Comments on "A New ML Based Interference Cancellation Technique for Layered Space-Time Codes"

is í µí±‚(í µí± 3) rather than the claimed í µí±‚(í µí± 2), where í µí± is the number of receive antennas. A MAXIMUM likelihood (ML) based interference cancellation (IC) detector was proposed in [1] for double space-time transmit diversity (DSTTD), which consists of two Alamouti's space-time block codes (STBC) units [2]. In many application areas of interest, the computational complexity of the detector in [1] can be less than that of the conventional minimum mean squared error (MMSE) IC detector for DSTTD [3]. However, the complexity claimed in [1] needs to be modified, as will be discussed in this comment. Let í µí± denote the number of receive antennas. In [1], the theoretical analysis gaves a complexity of í µí±‚(í µí± 2) (i.e. 7í µí± 2 + 62í µí± − 103 real multiplications and 12í µí± 2 + 47í µí± − 103 real additions) [1, Table I], while numerical experiments were not carried out to verify the given complexity. In what follows, we show that the complexity is not í µí±‚(í µí± 2), but í µí±‚(í µí± 3), and then give the exact complexity that is verified by our numerical experiments. Firstly, we show that a complexity of í µí±‚(í µí± 3) is required to perform the orthonormalization process by equations (9), (13), (14) and (15) in [1]. Let (•) í µí±‡ and (•) í µí°» denote transpose and conjugate transpose of a vector, respectively. Equation (9) in [1] defines the basis vectors v í µí±– = [ í µí±Ž í µí±– í µí± í µí±– e í µí±‡ í µí±– ] í µí±‡ , (1) where í µí±– = 1, 2, ⋅ ⋅ ⋅ , 2í µí± − 2, and e í µí±– is the (2í µí± − 2) × 1 vector with the í µí±– í µí±¡ℎ element to be 1 and all others to be zero. Equation (13) in [1] utilizes v 1 and v 2 , which is θ 1 = v 1 / ∥v 1 ∥ , θ 2 = v 2 / ∥v 2 ∥. Moreover, we represent equations (14) and (15) in [1] as ⎧   ⎨   ⎩ θ 2í µí±›−1 = (v 2í µí±›−1 − ∑ 2í µí±›−2 í µí±—=1 í µí± í µí±— 2í µí±›−1 θ í µí±—) / ∥⋅ ⋅ ⋅ ∥ , (3a) θ 2í µí±› = (v 2í µí±› − ∑ 2í µí±›−2 í …