MIMO capacity with channel state information at the transmitter

This paper presents analytical expressions for the capacity of single-user multi-antenna channels, known instantaneously by both transmitter and receiver, at moderate and high signal-to-noise ratios. Fading channels with both uncorrelated and correlated antennas are encompassed. The characterization is conducted primarily in the limit of large numbers of antennas, with accompanying examples that illustrate the validity of the results for even small numbers thereof. In the absence of correlation, the capacity is also tightly bounded for fixed numbers of antennas with compact closed-form expressions.

I. Introduction

The capacity of a MIMO (multi-input multi-output) channel is influenced by the degree of CSI (channel-state information) available to both transmitter and receiver. In most instances of multi-antenna communication, the receiver can accurately track the instantaneous state of the channel from pilot signals that are typically embedded within the transmissions. In terms of CSI at the transmitter, on the other hand, several scenarios are possible: •

In frequency-duplexed systems, where uplink and down-link are apart in frequency, the link fading is not reciprocal and thus the CSI must be conveyed through feedback, which may incur round-trip delays that are nonnegligible with respect to the coherence time of the CSI being re-ported. Consequently, the transmitter is usually deprived of instantaneous CSI.

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In time-duplexed systems, in contrast, the links are reciprocal as long as the coherence time of the fading process exceeds the duplex time. Thus, the transmitter may have access to reliable CSI at low and moderate levels of mobility.

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At high levels of mobility, even in time-duplexed systems the CSI becomes rapidly outdated.