  A cognitive radar adapts the transmit waveform in response to changes in the
radar and target environment. In this work, we analyze the recently proposed
sub-Nyquist cognitive radar wherein the total transmit power in a multi-band
cognitive waveform remains the same as its full-band conventional counterpart.
For such a system, we derive lower bounds on the mean-squared-error (MSE) of a
single-target time delay estimate. We formulate a procedure to select the
optimal bands, and recommend distribution of the total power in different bands
to enhance the accuracy of delay estimation. In particular, using Cram\'er-Rao
bounds, we show that equi-width subbands in cognitive radar always have better
delay estimation than the conventional radar. Further analysis using Ziv-Zakai
bound reveals that cognitive radar performs well in low signal-to-noise (SNR)
regions.
