FFT 1536

Computes fast-fourier-transform (FFT) for LTE standard transmission bandwidth of 15 MHz

Library:
Wireless HDL Toolbox / Modulation

Description

The FFT 1536 block is designed to support LTE standard transmission bandwidth of 15 MHz. This block is used in LTE OFDM Demodulator block operation. The block accepts input data, along with a valid control signal and outputs streaming data with a samplecontrol bus.

The block provides an architecture suitable for HDL code generation and hardware deployment.

Ports

Input

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`data` — Input data
scalar of real or complex values

Input data, specified as a scalar of real or complex values.

double and single input data are allowed for simulation but not for HDL code generation.

The more the fractional bits you provide in the input word length, the better the accuracy you receive in the output.

Data Types: double | single | int8 | int16 | int32 | fixed point
Complex Number Support: Yes

`valid` — Indicates valid input data
`Boolean` scalar

Indicates if the input data is valid. When the input valid is 1 (true), the block captures the value on the input data port. When the input valid is 0 (false), the block ignores the input data samples.

Data Types: Boolean

`reset` — Reset control signal
`Boolean` 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

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`data` — Frequency channel output data
scalar of real or complex values

Frequency channel output data, returned as a scalar of real or complex values.

When the input is of fixed point data type, the output data type is the same as the input data type. When the input is of integer type, the output data type is of fixed point type.

Data Types: double | single | int8 | int16 | int32 | fixed point
Complex Number Support: Yes

`ctrl` — Control signals accompanying sample stream
`samplecontrol` bus

Control signals accompanying the sample stream, returned as a samplecontrol bus. The bus includes the start, end, and valid control signals, which indicate the boundaries of the frame and the validity of the samples.

start — Indicates the start of the output frame
end — Indicates the end of the output frame
valid — Indicates that the data on the output data port is valid

Data Types: bus

Parameters

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Main

`Complex multiplication` — HDL implementation
`Use 3 multipliers and 5 adders` (default) | `Use 4 multipliers and 2 adders`

Specifies the complex multiplier type for HDL implementation. Each multiplication is implemented either with Use 3 multipliers and 5 adders or with Use 4 multipliers and 2 adders. The implementation speed depends on the synthesis tool and the target device that you use.

`Rounding method` — Rounding mode for internal fixed-point calculations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Zero`

Specifies the type of rounding method for internal fixed-point calculations. For more information about rounding methods, see Rounding Modes (DSP System Toolbox). When the input is any integer or fixed-point data type, this block uses fixed-point arithmetic for internal calculations. This parameter does not apply when the input data is single or double.

`Normalize butterfly output` — Output normalization
`off` (default) | `on`

When you select this parameter, the block divides the output by 1536. This option is useful when you want the output of the block to stay in the same amplitude range as its input. You require this option when the input is of fixed point type.

When you select this parameter, the output word length increases by 2 bits and when you clear this parameter the output word length increases by 11 bits.

Control Ports

`Enable reset input port` — Optional reset signal
`off` (default) | `on`

Select this parameter to enable the reset port.

Model Examples

Application of FFT 1536 block in LTE OFDM Demodulation

Use the FFT 1536 block in LTE OFDM demodulation.

Open Script

Algorithms

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To design an FFT 1536 block, radix-3 decimation-in-time (DIT) algorithm is implemented. The input sequence x(n) for all n = {0,1,2....1535} is divided into three DIT sequences, x(3n), x(3n+1), x(3n+2) for all n = {0,1,2....511}.

This equation defines FFT 1536 computation of a given sequence x(n).

$x (k) = \sum_{n = 0}^{1535} x (n) W_{1536}^{n k}; k = 0, 1, 2, ..., 1535$

The equation can be implemented by dividing it into three parts, where P(k), Q(k), R(k) are the N/3 (FFT 512) point FFT of x(3n), x(3n+1), and x(3n+2), respectively. Here, N = 1536, and k = 0,1,2,.....,511.

