In this manuscript we investigate the implications of adopting a double cyclic prefix in the orthogonal timefrequency space modulation. Our study first focuses on the analysis of the modulated signal and on the development of a useful model for the received signal in the presence of a doubly selective fading channel. On the one hand, our mathematical results allow us to accurately assess the impact of pulse shaping on the structure of the transmitted waveform and on its power spectral density, and to develop some simple rules for allocating multiple pilot symbols within each orthogonal time-frequency space symbol. On the other hand, they are exploited to develop a novel algorithm for pilot-aided channel estimation, whose output provides a detailed representation of the communication channel; for this reason, it can be used for sensing at the transmit side in integrated sensing and communication applications, or for channel equalization at the receive side in digital communications. Our numerical results evidence that our channel estimation & equalization algorithm outperforms the other related techniques available in the technical literature at the price of a limited increase in computational complexity.

In this manuscript, an innovative method for the detection and the estimation of multiple targets in a radar system employing orthogonal frequency division multiplexing is illustrated. The core of this method is represented by a novel algorithm for the detection of multiple superimposed two-dimensional complex tones in the presence of noise and the for estimation of their parameters. This algorithm is based on a maximum likelihood approach and combines a single tone estimator with a serial cancellation procedure. Our numerical results lead to the conclusion that the developed method can achieve a substantially better accuracy-complexity trade-off than various related techniques in the presence of closely spaced targets.