High-order approximation algorithm using Gram-Schmidt QR transformations coupled with an iterative correction process for tracking frequency drift in OFDM systems

EURASIP Journal on Wireless Communications and Networking

Table 1 Computation complexity comparison between various tracking algorithms

	Real multiplication	Real addition	Real division	Square roots
EM	(M + 1)(8vN + 13N - 1)	2(M + 1)(2vN + N - v - 2)	M + 1	0
JML-CFE	2N(13N + 2v + 8)	12N² + 2vN - 3N - 2v - 6	1	0
The first-order algorithm	$\begin{array}{l} (M + 1) (8 N^{2} + 13 N - 1) \\ + 4 vN \end{array}$	$\begin{array}{l} (M + 1) (4 N^{2} - 3) \\ + 2 v (N - 1) - 1 \end{array}$	M + 1	0
The K th-order algorithm (K ≥ 2)	$\begin{array}{l} (M + 1) {(20 K + 8) N^{2} \\ + (5 K + 4) N \\ + K [L (3 K^{2} - 1) - 1]} \\ + 4 vN \end{array}$	$\begin{array}{l} (M + 1) {2 (2 K + 1) N^{2} \\ - 2 (K + 1) N \\ + L (K - 1) (3 K^{2} + K / 2 - 1)} \\ + M + 2 v (N - 1) \end{array}$	$\begin{array}{l} (M + 1) \\ [LK (3 K - 1) / 2 + K] \end{array}$	(M + 1)LK