Performance Estimates of the Pseudo-Random Method for Radar Detection

A performance of the pseudo-random method for the radar detection is analyzed. The radar sends a pseudo-random sequence of length $N$, and receives echo from $r$ targets. We assume the natural assumptions of uniformity on the channel and of the square root cancellation on the noise. Then for $r \leq N^{1-\delta}$, where $\delta > 0$, the following holds: (i) the probability of detection goes to one, and (ii) the expected number of false targets goes to zero, as $N$ goes to infinity.