__all__ = [
"BPSK_MAP",
"BPSK_NOROT_MAP",
"BPSK_ROTATION",
"QPSK_MAP",
"QPSK_ROTATION",
"SLE_RRC_BETA",
"PSKDemodulator",
"PSKModulator",
"rrc_filter",
]
from functools import lru_cache
import numpy as np
# TXS-10002-2025 6.2.1.2 PSK调制
# 滚降系数 beta = 0.4
SLE_RRC_BETA = 0.4
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@lru_cache(maxsize=8)
def rrc_filter(beta: float, sps: int, span: int = 10) -> np.ndarray:
"""生成平方根升余弦脉冲成型滤波器。
:param beta: 滚降系数
:param sps: 每符号采样数
:param span: 单侧符号跨度
:returns: 滤波器系数, 归一化使得匹配滤波后采样点增益为1
"""
N = 2 * span * sps + 1
t = np.arange(-(N - 1) / 2, (N - 1) / 2 + 1) / sps
h = np.zeros(len(t))
for i, ti in enumerate(t):
if abs(ti) < 1e-10:
h[i] = 1.0 - beta + 4 * beta / np.pi
elif abs(abs(ti) - 1.0 / (4 * beta)) < 1e-10:
h[i] = (beta / np.sqrt(2)) * (
(1 + 2 / np.pi) * np.sin(np.pi / (4 * beta)) +
(1 - 2 / np.pi) * np.cos(np.pi / (4 * beta))
)
else:
num = np.sin(np.pi * ti * (1 - beta)) + 4 * beta * ti * np.cos(np.pi * ti * (1 + beta))
den = np.pi * ti * (1 - (4 * beta * ti) ** 2)
h[i] = num / den
# 归一化
h = h / np.sqrt(np.sum(h ** 2))
return h
# 标准中的PSK星座映射表
# BPSK: 0->90°, 1->-90°, 偶数符号额外顺时针旋转90°
BPSK_MAP = {
0: np.exp(1j * np.pi / 2),
1: np.exp(-1j * np.pi / 2),
}
BPSK_ROTATION = np.exp(-1j * np.pi / 2) # 偶数位顺时针90°
# QPSK: 00->45°, 01->135°, 11->-135°, 10->-45°
QPSK_MAP = {
0b00: np.exp(1j * np.pi / 4),
0b01: np.exp(1j * 3 * np.pi / 4),
0b11: np.exp(-1j * 3 * np.pi / 4),
0b10: np.exp(-1j * np.pi / 4),
}
QPSK_ROTATION = np.exp(-1j * np.pi / 4) # 偶数位顺时针45°
# 8PSK: 000->22.5°, 001->67.5°, 011->112.5°, 010->157.5°,
# 110->-157.5°, 111->-112.5°, 101->-67.5°, 100->-22.5°
_8PSK_MAP = {
0b000: np.exp(1j * np.deg2rad(22.5)),
0b001: np.exp(1j * np.deg2rad(67.5)),
0b011: np.exp(1j * np.deg2rad(112.5)),
0b010: np.exp(1j * np.deg2rad(157.5)),
0b110: np.exp(-1j * np.deg2rad(157.5)),
0b111: np.exp(-1j * np.deg2rad(112.5)),
0b101: np.exp(-1j * np.deg2rad(67.5)),
0b100: np.exp(-1j * np.deg2rad(22.5)),
}
_8PSK_ROTATION = np.exp(-1j * np.deg2rad(22.5)) # 偶数位顺时针22.5°
# 无相位旋转BPSK: 0->0°, 1->180°
BPSK_NOROT_MAP = {
0: np.exp(1j * 0),
1: np.exp(1j * np.pi),
}
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class PSKModulator:
"""TXS-10002-2025 6.2.1.2 PSK调制器。
支持 BPSK, QPSK, 8PSK 及无相位旋转BPSK。
"""
def __init__(self, mod_type: str = "QPSK", sps: int = 4,
beta: float = SLE_RRC_BETA, rrc_span: int = 10):
self.mod_type = mod_type.upper()
self.sps = sps
self.beta = beta
self.rrc_span = rrc_span
self._rrc = rrc_filter(beta, sps, rrc_span)
if self.mod_type == "BPSK":
self._map = BPSK_MAP
self._bits_per_symbol = 1
self._rotation = BPSK_ROTATION
elif self.mod_type == "QPSK":
self._map = QPSK_MAP
self._bits_per_symbol = 2
self._rotation = QPSK_ROTATION
elif self.mod_type == "8PSK":
self._map = _8PSK_MAP
self._bits_per_symbol = 3
