There is a presumed adverse effect on radar operation brought about from embedding communication signals in radar waveforms. Contrary to that presumption, we show in this paper that modulation of the radar pulse can indeed benefit both radar and communications in the dual system paradigm. This is shown by analyzing the impact of phase-shift keying (PSK) symbol embedding on the ambiguity function (AF) of a multiple-input multiple-output (MIMO) radar. Our analysis shows that the embedded PSK symbols yield reduction in the AF sidelobe peaks for a single pulse as well as for a series of radar pulses. To prove these results, we analyze the AF with and without the PSK symbol embedding. It is shown that the embedding of PSK symbols enable increasing the number of orthogonal transmit waveforms that can be used without increasing the sidelobe levels (SLL) of the corresponding AF.