Modulate signal by using BPSK method
Communications Toolbox / Modulation / Digital Baseband Modulation / PM
Communications Toolbox HDL Support / Modulation / PM
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 discretetime binaryvalued 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.
Data Types 

Multidimensional Signals 

VariableSize Signals 

^{[a]} ufix(ceil(log2(M))) only at the input for Mary modulation. ^{[b]} Fixedpoint outputs must be signed. 
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 Constellation Visualization.
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
$${s}_{n}(t)=\sqrt{\frac{2{E}_{b}}{{T}_{b}}}\mathrm{cos}\left(2\pi {f}_{c}t+{\varphi}_{n}\right),$$
for $$(n1){T}_{b}\le t\le n{T}_{b},\text{n}=\text{1},\text{2},\text{3},\dots $$where:
ϕ_{n} = πm, m∈{0,1}.
E_{b} is the energy per bit.
T_{b} is the bit duration.
f_{c} is the carrier frequency.
In MATLAB^{®}, the baseband representation of a BPSK signal is
$${s}_{n}(t)={e}^{i{\varphi}_{n}}=\mathrm{cos}\left(\pi n\right).$$
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 N_{0} is the noise power spectral density.