# MIMO Systems with Residual Hardware Impairments

[Licentiatavhandling]

Recent years have witnessed an unprecedented explosion in mobile data traffic, due to the expansion of numerous types of wireless devices, which have enabled a plethora of data-hungry applications. Novel techniques, such as large-scale multiple-input multiple-output (MIMO) systems, represent potential candidates to support the ever-growing demands. However, large-scale MIMO systems will be a viable solution only if low-cost and energy-efficient hardware is deployed, which is particularly prone to impairments. Previous works have reported effective calibration schemes and compensation algorithms to mitigate individual hardware impairments, such as I/Q imbalance, phase noise and amplifier nonlinearities. However, a certain amount of residual hardware impairments always persist. In this thesis, we aim at exploring the fundamental limits that residual hardware impairments have imposed on MIMO systems, and more interestingly, on large-scale MIMO systems. We consider both the cases whereof the receiver has perfect channel state information (CSI) and estimated CSI. Important insights are gained through the analysis of system performance indicators, such as ergodic channel capacity and achievable rates, channel estimation accuracy and energy efficiency. Paper A characterizes the ergodic channel capacity of Rayleigh fading channels in the presence of transceiver residual hardware impairments. Closed-form capacity formulas for MIMO systems with arbitrary number of antennas and signal-to-noise ratio (SNR) values are derived, while approximations at low and high SNRs are also presented. We further extend our results to large-scale MIMO systems, and derive the channel capacity in the asymptotic regime. Paper B, which is a journal version of Paper D, considers a training-based MIMO system with transmit residual hardware impairments. The impact of residual hardware impairments on channel estimation accuracy and achievable rates with different linear receivers is theoretically analyzed. The achievable-rate-maximizing training lengths are thereafter presented. For large-scale MIMO systems, we derive deterministic equivalents of the achievable rates, and the corresponding optimal training lengths. In paper C, we assess residual hardware impairments from an energy-efficiency perspective. Assuming estimated CSI and zero-forcing (ZF) receivers, we find the optimal training lengths, as well as, the number of transmit and receive antennas that maximize the system energy efficiency at any given SNR, through a proposed iterative sequential optimization algorithm.

**Nyckelord: **Achievable rate, channel capacity, channel estimation, energy efficiency, large-scale MIMO, residual hardware impairments, training length.

Denna post skapades 2014-12-19. Senast ändrad 2015-02-11.

CPL Pubid: 208611