle the extra/missing interpolants. You can refer to Chapter 8.4.4 of [ 1 ] for details of bit stuffing/skipping.

The timing recovery loop normally generates 100 QPSK symbols per frame, one output symbol for every two input samples. It also outputs a timing strobe that runs at the input sample rate. Under normal circumstances, the strobe value is simply a sequence of alternating ones and zeroes. However, this occurs only when the relative delay between Tx and Rx contains some fractional part of one symbol period and the integer part of the delay (in symbols) remains constant. If the integer part of the relative delay changes, the strobe value can have two consecutive zeroes or two consecutive ones. In that case, the timing recovery loop generates 99 or 101 QPSK output symbols per frame. However, the downstream processing must use a frame size of 100 symbols, which is ensured by the Modified Buffer subsystem.

The Modified Buffer subsystem uses the strobe to fill up a delay line with properly sampled QPSK symbols. As each QPSK symbol is added to the delay line, a counter increments the number of symbols in the line. At each sampling instant, the delay line outputs a frame of size 100 to the Data Decoding subsystem. However, the Data Decoding subsystem runs on its received data only when its enable signal goes high. This occurs when both the counter value reaches 100 and the strobe is high, i.e. each time exactly 100 valid QPSK symbols are present at the Modified Buffer.

Data Decoding

The Data Decoding subsystem performs frame synchronization, phase ambiguity resolution, demodulation and text message decoding. The subsystem uses a QPSK-modulated Barker code, generated by the Bits Generation subsystem, to correlate against the received QPSK symbols and achieve frame synchronization. The Compute Delay subsystem correlates the data input with the QPSK modulated Barker code, and uses the index of the peak amplitude to find the delay.

The carrier phase PLL of the Fine Frequency Compensation subsystem may lock to the unmodulated carrier with a phase shift of 0, 90, 180, or 270 degrees, which can cause a phase ambiguity. For details of phase ambiguity and its resolution, refer to Chapter 7.2.2 and 7.7 in [ 1 ]. The Phase Offset Estimator subsystem determines this phase shift. The Phase Ambiguity Correction & Demodulation subsystem rotates the input signal by the estimated phase offset and demodulates the corrected data. The payload bits are descrambled, and the first 105 payload bits are extracted and stored in a workspace variable. All the stored bits are converted to characters and printed out at the MATLAB command window while the simulation is running.

Things to Try

The example allows you to experiment with multiple system capabilities to examine their effect on bit error rate performance. You can make changes to the receiver algorithms behaviors using the Model Parameters block.

  • You can tune the FFT Size and Number of Spectrum Averages for the Coarse Frequency Compensation subsystem to see the effect of the estimation accuracy and the tolerance to a high noise level. The resolution of the estimate is the frequency spacing between two adjacent FFT points. There is a speed versus accuracy tradeoff when choosing the value of FFT Size. To get a more accurate frequency estimate usually requires a larger FFT Size. However, a larger FFT Size also incurs a higher computational burden. If the resolution of the Coarse Frequency Compensation subsystem is low, then the Fine Frequency Compensation subsystem must have a wider frequency tracking range.

  • Due to the existence of noise and zero padding of the input, the FFT output might have some outliers in the estimation results. To ease the effect of these bad estimates, you can adjust the Number of Spectrum Averages to average the FFT result across multiple frames. The larger Number of Spectrum Averages improves the robustness of the coarse frequency estimation, but this also incurs a greater computational burden. Also, the fourth-power operation can correctly estimate an offset only if the offset satisfies the following inequality:

$4*\Delta f_{\max} \le f_s/2$, or

$4*\Delta f_{\max} \le 2*R_{sym}/2$, or

$\Delta f_{\max} \le R_{sym}/4$.

  • The FFT-based Coarse Frequency Compensation subsystem was designed for a scenario with a static frequency offset. In practice, the frequency offset might vary over time. This model can still track a time-varying frequency drift by the Coarse Frequency Compensation subsystem. However, the coarse frequency estimates take on discrete values, separated by the frequency resolution of the subsystem. You might observe jumps between frequency estimates. You can also implement coarse frequency compensation with a filter to get a smoother estimation output.

  • You can adjust the PLL design parameters such as Loop Bandwidth and Damping Factor in both Fine Frequency Compensation and Timing Recovery subsystems to see their effect on pull-in range, convergence time and the estimation accuracy. With a large Loop Bandwidth and Damping Factor, the PLL can acquire over a greater frequency offset range. However a large Loop Bandwidth allows more noise, which leads to a large mean squared error in the phase estimation. "Underdamped systems (with Damping Factor less than one) have a fast settling time, but exhibit overshoot and oscillation; overdamped systems (with Damping Factor greater than one) have a slow settling time but no oscillations." [ 1 ]. For more detail on the design of these PLL parameters, you can refer to Appendix C in [ 1 ].

  • The Timing Recovery subsystem relies on a stable constellation which does not rotate over time. This requires an accurate frequency offset compensation. In this model, if the actual frequency offset exceeds the maximum frequency offset that can be tracked by the current coarse compensation subsystem, you can increase its tracking range by increasing the oversampling factor. Another way to adjust the tracking range is to implement a rotationally-invariant timing error detector (e.g., Gardner timing error detector described in Chapter 8.4.1 of [ 1 ]) first and correct the rotation afterwards.

Alternative Implementations

This example describes the Simulink implementation of a QPSK receiver with SDR Hardware.

You can also explore a non-hardware QPSK transmitter and receiver example that models a general wireless communication system using an AWGN channel and simulated channel impairments with QPSK Transmitter and Receiver in Simulink.

Troubleshooting the Example

If you fail to successfully receive any 'Hello world' messages, try the troubleshooting steps below:

  • If the example runs slower than real time, you can try using Burst Mode.

  • The ability to decode the received signal depends on the received signal strength. If the message is not properly decoded by the receiver system, you can vary the gain applied to the received signal by changing the Gain parameter in the SDR receiver block.

  • A large relative frequency offset between the transmit and receive radios can prevent the receiver from properly decoding the message. If that happens, you can determine the offset by sending a tone at a known frequency from the transmitter to the receiver, and then measuring the offset between the transmitted and received frequency. This value can then be used to compensate the center frequency of the receiver block. See the Frequency Offset Calibration Using USRP E3xx example.

If you still fail to receive any messages, see Common Problems and Fixes.

List of Example Helper Files

This example uses the following helper files:

  • usrpe3xxQPSKRxSL_init.m: returns a structure of variables used to control constant parameters in the model.

  • usrpe3xxqpskrx_mask.m: controls the Model Parameters mask and updates the model depending on the parameters supplied in the mask.


1. Michael Rice, "Digital Communications - A Discrete-Time Approach", Prentice Hall, April 2008.