Phase/Frequency Offset

Apply phase and frequency offsets to complex baseband signal

Libraries:
Communications Toolbox / RF Impairments Correction
Communications Toolbox / RF Impairments and Components

Description

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

This icon shows the block with all ports enabled. Phase/Frequency Offset block with optional frequency offset input port

Examples

expand all

Apply Phase/Frequency Offset to QAM Modulated Signal

This example uses:

Open Model

The model applies phase and frequency offsets to a 16-ary quadrature amplitude modulation (16-QAM) signal. The Phase/Frequency Offset block applies phase and frequency offsets to the input signal based on parameter settings specified in the Model Parameters block. The effects of updating the offset settings are illustrated by constellation diagrams of a 16-QAM signal.

This constellation diagram shows the 16-QAM constellation with no phase or frequency offset impairing the modulated signal. The constellation diagram shows symbols with no impairments.

Modulation order: 16
Sample time: 1.00e-03
Phase Offset (deg): 0.00
Frequency Offset (Hz): 0.00

A phase offset impairs each point in the constellation, causing a rotation in the counterclockwise direction for a positive phase offset. The constellation shows the signal impaired by these settings.

Phase Offset (deg): 20.00
Frequency Offset (Hz): 0.00

A frequency offset changes the angles of points in the constellation linearly over time, causing points in the constellation to shift radially in the counterclockwise direction for a positive frequency offset. Although the points are radially shifted, their magnitude is unchanged. The constellation shows the signal impaired by these settings.

Phase Offset (deg): 0.00
Frequency Offset (Hz): 0.50

Apply both phase and frequency offset. The constellation shows the signal impaired by these settings.

Phase Offset (deg): 20.00
Frequency Offset (Hz): 0.50

Ports

Input

expand all

In — Complex signal
scalar | vector | matrix

Complex signal, specified as a scalar, vector, or matrix. The port is unnamed until you enable the Frequency offset from port parameter.

Data Types: double | single
Complex Number Support: Yes

Frq — Frequency offset
scalar | vector | matrix

Frequency offset, specified as a scalar, a vector with the same number of rows or columns as the input signal, or a matrix with the same dimensions as the input signal. For more information, see Interdependent Parameter-Port Dimensions.

Dependencies

To enable this port, select the Frequency offset from port parameter.

Data Types: double | single

Output

expand all

Out1 — Output signal
scalar | vector | matrix

Output signal, returned as a scalar, vector, or matrix. This output is the same dimension and data type as the input signal.

Parameters

expand all

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Phase offset (deg) — Phase offset
`0` (default) | scalar | vector | matrix

Phase offset in degrees, specified as a scalar, vector, or matrix.

If Phase offset (deg) and Frequency offset (Hz) are both nonscalar, they must be the same size.

Tunable: Yes

Frequency offset from port — Option to add port to set frequency offset
`off` (default) | on

Select this parameter to add the Frq port.

When you select this parameter, the Frq port specifies the frequency offset.
When you clear this parameter, the Frequency offset (Hz) parameter specifies the frequency offset.

Frequency offset (Hz) — Frequency offset
`0` (default) | scalar | vector | matrix

Frequency offset in hertz, specified as a scalar, a vector with the same number of rows or columns as the input signal, or a matrix with the same dimensions as the input signal. For more information, see Interdependent Parameter-Port Dimensions.

If Phase offset (deg) and Frequency offset (Hz) are both nonscalar, they must be the same size.

Tunable: Yes

Dependencies

To enable this port, clear the Frequency offset from port parameter.

Block Characteristics

Data Types	`double` \| `single`
Multidimensional Signals	`no`
Variable-Size Signals	`no`

More About

expand all

Interdependent Parameter-Port Dimensions

This table outlines the interdependency of parameter-to-port dimensions.

