Frequency division multiplexing technique for composite ambiguity function approximation

In this paper, we propose a frequency division multiplexing (FDM) diversity waveform technique to achieve a delay-Doppler response that approximates the composite ambiguity function (CAF) in a multiple target scenario. First, a channel estimate based on maximum likelihood estimation (MLE) for each subband is provided, and the signal to noise power ratio (SNR) needed to achieve the specific variance requirement of the MLE is derived. Next, using the Doppler transformation, we show how to combine the output response of each subband undergoing a different Doppler shift. Then the CAF approximation of each detected target is derived based on the coherent CLEAN algorithm. Finally, the CAF approximation of all the targets is attained, having the improved delay-Doppler resolution and thus providing a way to resolve initially undetected targets using a recursive procedure.