On the near-equivalence of envelope and square-law detection of correlated Gaussian noise

Postdetection integration of radar signals in correlated noise background results in degraded detection performance which is analytically tractable for a square-law detector, but not for the linear envelope detector usually employed in practical radar receivers. It is shown that for stationary Gaussian input noise with arbitrary correlation, the "effective number of integrated independent noise samples" (N
e
) satisfies: 1 ≤ N
e
(envelope)/N
e
(square-law) ≤ 4(4 - π)π ≈ 1.093, thus suggesting near-equivalence of the detection performance and justifying results previously obtained by simulation techniques.