OFDM Demodulator
Demodulate time-domain OFDM samples and return subcarriers for custom communication protocols
Libraries:
Wireless HDL Toolbox /
Modulation
Description
The OFDM Demodulator block demodulates time-domain orthogonal frequency division multiplexing (OFDM) samples and outputs subcarriers based on the OFDM parameters. The block supports 5G new radio (NR) standard, long term evolution (LTE) [1], wireless local area network (WLAN 802.11a/g/n/ac) [2], WiMAX, digital video broadcast (DVB), and digital audio broadcast (DAB) standards.
The block accepts input data along with a valid control signal and these OFDM parameters:
FFT length, CP length, and the number of right and left guard subcarriers. The block outputs
demodulated data along with valid and ready controls signals. The block enables the ready output port only when these OFDM parameters are provided to the
block through input ports. The block samples the corresponding OFDM parameters only when the
ready port is 1
(high) and the first
valid port of each OFDM symbol is 1
(high).
The block supports scalar and vector inputs. You can use a vector input to increase the data throughput and achieve a giga-sample-per-second (GSPS) throughput. The block provides an interface and architecture suitable for HDL code generation and hardware deployment.
Examples
OFDM Demodulation of Streaming Samples
Demodulate complex time-domain OFDM samples to subcarriers.
Modulate and Demodulate OFDM Streaming Samples
Modulate and demodulate OFDM streaming samples.
Ports
Input
data — Input data
scalar | column vector
Input data, specified as a scalar or column vector of real or complex values. The vector size must be a power of 2, in the range from 1 to 64, and less than or equal to the FFT length.
The software supports double
and
single
data types for simulation, but not for HDL code generation.
Data Types: single
| double
| int8
| int16
| int32
| signed fixed point
Complex Number Support: Yes
valid — Indicates valid input data
scalar
Indicates valid input data, specified as a scalar.
This port is a control signal that indicates when the sample from the
data input port is valid. When this value is
1
, the block captures the values on the data
input port. When this value is 0
, the block ignores the values on
the data input port.
Data Types: Boolean
FFTLen — Length of FFT
scalar
Length of the FFT, specified as a scalar. The FFT length must be power of 2 and in the range from 8 to 65,536. This value must be less than or equal to the Maximum FFT length parameter value.
To support the minimum FFT length of 8, the FFTLen data type
must be fixdt(0,k,0)
, where k is greater than or
equal to 4.
Dependencies
To enable this port, set the OFDM parameters source
parameter to Input port
.
Data Types: single
| double
| uint8
| uint16
| uint32
| unsigned fixed point
CPLen — Length of cyclic prefix
scalar
Length of the cyclic prefix, specified as a scalar in the range from 0 to FFTLen.
To support the minimum FFT length of 8, the CPLen data type
must be fixdt(0,k,0)
, where k is greater than or
equal to 4.
Dependencies
To enable this port, set the OFDM parameters source
parameter to Input port
.
Data Types: single
| double
| uint8
| uint16
| uint32
| unsigned fixed point
numLgSc — Number of left guard carriers of OFDM symbol
scalar
Number of left guard carriers of OFDM symbol, specified as a scalar in the range from 0 to (FFTLen/2) – 1.
To support the minimum FFT length of 8, the numLgSc data type
must be fixdt(0,k,0)
, where k is greater than or
equal to 2.
Dependencies
To enable this port, set the OFDM parameters source
parameter to Input port
.
Data Types: single
| double
| uint8
| uint16
| uint32
| unsigned fixed point
numRgSc — Number of right guard carriers of OFDM symbol
scalar
Number of right guard carriers of OFDM symbol, specified as a scalar in the range from 0 to (FFTLen/2) – 1.
To support the minimum FFT length of 8, the numRgSc data type
must be fixdt(0,k,0)
, where k is greater than or
equal to 2.
Dependencies
To enable this port, set the OFDM parameters source
parameter to Input port
.
Data Types: single
| double
| uint8
| uint16
| uint32
| unsigned fixed point
CPFraction — CP Fraction
real positive scalar
CP Fraction, specified as a real positive scalar in the range [0, 1].
