Precoding algorithms are used in massive multiple-input multiple-output (mMIMO) communication systems to ensure effective signal transmission. The zero-forcing (ZF) is one of the most common linear precoding algorithms used in MIMO and mMIMO systems. ZF precoding is complex to implement because it requires direct matrix inversion of the gram matrix. Iterative algorithms have been proposed for approximating matrix inversions. However, iterative algorithms require initial conditions and pre-computations to converge to the optimal transmitted signal vector. This paper proposes a new improved iterative algorithm that guarantees convergence under any circumstances without dependency on any optimized initial parameter or condition. The proposed algorithm is based on a three-step iterative and iterative generalized inverse matrix approximation algorithm. The proposed algorithm was verified using a new correlated channel model that included mutual coupling effects and gain and phase variances caused by radio frequency elements at a base station (BS). The computational complexity of the proposed algorithm was then computed. This study analyzes and compares the bit error rate (BER) performance of the proposed algorithm with that of prominent existing algorithms. Moreover, the sum-rate performance of the proposed algorithm was analyzed. Simulations were performed under both correlated and uncorrelated channel conditions, for comparison and analysis. The simulation results demonstrate that the proposed algorithm outperforms the compared algorithms in terms of the convergence and convergence rates.INDEX TERMS Adaptive antenna system, approximate matrix inversion, iterative algorithms, massive MIMO, ZF precoding.

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