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Table 1 Signal model parameters defined within a symbol duration

From: Efficient phase estimation for the classification of digitally phase modulated signals using the cross-WVD: a performance evaluation and comparison with the S-transform

Signal Normalized frequency (Hz) Symbol duration (s) Phase mapping
BPSK1 1/16 f s /80 ϕ k (t) = π for s = 1
ϕ k (t) = 0  for s = 0
BPSK2 1/8   
QPSK1 1/16 f s /80 ϕ k (t) = π/4  for s = 11
ϕ k (t) = 3π/4  for s = 01
ϕ k (t) = 5π/4  for s = 00
ϕ k (t) = 7π/4  for s = 10
QPSK2 1/8   
8PSK1 1/16 f s /80 ϕ k (t) = π/8  for s = 000
ϕ k (t) = 3π/8  for s = 001
ϕ k (t) = 5π/8  for s = 010
ϕ k (t) = 7π/8  for s = 011
ϕ k (t) = 9π/8  for s = 100
ϕ k (t) = 11π/8  for s = 101
ϕ k (t) = 13π/8  for s = 110
ϕ k (t) = 15π/8  for s = 111
8PSK2 1/8