The Role of Correlation in Communication over Fading Channels

In wireless communication systems with no channel state information (CSI) available at the transmitter or receiver, channel correlation plays a pivotal role in analyzing system behavior. This thesis explores the theme of channel correlation in several scenarios.

The first part of the thesis investigates a Rayleigh fading channel without correlation in time. Using a suitable logarithmic transformation, the channel model can be converted into an equivalent channel model with additive noise only. Such a perspective lends geometric intuition and often substantially reduces mathematical machinery to evaluate performance in terms of achievable rates and capacity. On one hand, a series of known results are revisited and reinterpreted; and on the other hand, several new results are obtained using this induced additive-noise perspective.

The second part of the thesis focuses on channel correlation in time. Using a block decision-feedback architecture, the original channel is decomposed into a series of parallel sub-channels, each being conditionally coherent linear Gaussian. Both discrete-time and continuous-time channels are examined, and the asymptotics of mutual information at low signal-to-noise ratio (SNR) are obtained. Compared to known capacity upper bounds under peak constraints, these asymptotics lead to negligible loss in the low-SNR regime for slowly time-varying fading channels.

The third part of the thesis studies channel correlation in space, {it i.e.}, across multiple transmit and receive antennas. In the low-SNR regime, it is shown using asymptotic analysis that spatially correlated antennas lead to both multiplicative rate gain as well as peak power reduction, at no cost of additional transmit power. Then a low-complexity communication scheme employing on-off signaling with hard-decision demodulation is evaluated, which demonstrates that most of the benefits promised by asymptotic analysis are realizable.

Finally, the last part of the thesis summarizes the main contributions and points out directions for future work.