Rectangular QAM Modulator Baseband
Modulate using rectangular quadrature amplitude modulation
Library
AM, in Digital Baseband sublibrary of Modulation
Description
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.
IntegerValued Signals and BinaryValued Signals
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.
Constellation Size and Scaling
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 
Parameters
 Mary 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
Userdefined
displays the field Constellation mapping, which allows for userspecified mapping. Constellation 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. Normalization method
Determines how the block scales the signal constellation. Choices are
Min. distance between symbols
,Average Power
, andPeak 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
,Fixedpoint
,Userdefined
, orInherit via back propagation
.Setting this parameter to
Fixedpoint
orUserdefined
enables fields in which you can further specify details. Setting this parameter toInherit 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 fixedpoint output data type. This parameter is only visible when you select
Fixedpoint
for the Output data type parameter. Userdefined data type
Specify any signed builtin or signed fixedpoint data type. You can specify fixedpoint data types using the
fixdt
(Simulink) function. This parameter is only visible when you selectUserdefined
for the Output data type parameter. Set output fraction length to
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 selectUserdefined
and the specified output data type is a fixedpoint data type. Output fraction length
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
orUserdefined
for the Output data type parameter andUserdefined
for the Set output fraction length to parameter.
Examples
Supported Data Types
Port  Supported Data Types 

Input 

Output 

Pair Block
References
[1] Smith, Joel G., “OddBit Quadrature AmplitudeShift Keying,” IEEE Transactions on Communications, Vol. COM23, March 1975, 385–389.
More About
Extended Capabilities
Version History
Introduced before R2006a