Long-Time Signal Nonlinear Integration with Arbitrary Complex Envelope

The migration of echo envelop and the complex underwater acoustic environment are challenging issues in long-time signal integration. In previous studies of long-time coherent integration, researchers usually constructed multi-pulse echo model with linear frequency modulation (LFM) signal to deduce perfect analytical formula, it has no generality when other sonar waveforms are used. Aiming to solve the problems, a nonlinear pulse integration method with arbitrary complex envelope form is discussed in this paper. The nonlinear procedure is to utilize multiply operation instead of add operation to accumulate the power of the received signals in various returns from the detected target moving with a uniform velocity. And a general expression of the integration output of the signal with arbitrary waveform envelope is given in the form of wideband ambiguity function.