# Copyright (c) IMToolkit Development Team
# This toolkit is released under the MIT License, see LICENSE.txt
import numpy as np
import scipy
from .Util import getDFTMatrixNumpy, CayleyTransform, getRandomHermitianMatrix
[docs]class Basis(object):
"""This class generates a basis set for nonsquare differential encoding and decoding, which is proposed in [1,2].
- [1] N. Ishikawa, R. Rajashekar, C. Xu, S. Sugiura, and L. Hanzo, ``Differential space-time coding dispensing with channel-estimation approaches the performance of its coherent counterpart in the open-loop massive MIMO-OFDM downlink,'' IEEE Trans. Commun., vol. 66, no. 12, pp. 6190–6204, 2018.
- [2] N. Ishikawa, R. Rajashekar, C. Xu, M. El-Hajjar, S. Sugiura, L. L. Yang, and L. Hanzo, ``Differential-detection aided large-scale generalized spatial modulation is capable of operating in high-mobility millimeter-wave channels,'' IEEE J. Sel. Top. Signal Process., in press.
"""
def __init__(self, type, M, T):
"""
Args:
type (string): the basis type, such as i (IdentityBasis) and d (DFTBasis).
M (int): the number of transmit antennas.
T (int): the number of reduced time slots.
"""
self.type = type
self.M = M
self.T = T
# initialize a unitary matrix that generates a set of bases
if type[0].lower() == 'i':
# Identity basis
U = np.eye(M, dtype=np.complex)
elif type[0].lower() == 'd':
# DFT basis
U = np.array(getDFTMatrixNumpy(M))
elif type[0].lower() == 'r':
# Random basis
U = CayleyTransform(getRandomHermitianMatrix(M))
elif type[0].lower() == 'h':
P = int(type.replace('h', ''))
W = getDFTMatrixNumpy(P)
U = np.zeros((M, M), dtype=complex)
for i in range(int(M / P)):
U[(i * P): (i * P + P), (i * P): (i * P + P)] = W
self.bases = self.convertUnitaryToBases(U) # (M/T) \times M \times T
[docs] def convertUnitaryToBases(self, U):
return np.array(np.hsplit(U, self.M / self.T))