$x (k) = P (k) + W_{N}^{k} Q (k) + W_{N}^{2 k} R (k)$

$x (k + N / 3) = P (k) + W_{3}^{1} W_{N}^{k} Q (k) + W_{3}^{2} W_{N}^{2 k} R (k)$

$x (k + 2 N / 3) = P (k) + W_{3}^{2} W_{N}^{k} Q (k) + W_{3}^{1} W_{N}^{2 k} R (k)$

This diagram shows the internal architecture of the block and how the input sequence streams through the components of the block.

The input sequence x(n) is demultiplexed into three DIT sequences, x(3n), x(3n+1), x(3n+2), each of length 512. Three first-input first-output (FIFO) memories store these sequences. These DIT sequences are serialized and streamed through the FFT 512 block.

Latency

This image shows the output waveform of the block when operated with default configuration parameters. The block provides output data after a latency of 3180 clock cycles. The length of the output data between start (Ctrl.(1)) and end (Ctrl.(2)) output control signals is 1536 clock cycles.

Performance

The performance of the synthesized HDL code varies with your target and synthesis options. This table shows the resource and performance data synthesis results of the block with default configuration parameters, along with normalization feature enabled, and with an input data in fixdt(1,17,15) format. The generated HDL is targeted to Xilinx^® Zynq^® XC7Z045-FFG900-2 FPGA board. The design achieves a clock frequency of 355 MHz.

Resource	Number Used
LUTs	7330
Registers	9325
Block RAMs	18
DSPs	36

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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has a single, default HDL architecture.

HDL Block Properties

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 `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
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 `0`. For more details, see InputPipeline (HDL Coder).
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 `0`. For more details, see OutputPipeline (HDL Coder).

Documentation

FFT 1536

Description

Ports

Input

`data` — Input data
scalar of real or complex values

`valid` — Indicates valid input data
`Boolean` scalar

`reset` — Reset control signal
`Boolean` scalar

Dependencies

Output

`data` — Frequency channel output data
scalar of real or complex values

`ctrl` — Control signals accompanying sample stream
`samplecontrol` bus

Parameters

Main

`Complex multiplication` — HDL implementation
`Use 3 multipliers and 5 adders` (default) | `Use 4 multipliers and 2 adders`

`Rounding method` — Rounding mode for internal fixed-point calculations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Zero`

`Normalize butterfly output` — Output normalization
`off` (default) | `on`

Control Ports

`Enable reset input port` — Optional reset signal
`off` (default) | `on`

Model Examples

Application of FFT 1536 block in LTE OFDM Demodulation

Algorithms

Latency

Performance

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Architecture

HDL Block Properties

See Also

Blocks

Introduced in R2019b

Wireless HDL Toolbox Documentation

Support

Documentation

FFT 1536

Description

Ports

Input

data — Input data scalar of real or complex values

valid — Indicates valid input data Boolean scalar

reset — Reset control signal Boolean scalar

Dependencies

Output

data — Frequency channel output data scalar of real or complex values

ctrl — Control signals accompanying sample stream samplecontrol bus

Parameters

Main

Complex multiplication — HDL implementation Use 3 multipliers and 5 adders (default) | Use 4 multipliers and 2 adders

Rounding method — Rounding mode for internal fixed-point calculations Floor (default) | Ceiling | Convergent | Nearest | Round | Zero

Normalize butterfly output — Output normalization off (default) | on

Control Ports

Enable reset input port — Optional reset signal off (default) | on

Model Examples

Application of FFT 1536 block in LTE OFDM Demodulation

Algorithms

Latency

Performance

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Architecture

HDL Block Properties

See Also

Blocks

Introduced in R2019b

Wireless HDL Toolbox Documentation

Support

`data` — Input data
scalar of real or complex values

`valid` — Indicates valid input data
`Boolean` scalar

`reset` — Reset control signal
`Boolean` scalar

`data` — Frequency channel output data
scalar of real or complex values

`ctrl` — Control signals accompanying sample stream
`samplecontrol` bus

`Complex multiplication` — HDL implementation
`Use 3 multipliers and 5 adders` (default) | `Use 4 multipliers and 2 adders`

`Rounding method` — Rounding mode for internal fixed-point calculations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Zero`

`Normalize butterfly output` — Output normalization
`off` (default) | `on`

`Enable reset input port` — Optional reset signal
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.