self._rotation = _8PSK_ROTATION
elif self.mod_type == "BPSK_NOROT":
self._map = BPSK_NOROT_MAP
self._bits_per_symbol = 1
self._rotation = None
else:
raise ValueError(f"不支持的调制方式: {mod_type}")
@property
def bits_per_symbol(self) -> int:
return self._bits_per_symbol
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def map_symbols(self, bits: np.ndarray) -> np.ndarray:
"""比特到星座符号的映射（含相位旋转）。"""
bps = self._bits_per_symbol
n_pad = (-len(bits)) % bps
if n_pad:
bits = np.concatenate([bits, np.zeros(n_pad, dtype=int)])
n_symbols = len(bits) // bps
symbols = np.zeros(n_symbols, dtype=complex)
for i in range(n_symbols):
idx = 0
for b in range(bps):
idx = (idx << 1) | int(bits[i * bps + b])
symbols[i] = self._map[idx]
# 偶数符号位额外旋转（标准中第一个符号处于奇数位，索引0为奇数位）
if self._rotation is not None and (i % 2 == 1):
symbols[i] *= self._rotation
return symbols
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def modulate(self, bits: np.ndarray) -> np.ndarray:
"""PSK调制并进行RRC脉冲成型。
:returns: 复基带IQ信号
"""
symbols = self.map_symbols(bits)
# 上采样
upsampled = np.zeros(len(symbols) * self.sps, dtype=complex)
upsampled[::self.sps] = symbols
# RRC脉冲成型
signal = np.convolve(upsampled, self._rrc, mode='same')
return signal
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class PSKDemodulator:
"""PSK解调器（匹配滤波+最近邻判决）。"""
def __init__(self, mod_type: str = "QPSK", sps: int = 4,
beta: float = SLE_RRC_BETA, rrc_span: int = 10):
self.mod_type = mod_type.upper()
self.sps = sps
self._rrc = rrc_filter(beta, sps, rrc_span)
if self.mod_type == "BPSK":
self._map = BPSK_MAP
self._bits_per_symbol = 1
self._rotation = BPSK_ROTATION
elif self.mod_type == "QPSK":
self._map = QPSK_MAP
self._bits_per_symbol = 2
self._rotation = QPSK_ROTATION
elif self.mod_type == "8PSK":
self._map = _8PSK_MAP
self._bits_per_symbol = 3
self._rotation = _8PSK_ROTATION
elif self.mod_type == "BPSK_NOROT":
self._map = BPSK_NOROT_MAP
self._bits_per_symbol = 1
self._rotation = None
else:
raise ValueError(f"不支持的调制方式: {mod_type}")
# 构建星座参考
self._constellation_keys = sorted(self._map.keys())
self._constellation_vals = np.array([self._map[k] for k in self._constellation_keys])
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def demodulate(self, signal: np.ndarray) -> np.ndarray:
"""PSK解调。
:param signal: 复基带IQ信号
:returns: 解调后的比特序列
"""
# 匹配滤波
filtered = np.convolve(signal, self._rrc, mode='same')
# 降采样（取峰值点）
symbols = filtered[::self.sps]
# 反旋转 + 最近邻判决
bps = self._bits_per_symbol
bits = []
for i, sym in enumerate(symbols):
# 反相位旋转
if self._rotation is not None and (i % 2 == 1):
sym = sym * np.conj(self._rotation)
# 最近邻判决
distances = np.abs(sym - self._constellation_vals)
idx = self._constellation_keys[np.argmin(distances)]
# 解码比特
bits.extend((idx >> b) & 1 for b in range(bps - 1, -1, -1))
return np.array(bits, dtype=int)