# Documentation

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## RF Impairments

### Illustrate RF Impairments That Distort a Signal

This section presents scatter plots that illustrate how blocks in the RF Impairments library distort a signal modulated by 16-ary quadrature amplitude modulation (QAM). The usual 16-ary QAM constellation without distortion is shown in the following figure.

As the scatter plots show, the first two blocks distort both the magnitude and angle of points in the constellation, while the last two alter just the angle.

You can create these scatter plots with models similar to the following, which produces the scatter plot for the Memoryless Nonlinearity block:

#### 16-ary QAM Model

The model uses the Rectangular QAM Modulator Baseband block, from AM in the Digital Baseband Modulation sublibrary of the Modulation library. You control the power of the block's output signal with the Normalization method parameter. To ```open this model```, enter `doc_16qam_plot` at the MATLAB® command line.

#### I/Q Imbalance Block

You can generate the next scatter plot by replacing the Memoryless Nonlinearity block in the 16-ary QAM Model with the I/Q Imbalance block. Set the block's I/Q amplitude imbalance (dB) parameter to `10` and the I/Q phase imbalance (deg) parameter to `30`.

For more examples of scatter plots produced using this block, see the I/Q Imbalance block reference page.

#### Phase/Frequency Offset Block

You can generate the next scatter plot by replacing the Memoryless Nonlinearity block in the 16-ary QAM Model with the Phase/Frequency Offset block. Set the block's Frequency offset (Hz) parameter to `0` and the Phase offset (deg) parameter to `70`.

The Frequency offset (Hz) parameter adds a constant to the phase of the signal. The scatter plot corresponds to the standard constellation rotated by a fixed angle of 70 degrees.

The Frequency offset (Hz) parameter determines the rate of change of the signal's phase. In this example, Frequency offset (Hz) is set to `0`, so the scatter plot always falls on the grid shown in the preceding figure. If you set Frequency offset (Hz) to a positive number, the points on the scatter plot fall on a rotating grid, corresponding to the standard constellation, which revolves at a constant rate in the counterclockwise direction. For an example, see the Phase/Frequency Offset block reference page.

#### Phase Noise Block

You can generate the next scatter plot by replacing the Memoryless Nonlinearity block in the 16-ary QAM Model with the Phase Noise block. Set the Phase noise level (dBc/Hz) parameter to `-60` and the Frequency offset (Hz) parameter to `100`.

The phase noise adds a random error to the signal's phase, so that the points in the scatter plot are spread in a radial pattern around the constellation points.

### Phase/Frequency Offsets and Phase Noise

The RF Impairments library contains two blocks that simulate phase/frequency offsets and phase noise:

• The Phase/Frequency Offset block applies phase and frequency offsets to a signal.

• The Phase Noise block applies phase noise to a signal.

The Phase/Frequency Offset block and the Phase Noise block alter only the phase and frequency of the signal.

### Receiver Thermal Noise and Free Space Path Loss

The RF Impairments Library contains two blocks that simulate signal impairments due to thermal noise and signal attenuation due to the distance from the transmitter to the receiver:

• The Receiver Thermal Noise block simulates the effects of thermal noise on a complex baseband signal.

• The Free Space Path Loss block simulates the loss of signal power due to the distance from the transmitter and signal frequency.

### Nonlinearity and I/Q Imbalance

The following two blocks model signal impairments due to nonlinear devices or imbalances between the in-phase and quadrature components of a modulated signal:

• The Memoryless Nonlinearity block models the AM-to-AM and AM-to-PM distortion in nonlinear amplifiers.

• The I/Q Imbalance block models imbalances between the in-phase and quadrature components of a signal caused by differences in the physical channels carrying the separate components.

These blocks distort both the phase and amplitude of the signal.

### Apply Nonlinear Distortion to Input Signal

The Memoryless Nonlinearity block applies a nonlinear distortion to the input signal. This distortion models the AM-to-AM and AM-to-PM conversions in nonlinear amplifiers. The block provides several methods, which you specify by the Method parameter, for modeling the nonlinear characteristics of amplifiers:

• Cubic polynomial

• Hyperbolic tangent

• Saleh model

• Ghorbani model

• Rapp model

In the model shown in the preceding figure, the Method parameter is set to `Ghorbani model`. The following figure shows the scatter plot the model generates.

For another example of a scatter plot produced using this block, see the Memoryless Nonlinearity block reference page.

### Simulate RF Impairments to a DQPSK Signal

The model shown in the following figure simulates RF impairments to a signal modulated by differential quaternary phase shift keying (DQPSK).

You can open this model by typing `doc_receiverimpairments_dqpsk` at the MATLAB command line.

#### Overview of the Model

The model does the following:

• Modulates a random signal using DQPSK modulation.

• Applies impairments to the signal using the blocks from the RF Impairments library.

• Forks the signal into two paths, and processes one path with an automatic gain control (AGC) to compensate for the free space path loss and the I/Q imbalance.

• Displays the trajectory of the signal with AGC and the trajectory of the signal without AGC.

• Demodulates both signals and calculates their error rates.

You can see the effect of the automatic gain by comparing the trajectories of the signals with and without AGC, as shown in the following figure.

Signal With (Left) and Without (Right) AGC

The trajectory of the signal with AGC more closely matches the undistorted trajectory for DQPSK, shown in the following figure, than does than the signal without AGC. Consequently, the error rate for the signal with AGC is much lower than the error rate for the signal without AGC.

In this example, the error rate for the demodulated signal without AGC is primarily caused by free space path loss and I/Q imbalance. The QPSK modulation minimizes the effects of the other impairments.

### View Phase Noise Effects on Signal Spectrum

This example shows the effects spectral and phase noise have on a 128 Hz carrier frequency.

1. Type `doc_phasenoise` at the MATLAB command line to open the model.

2. Click Simulation > Run.

The model generates four figure windows. Notice the position of the 128 Hertz signal, and the respective noise floor on the different plots. Take note of the numeric value that the RMS Phase Noise block displays.

3. In the Noisy dBw figure window, click .

4. Move the mouse pointer to the figure window and then click-and-drag to zoom in on the 128 Hz signal.

6. Change the value of the Phase noise level block parameter to `[-40 -100]`

7. Change the value of the Frequency offset block parameter to `[100 400]`

8. Click .

9. Click .

10. Observe how changing the phase noise and frequency offset vectors effects the 128 Hz signal.

As you add noise, the spectrum shape changes. With more noise, 128 Hz signal becomes less distinct, as the side lobes increase in amplitude. Similarly, as you add phase noise, the measured value in the RMS Phase Noise block also increases.

### Selected Bibliography for Channel Modeling

[1] Simon, M. K., and Alouini, M. S., Digital Communication over Fading Channels – A Unified Approach to Performance Analysis, 1st Ed., Wiley, 2000.

[2] 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA), Base Station (BS) radio transmission and reception, Release 10, 3GPP TS 36.104, v10.0.0, 2010-09.

[3] 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA), User Equipment (UE) radio transmission and reception, Release 10, 3GPP TS 36.101, v10.0.0, 2010-10.