Rectangular QAM Modulator Baseband

Modulate using rectangular quadrature amplitude modulation

Libraries:
Communications Toolbox / Modulation / Digital Baseband Modulation / AM
Communications Toolbox HDL Support / Modulation / AM

Description

The Rectangular QAM Modulator Baseband block modulates the input signal using M-ary quadrature amplitude modulation with a constellation on a rectangular lattice. The output is a baseband representation of the modulated signal.

Note

All values of power assume a nominal impedance of 1 ohm.

Examples

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Plot Noisy 16-QAM Constellation in Simulink

This example uses:

Open Model

The doc_qam_mod model uses the Rectangular QAM Modulator Baseband block to modulate random data and applies noise to the signal by using the AWGN Channel block. After passing the symbols through a noisy channel, the model produces a constellation diagram of the noisy data by using the Constellation Diagram block. When you increase the noise level, the constellation points show increased signal distortion.

A Random Integer Generator block generates integers in the range [0,15] for a modulator configured to apply 16-QAM. The modulated signal passes through an AWGN channel, and a constellation diagram displays the resulting symbols.

Run the model with Eb/N0 set to 20 dB in the AWGN channel.

Change the Eb/No from 20 dB to 10 dB. Observe the increase in the noise.

Ports

Input

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In — Input data
scalar | column vector

Input data, specified as a scalar or column vector. The input data must be binary values or integers in the range [0, (M – 1)], where M is the modulation order as specified by M-ary number. Use Input type to specify the input data as Integer or Bit.

Output

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Out — Output data
scalar | column vector

Rectangular QAM-modulated baseband signal, returned as a scalar or vector. Use the Output data type parameter to specify the output data type.

Data Types: single | double | fixed point

Parameters

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

Main

M-ary number — Modulation order
`16` (default) | positive integer

Modulation order, specified as a positive integer power of two. The modulation order specifies the number of points in the signal constellation. For more information, see Constellation Size and Scaling.

Input type — Input type
`Integer` (default) | `Bit`

Input type, specified as Integer or Bit to indicate whether the input consists of integers or groups of bits.

To use Integer, the input signal must consist of integers in the range [0, (M – 1)]. M is M-ary number.
To use Bit, the input signal must contain binary values, and the number of rows must be an integer multiple of log₂(M).

For more information, see Integer-Valued Signals and Binary-Valued Signals.

Constellation ordering — Mapping order of symbols
`Gray` (default) | `Binary` | `User-defined`

Mapping order of the symbols, specified as Gray, Binary, or User-defined. This parameter determines how the block maps each symbol to constellation points. Based on setting of Input type, the block maps input integers or groups of log₂(M) input bits onto a symbol. For bits, the first bit represents the MSB and the last bit represents the LSB. M is M-ary number. For more information, see Integer-Valued Signals and Binary-Valued Signals.

Constellation mapping — User-defined constellation mapping
`[0:15]` (default) | vector

Constellation mapping that you define, specified as an M-element vector containing unique integer values in the range [0, (M – 1)]. M is M-ary number.

The first element of this vector corresponds to the top-leftmost point of the constellation, with subsequent elements running down column-wise, from left to right. The last element corresponds to the bottom-rightmost point.

Dependencies

This parameter appears when you set Constellation ordering to User-defined.

Normalization method — Scaling method for constellation
`Min. distance between symbols` (default) | `Average Power` | `Peak Power`

Scaling method for constellation, specified as Min. distance between symbols, Average Power, or Peak Power. For more information, see Constellation Size and Scaling

Minimum distance — Distance between two nearest constellation points
`2` (default) | positive scalar

Distance between the two nearest constellation points, specified as a positive scalar.

Dependencies

This parameter appears when you set Normalization method to Min. distance between symbols.

Average power, referenced to 1 ohm (watts) — Average power
`1` (default) | positive scalar

Average power of the symbols in the constellation in watts, specified as a positive scalar. Power values assume a nominal impedance of 1 ohm.

Dependencies

This parameter appears when you set Normalization method to Average Power.

Peak power, referenced to 1 ohm (watts) — Maximum power
`1` (default) | positive scalar

Maximum power of the symbols in the constellation in watts, specified as a positive scalar. Power values assume a nominal impedance of 1 ohm.

Dependencies

This parameter appears when you set Normalization method to Peak Power.

Phase offset (rad) — Rotation of signal constellation
`0` (default) | numeric scalar

Rotation of the signal constellation in radians, specified as a numeric scalar.

View constellation — Option to plot reference constellation
button

Click View Constellation on the block mask to visualize a signal constellation for the specified block parameters. Before viewing a constellation, apply the parameter settings. For more information, see View Constellation of Modulator Block.

Data Types

Output data type — Output data type
`double` (default) | `single` | `fixdt(1,16)` | `fixdt(1,16,0)` | `Inherit: Inherit via back propagation` | `<data type expression>`

Output data type, specified as double, single, fixdt(1,16), fixdt(1,16,0), Inherit: Inherit via back propagation, or <data type expression>.

fixdt(1,16), fixdt(1,16,0), or <data type expression> enables parameters in which you can further specify details.
Inherit: Inherit via back propagation sets the output data type and scaling to match the following block.

For information about specifying data types, see Data Type Assistant.

