# BPSK Modulator Baseband

Modulate signal by using BPSK method

• Library:
• Communications Toolbox / Modulation / Digital Baseband Modulation / PM

Communications Toolbox HDL Support / Modulation / PM

## Description

The BPSK Modulator Baseband block modulates a signal by using the binary phase shift keying (BPSK) method. The output is a baseband representation of the modulated signal.

The input signal must be a discrete-time binary-valued signal. If the input bit is 0 or 1, then the modulated symbol is exp(jθ) or -exp(jθ), respectively, where θ represents the Phase offset (rad) parameter.

## Ports

### Input

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Input signal, specified as a scalar or vector.

• If you specify a scalar, it must be an integer from 0 to M – 1, where M is the modulation order.

• If you specify a vector, the elements must be either integers from 0 to M-1 or binary values. If you specify a binary vector, the number of elements must be an integer multiple of the number of bits per symbol. The number of bits per symbol is equal to log2(M).

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

### Output

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BPSK-modulated baseband signal, returned as a complex scalar or vector of complex values.

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

## Parameters

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Specify a finite real-valued scalar for the phase of the zeroth point of the constellation in radians.

Example: `pi/4`

Data type of output,. Set this parameter to one of the fixed point options or `<data type expression>` to enable parameters in which you specify additional details. Set this parameter to `Inherit via back propagation`, to match the output data type and scaling to the following block in the model.

## Block Characteristics

 Data Types `Boolean` | `double` | `fixed point[a][b]` | `integer` | `single` Multidimensional Signals `no` Variable-Size Signals `yes` [a] ufix(ceil(log2(M))) only at the input for M-ary modulation.[b] Fixed-point outputs must be signed.

## Tips

The BPSK Modulator Baseband block provides the capability to visualize a signal constellation from the block mask. This constellation visualization feature allows you to visualize a signal constellation for the specified block parameters. For more information, see the Constellation Visualization section of the Communications Toolbox™ User's Guide.

## Algorithms

Phase modulation is a linear baseband modulation technique in which the message modulates the phase of a constant amplitude signal. Binary Phase Shift Keying (BPSK) is a two phase modulation scheme, where the 0’s and 1’s in a binary message are represented by two different phase states in the carrier signal

`${s}_{n}\left(t\right)=\sqrt{\frac{2{E}_{b}}{{T}_{b}}}\mathrm{cos}\left(2\pi {f}_{c}t+\pi \left(1-n\right)\right);\text{\hspace{0.17em}}n\in \left\{0,1\right\},$`

where:

• Eb is the energy per bit.

• Tb is the bit duration.

• fc is the carrier frequency.

In MATLAB®, the baseband representation of a BPSK signal is

`${s}_{n}\left(t\right)=\mathrm{cos}\left(\pi n\right);\text{\hspace{0.17em}}n\in \left\{0,1\right\}.$`

The BPSK signal has two phases: 0 and π.

The probability of a bit error in an AWGN channel is

`${P}_{b}=Q\left(\sqrt{\frac{2{E}_{b}}{{N}_{0}}}\right),$`

where N0 is the noise power spectral density.

## Extended Capabilities

### C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™.

Introduced before R2006a