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Table 1 Order of computation complexity for proposed TDE and conventional FDE methods

From: Time domain equalization method for TS-OFDM signal under higher mobile environments

 

Equalization methods with direct inverse matrix calculation

Methods

Removing ISI

Construction of channel matrix

Calculation of inverse

Equalization

 

from TS

and received signal matrix

matrix

 

MMSE-FDE [9]

N/A

O[ N 3+2N 2log2 N+N 2+Nlog2 N]

O[ N 3]

O[ N 2]

OLA-MMSE-FDE [14]

O[ S 2S]

O[ N 3+2N 2log2 N+N 2+Nlog2 N]

O[ N 3]

O[ N 2]

FAST-MMSE-FDE [14]

O[ S 2S]

O[ P 3+2SP 2+2P 2]

O[ P 3]

O[ P 2+N 2]

Proposed TDE

O[ S 2S]

O[ NS 2+NS]

O[ N 3]

O[ N 2+Nlog2 N]

Equalization methods with complexity reduction algorithms

 

MMSE-FDE [10]

N/A

O[ (2Q 1+2)Nlog2 N+N(Q 1+1)2

O[ 3N(Q 1+1)2]

O[ N 2]

  

+N(Q 1+1)+Nlog2 N]

  

OLA-MMSE-FDE [14]

O[ S 2S]

O[ Nlog2 N+3N]

O[ 2Q 2 Nlog2 N+(2Q 2+3)N]

FAST-MMSE-FDE [14]

O[ S 2S]

O[ P 2+3P]

O[ N 2+(2Q 2+1)P 2+(2Q 2+3)P]

Proposed TDE

O[ S 2S]

O[ NS 2+NS]

O[ 3NS 2]

O[ N 2+Nlog2 N]

  1. N is the number of FFT/IFFT points, S is the length of TS, Q 1 is the bandwidth of CFR matrix [10], Q 2 is the order of Maclaurin’s expansion [14], and P=N+S−1