# Copyright (c) IMToolkit Development Team
# This toolkit is released under the MIT License, see LICENSE.txt
import itertools
import numpy as np
from .Modulator import Modulator
[docs]class OSTBCode(object):
"""Orthogonal space-time block code (OSTBC). A seminal research can be found in [1].
- [1] S. Alamouti, ``A simple transmit diversity technique for wireless communications,'' IEEE J. Sel. Areas Commun., vol. 16, no. 8, pp. 1451--1458, 1998.
"""
def __init__(self, M, modtype, L, nsymbols=1):
"""
Args:
M (int): the number of transmit antennas.
modtype (string): the constellation type.
L (int): the constellation size.
nsymbols (int): the number of embedded symbols.
"""
self.M = M
mod = Modulator(modtype, L)
if M == 2:
nsymbols = M
elif M == 4:
if modtype == "PSK" or modtype == "SQAM":
if nsymbols != 2 and nsymbols != 3:
print("Please specify nsymbols = 2 or 3. I use nsymbols = 2.")
nsymbols = 2
elif modtype == "PAM":
nsymbols = M
elif M == 8:
if modtype == "PSK" or modtype == "SQAM":
print("OSTBC with M=8 and PSK is not supported")
elif modtype == "PAM":
nsymbols = M
elif M == 16:
nsymbols = M
self.B = nsymbols * np.log2(L)
self.Nc = int(2 ** self.B)
# initialize codes
kfoldsymbols = np.array(list(itertools.product(mod.symbols, repeat=nsymbols))) # L^nsymbols \times nsymbols
self.codes = np.zeros((self.Nc, M, M), dtype=complex)
for i in range(kfoldsymbols.shape[0]):
s = kfoldsymbols[i, :]
if M == 2:
self.codes[i] = [[s[0], s[1]], [-np.conj(s[1]), np.conj(s[0])]]
self.codes[i] /= np.sqrt(nsymbols)
if M == 4:
if modtype == "PSK" or modtype == "SQAM":
if nsymbols == 2:
self.codes[i, 0, 0] = s[0]
self.codes[i, 0, 1] = s[1]
self.codes[i, 1, 0] = -np.conj(s[1])
self.codes[i, 1, 1] = np.conj(s[0])
self.codes[i, 2, 2] = s[0]
self.codes[i, 2, 3] = s[1]
self.codes[i, 3, 2] = -np.conj(s[1])
self.codes[i, 3, 3] = np.conj(s[0])
self.codes[i] /= np.sqrt(nsymbols)
elif nsymbols == 3:
self.codes[i, 0, 0] = s[0]
self.codes[i, 0, 1] = s[1]
self.codes[i, 0, 2] = s[2]
self.codes[i, 1, 0] = -np.conj(s[1])
self.codes[i, 1, 1] = np.conj(s[0])
self.codes[i, 1, 3] = s[2]
self.codes[i, 2, 0] = np.conj(s[2])
self.codes[i, 2, 2] = -np.conj(s[0])
self.codes[i, 2, 3] = s[1]
self.codes[i, 3, 1] = np.conj(s[2])
self.codes[i, 3, 2] = -np.conj(s[1])
self.codes[i, 3, 3] = -s[0]
self.codes[i] /= np.sqrt(nsymbols)
elif modtype == "PAM":
self.codes[i, 0, 0] = s[0]
self.codes[i, 0, 1] = s[1]
self.codes[i, 0, 2] = s[2]
self.codes[i, 0, 3] = s[3]
self.codes[i, 1, 0] = -s[1]
self.codes[i, 1, 1] = s[0]
self.codes[i, 1, 2] = -s[3]
self.codes[i, 1, 3] = s[2]
self.codes[i, 2, 0] = -s[2]
self.codes[i, 2, 1] = s[3]
self.codes[i, 2, 2] = s[0]
self.codes[i, 2, 3] = -s[1]
self.codes[i, 3, 0] = -s[3]
self.codes[i, 3, 1] = -s[2]
self.codes[i, 3, 2] = s[1]
self.codes[i, 3, 3] = s[0]
self.codes[i] /= np.sqrt(nsymbols)
elif M == 8:
if modtype == "PAM":
self.codes[i, 0] = [+s[0], +s[1], +s[2], +s[3], +s[4], +s[5], +s[6], +s[7]]
self.codes[i, 1] = [-s[1], +s[0], +s[3], -s[2], +s[5], -s[4], -s[7], +s[6]]
self.codes[i, 2] = [-s[2], -s[3], +s[0], +s[1], +s[6], +s[7], -s[4], -s[5]]
self.codes[i, 3] = [-s[3], +s[2], -s[1], +s[0], +s[7], -s[6], +s[5], -s[4]]
self.codes[i, 4] = [-s[4], -s[5], -s[6], -s[7], +s[0], +s[1], +s[2], +s[3]]
self.codes[i, 5] = [-s[5], +s[4], -s[7], +s[6], -s[1], +s[0], -s[3], +s[2]]
self.codes[i, 6] = [-s[6], +s[7], +s[4], -s[5], -s[2], +s[3], +s[0], -s[1]]
self.codes[i, 7] = [-s[7], -s[6], +s[5], +s[4], -s[3], -s[2], +s[1], +s[0]]
self.codes[i] /= np.sqrt(nsymbols)
elif M == 16:
for k in range(8):
self.codes[i, 0 + k * 2, 0 + k * 2] = s[0 + k * 2]
self.codes[i, 0 + k * 2, 1 + k * 2] = s[1 + k * 2]
self.codes[i, 1 + k * 2, 0 + k * 2] = -np.conj(s[1 + k * 2])
self.codes[i, 1 + k * 2, 1 + k * 2] = np.conj(s[0 + k * 2])
self.codes[i] /= np.sqrt(2)
[docs] def putRate(self):
print("B / M = %d / %d = %d [bit/symbol]" % (self.B, self.M, self.B / self.M))
