Waveform design with stopband and correlation constraints for cognitive radar

Abstract

One of the main objectives of cognitive radar is to adapt the spectrum of transmit waveforms to certain needs, such as avoiding reserved frequency bands or narrowband interferences. Besides spectral requirements, good correlation properties of the transmit waveforms are also desired in specific applications, such as range compression. Moreover, practical hardware constraints usually require the transmit waveforms be unimodular (i.e. only phase-modulated). In this paper, we propose a new algorithm named SCAN (stopband cyclic algorithm new) to design unimodular sequences with spectral power suppressed in arbitrary bands and with low correlation sidelobes as well. The SCAN algorithm, which starts from random initializations, can generate many sequences possessing similarly good properties. Furthermore, the SCAN algorithm is based on FFT (fast Fourier transform) operations and thus is computationally efficient, which facilitates long-sequence design and real-time waveform update.

Synthesizing Low Autocorrelation and Low PAPR OFDM Sequences Under Spectral Constraints Through Convex Optimization and GS Algorithm

“…3) Fix and ; update the value of by the optimal one that minimizes the cost function . This optimal value can be derived by expanding the cost function as [25] (55) where is a constant. Then the optimal is given by (56) where is the th element of , and is the th element of .…”

“…When PAPR is further considered, similar to the method used in [24] and [25], we try to find a solution set that minimizes the following cost function:…”

“…The design objective can also be a certain convex function of the sequence AC sidelobes. The two metrics PSL and WSSL had been adopted as design criteria in [21], [22], [25]- [27]. To demonstrate an example of practical application, we will present the connection between the AC metrics and the channel estimation error when the proposed sequence is applied as the training sequence for channel estimation.…”

“…However, because the filtered sequences are not explicitly optimized toward the desired AC property under the constraints specified by the spectrum mask, the AC properties of the filtered sequences are not as good as those of the original sequences. A recent work [25] considered the waveform design for cognitive radar system. The method presented in [25] is used to obtain unimodular sequences with suppressed power in arbitrarily chosen bands and with low aperiodic AC sidelobe level.…”

“…A recent work [25] considered the waveform design for cognitive radar system. The method presented in [25] is used to obtain unimodular sequences with suppressed power in arbitrarily chosen bands and with low aperiodic AC sidelobe level. In contrast to that work, we focus on designing the sequences strictly satisfying the given spectral constraints.…”