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A simple and effective modification of the high-order ambiguity function (HAF) is introduced. The number of phase differentiations is decreased to two with respect to the HAF. The obtained signal has a cubic phase, the parameters of which can be estimated using the cubic phase function (CPF) in the final stage. The SNR threshold of the proposed modification is reduced for 9 dB with respect to the HAF, while the MSE is about 2 dB less.