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 can be transformed into an unconstrained optimization problem then solved by efficient numerical algorithms in iterative way. Three low-complexity Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton methods are proposed to iteratively realize MIMO without inversion. The reduced from O ( K 3 ) $\mathcal {O}(K^{3})$ L 2 {O}(LK^{2})$ , where denote number of users iterations, respectively. Leveraging special properties MIMO, authors first explore simplified BFGS method (named S-BFGS) alleviate computational burden search direction. For lower complexity, with unit step size U-BFGS) is presented subsequently. When base station (BS)-to-user-antenna ratio (BUAR) large enough, two integrated U-S-BFGS) further reduce complexity. In addition, initialization strategy devised accelerate convergence. Simulation results verify that scheme achieve near-MMSE small iterations as low or 3.