Low-Complexity Algorithm for Log Likelihood Ratios in Coded MIMO-OFDM Communications

Abstract

This paper proposes a low-complexity algorithm to calculate log likelihood ratios (LLRs) of coded bits, which is necessary for channel decoding in coded MIMO-OFDM mobile communications. An approximate LLR needs to find a pair of transmitted signal candidates that can maximize the log likelihood function under a constraint that a coded bit be equal to either one or zero. The proposed algorithm can find such a pair simultaneously, whereas conventional ones find them individually. Specifically, the proposed method searches for such candidates in directions of the noise enhancement with the MMSE detection as a starting point. First, an inverse matrix which the MMSE weight matrix includes is obtained and then the power method derives eigenvectors of the inverse matrix as the directions of the noise enhancement. With some eigenvectors, one-dimensional search and hard decision are performed. From the resultant signals, the transmitted signal candidates to be required are selected on the basis of the log likelihood function. Computer simulations with 4 × 4 MIMO-OFDM, 16QAM, and a half-rate convolutional code demonstrate that the proposed algorithm requires only 1.0 dB more E b /N0 than that of the maximum likelihood detection (MLD) in order to achieve packet error rate of 10 −3 , while reducing the complexity to about 0.2% of that of MLD.

Near-Optimal Signal Detection Based on the MMSE Detection Using Multi-Dimensional Search for Correlated MIMO Channels

“…The detected signal is selected from hard decisions of both the MMSE detection result and the unquantized signal candidates on the basis of the log likelihood function. Computer simulations under a correlated Rayleigh flat fading channel have shown that the proposed scheme provides an excellent trade-off between BER performance and complexity, and that it outperforms conventional one-dimensional search algorithms, PM [5] and plural PM [7] while requiring much less complexity than the conventional algorithms. It was also shown that the proposed algorithm can reduce the complexity about 7.4% of that required by GD, 12.1% of that required by PM, and 5.4% of that required by plural PM, when the number of receive or transmit antennas is equal to 8, QPSK is used as the modulation scheme, and average E b /N 0 is equal to 30 dB.…”

“…Note that (52) coincides with the one-dimensional search in [5], which is referred to as the projection method (PM). PM can be extended into plural one-dimensional search, plural PM [7] aŝ…”

“…The simulation parameters are listed in Table 2. As conventional algorithms, MMSE, PM [5], plural PM [7], GD with twodimensional search [6], sphere decoding (SD) [3], and MLD were also investigated.…”

“…Unfortunately, the computational complexity of MLD is prohibitive because it increases exponentially with the number of data streams. Thus, suboptimal detection algorithms that can reduce the complexity are required [3]- [7].…”