  In this paper, we derive an ambiguity function (AF) for the transmit
beamspace (TB)-based multipleinput multiple-output (MIMO) radar for the case of
far-field targets and narrow-band waveforms. The effects of transmit coherent
processing gain and waveform diversity are incorporated into the AF definition.
To cover all the phase information conveyed by different factors, we introduce
the equivalent transmit phase centers. The newly defined AF serves as a
generalized AF form for which the phased-array (PA) and traditional MIMO radar
AFs are important special cases. We establish relationships among the defined
TB-based MIMO radar AF and the existing AF results including the Woodward's AF,
the AFs defined for the traditional colocated MIMO radar, and also the PA radar
AF, respectively. Moreover, we compare the TB-based MIMO radar AF with the
square-summation-form AF definition and identify two limiting cases to bound
its 'clear region' in Doppler-delay domain that is free of sidelobes.
Corresponding bounds for these two cases are derived, and it is shown that the
bound for the worst case is inversely proportional to the number of transmitted
waveforms K, whereas the bound for the best case is independent of K. The
actual 'clear region' of the TB-based MIMO radar AF depends on the array
configuration and is in between of the worst- and best-case bounds. We propose
a TB design strategy to reduce the levels of the AF sidelobes, and show in
simulations that proper design of the TB matrix leads to reduction of the
relative sidelobe levels of the TB-based MIMO radar AF.
