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Table 1 Comparison of number of complex arithmetic operations for ZF, MMSE, QR decomposition and LC-QR decomposition detection mechanisms

From: A low computational complexity V-BLAST/STBC detection mechanism in MIMO system

Complex arithmetic operation

ZF with H

MMSE with H

QR decomposition with H

LC-QR with H

Addition

4(4 N − 1) × (M − 1)2 − 2(M − 1)

4(4 N − 1) × (M − 1)2

2(2 N − 1) × (M − 1) + (M − 2) × (2 M − 3)

N(3 M − 2) + (M − 3) × (M − 1)

Subtraction

-

-

2 M − 3

2(M − 2) + 2 N + 1

Multiplication

4 N(M − 1) × (4 M − 3)

4 N(M − 1) × (4 M − 3)

(M − 1) × (4 N + 2 M − 3)

M2 + 3MN − M + 4

Division

-

-

2(M − 1)

2(M − 2)

Householder reflection

-

-

8 N(M − 1)2 − (8/3)(M − 1)3

NM2 − M3/ 3

Gaussian elimination

8(M − 1)3

8(M − 1)3

-

-

Total

8(M − 1)3 + 4(8 N − 1)(M − 1)2 + 2(2 N − 1)(M − 1)

8(M − 1)3 + 4(8 N − 1)(M − 1)2 + 4 N(M − 1)

8 N(M − 1)2 − (8/3)(M − 1)3 + (2 M − 3)2 + 2(M − 1)(4 N + 1) − 1

NM2 − M3/ 3 + (M + 2)(2 N − 1) + 2(M − 2)(M + 2) + 4 N (M − 1) + 10