  This paper focuses on waveform design for joint radar and communication
systems and presents a new subset selection process to improve the
communication error rate performance and global accuracy of radar sensing of
the random stepped frequency permutation waveform. An optimal communication
receiver based on integer programming is proposed to handle any subset of
permutations followed by a more efficient sub-optimal receiver based on the
Hungarian algorithm. Considering optimum maximum likelihood detection, the
block error rate is analyzed under both additive white Gaussian noise and
correlated Rician fading. We propose two methods to select a permutation subset
with an improved block error rate and an efficient encoding scheme to map the
information symbols to selected permutations under these subsets. From the
radar perspective, the ambiguity function is analyzed with regards to the local
and the global accuracy of target detection. Furthermore, a subset selection
method to reduce the maximum sidelobe height is proposed by extending the
properties of Costas arrays. Finally, the process of remapping the frequency
tones to the symbol set used to generate permutations is introduced as a method
to improve both the communication and radar performances of the selected
permutation subset.
