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 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
(Simulink), sint
(Simulink), sfrac
(Simulink), and fixdt
(Simulink) 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 

[1] Smith, Joel G., “OddBit Quadrature AmplitudeShift Keying,” IEEE Transactions on Communications, Vol. COM23, March 1975, 385–389.