Abstract-In this paper, a field programmable gate array (FPGA) implementation of a linear minimum mean square error (LMMSE) detector is considered for MIMO-OFDM systems. Two square root free algorithms based on QR decomposition (QRD) are introduced for the implementation of LMMSE detector. Both algorithms are based on QRD via Givens rotations, namely coordinate rotation digital computer (CORDIC) and squared Givens rotation (SGR) algorithms. Linear and triangular shaped array architectures are considered to exploit the parallelism in the computations. An FPGA hardware implementation is presented and computational complexity of each implementation is evaluated and compared.
A list sphere detector (LSD) can be used to approximate the optimal maximum a posteriori (MAP) detection. The total complexity of the LSD algorithms is relative to the number of visited nodes in the search tree. We compare the differences between real and complex signal model in the LSD algorithm implementation and study its impact on the complexity and performance with different search strategies. In hardware implementation, the number of visited nodes needs to be bounded in order to determine the complexity and the latency of the implementation. Thus, we study the performance of LSD algorithms with a limited number of nodes in the search. We show that the algorithms with real signal model are less complex compared to the complex signal model, and that the performance may suffer significantly with limited search depending on the search strategy.
The optimal detection for coded system requires the use of a maximum a posteriori (MAP) detection. A list sphere detector (LSD) can be used to approximate the MAP detector. Depending on the used list size, LSD provides a tradeoff between the performance and the computational complexity. The LSD output candidate list is used to calculate the approximation of the probability log-likelihood ratio (LLR) of each transmitted bit. The list should be large enough and it should include at least one candidate for both possible bits for good approximation. The use of a small list size causes inaccurate and, especially, very large LLRs that prevent the decoder from correcting the falsely detected signals and, thus, degrades performance. We study the effect of the LLR clipping to the performance and complexity of the LSD algorithm. We show that by limiting the dynamic range of the LLR the required LSD list size can be decreased, and, thus, the complexity of the algorithms is decreased. The optimal dynamic range values for LLR clipping are determined and the effect of the clipping to the complexity of the LSD algorithms is analyzed.
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