Beamforming Algorithms for Multiuser MIMO Uplink Systems: Parallel and Serial Approaches Abstract: Joint transmitter and receiver beamforming algorithms for uplink multiuser multi-input multi-output (MIMO) communication systems are proposed in this paper based on maximizing an utility function, which is defined based on the difference between desired signal power and interference plus noise power . Two iterative beamforming algorithms are developed by maximizing the utility function of each user via parallel and serial methods. In parallel method, the transmitter and receiver beamforming vectors of each user are iteratively updated by maximizing its utility function. However in serial method, at first step, the transmitter beamforming vectors of all users are iteratively updated by maximizing the utility function of each user and then receiver beamforming vectors of users are calculated. By computer simulations, the performances of the proposed beamforming algorithms are evaluated and also compared with the performance of the duality method (DM) based beamforming algorithm. With respect to bit error rate (BER) and convergence rate, the results show that the new proposed beamforming algorithms have superior performances in comparison with the DM based beamforming algorithm. Also, for some cases, the serial method achieves better performances in comparison with the parallel method. Keywords: Multiuser, MIMO systems, uplink, beamforming. 1. Introduction In multiuser environment, interference is the most challenging issue in communication system design. Employing multiple antennas at the transmitter and receiver sides is a technology which is able to overcome multiuser interference (MUI) in addition to achieve high data rate. To eliminate the MUI in the multiuser multi-input multi-output (MIMO) system, different criteria have been proposed to design transmitter and receiver beamforming algorithms [1-7]. Maximizing mutual information between transmitter and receiver has been considered in [1-3] for multiuser system design. The signal to interference plus noise (SINR) maximization is another criterion employed in joint transmitter and receiver beamfoming algorithms [4-5]. Based on duality relation between downlink and uplink, an iterative beamfoming algorithm has been proposed in [6] that minimizes minimum mean square error (MMSE) in symbol detection. In duality method (DM), the transmit and receive beamfomers are designed based on using downlink and uplink MMSE criteria, respectively. In [7], by defining the difference between desired signal power and interference plus noise power as an utility function, iterative beamforming algorithms, which maximize the utility function, have been proposed for multiuser MIMO downlink systems. In this paper we propose a beamformer design for multiuser MIMO uplink systems based on maximizing the defined utility function in [7]. We develop two iterative beamfoming algorithms in order to maximum the utility function via parallel and serial methods. In the parallel method (PM), the transmit and receive beamformers of each user are estimated iteratively. In serial method (SM), only the transmit beamformers of all users are estimated in an iterative manner and after that the receive beamformers of users are calculated at one iteration. Simulation results show the superiority in performances of the proposed methods compared with the previously proposed duality method (DM) in [6]. The rest of this paper is organized as follows. The uplink multiuser MIMO system is modelled in section 2. In section 3, the utility function is proposed and then the PM and SM methods are derived. We present some simulation results in section 4 and then draw some conclusions in section 5. 2. System Model We consider an uplink multiuser MIMO system with K users where the number of transmitting antennas of each user is N and the number of receiving antennas of the base station (BS) is M . User m transmits data vector ,1 ,2 , [ , ,..., ] T m m m mJ d d d = d , which has J N ≤ data streams, such that [ ] H m m J E =Ι d d , where J Ι is J J × unitary matrix and (.) H represents complex conjugating operation. Beamforming matrix S.M.J. Asgari Tabatabaee 1,2 and H. Zamiri-Jafarian 1 1 Electrical Engineering Department, Ferdowsi University of Mashhad 2 Communications and Computer Research Centre, Ferdowsi University of Mashhad 978-1-4673-5634-3/13/$31.00 ©2013 IEEE