Bit Modulated Frequency Permutation Waveforms for Joint Communications and Radar

In this paper, we propose the selection of a subset of waveforms based on the random stepped frequency permutation waveform to support joint radar and communication. More specifically, we solve two critical implementation problems arising from the subset selection which is motivated by the fundamental bit level operation requirements of communication systems. Noting that the practicality of any selected subset depends on the feasibility of efficient implementation, we focus on finding a specific subset for which we can design an efficient mapping process and a receiver implementation. More specifically, we propose an efficient process to map information bits to waveforms based on the factorial number system. An efficient optimal communication receiver that utilizes the Hungarian algorithm is also designed. For additive white Gaussian noise and correlated Rician fading channels, the bit error rate is analyzed in accordance with the optimum maximum likelihood detection.