BPSK Demodulator Baseband

R2026b

Demodulate BPSK-modulated data

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BPSK Demodulator Baseband block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Communications Toolbox HDL Support / Modulation / PM
Communications Toolbox / Modulation / Digital Baseband Modulation / PM

Description

The BPSK Demodulator Baseband block demodulates a signal that was modulated using the binary phase shift keying (BPSK) method. The input is a baseband representation of the modulated signal. This block accepts a scalar or column vector input signal. The input signal must be a discrete-time complex signal. The block maps the points exp(jϕ) or -exp(jϕ) to 0 and 1, respectively. The Phase offset (rad) parameter specifies the value of ϕ.

Examples

Cyclic Redundancy Check of Noisy BPSK Data Frames in Simulink

Use a CRC code to detect frame errors in a noisy BPSK signal.

In the cm_ex_crc_noisy_bpsk_frames model, the CRC generator and detector pair use a standard CRC-4 polynomial, . The length of the CRC is 4 bits as determined by the degree of the polynomial. The number of checksums per frame is 1, so the full transmission frame has one CRC appended at the end.

A binary signal frame gets a CRC code appended to the end of the frame. BPSK modulation is applied to the signal and the signal passes through an AWGN channel. The signal is demodulated, and then a CRC syndrome detector removes the CRC and calculates the CRC errors.

Generate 12-bit frames of binary data and append CRC bits. Based on the degree of the polynomial, 4 bits are appended to each frame. Apply BPSK modulation and pass the signal through an AWGN channel. Demodulate and use the CRC detector to determine if the frame is in error.

The results of the CRC detection are compared to a BER calculation.

Number of bit errors detected:  6
Number of crc errors detected:  5

Extended Examples

Frame Synchronization Using Barker Code Preamble

Use a length 13 Barker code frame preamble for frame synchronization of data bits.

• Open Model

Ports

Input

In — BPSK-modulated baseband signal

scalar | vector | matrix

BPSK-modulated baseband signal, specified as a scalar, vector, or matrix. When this input is a matrix, each column is treated as an independent channel. This port is unnamed until the Var port is enabled.

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

Var — Noise Variance

positive scalar | vector of positive values

Noise variance, specified as a positive scalar or vector of positive values.

Dependencies

To enable this parameter, set the Noise variance source parameter to Port.

Data Types: double

Output

Out — Demodulated signal

scalar | vector

Demodulated signal, returned as a scalar or vector. If the output is a scalar, the value is an integer. If the output is a vector, it is an integer-valued or binary-valued vector.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

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

Decision type — Decision type

Hard decision (default) | Log-likelihood ratio | Approximate log-likelihood ratio

Decision type used during demodulation, specified as Hard decision, Log-likelihood ratio or Approximate log-likelihood ratio. For more information, see BPSK Hard-Decision Demodulation and BPSK Soft Demodulation.

The output matches the data type of the input values when Decision type is set to Log-likelihood ratio or Approximate log-likelihood ratio.

Noise variance source — Noise variance source

Dialog (default) | Port

Noise variance source, specified as Dialog or Port.

• Dialog — The noise variance is set using the Noise variance parameter.

• Port — The noise variance is set using the Var input port.

Noise variance — Noise Variance

1 (default) | positive scalar | vector of positive values

Noise variance, specified as a positive scalar or vector of positive values.

• When specified as a scalar, that value is used on all elements in the input signal.

• When specified as a vector, the vector length must be equal to the number of columns in the input signal. Each noise variance vector element is applied to its corresponding column in the input signal.

This parameter is tunable in normal mode, accelerator mode and rapid accelerator mode. If you use the Simulink Coder™ rapid simulation (RSIM) target to build an RSIM executable, then you can tune the parameter without recompiling the model. This is useful for Monte Carlo simulations, in which you run the simulation multiple times (perhaps on multiple computers) with different amounts of noise.

Tunable: Yes

Dependencies

To enable this parameter, set the Decision type parameter to set to either Log-likelihood ratio or Approximate log-likelihood ratio and set the Noise variance source parameter to Dialog.

Phase offset (rad) — Phase of zeroth point

0 (default) | real-valued scalar

Phase of the zeroth point, specified as a real-valued scalar. Units are in radians.

Example: pi/4

Data Types

Output data type — Output data type

Inherit via internal rule (default) | Smallest unsigned integer | double | single | ...

Output data type, specified as one of these options

• When you set the Decision type parameter to Hard decision:

  • Inherit via internal rule — The block inherits the output data type from the input port. If the input is a floating-point type (single or double), the output data type is the same as the input data type. If the input data type is fixed-point, the output data type works as if you set this parameter to Smallest unsigned integer.

  • Smallest unsigned integer — The block selects the output data type based on the settings used in the Hardware Implementation pane of the Configuration Parameters dialog box of the model. If you select ASIC/FPGA in the Hardware Implementation pane, the output data type is the ideal minimum one-bit size, that is, ufix(1). For all other selections, the output data type is an unsigned integer with the smallest available word length large enough to fit one bit, usually corresponding to the size of a character (for example, uint8).

  • double

  • single

  • int8

  • uint8

  • int16

  • uint16

  • int32

  • uint32

  • boolean

• When you set the Decision type parameter to Log-likelihood ratio or Approximate log-likelihood ratio — The block inherits the output data type matches the data type of the input.

For information about specifying data types, see Data Type Assistant.

Derotate factor — Derotate factor

Same word length as input (default) | Specify word length

Derotate factor, specified as Same word length as input or Specify word length.

Dependencies

This parameter applies only when the input is fixed-point and the Phase offset (rad) parameter is not a multiple of π/2.

Block Characteristics

Data Types	Boolean | double | fixed pointa, b | integer | single
Multidimensional Signals	no
Variable-Size Signals	yes
a Fixed-point inputs must be signed. b ufix(1) only at the output when ASIC/FPGA is selected in the Hardware Implementation Pane.

Programmatic Use: Add Block

To add the block programmatically, use the add_block function with one of these library block paths as the source.

"commhdldigbbndpm/BPSK Demodulator Baseband"

"commdigbbndpm3/BPSK Demodulator Baseband"

Example: add_block("commhdldigbbndpm/BPSK Demodulator Baseband","myModel/myBlock",MakeNameUnique="on")

More About

Data Type Assistant

The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Algorithms

BPSK Hard-Decision Demodulation

When applying hard demodulation, the input signal type and phase offset are considered.

This figure shows the hard decision BPSK demodulator for a floating-point or fixed-point signal and trivial phase offset (multiple of π/2)

This figure shows the hard decision BPSK demodulator for a floating-point signal and nontrivial phase offset

This figure shows the hard decision BPSK demodulator for a fixed-point signal and nontrivial phase offset.

BPSK Soft Demodulation

For soft demodulation, two soft-decision log-likelihood ratio (LLR) algorithms are available: exact LLR and approximate LLR. The exact LLR algorithm is more accurate but has slower execution speed than the approximate LLR algorithm. For further description of these algorithms, see the Hard- vs. Soft-Decision Demodulation topic.

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.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays in the design. Distributed pipelining does not redistribute these registers. The default value 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 value 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 value is 0. For more details, see OutputPipeline (HDL Coder).

Version History

Introduced before R2006a

R2026b: Update exact LLR algorithm to use LogSumExp for improved numerical stability

Starting in R2026b, the exact LLR algorithm uses LogSumExp for improved numerical stability, returning finite values for extreme noise variance or signal power conditions. Previously, outputs could be Inf, –Inf, or NaN in these cases. For more information, see Exact LLR Algorithm.