Skip to main content

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