A Codeword Search Scheme for Massive MIMO Systems

In limited-feedback systems, conventional codeword search scheme targets the entire codebook to find a codeword, which maximizes an inner product norm with a channel direction. Since the computational complexity of the conventional codeword search scheme is proportional to the multiplication of the number of antennas and the codebook size, it spends too much time in the massive MIMO systems. From a geometric observation, we propose a fast codeword search scheme that stops search when an inner product norm between a codeword and a channel direction is larger than a threshold to reduce the search time. We derive an optimal threshold that can reduce the average number of searches without search accuracy loss and a suboptimal threshold that can reduce the average number of searches largely at the cost of search accuracy. We analyze the performances of the proposed scheme as functions of the thresholds, and show that the optimal threshold loses its benefit in the massive MIMO systems and the suboptimal threshold can reduce the number of searches by e^-1 ≈ 37% without performance loss when the number of antennas is infinite. The simulation results show that our theoretical analysis is accurate.