Block Characteristics

Data Types	`Boolean` \| `double` \| `fixed point^a,^b,^c` \| `integer` \| `single`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`
^a Square QAM only. ^b ufix(1) at the input if ''input type'' is set to ''bit''. ufix(ceil(log2(M))) at input if ''input type'' is set to ''integer'' for M-ary modulation. ^c Fixed-point outputs must be signed.

More About

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Data Type Assistant

The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Algorithms

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Integer-Valued Signals and Binary-Valued Signals

When you set the Input type parameter to Integer, the block accepts integer values in the range [0, (M-1)]. M is the modulation order as specified by the M-ary number block parameter.

When you set the Input type parameter to Bit, the block accepts binary-valued inputs that represent integers. The block collects binary-valued signals into groups of K = log₂(M) bits, where K is the number of bits per symbol and M is the modulation order. The input vector length must be an integer multiple of K. In this configuration, the block accepts a group of K bits and maps that group onto a symbol at the block output. The block outputs one modulated symbol for each group of K bits.

The Constellation ordering parameter indicates how the block assigns binary words to points of the signal constellation. Such assignments apply independently to the in-phase and quadrature components of the input:

If Constellation ordering is set to Binary, the block uses a binary-coded constellation.
If Constellation ordering is set to Gray and K is even, the block uses a Gray-coded constellation.
If Constellation ordering is set to Gray and K is odd, the block codes the constellation so that pairs of nearest points differ in one or two bits. The constellation is cross-shaped, and the schematic below indicates which pairs of points differ in two bits. The schematic uses M = 128 but suggests the general case.

For details about Gray coding and symbol mapping, see Digital Baseband Modulation, View Constellation of Modulator Block, and [1]. Because the in-phase and quadrature components are assigned independently, the Gray and binary orderings coincide when M = 4.

Constellation Size and Scaling

The signal constellation has M points, where M is the M-ary number parameter. M must have the form 2^K for some positive integer K. The block scales the signal constellation based on how you set the Normalization method parameter.

Value of Normalization Method Parameter	Scaling Condition
`Min. distance between symbols`	The nearest pair of points in the constellation is separated by the value of the Minimum distance parameter.
`Average Power`	The average power of the symbols in the constellation is the Average power, referenced to 1 ohm (watts) parameter.
`Peak Power`	The maximum power of the symbols in the constellation is the Peak power, referenced to 1 ohm (watts) parameter.

References

[1] Smith, J. G. "Odd-Bit Quadrature Amplitude-Shift Keying." IEEE^® Transactions on Communications 23, no. 3 (March 1975): 385–89.

[2] Proakis, John G. Digital Communications. 4th ed. New York: McGraw Hill, 2001.

Extended Capabilities

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

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).

Restrictions

The block does not support single or double data types for HDL code generation.
When Input Type is set to Bit, the block does not support HDL code generation for input types other than boolean or ufix1.

When the input type is set to Bit, but the block input is actually multibit (uint16, for example), the Rectangular QAM Modulator Baseband block does not support HDL code generation.

Version History

Introduced before R2006a

Rectangular QAM Modulator Baseband

Description

Examples

Plot Noisy 16-QAM Constellation in Simulink

Ports

Input

In — Input data scalar | column vector

Output

Out — Output data scalar | column vector

Parameters

Main

M-ary number — Modulation order 16 (default) | positive integer

Input type — Input type Integer (default) | Bit

Constellation ordering — Mapping order of symbols Gray (default) | Binary | User-defined

Constellation mapping — User-defined constellation mapping [0:15] (default) | vector

Dependencies

Normalization method — Scaling method for constellation Min. distance between symbols (default) | Average Power | Peak Power

Minimum distance — Distance between two nearest constellation points 2 (default) | positive scalar

Dependencies

Average power, referenced to 1 ohm (watts) — Average power 1 (default) | positive scalar

Dependencies

Peak power, referenced to 1 ohm (watts) — Maximum power 1 (default) | positive scalar

Dependencies

Phase offset (rad) — Rotation of signal constellation 0 (default) | numeric scalar

View constellation — Option to plot reference constellation button

Data Types

Output data type — Output data type double (default) | single | fixdt(1,16) | fixdt(1,16,0) | Inherit: Inherit via back propagation | <data type expression>

Block Characteristics

More About

Data Type Assistant

Algorithms

Integer-Valued Signals and Binary-Valued Signals

Constellation Size and Scaling

References

Extended Capabilities

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

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Version History

See Also

Blocks

Functions

In — Input data
scalar | column vector

Out — Output data
scalar | column vector

M-ary number — Modulation order
`16` (default) | positive integer

Input type — Input type
`Integer` (default) | `Bit`

Constellation ordering — Mapping order of symbols
`Gray` (default) | `Binary` | `User-defined`

Constellation mapping — User-defined constellation mapping
`[0:15]` (default) | vector

Normalization method — Scaling method for constellation
`Min. distance between symbols` (default) | `Average Power` | `Peak Power`

Minimum distance — Distance between two nearest constellation points
`2` (default) | positive scalar

Average power, referenced to 1 ohm (watts) — Average power
`1` (default) | positive scalar

Peak power, referenced to 1 ohm (watts) — Maximum power
`1` (default) | positive scalar

Phase offset (rad) — Rotation of signal constellation
`0` (default) | numeric scalar

View constellation — Option to plot reference constellation
button

Output data type — Output data type
`double` (default) | `single` | `fixdt(1,16)` | `fixdt(1,16,0)` | `Inherit: Inherit via back propagation` | `<data type expression>`

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

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.