Number of Dimensions	Data I/O Dimension	Frame Size	Number of Channels	Frequency/Phase Offset Parameter Dimension	Frequency Offset Input Port Dimension
Any	Scalar	1	1	Scalar	Scalar
2	M-by-1	M	1	M-by-1 1-by-M 1-by-1	M M-by-1 1 1-by-1
2	1-by-N	1	N	N-by-1 1-by-N 1-by-1	N 1-by-N 1 1-by-1
2	M-by-N	M	N	M-by-N N-by-1 1-by-N M-by-1 1-by-M 1-by-1	M-by-N N 1-by-N 1 1-by-1 M M-by-1

For example:

When you specify a scalar offset parameter, the block applies the same offset to all elements of the input signal
When you specify a 2-by-1 offset parameter for a 2-by-3 input signal (one offset value per sample), the block applies the same sample offset across the three channels.
When you specify a 1-by-3 offset parameter for a 2-by-3 input signal (one offset value per channel), the same channel offset is applied across the two samples of a channel.
When you specify a 2-by-3 offset parameter for a 2-by-3 input signal (one offset value per sample for each channel), the offsets are applied element-wise to the input signal.

Algorithms

If the input signal is u(t), then the output signal is

$y (t) = u (t) \cdot (\cos (2 π \int_{0}^{t} f (τ) d τ + φ (t)) + j \sin (2 π \int_{0}^{t} f (τ) d τ + φ (t))),$

where f(t) is the frequency offset, and φ(t) is the phase offset.

The discrete-time output is given by

$\begin{array}{l} y (0) = u (0) (\cos (φ (0)) + j \sin (φ (0))) and \\ y (i) = u (i) (\cos (2 π \sum_{n = 0}^{i - 1} f (n) Δ t + φ (i)) + j \sin (2 π \sum_{n = 0}^{i - 1} f (n) Δ t + φ (i))), \end{array}$

where i > 0, and Δt is the sample time.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

The Frequency offset (Hz) and Phase offset (deg) parameters are tunable in Normal mode, Accelerator mode, and Rapid Accelerator mode. If you use the Simulink Coder™ rapid simulation (RSIM) target to build an RSIM executable, then you can tune these parameters without recompiling the model. For more information, see Tunable Parameters (Simulink).

Version History

Introduced before R2006a

Phase/Frequency Offset

Description

Examples

Apply Phase/Frequency Offset to QAM Modulated Signal

Ports

Input

In — Complex signal
scalar | vector | matrix

Frq — Frequency offset
scalar | vector | matrix

Dependencies

Output

Out1 — Output signal
scalar | vector | matrix

Parameters

Phase offset (deg) — Phase offset
`0` (default) | scalar | vector | matrix

Frequency offset from port — Option to add port to set frequency offset
`off` (default) | on

Frequency offset (Hz) — Frequency offset
`0` (default) | scalar | vector | matrix

Dependencies

Block Characteristics

More About

Interdependent Parameter-Port Dimensions

Algorithms

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Phase/Frequency Offset

Description

Examples

Apply Phase/Frequency Offset to QAM Modulated Signal

Ports

Input

In — Complex signal scalar | vector | matrix

Frq — Frequency offset scalar | vector | matrix

Dependencies

Output

Out1 — Output signal scalar | vector | matrix

Parameters

Phase offset (deg) — Phase offset 0 (default) | scalar | vector | matrix

Frequency offset from port — Option to add port to set frequency offset off (default) | on

Frequency offset (Hz) — Frequency offset 0 (default) | scalar | vector | matrix

Dependencies

Block Characteristics

More About

Interdependent Parameter-Port Dimensions

Algorithms

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

In — Complex signal
scalar | vector | matrix

Frq — Frequency offset
scalar | vector | matrix

Out1 — Output signal
scalar | vector | matrix

Phase offset (deg) — Phase offset
`0` (default) | scalar | vector | matrix

Frequency offset from port — Option to add port to set frequency offset
`off` (default) | on

Frequency offset (Hz) — Frequency offset
`0` (default) | scalar | vector | matrix

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.