Suppose that a multiinput/multioutput channel is described by a time-invariant, linear operator H, which maps an input vector waveform u(•) to an output vector waveform y(•). The input u(•) is assumed to be bounded in energy (L2 norm) on the time interval [0,T]. Let Nmax(T,∊) denote the maximum number of inputs to H for which any pair of distinct outputs are separated by at least e in L2 norm. The limit of [log2 Nmax(T,∊)]/ T as T →∞ is known as “∊-rate.” Here we extend the bounds on ∊-rate given by Root for single-input/ single-output channels to multiinput/multioutput channels. This extension uses a result due to Lerer on the eigenvalue distribution of a convolution operator with a matrix kernel (impulse response). Our results are used to assess the increase in data rate attainable by designing input signals which exploit the multidimensional nature of the channel, relative to treating each constituent channel in isolation. Numerical results based upon a simple model for two coupled twisted-pair wires are presented.
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences