Modulate using rectangular quadrature amplitude modulation
AM, in Digital Baseband sublibrary of Modulation
The Rectangular QAM Modulator Baseband block modulates using Mary 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. 
When you set the Input type parameter to Integer
,
the block accepts integer values between 0
and M1
. M represents
the Mary number block parameter.
When you set the Input type parameter to Bit
,
the block accepts binaryvalued inputs that represent integers. The
block collects binaryvalued signals into groups of K =
log_{2}(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 inphase and quadrature components of the input:
If Constellation ordering is
set to Binary
, the block uses a natural
binarycoded constellation.
If Constellation ordering is
set to Gray
and K is even, the block uses
a Graycoded 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 crossshaped, 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 MPSK Modulator Baseband block and the paper listed in References. Because the inphase and quadrature components are assigned independently, the Gray and binary orderings coincide when M = 4.
The signal constellation has M points, where M is the Mary 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 
The Rectangular QAM Modulator Baseband block provides the capability to visualize a signal constellation from the block mask. This Constellation Visualization feature allows you to visualize a signal constellation for specific block parameters. For more information, see the Constellation Visualization section of the Communications System Toolbox™ User's Guide.
The number of points in the signal constellation. It must have the form 2^{K} for some positive integer K.
Indicates whether the input consists of integers or groups of bits.
Determines how the block maps each symbol to a group of output bits or integer.
Selecting Userdefined
displays the field Constellation
mapping, which allows for userspecified mapping.
This parameter is a row or column vector of size M and must
have unique integer values in the range [0, M1]. The values must
be of data type double
.
The first element of this vector corresponds to the topleftmost point of the constellation, with subsequent elements running down columnwise, from left to right. The last element corresponds to the bottomrightmost point.
This field appears when Userdefined
is selected
in the dropdown list Constellation ordering.
Determines how the block scales the signal constellation. Choices
are Min. distance between symbols
, Average
Power
, and Peak Power
.
The distance between two nearest constellation points. This
field appears only when Normalization method is
set to Min. distance between symbols
.
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
.
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
.
The rotation of the signal constellation, in radians.
The output data type can be set to double
, single
, Fixedpoint
, Userdefined
,
or Inherit via back propagation
.
Setting this parameter to Fixedpoint
or Userdefined
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.
Specify the word length, in bits, of the fixedpoint output
data type. This parameter is only visible when you select Fixedpoint
for
the Output data type parameter.
Specify any signed builtin or signed fixedpoint data type.
You can specify fixedpoint data types using the sfix
, sint
, sfrac
, and fixdt
functions
from FixedPoint Designer™ software. This parameter is only visible
when you select Userdefined
for the Output
data type parameter.
Specify the scaling of the fixedpoint 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 Userdefined
to
specify the output scaling in the Output fraction length parameter.
This parameter is only visible when you select Fixedpoint
for
the Output data type parameter or when you select Userdefined
and
the specified output data type is a fixedpoint data type.
For fixedpoint 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 Fixedpoint
or Userdefined
for
the Output data type parameter and Userdefined
for
the Set output fraction length to parameter.
Port  Supported Data Types 

Input 

Output 

This block supports HDL code generation using HDL Coder™. HDL Coder provides additional configuration options that affect HDL implementation and synthesized logic. For more information on implementations, properties, and restrictions for HDL code generation, see Rectangular QAM Modulator Baseband in the HDL Coder documentation.
[1] Smith, Joel G., "OddBit Quadrature AmplitudeShift Keying," IEEE Transactions on Communications, Vol. COM23, March 1975, 385–389.