252 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 1, JANUARY 2011 Correlation Rotation Linear Precoding for MIMO Broadcast Communications Christos Masouros, Member, IEEE Abstract—A simple linear precoding technique is proposed for multiple input multiple output (MIMO) broadcast systems using phase shift keying (PSK) modulation. The proposed technique is based on the fact that, on an instantaneous basis, the interference between spatial links in a MIMO system can be constructive and can contribute to the power of the useful signal to improve the per- formance of signal detection. In MIMO downlinks this co-channel interference (CCI) can be predicted and characterised prior to transmission. Contrary to common practice where knowledge of the interference is used to eliminate it, the main idea proposed here is to use this knowledge to influence the interference and benefit from it, thus gaining advantage from energy already existing in the communication system that is left unexploited otherwise. The pro- posed precoding aims at adaptively rotating, rather than zeroing, the correlation between the MIMO substreams depending on the transmitted data, so that the signal of interfering transmissions is aligned to the signal of interest at each receive antenna. By doing so, the CCI is always kept constructive and the received signal to interference-plus-noise ratio (SINR) delivered to the mobile units (MUs) is enhanced without the need to invest additional signal power per transmitted symbol at the MIMO base station (BS). It is shown by means of theoretical analysis and simulations that the proposed MIMO precoding technique offers significant performance and throughput gains compared to its conventional counterparts. Index Terms—Adaptive transmission, channel inversion, in- terference multiuser channels, multiple input multiple output (MIMO) systems, precoding. I. INTRODUCTION T HE pursuit of cost-effective and power-efficient mobile units (MUs) in wireless communications systems has re- cently stimulated research on precoding techniques for mul- tiple input multiple output (MIMO) downlink transmission, as a means of transferring the signal processing complexity to the base stations (BSs). Simple forms of precoding schemes al- ready appear in communication standards such as the 3 GPP long term evolution (LTE) [1] and are expected to dominate future implementations of telecommunications networks. Re- ceiver based techniques [2]–[5] that have been traditionally ap- plied to counteract the impediments of MIMO systems, tend to involve quite complex detection processing which renders Manuscript received August 20, 2010; accepted October 12, 2010. Date of publication October 18, 2010; date of current version December 17, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiang-Gen Xia. The author is with the School of Electronics, Electrical Engineering and Com- puter Science, Queen’s University Belfast, BT3 9DT, Belfast, U.K. (e-mail: chris.masouros@ieee.org). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2010.2088395 them impractical for use in the MUs in downlink communi- cations. In order to shift the signal enhancement processing to the BS during downlink transmission, various precoding tech- niques have been developed with the view to maintain simple low-cost MUs. The least complexity of the techniques available is offered by linear precoding in the form of channel inversion (CI) [6]. It was shown, however, in [7] that the transmission rate and throughput delivered with CI are limited and do not im- prove with the increase in the number of antennas. Regularized channel inversion (RCI) proposed in [7], provides some perfor- mance and capacity gains with respect to the conventional CI. Nevertheless, the transmission rates offered by this scheme are still far from reaching the theoretical channel capacity. Based on the initial information theoretical analysis in [8], a number of nonlinear dirty paper coding (DPC) techniques [9]–[12] have been proposed to further increase transmission rates. Despite the significant capacity benefits they offer, the DPC methods de- veloped so far are complex as they require sophisticated signal processing at the transmitter. The fact that sphere-search algo- rithms [13] as complex as the ones used in MIMO detection [2], [3] are employed for determining the data perturbation quantity, renders DPC techniques rather impractical in their present state. Joint transmit-receive beamforming (e.g., [14]) is a promising alternative. However, while less complex than DPC, this group of techniques has two main disadvantages compared to purely transmitter-based precoding. First, they require receive antenna cooperation which limits their applications in realistic scenarios. Moreover, the most robust beamforming schemes entail iterative communication between the transmitter and receiver for the op- timization of the joint processing and the system configuration. This needs to be done every time the channel characteristics change and hence, in fast fading environments, introduces con- siderable latency to the MIMO downlink system. As a result of the above, the advantageous tradeoff between performance and complexity of the linear CI and RCI precoding schemes renders them practical and appropriate for contemporary MIMO broad- cast systems. In line with this, recent work has investigated the exploitation of co-channel interference (CCI) in order to glean useful signal energy and attain more power-efficient communication systems. The work is based on the concept that for PSK, the instanta- neous interference can be separated into constructive and de- structive, as previously presented in [15] by mathematical anal- ysis. Since all the data symbols to be transmitted are known at the BS prior to downlink transmission the resulting interference can be predicted. In [15] an adaptation of CI, namely selective CI (SCI), was proposed where the precoding was applied solely to eliminate destructive interference, while constructive interfer- ence was allowed at the receiver in order to enhance the power 1053-587X/$26.00 © 2010 IEEE