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 Mary 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
Plot Noisy 16QAM 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 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 16QAM. 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
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 Mary
number. Use Input
type to specify the input data as
Integer
or
Bit
.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
Output
Out — Output data
scalar  column vector
Rectangular QAMmodulated 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
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
Mary 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 Mary number.To use
Bit
, the input signal must contain binary values, and the number of rows must be an integer multiple of log_{2}(M).
For more information, see IntegerValued Signals and BinaryValued Signals.
Constellation ordering — Mapping order of symbols
Gray
(default)  Binary
 Userdefined
Mapping order of the symbols, specified as Gray
,
Binary
, or
Userdefined
. 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 log_{2}(M) input bits onto a symbol. For bits, the first bit
represents the MSB and the last bit represents the LSB.
M is Mary
number. For more information, see IntegerValued Signals and BinaryValued Signals.
Constellation mapping — Userdefined constellation mapping
[0:15]
(default)  vector
Constellation mapping that you define, specified as an Melement vector containing unique integer values in the range [0, (M – 1)]. M is Mary number.
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.
Dependencies
This parameter appears when you set Constellation ordering to
Userdefined
.
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.
The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click Show data type assistant . For more information, see Specify Data Types Using Data Type Assistant (Simulink).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

^{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 Mary modulation. ^{c} Fixedpoint outputs must be signed. 
Algorithms
IntegerValued Signals and BinaryValued Signals
When you set the Input type parameter to
Integer
, the block accepts integer values in the range [0
, (M1
)]. M is the modulation order as specified by 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 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 inphase and quadrature components of the input:
If Constellation ordering is set to
Binary
, the block uses a 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 Gray coding and symbol mapping, see Digital Baseband Modulation, View Constellation of Modulator Block, and [1]. 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.
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., "OddBit Quadrature AmplitudeShift Keying," IEEE Transactions on Communications, Vol. COM23, March 1975, pp. 385–389.
[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.
This block has one default HDL architecture.
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

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

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

The block does not support
single
ordouble
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 thanboolean
orufix1
.
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
See Also
Blocks
Functions
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