Low-complexity linear massive MIMO detection based on the improved BFGS method

Linear minimum mean square error (MMSE) detection achieves a good trade-off between performance and complexity for massive multiple-input multiple-output (MIMO) systems. To avoid the high-dimensional matrix inversion involved, MMSE detection can be transformed into an unconstrained optimization problem and then solved by efficient numerical algorithms in an iterative way. Three low-complexity Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton methods are proposed to iteratively realize massive MIMO MMSE detection without matrix inversion. The complexity can be reduced from O(K3)$\mathcal {O}(K<^>{3})$ to O(LK2)$\mathcal {O}(LK<^>{2})$, where K and L denote the number of users and iterations, respectively. Leveraging the special properties of massive MIMO, the authors first explore a simplified BFGS method (named S-BFGS) to alleviate the computational burden in the search direction. For lower complexity, BFGS method with the unit step size (named U-BFGS) is presented subsequently. When the base station (BS)-to-user-antenna ratio (BUAR) is large enough, the two proposed BFGS methods can be integrated (named U-S-BFGS) to further reduce complexity. In addition, an efficient initialization strategy is devised to accelerate convergence. Simulation results verify that the proposed detection scheme can achieve near-MMSE performance with a small number of iterations L as low as 2 or 3.