### BPSK

Diagrams for hard-decision demodulation of BPSK signals follow.

**Hard-Decision BPSK Demodulator Signal Diagram for Trivial Phase
Offset (multiple of )**

**Hard-Decision BPSK Demodulator Floating-Point Signal Diagram
for Nontrivial Phase Offset**

**Hard-Decision BPSK Demodulator Fixed-Point Signal Diagram for
Nontrivial Phase Offset**

### QPSK

Diagrams for hard-decision demodulation of QPSK signals follow.

**Hard-Decision QPSK Demodulator Signal Diagram for Trivial Phase
Offset (odd multiple of )**

**Hard-Decision QPSK Demodulator Floating-Point Signal Diagram
for Nontrivial Phase Offset**

**Hard-Decision QPSK Demodulator Fixed-Point Signal Diagram for
Nontrivial Phase Offset**

### Higher-Order PSK

Diagrams for hard-decision demodulation of higher-order (*M* ≥
8) signals follow.

**Hard-Decision 8-PSK Demodulator Floating-Point Signal Diagram**

**Hard-Decision 8-PSK Demodulator Fixed-Point Signal Diagram**

**Hard-Decision M-PSK Demodulator (M > 8) Floating-Point Signal
Diagram for Nontrivial Phase Offset**

For *M* > 8, in order to improve speed and
implementation costs, no derotation arithmetic is performed when **Phase
offset** is 0, $$\pi /2$$, $$\pi $$, or $$3\pi /2$$ (i.e., when it is trivial).

Also, for *M* > 8, this block will only
support inputs of type `double`

and `single`

.

### Log-likelihood Ratio and Approximate Log-likelihood Ratio

The exact LLR and approximate LLR algorithms (soft-decision)
are described in Phase Modulation.