Generating and Detecting Solvable Chaos at Radio Frequencies with Consideration to MultiUser Ranging High entropy waveforms exhibit desirable correlation properties in radar and sonar applications when multiple systems are used in close proximity. Unfortunately, the information content of these signals can impose high sampling requirements for digital detection techniques. Solvable chaotic oscillators have been proposed to address such issues due to their simple, matched filters, where hardware has been demonstrated with a bandwidth of 10xe2x80x9320 kHz. To extend applications of these systems, we present theory, design, and experimental verification of solvable chaos at 1 MHz using simple offtheshelf components. The waveforms produced by this system were propagated over a 2.45 GHz RF link and detected with an RLCbased, purely analog matched filter. Further, we show that properties of this special class of chaotic systems can be exploited to yield RF noise sources that are generally advantageous for multiuser ranging applications when compared to conventional techniques. The result is a simple, lowcost, and potentially lowpower RF ranging system that requires very little digital signal processing.

Extended Logarithmic Frequency Domain Rulers for Joint RadarCommunications This paper studies the design and performance of a new class of Doppler estimation capable waveforms called Extended Logarithmic Frequency Domain Rulers (ELFDRs) for joint radarcommunications. ELFDRs are multicarrier waveforms whose carriers are spaced according to an Extended Golomb Ruler after a logarithmic warping of the frequency axis. The multiplicative Doppler shift additively translates the waveformxe2x80x99s logarithmically warped spectrum, which allows simultaneous signal detection and Doppler shift estimation via convolutional matched filtering of the logarithmically warped power spectrum. We propose to use these waveforms for communications by phase modulating the carriers and using the estimated Doppler shift to adjust a pilot tone time domain matched filter for fine symbol synchronization. The synchronized waveform is then sent to a communications module for symbol decoding. This paper gives an example of these waveforms, details their design, illustrates a receiver, and explores their bit error rate in AWGN and multipath.