  Motivated by the ideal peak-to-average-power ratio and radar sensing
capability of traditional frequency-coded radar waveforms, this paper considers
the frequency shift keying (FSK) based waveform for joint communications and
radar (JCR). An analysis of the probability distributions of its ambiguity
function (AF) sidelobe levels (SLs) and peak sidelobe level (PSL) is conducted
to study the radar sensing capability of random FSK. Numerical results show
that the independent frequency modulation introduces uncontrollable AF PSLs. In
order to address this problem, the initial phases of waveform sub-pulses are
designed by solving a min-max optimisation problem. Numerical results indicate
that the optimisation-based phase design can effectively reduce the AF PSL to a
level close to well-designed radar waveforms while having no impact on the data
rate and the receiver complexity. For large numbers of waveform sub-pulses and
modulation orders, the impact on the error probability is also insignificant.
