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 ≤ N
^1-δ
, where δ > 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.