To support maximum precision, the CPFraction data type must
be fixdt(0,k,p)
, where k is less than or equal
to 16 and p is equal to k - 1.
Dependencies
To enable this port, select the Enable CP fraction
parameter and set the CP fraction source parameter to
Input port
.
Data Types: single
| double
| unsigned fixed point
reset — Clear internal states
scalar
Clear internal states, specified as a scalar. When this value is
1
(true), the block stops the current calculation and clears all
internal states.
Dependencies
To enable this port, select the Enable reset input port parameter.
Data Types: Boolean
Output
data — Demodulated output data
scalar | column vector
Demodulated output data, returned as a complex-valued scalar or column vector. Output data type is dependent on the data type of the input data port.
When you set the OFDM parameters source parameter to
Property
and clear the Divide butterfly outputs by two parameter, the output word length increases by log2(FFT length) bits.When you set the OFDM parameters source parameter to
Input port
and clear the Divide butterfly outputs by two parameter, the output word length increases by log2(Maximum FFT length) bits.
To avoid overflow, select the Divide butterfly outputs by two parameter.
Data Types: single
| double
| int8
| int16
| int32
| signed fixed point
Complex Number Support: Yes
valid — Indicates valid output data
scalar
Indicates valid input data, returned as a scalar.
This port is a control signal that indicates when the data
output port is valid. The block sets this value to 1
when the data
samples are available on the data output port. When you select
the Remove DC subcarrier parameter, this value is set to
0
at the center of the output samples to exclude the DC
carrier.
Data Types: Boolean
ready — Indicates block is ready
scalar
Control signal that indicates when the block is ready for new input data. When
this value is 1
, the block accepts input data in the next time
step. When this value is 0
, the block ignores input data in the
next time step.
Dependencies
To enable this port, set the OFDM parameters source
parameter to Input port
.
Data Types: Boolean
Parameters
Main
OFDM parameters source — Source of OFDM parameters
Property
(default) | Input port
You can set OFDM parameters with an input port or by selecting a value for the parameter.
Select Property
to enable the FFT
length, Cyclic prefix length, Number of
left guard subcarriers, and Number of right guard
subcarriers parameters.
Select Input port
to enable the
FFTLen, CPLen,
numLgSc, numRgSc input ports and the
Maximum FFT length parameter. The Maximum
FFT length parameter sets the upper bound of the range of valid values
for the FFTLen input port.
Maximum FFT length — Maximum length of FFT length
64
(default) | power of 2 in range from 8 to 65,536
Specify the maximum length of the FFT.
Dependencies
To enable this parameter, set the OFDM parameters source
parameter to Input port
.
FFT length — Length of FFT
64
(default) | power of 2 in range from 8 to 65,536
Specify the FFT length. When you set the OFDM parameters
source parameter to Property
, the block uses
this FFT length value as the maximum FFT length.
Dependencies
To enable this parameter, set the OFDM parameters source
parameter to Property
.
Cyclic prefix length — Length of cyclic prefix
16
(default) | integer in range from 0 to FFT length
Specify the length of the cyclic prefix.
Dependencies
To enable this parameter, set the OFDM parameters source
parameter to Property
.
Number of left guard subcarriers — Number of guard band subcarriers in left extreme of OFDM symbol
6
(default) | integer in range from 0 to (FFT length/2) – 1
Specify the number of left guard subcarriers.
Dependencies
To enable this parameter, set the OFDM parameters source
parameter to Property
.
Number of right guard subcarriers — Number of guard band subcarriers in right extreme of OFDM symbol
5
(default) | integer in range from 0 to (FFT length/2) – 1
Specify the number of right guard subcarriers.
Dependencies
To enable this parameter, set the OFDM parameters source
parameter to Property
.
Enable CP fraction — CP fraction enabler
off
(default) | on
Select this parameter to enable the CP fraction either through
Property
or through Input
port
.
CP fraction source — CP fraction source type
Property
(default) | Input port
You can set CP fraction with an input port or by selecting a value for the parameter.
Select Property
to enable the CP
fraction parameter.
Select Input port
to enable the
CPFraction input port.
Dependencies
To enable this parameter, select the Enable CP fraction parameter.
