Circulant MIMO Structures

Multiple-input, multiple-output (MIMO) systems allow increased capacity over single port antenna systems in the presence of multipath fading environments. The challenging areas in a MIMO system overlap between the propagation channel, the antennas and the signal processing. In this dissertation two aspects of MIMO theory are investigated. Firstly, the effect of systematic correlation on the capacity efficiency is analyzed in detail. This analysis has been undertaken through the introduction of a specific correlated structure, namely the circulant. Compared to the completely random (i.i.d.) structure, the circulant shows a clear capacity increase both in the theoretical Shannon limit and also in the practicable, QAMincluded case. This fascinating behavior can be fully explained through investigation of the pdfs of the eigenvalues of the channel matrices. The investigation shows that the capacity increase arises from the more similar eigenvalues of the circulant structure. The empirical pdfs of the eigenvalues are presented and parameters are introduced to compare the similarity between the eigenvalues. Furthermore, the basic hypothesis of parallel channel capacity is clarified with respect to the water-filling of MIMO eigenchannels. Other advantages of the circulant structure, based on its fixed eigenvectors, have been developed. In particular, it is possible to reduce the degradation caused by errors in the channel estimation for circulant channels. While this first aspect of MIMO theory concerns the channel modeling and signal processing, the second aspect focuses on the important practical issue of power allocation between eigenchannels. The optimum power allocation is the non-linear strategy of water filling, but this is expensive in processing power to implement. Therefore it is of interest to decrease the complexity of water filling using a sub-optimum method. It is shown here that it is reasonable to circumvent the complexity of water filling by simply using equal powers. Again, this simplification is feasible because of the arrangement of the eigenvalues in the channel matrix. For differently dimensioned MIMO systems, there is a different power threshold above which we can substitute equal powers instead of water filling powers. An experimental rule for this power threshold has been derived.