Rectangular QAM Modulator Baseband

Modulate using rectangular quadrature amplitude modulation

Library

AM, in Digital Baseband sublibrary of Modulation

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Description

The Rectangular QAM Modulator Baseband block modulates using M-ary quadrature amplitude modulation with a constellation on a rectangular lattice. The output is a baseband representation of the modulated signal. This block accepts a scalar or column vector input signal. For information about the data types each block port supports, see Supported Data Types.

Note

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

Integer-Valued Signals and Binary-Valued Signals

When you set the Input type parameter to Integer, the block accepts integer values between 0 and M-1. M represents 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 represents the number of bits per symbol.

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 natural 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 the Gray coding, see the reference page for the M-PSK Modulator Baseband block and the paper listed in References. 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. The following table lists the possible scaling conditions.

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 parameter
Peak Power	The maximum power of the symbols in the constellation is the Peak power parameter

Parameters

M-ary number

The number of points in the signal constellation. It must have the form 2^K for some positive integer K.

Input type

Indicates whether the input consists of integers or groups of bits.

Constellation ordering

Determines how the block maps each symbol to a group of output bits or integer.

Selecting User-defined displays the field Constellation mapping, which allows for user-specified mapping.

Constellation mapping

This parameter is a row or column vector of size M and must have unique integer values in the range [0, M-1]. The values must be of data type double.

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.

This field appears when User-defined is selected in the drop-down list Constellation ordering.

Normalization method

Determines how the block scales the signal constellation. Choices are Min. distance between symbols, Average Power, and Peak Power.

Minimum distance

The distance between two nearest constellation points. This field appears only when Normalization method is set to Min. distance between symbols.

Average power, referenced to 1 ohm (watts)

The average power of the symbols in the constellation, referenced to 1 ohm. This field appears only when Normalization method is set to Average Power.

Peak power, referenced to 1 ohm (watts)

The maximum power of the symbols in the constellation, referenced to 1 ohm. This field appears only when Normalization method is set to Peak Power.

Phase offset (rad)

The rotation of the signal constellation, in radians.

Output data type

The output data type can be set to double, single, Fixed-point, User-defined, or Inherit via back propagation.

Setting this parameter to Fixed-point or User-defined enables fields in which you can further specify details. Setting this parameter to Inherit via back propagation, sets the output data type and scaling to match the following block.

Output word length

Specify the word length, in bits, of the fixed-point output data type. This parameter is only visible when you select Fixed-point for the Output data type parameter.

User-defined data type

Specify any signed built-in or signed fixed-point data type. You can specify fixed-point data types using the fixdt (Simulink) function. This parameter is only visible when you select User-defined for the Output data type parameter.

Set output fraction length to

Specify the scaling of the fixed-point output by either of the following methods:

• Choose Best precision to have the output scaling automatically set such that the output signal has the best possible precision.

• Choose User-defined to specify the output scaling in the Output fraction length parameter.

This parameter is only visible when you select Fixed-point for the Output data type parameter or when you select User-defined and the specified output data type is a fixed-point data type.

Output fraction length

For fixed-point output data types, specify the number of fractional bits, or bits to the right of the binary point. This parameter is only visible when you select Fixed-point or User-defined for the Output data type parameter and User-defined for the Set output fraction length to parameter.

Examples

Plot Noisy 16-QAM Constellation in Simulink

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. When the noise level is increased, 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.

Supported Data Types

Port	Supported Data Types
Input	Double-precision floating point Single-precision floating point Boolean when Input type is Bit 8-, 16-, 32-bit signed integers 8-, 16-, 32-bit unsigned integers $$ufix\left({\log }_{2}M\right)$$ when Input type is Integer
Output	Double-precision floating point Single-precision floating point Signed fixed-point

Pair Block

Rectangular QAM Demodulator Baseband

References

[1] Smith, Joel G., “Odd-Bit Quadrature Amplitude-Shift Keying,” IEEE Transactions on Communications, Vol. COM-23, March 1975, 385–389.

More About

Constellation Visualization

Click View Constellation on the block mask to visualize a signal constellation for the specified block parameters. Parameter settings must be applied before viewing a constellation. For more information, see View Constellation of Modulator Block.

Extended Capabilities

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

HDL Code Generation

Generate Verilog and VHDL 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