Low-complexity soft-output signal detector based on adaptive pre-conditioned gradient descent method for uplink multiuser massive MIMO systems

Abstract

In multiuser massive Multiple Input Multiple Output (MIMO) systems, a large amount of antennas are deployed at the Base Station (BS). In this case, the Minimum Mean Square Error (MMSE) detector with soft-output can achieve the near-optimal performance at the cost of a large-scale matrix inversion operation. The optimization algorithms such as Gradient Descent (GD) method have received a lot of attention to realize the MMSE detection efficiently without a large scale matrix inversion operation. However, they converge slowly when the condition number of the MMSE filtering matrix (the coefficient matrix) increases, which can compromise the efficiency of their implementation. Moreover, their soft information computation also involves a large-scale matrix-matrix multiplication operation. In this paper, a low-complexity soft-output signal detector based on Adaptive Pre-conditioned Gradient Descent (APGD-SOD) method is proposed to realize the MMSE detection with soft-output for uplink multiuser massive MIMO systems. In the proposed detector, an Adaptive Pre-conditioner (AP) matrix obtained through the Quasi-Newton Symmetric Rank One (QN-SR1) update in each iteration is used to accelerate the convergence of the GD method. The QN-SR1 update supports the intuitive notion that for the quadractic problem one should strive to make the pre-conditioner matrix close to the inverse of the coefficient matrix, since then the condition number would be close to unity and the convergence would be rapid. By expanding the signal model of the massive MIMO system and exploiting the channel hardening property of massive MIMO systems, the computational complexity of the soft information is simplified. The proposed AP matrix is applied to the GD method as a showcase. However, it also can be used by Conjugate Gradient (CG) method due to its generality. It is demonstrated that the proposed detector is robust and its convergence rate is superlinear. Simulation results show that the proposed detector converges at most four iterations. Simulation results also show that the proposed approach achieves a better trade-off between the complexity and the performance than several existing detectors and achieves a near-optimal performance of the MMSE detector with soft-output at four iterations without a complicated large scale matrix inversion operation, which entails a big challenge for the efficient implementation.