Documentation 
The BPSK Demodulator Baseband block demodulates a signal that was modulated using the binary phase shift keying 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 be a discretetime complex signal. The block maps the points exp(jθ) and exp(jθ) to 0 and 1, respectively, where θ is the Phase offset parameter.
For information about the data types each block port supports, see Supported Data Types.
HardDecision BPSK Demodulator Signal Diagram for Trivial Phase Offset (multiple of )
HardDecision BPSK Demodulator FloatingPoint Signal Diagram for Nontrivial Phase Offset
HardDecision BPSK Demodulator FixedPoint Signal Diagram for Nontrivial Phase Offset
The exact LLR and approximate LLR cases (softdecision) are described in Exact LLR Algorithm and Approximate LLR Algorithm in the Communications System Toolbox™ User's Guide.
The phase of the zeroth point of the signal constellation.
Specifies the use of hard decision, LLR, or approximate LLR during demodulation. The output values for Loglikelihood ratio and Approximate loglikelihood ratio are of the same data type as the input values. See Exact LLR Algorithm and Approximate LLR Algorithm in the Communications System Toolbox User's Guide for algorithm details.
This field appears when Approximate loglikelihood ratio or Loglikelihood ratio is selected for Decision type.
When set to Dialog, the noise variance can be specified in the Noise variance field. When set to Port, a port appears on the block through which the noise variance can be input.
This parameter appears when the Noise variance source is set to Dialog and specifies the noise variance 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.
The LLR algorithm involves computing exponentials of very large or very small numbers using finite precision arithmetic and would yield:
Inf to Inf if Noise variance is very high
NaN if Noise variance and signal power are both very small
In such cases, use approximate LLR, as its algorithm does not involve computing exponentials.
Data Types Pane for HardDecision
When Decision type is set to Hard decision, the output data type can be set to 'Inherit via internal rule', 'Smallest unsigned integer', double, single, int8, uint8, int16, uint16, int32, uint32, or boolean.
When this parameter is set to 'Inherit via internal rule' (default setting), the block will inherit the output data type from the input port. The output data type will be the same as the input data type if the input is a floatingpoint type (single or double). If the input data type is fixedpoint, the output data type will work as if this parameter is set to 'Smallest unsigned integer'.
When this parameter is set to 'Smallest unsigned integer', the output data type is selected based on the settings used in the Hardware Implementation pane of the Configuration Parameters dialog box of the model. If ASIC/FPGA is selected in the Hardware Implementation pane, the output data type is the ideal minimum onebit size, i.e., ufix(1). For all other selections, it is an unsigned integer with the smallest available word length large enough to fit one bit, usually corresponding to the size of a char (e.g., uint8).
This parameter only applies when the input is fixedpoint and Phase offset is not a multiple of $$\frac{\pi}{2}$$.
This can be set to Same word length as input or Specify word length, in which case a field is enabled for user input.
Data Types Pane for SoftDecision
When Decision type is set to Loglikelihood ratio or Approximate loglikelihood ratio, the output data type is inherited from the input (e.g., if the input is of data type double, the output is also of data type double).
Port  Supported Data Types 

Input 

Var 

Output 

This block supports HDL code generation using HDL Coder™. HDL Coder provides additional configuration options that affect HDL implementation and synthesized logic. For more information on implementations, properties, and restrictions for HDL code generation, see BPSK Demodulator Baseband in the HDL Coder documentation.