Signal design and convolutional coding for noncoherent space-time communication on the block-Rayleigh-fading channel

We consider the problem of designing signal constellations for the multiple transmit-multiple receive antenna Rayleigh-fading communication channel, when neither the transmitter nor the receiver know the fading. In particular, by employing the asymptotic union bound (AUB) on the probability of error, we give a new formulation of the problem of signal design for the noncoherent fading channel. Since unitary signals are optimal for this channel (in the limit of large signal-to-noise ratios SNRs), the problem can be posed in terms of packings on the Grassmanian manifold. A key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound. As a consequence of our use of this distance measure, we obtain signal designs that are guaranteed to achieve the full diversity order of the channel, a result that does not hold when the chordal distance is used. We introduce a new method of recursively designing signals, termed successive updates, to approximately optimize this performance measure. We then examine the use of our signals with several convolutional codes over the fading channel. An upper bound on the bit error probability of the maximum-likelihood decoder is presented together with an asymptotic analysis of that bound.