# A Robust Hybrid Iterative Linear Detector for Massive MIMO Uplink Systems
## 1 Introduction  
In last few years, a vast development in telecommunication systems has been witnessed to offer data-oriented services. In fifth-generation (5G) wireless communication systems, massive multiple-input multiple-output (mMIMO) is utilized to attain high data rate, reliability, robustness, energy efficiency, and spectral efficiency [1; 2; 3]. The mMIMO technology is also a strong candidate to be used in beyond-5G systems. However, computational complexity is remaining a challenge in implementation of the mMIMO system where large number of antennas are deployed at the base station (BS) to serve many users in a single cell [4]. The complexity is exponentially increases as the number of antenna elements increases. Therefore, a design of efficient low complexity detector for mMIMO uplink (UL) system requires a sophisticated signal processing. It is well known that the maximum likelihood (ML) obtains the lowest bit-error-rate (BER), but requires a very high computational complexity, which is not desirable in implementation. For instance, in a mMIMO system with 64 transmit antennas, ML detector exhaustively searches \(1.84\times 10^{19}\) solutions to find the optimal result which is not practical [5]. In addition, computational complexity of the ML detectorremarkably increases as the number of users increases. Sub-optimum detectors have been proposed to attain a considerable performance and complexity trade-off where a comprehensive survey can be found in [6]. Nonlinear algorithms like the \(K\)-best [6] and sphere decoding (SD) [7] are proposed for MIMO, but they include a QR decomposition which increases required signal processing operations, and therefore the computational complexity increases unfavorably with the system's size. The case of utilizing the \(K\)-best and the SD algorithms in mMIMO system is being worse because of the large system's size. The successive interference cancellation (SIC) cannot achieve a quasi-optimum performance close to the ML based detector [5]. Other nonlinear algorithms are also proposed such as the expectation propagation detector and the message passing detector [8]. However, myriad area and high power are required for real implementation in case of nonlinear algorithms. In addition, the belief propagation (BP)-based detector achieves low performance when the ratio between the BS-to-user-antenna ratio (BUAR) is close to 1 [9]. It is also hard to obtain the optimal damping factor. However, the convergence may not be achievable under certain circumstances. In [10], a detection algorithm based on the BP and neural networks have been proposed. Unfortunately, the computational complexity is greatly increased as the number of layers and neurons increased. The approximate message passing (AMP) and generalized approximate message passing (GAMP) algorithms are not robust and they obtain a poor performance outside the situation of the zero-mean independent and identically distributed (i.i.d) sub-Gaussian matrix [11]. Linear detection methods have been proposed to achieve a quasi-optimal performance and relieve some of the burden of the computational complexity in mMIMO systems. They work properly when the number of users is small. For instance, a minimum mean square error (MMSE) achieves a near-optimal performance when the BUAR is large enough [1]. Unfortunately, the MMSE algorithm includes undesirable and complicated matrix inversion, which is a critical task in the computational complexity, particularly when the number of antennas is large. The complexity of utilizing the MMSE algorithm is \(\mathcal{O}\left(K^{3}\right)\), where \(K\) is the number of users. Alternative detection algorithms have been illustrated such as the MMSE-parallel-interference-cancellation (MMSE-PIC) to achieve a satisfactory performance. However, complexity of the MMSE-PIC algorithm is still \(\mathcal{O}\left(K^{3}\right)\) for computing the matrix inversion [12].