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Abstract-In this paper we examine convergence properties of massive MIMO systems with the aim of determining the number of antennas required for massive MIMO gains. We consider three characteristics of a channel matrix and study their asymptotic behaviour. Furthermore, we derive ZF SNR and MF SINR for a scenario of unequal receive powers. In our results we include the effects of spatial correlation. We show that the rate of convergence of channel metrics is much slower than that of the ZF/MF precoder properties.

Abstract-A spatially correlated large antenna array operating at millimeter-wave (mmWave) frequencies is considered. Based on a Saleh-Valenzuela channel model, closed-form expressions of the three-dimensional spatial correlation (SC) for wide, narrow and Von Mises power elevation spectra (PES) are analytically derived. The effects of the PES on the convergence to massive multipleinput-multiple-output (MIMO) properties is then illustrated by defining and deriving a diagonal dominance metric. Numerically, the effects of antenna element mutual coupling (MC) is shown on the effective SC, eigenvalue structure and mmWave user rate for different antenna topologies. It is concluded that although MC can significantly reduce SC for side-by-side dipole antenna elements, the change in antenna effective gain (and therefore signal-to-noise ratio) caused by MC becomes a dominating effect and ultimately determines the antenna array performance. The user rate of a mmWave system with hybrid beamforming (HBF), using an orthogonal matching pursuit (OMP) algorithm, is then shown for different antenna topologies with dipole and crosspolarized (x-pol) antenna elements. It is seen that even for small numbers of radio-frequency chains, the OMP algorithm works well relative to the fully digital case for channels with high SC, such as the x-pol antenna array.

Abstract-Approximate expressions for the spatial correlation of cylindrical and uniform rectangular arrays (URA) are derived using measured distributions of angles of departure (AOD) for both the azimuth and zenith domains. We examine massive multiple-input-multiple-output (MIMO) convergence properties of the correlated channels by considering a number of convergence metrics. The per-user matched filter (MF) signal-tointerference-plus-noise ratio (SINR) performance and convergence rate, to respective limiting values, of the two antenna topologies is also explored.

Abstract-In this paper we examine a number of deployment issues which arise from practical considerations in massive multiple-input-multiple-output (MIMO) systems. We show both spatial correlation and line-of-sight (LOS) introduce an interference component to the system which causes non-orthogonality between user channels. Distributing the antennas into multiple clusters is shown to reduce spatial correlation and improve performance. Furthermore, due to its ability to minimize interference, zero forcing (ZF) precoding performs well in massive MIMO systems compared to matched filter (MF) precoding which suffers large penalties. However, the noise component in the ZF signal-to-noise-ratio (SNR) increases significantly in the case of imperfect transmit channel state information (CSI).