CP fraction — Percent of cyclic prefix to remove
0.55
(default) | range from 0 to 1
Cyclic prefix fraction, specified as a value from 0 to 1, inclusive. This parameter specifies the percentage of CP samples that the block removes from the start of the OFDM symbol. The block shifts the remaining CP samples to the end of the OFDM symbol.
When this parameter is 0.55
, the block removes 55% of the CP
from the beginning of the symbol, and shifts 45% to the end of the symbol. When you
set this parameter to 1
, the block removes 100% of the CP from the
start of the OFDM symbol, and does not shift any samples to the end.
Dependencies
To enable this parameter, select the Enable CP fraction
parameter and the set the CP fraction source parameter to
Property
.
Remove DC subcarrier — Exclude or include DC subcarrier
on
(default) | off
When you select this parameter, the block excludes the DC subcarrier in the output
by setting the output valid signal to 0
for the center of the
output subcarriers.
Enable reset input port — Reset signal
off
(default) | on
Select this parameter to enable the reset input port.
FFT Parameters
Divide butterfly outputs by two — Divide FFT butterfly outputs by two
off
(default) | on
This parameter controls the scaling option of the FFT block inside the OFDM Demodulator block.
When you select this parameter, the FFT implements an overall 1/N scale factor by dividing the output of each butterfly multiplication by two. This adjustment keeps the output of the FFT in the same amplitude range as its input. If you clear this parameter, the block avoids overflow by increasing the word length by one bit after each butterfly multiplication.
Rounding Method — Rounding mode for internal fixed-point calculations
Floor
(default) | Ceiling
| Convergent
| Nearest
| Round
| Zero
This parameter specifies the type of rounding mode for internal fixed-point
calculations. For more information about rounding modes, see Rounding Modes. When the input is any integer data
type or fixed-point data type, the FFT algorithm uses fixed-point arithmetic for
internal calculations. This parameter does not apply when the input is of data type
single
or double
. Rounding applies to
twiddle-factor multiplication and scaling operations.
Algorithms
The OFDM Demodulator block operation sequence is implemented using these blocks: Ready Generator, Cyclic Prefix Remover, Sample Repeater, FFT Shifter, FFT, Down Sampler, and Subcarrier Selector. The parameters shown in this figure configure the behavior of the block.
Ready Generator
This block enables a ready port when you set the
OFDM parameters source parameter to Input
port
. This ready port controls the input
samples based on the maximum FFT length.
The following equations apply.
Nh =
ceil
((Nr + FFTLen + CPLen)/vecLen)Nl =
ceil
((Nr + Maximum FFT length + CPLen)/vecLen) – Nh
In these equations,
Nh is the number of high ready clock cycles
Nl is the number of low ready clock cycles
Nr is the number of remaining samples from the previous OFDM symbol. Initially, this value is
0
. In the subsequent operations, the block calculates Nr using the equation, (Nr + FFTLen + CPLen) - (floor
((Nr + FFTLen + CPLen) / vecLen) x vecLen)vecLen is the length of the vector
Cyclic Prefix Remover
This block removes CP samples from an OFDM symbol for extracting constellation symbols. The block performs CP removal based on these parameters: CP length, CP fraction (when enabled), and the FFT length.
This block supports windowed transmission by implementing fractional cyclic prefix removal. Windowing reduces out-of-band emissions. A transmitter performs windowing by overlapping the tail of each OFDM symbol with the head of the next OFDM symbol. A receiver must avoid these overlapped samples in the FFT calculation. Fractional CP solves this problem by removing part of the CP at the start of a symbol and the remainder of the CP at the end of the symbol. Implementing a CP-fraction algorithm also makes this block less sensitive to timing offset.
The block handles the CP in two stages. First, the block calculates the number of CP samples to remove, Nr, and removes those samples from the input samples. In this case, Nr = CP fraction x CP length.
Next, the block calculates the number of samples to shift, Ns, and shifts those samples to the end of OFDM symbol in the time domain. Where, Ns = CP length – (CP fraction x CP length).
These two segments together make up the total cyclic prefix length,
Ncp =
Ns +
Nr. The CP fraction
parameter controls how many samples the block removes at the beginning of the symbol. The
block shifts the remainder of the cyclic prefix from the start of the symbol to the end of
the symbol. The block quantizes the CP fraction parameter as
fi(0,11,10)
. To achieve an integer number of samples, the block
calculates Nr = floor
(Ncp x CP fraction).
