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Performance Analysis of MIMO Systems in Spatially Correlated Fading Using MatrixMonotone Functions
Eduard A. JORSWIECK Holger BOCHE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89A
No.5
pp.14541472 Publication Date: 2006/05/01 Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.5.1454 Print ISSN: 09168508 Type of Manuscript: PAPER Category: Information Theory Keyword: average mutual information, minimum meansquare error, multiple antenna system, optimal transmit strategies, matrixmonotone functions, convex optimization, spatial correlation,
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Summary:
The average performance of a singleuser MIMO system under spatially correlated fading and with different types of CSI at the transmitter and with perfect CSI at the receiver was studied in recent work. In contrast to analyzing a single performance metric, e.g. the average mutual information or the average bit error rate, we study an arbitrary representative of the class of matrixmonotone functions. Since the average mutual information as well as the average normalized MSE belong to that class, this universal class of performance functions brings together the information theoretic and signal processing performance metric. We use Lowner's representation of operator monotone functions in order to derive the optimum transmission strategies as well as to characterize the impact of correlation on the average performance. Many recent results derived for average mutual information generalize to arbitrary matrixmonotone performance functions, e.g. the optimal transmit strategy without CSI at the transmitter is equal power allocation. The average performance without CSI is a Schurconcave function with respect to transmit and receive correlation. In addition to this, we derive the optimal transmission strategy with longterm statistics knowledge at the transmitter and propose an efficient iterative algorithm. The beamformingrange is the SNR range in which only one data stream spatially multiplexed achieves the maximum average performance. This range is important since it has a simple receiver structure and well known channel coding. We entirely characterize the beamformingrange. Finally, we derive the generalized waterfilling transmit strategy for perfect CSI and characterize its properties under channel correlation.

