OFDM Demodulator

Demodulate time-domain OFDM samples and return subcarriers for custom communication protocols

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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.

• Open Script

Modulate and Demodulate OFDM Streaming Samples

Modulate and demodulate OFDM streaming samples.

• Open Script

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.

• N_h = ceil((N_r + FFTLen + CPLen)/vecLen)

• N_l = ceil((N_r + Maximum FFT length + CPLen)/vecLen) – N_h

In these equations,

• N_h is the number of high ready clock cycles

• N_l is the number of low ready clock cycles

• N_r is the number of remaining samples from the previous OFDM symbol. Initially, this value is 0. In the subsequent operations, the block calculates N_r using the equation, (N_r + FFTLen + CPLen) - (floor((N_r + 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, N_r, and removes those samples from the input samples. In this case, N_r = CP fraction x CP length.

Next, the block calculates the number of samples to shift, N_s, and shifts those samples to the end of OFDM symbol in the time domain. Where, N_s = CP length – (CP fraction x CP length).

These two segments together make up the total cyclic prefix length, N_cp = N_s + N_r. 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 N_r = floor (N_cp 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

$$X(k)=F[x(n)]={\displaystyle \sum _{n=0}^{N-1}x(n)e^{-\frac{j2\pi nk}{N}}}$$

For an FFT shift of N/2 carriers in either direction, substitute $$k=k-\frac{N}{2}$$, resulting in

$$X(k-\frac{N}{2})={\displaystyle \sum _{n=0}^{N-1}x(n)e^{-\frac{j2\pi n(k-\frac{N}{2})}{N}}}$$

This equation simplifies to

$$X(k-\frac{N}{2})={\displaystyle \sum _{n=0}^{N-1}{e}^{j\pi n}x(n)e^{-\frac{j2\pi nk}{N}}}$$

Since $${\displaystyle \sum _{n=0}^{N-1}x(n)e^{-\frac{j2\pi nk}{N}}}$$ is equivalent to $$F[x(n)]$$, and $$e^{j\pi }=-1$$, this equation simplifies to

$$X(k-\frac{N}{2})=F[{{\displaystyle (-1)}}^{n}x(n)]$$

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.

Scalar Input

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).

Vector Input

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 R2019b

R2023a: 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.