For example, if the FFT length is 128 and CP length is 10, the block receives 128 samples plus the cyclic prefix size.
Sample Repeater
This block repeats FFT-length number of samples until it forms the maximum FFT length.
For this operation, the block buffers the input samples first and then repeats the samples
based on the maximum FFT length value. This repetition mechanism helps to avoid scaling at
the FFT block input. This block is optional and available only when you set the
OFDM parameters source parameter to Input
port
. When you set the OFDM parameters source parameter
to Property
, the FFT length value provided in the block mask is
set as the maximum FFT length. The block does not need to repeat the samples in this
context.
For example, if the FFT length is 128 and the maximum FFT length is 2048, each OFDM symbol consists of 128 samples. The block converts these 128 samples to 2048 samples by repeating the 128 samples 16 times. After the block generates 2048 data samples, it sends data and valid input signals to the next block.
Time-Domain FFT Shifter
Conventionally, receivers perform the FFT shift in the frequency domain. However, this method requires memory and introduces latency related to the size of the FFT. Instead, a receiver can execute the same operation in the time domain by using the frequency shifting property of Fourier transforms. Shifting a function in one domain corresponds to a multiplication by a complex exponential function in the other domain. To reduce hardware resources and latency, this block performs the FFT shift by multiplying the time-domain samples by a complex exponential function.
These equations describe an FFT shift. The equation for an N-point FFT is
For an FFT shift of N/2 carriers in either direction, substitute , resulting in
This equation simplifies to
Since is equivalent to , and , this equation simplifies to
The final equation shows that an FFT shift in the time domain simplifies to multiplication by (–1)n. As a result, the block implements the FFT shift by multiplying the time-domain samples by either +1 or –1.
FFT
This block converts a time-domain signal to a frequency-domain signal based on the maximum FFT length provided for the block. You can provide the FFT length value either through a parameter or through an input port. The output of the FFT shift subsystem is fed to an FFT block. The block calculates the maximum FFT for all the FFT length and CP length values.
The Divide butterfly outputs by two parameter sets whether the FFT implements an overall 1/N scale factor by dividing the output of each butterfly multiplication by two. This adjustment keeps the output of the FFT in the same amplitude range as its input. When you clear the Divide butterfly outputs by two parameter, the block avoids overflow by increasing the word length by one bit after each butterfly multiplication.
Down Sampler
This block down samples maximum-FFT-length number of samples to FFT-length number of
samples. This block is optional and available only when you set the OFDM
parameters source parameter to Input port
. When you
set the OFDM parameters source parameter to
Property
, the FFT length value provided in the block mask sets
the maximum FFT length. The block does not need to downsample the samples in this
context.
For example, if the FFT length is 128 and the maximum FFT length is 2048, the input is 2048 samples and must be downsampled with respective to the FFT length of 128. In this case, the block samples 1 sample for every 16 samples.
Subcarrier Selector
The output subcarriers are categorized into data, DC, and guard subcarriers. Data subcarriers contains useful data. This block selects subcarriers by removing the number of left guard subcarriers and right guard subcarriers provided for the block. The number of guard subcarriers to set varies with standards.
If you select the Remove DC subcarrier parameter, the block
excludes the DC subcarrier from output. The block excludes the DC subcarrier by setting the
valid port to 0
(false) for the center cycle of
the output subcarriers.
Latency
The block captures output data at valid cycles based on the type of input: scalar or vector.
This figure shows a sample output and latency of the OFDM Demodulator
block when you specify a scalar input, set the OFDM parameters source
parameter to Property
and use default settings for the other
block parameters. In this example, the FFTLen parameter is set to
64
, Cyclic prefix length parameter is set to
16
, Number of left guard subcarriers parameter
is set to 6
, and Number of right guard subcarriers
parameter is set to 5
.
In this example, the latency of the block is calculated using this formula: Cyclic prefix length + FFTLatency + Number of left guard subcarriers + 12, where FFTLatency is the latency of FFT block for the specified FFT length, and 12 is the number of pipeline delays.
