Assume that the receiver estimates the propagation matrix from a known set of transmitted training signals, and then uses the estimate as though it were correct for nulling and cancellation. How much training is needed for satisfactory operation?

The optimal training signals are orthogonal with respect to time among the transmit antennas, and each transmit antenna is fed equal energy. Errors in estimating the propagation matrix manifest themselves as crosstalk among the virtual subchannels. If its magnitude is too large, the crosstalk constitutes an outage event that is independent of the primary outage event (e.g., that the value of the propagation matrix cannot support the transmission rate). We show that the training interval required to control the probability of the estimation-error induced outage is approximately proportional to the number of transmit antennas, and is independent of the number of receive antennas. Contrary to what is implied by their names, the operations of nulling and cancellation are, in fact, robust with respect to estimation errors.

Our results have an interesting implication for BLAST, either in a mobile environment, or for TDMA, where both training and data transmission have to occur within a fixed interval: if one wishes to maximize the overall transmission rate, then the number of transmit antennas should be chosen such that half of the interval is used for training, and half of the interval for data transmission.

Status: Appears in Proceedings of 1999 Allerton Conference, Monticello, IL.

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