Randomized Kaczmarz Algorithm Applied D’Hondt Method for Extremely Massive MIMO Wireless Communication Systems

Extremely massive MIMO (Multiple-Input Multiple-Output) is a technique to enable the spatial diversity. The systems employ a large number of antennas at the base stations, resulting in high computational complexity in various processes of wireless communications. The precoding process is one of them because the process requires the calculation of matrix inversion. The randomized Kaczmarz algorithm(rKA) is an iterative method to obtain the approximation so the computational time of precoding can be decreased. Some improvements of rKA were proposed so far, the iteration number required to obtain the approximation of inverse matrix is not so small. In this paper, we propose a new rKA method that applies the D’Hondt method, typically used for seat allocation in elections. In rKA process, the row vector is selected to use for updating approximation. Our method selects the row vector based on the D’Hondt method while the conventional rKA methods select the row vector probabilistic. Some results of simulation showed that the bit error ratio (BER) performance of our method is superior to other rKA methods at higher normalized transmit powers (NTP). The results also showed that the BER performances of our method with small number of iterations are more accurate than the others especially at high NTPs. That means our method can achieve the same BER performance with smaller number of iterations as the others, so the computational complexity of precoding with rKA is decreased.