The essential degrees of freedom in space-time fading channels

The key to reliable communication is a fundamental understanding of the interaction between the signal space and the channel. In time- and frequency-selective multi-antenna (space-time) fading channels this interaction happens in time, frequency and space. In this paper we propose a four-dimensional Karhunen-Loeve-like Fourier series representation for space-time channels that captures the essence of such interaction and exposes the intrinsic degrees of freedom in the channel. The four dimensions are: time, frequency and the two spatial dimensions at the transmitter and receiver. The key signal space parameters are the signaling duration, bandwidth and the two array apertures. The corresponding channel parameters are the delay, Doppler and the two angular spreads associated with the scattering environment. The representation induces a virtual partitioning of propagation paths in-time, frequency and space that reveals their contribution to channel capacity and diversity. It also exposes fundamental dependencies between time, frequency and space thereby revealing the essential independent degrees of freedom in the channel.