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Table 2 Expresions for the complexity per user for the different receiver components, as well as the required number of complex multiplications per information bit

From: Iterative receivers with channel estimation for multi-user MIMO-OFDM: complexity and performance

Algorithm

Total no. of complex mult.*

Mult. per bit

Channel estimators

  

SAGE ML

2MNS +2MNL +IN

24

Joint MMSE

MS(3 + K) + KMI(1 + I) + K2I3 + N(MS + 2MI + KI2)

465

Krylov MMSE

3MS + MSN + 2IMN + CAx(S k + 1) + IN(5S k + 2) + 3NS k /K

145

with

CAx = 3MSN+ IN(M +1)

 

Multi-user detection

  

PIC-MF

2MSN+4MS+MNK

13

PIC-MMSE

4SM + 3SMN + SMNK + SMK3 + MNK

97

MAP

SMN22K/K

256

SISO decoder

  

MAP**

(42M(S - Sp))/3

56

  1. The latter is given for the case of N = 4 receive antennas, K = 4 users, M = 256 subcarriers, S = 20 and S p = 1 OFDM symbol, and I = 36 DPS sequences. Further, QPSK and a code rate of 1/2 is assumed. The subspace order in Krylov MMSE is set to S K = 5.
  2. *The expressions are given per user and per transmitted data block.
  3. **Expression valid for QPSK and a code rate of R = 1/2, and a factor of 3 is included for conversion between real and complex multiplications.