After calculation, the latency of the block is 207 clock cycles, as shown in the following figure.
This figure shows a sample output and latency of the block when you specify a scalar
input and set the OFDM parameters source parameter to
Input port
. In this example, the FFTLen
port is set to 64
, CPLen port is set to
16
, numLgSc port is set to 6
and numRgSc port is set to 5
, and
Maximum FFT length parameter is set to
128
.
The latency of the block is calculated using the formula CPLen + FFTLen + FFTLatency + numLgSc x (Maximum FFT length/FFTLen) + 25, where FFTLatency is the latency of FFT block for the specified maximum FFT length, and 25 is the number of pipeline delays.
After calculation, the latency of the block is 424 clock cycles, as shown in this figure.
The block accepts input only when the ready is
1
(high). In this case, the block captures parameters on the first
cycle when the input valid port is 1
(high).
This figure shows a sample output and latency of the OFDM Demodulator
block when you specify a two-element column vector input and set the OFDM
parameters source parameter to Property
and use
default settings for the other block parameters. FFTLen is set to
64
, Cyclic prefix length is set to
16
, and Number of left guard subcarriers and
Number of right guard subcarriers are set to 6
and 5
, respectively.
In this example, the latency of the block is calculated using this formula:
floor
(Cyclic prefix
length/vecLen) + vecFFTLatency +
floor
(Number of left guard
subcarriers/vecLen) + 12, where
vecFFTLatency is the latency of FFT block for the
specified FFT length and vector length, vecLen is the length of the
vector, and 12 is the number of pipeline delays.
This calculation shows that the latency of the block is 142 clock cycles, as shown in this figure.
This figure shows a sample output and latency of the block when you specify a
two-element column vector input and set the OFDM parameters source
parameter to Input port
. For this example,
FFTLen is set to 64
, CPLen
is set to 16
, numLgSc is set to
6
, numRgSc is set to 5
, and
Maximum FFT length is set to 128
.
In this example, the latency of the block is calculated using this formula:
floor
(CPLen/vecLen) +
FFTLen/vecLen + vecFFTLatency
+ floor
(numLgSc/vecLen) x
(Maximum FFT length/FFTLen) + 26, where
vecFFTLatency is the latency of FFT block for the
specified maximum FFT length and vector length, vecLen is the length of
the vector, and 26 is the number of pipeline delays.
After calculation, the latency of the block is 266 clock cycles, as shown in this figure.
The block accepts input only when the ready is
1
(high). In this case, the block captures parameters on the first
cycle when the input valid port is 1
(high).
Performance
The performance of the synthesized HDL code varies with your target and synthesis
options. The input data type used in this example for generating HDL code is
fixdt(1,16,14)
.
This table shows the resource and performance data synthesis results when using the block with a scalar or two-element column vector input for default configuration values. The generated HDL is targeted to the AMD® Zynq®- 7000 ZC706 evaluation board.
Input Data | Slice LUTs | Slice Registers | DSPs | Block RAM | Maximum Frequency in MHz |
---|---|---|---|---|---|
Scalar | 2434 | 4161 | 8 | 1 | 340 |
Vector | 4890 | 7764 | 16 | 0 | 235 |
References
[1] 3GPP TS 36.211 version 14.2.0 Release 14. "Physical channels and modulation." LTE - Evolved Universal Terrestrial Radio Access (E-UTRA).
[2] "Wireless LAN Medium Access Control (MAC) and Physical layer (PHY) Specifications." IEEE Std 802.11 – 2012.
[3] Stefania Sesia, Issam Toufik, and Matthew baker. LTE - THE UMTS Long Term Evolution from theory to practice.
[4] Erik Dahlman, Stefan Parkvall, and Johan Skold. 4G - LTE/LTE - Advanced for Mobile broadband Second edition.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
This block supports C/C++ code generation for Simulink® accelerator and rapid accelerator modes and for DPI component generation.
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 does not have any HDL Block Properties.
Version History
Introduced in R2019bR2023a: CP fraction as input port
You can now specify the CP fraction through port. To enable this port, select the
Enable CP fraction parameter and set the CP fraction
source parameter to Input port
.
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