Impact of antenna correlation on multi-user MIMO systems

Abstract

Multiple-input multiple-output (MIMO) techniques provide a promising solution to enhance the performance of wireless communication systems. Antenna correlation exists in practical MIMO systems for two reasons. First, there may be no sufficient space to separate antenna elements due to the limited physical sizes of the transmitters and/or the receivers. Second, the practical propagation environments may not provide sufficient scatters. In a conventional single-user MIMO system, since antenna correlation results in reduced degrees of freedom (DOF) and may severely degrade the system capacity, it has been generally regarded as a negative factor. However, the impact of antenna correlation in multi-user environments is still limited explored. In this thesis, we make a comprehensive study on theoretical and practical aspects of multi-user MIMO systems with correlated fading. In the first contribution, the capacity of correlated MIMO systems with full channel state information (CSI) at both the transmitters and the receiver over multiple access channels (MACs) (i.e. uplink multi-user MIMO systems) is analyzed. In contrast to the common views, we show that antenna correlation is potentially beneficial in a multi-user environment. The key is that the spatial diversity related to user locations (i.e., multi-user diversity) can compensate the loss of DOF due to antenna correlation. More specifically, it is shown numerically that there is a cross point between the capacity curves for systems with and without correlation. Below this point, correlation is advantageous and vice versa. Moreover, such a point occurs at a rate increasing with the number of mobile units (MUs) (denoted by K in this thesis), which implies that the range where antenna correlation is beneficial increases with K. We also quantify this advantage analytically in the limiting case of K → ∞. In the meanwhile, it is shown numerically and analytically that there is a similar advantage from antenna correlation for MIMO MACs with rate constraints. (We call this advantage correlation gain in this thesis.) In the second contribution, we study the impact of antenna correlation on the capacity of MIMO MACs with imperfect CSI at the transmitter (CSIT). We first consider the case of no CSIT.We prove that isotropic inputs (i.e., the covariance of transmitted signal for each MU is identity matrix) are the most robust and optimal ones, and therefore achieve the capacity of such systems. Both numerical results and theoretical analysis show that although antenna correlation is detrimental in all rate or power range, the capacity degradation decreases with K increasing and vanishes when K → ∞. These results imply that besides multi-user diversity, CSIT also plays an important role in exploiting correlation gain. We then study the systems with partial CSIT in form of channel covariance information (CCI). Our major finding is that, similar to the scenario of perfect CSIT, antenna correlation is potentially beneficial in a multi-user environment. We also prove that, when antennas at MUs are fully correlated, systems with CCI at transmitters can obtain exact the same correlation gain as that in systems with perfect CSIT. This indicates that CCI may be enough to exploit the potential benefit of antenna correlation. In the third contribution, we extend the results from the MAC scenario to the broadcast channel (BC) scenario (i.e., downlink multi-user MIMO systems). Numerical results show that, similar to MIMO MACs, antenna correlation can potentially improve the capacity of MIMO BCs. We point out that, besides multiuser diversity and power focusing effect, such a gain mainly comes from the fact that antenna correlation can increase the variance of the channel gain, which has already been regarded as a advantageous factor in systems with user scheduling. We also quantify the correlation gain in BCs for the limiting case of K → ∞ when antennas at the base station (BS) and/or MUs are fully correlated. Theoretical analysis shows that the asymptotic correlation gain for the case of full correlation at both the BS and MUs grows linearly and logarithmically with the antenna number at the BS, and logarithmically with the antenna number at each MU. In the final contribution, we consider the practical implementation aspects of correlation gain in coded MIMO multiple-access systems. To decrease the complexity of MIMO transmission under imperfect CSIT, we propose two types of low-cost but asymptotically optimal strategies, i.e. the instantaneous maximum eigenmode beamforming (MEB) and statistical MEB strategy. Interleave-division multiple-access (IDMA) technique, as a low-cost iterative multi-user detection (MUD) approach, is adopted to alleviate inter-user interference resulting from multi-user concurrent transmission. Simulation results demonstrate that our proposed transceiver (i.e., MEB-based IDMA system) is an effective platform in practice to obtain the aforementioned correlation gain. In summary, this thesis presents a comprehensive study on antenna correlation in multi-user MIMO systems. Both numerical and analytical results show that antenna correlation is potential advantageous in a multi-user environment. Such an advantage mainly comes from three aspects. First, the loss of the spatial DOF due to antenna correlation is compensated by multi-user diversity. Second, antenna correlation enables focusing power. Third, the variance of the channel gain is enlarged by antenna correlation, which is beneficial in systems with user scheduling. The finding in this thesis is useful in practice as minimizing the physical size of MUs and/or the BS is highly desirable, but it may result in antenna correlation.

Date of Award	15 Feb 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Ping LI (Supervisor)