Time limited and bandwidth constrained signal design for the fast fading noncoherent MIMO channel

We address the problem of bandwidth constrained space-time signal design for the noncoherent Rayleigh block-fading channel. Existing design techniques for this channel subdivide the coherence interval into smaller time blocks and use repetitions of a basic waveform to signal in each sub-block. When the coherence time of the channel is short this access technique becomes questionable, due to the inverse relationship between bandwidth and time support. In particular, there may not be sufficient time support to allow matched filtered reception with finite (or nearly finite) Shannon bandwidth waveforms. To address this problem, we consider other notions of bandwidth, such as the root-mean square (RMS) bandwidth and fractional out of band energy (FOBE), which are appropriate for signals with finite time support. We extend our previous work on unconstrained signal designs for the block fading channel to incorporate such bandwidth constraints. The resulting signal constellations can be used 1) as a comparison point for any signal design procedure and 2) to conclude that there is a performance advantage to be had when signals are properly matched to the finite time support of the channel.