  Dual function radar communication (DFRC) systems can achieve significant
improvements in spectrum efficiency, system complexity and energy efficiency,
and are attracting a lot of attention for next generation wireless system
design. This paper considers DFRC systems using MIMO radar with a sparse
transmit array, transmitting OFDM waveforms, and assigning shared and private
subcarriers to active transmit antennas. Subcarrier sharing allows antennas to
modulate data symbols onto the same subcarriers and enables high communication
rate, while the use of private subcarriers trades-off communication rate for
sensing performance by enabling the formulation of a virtual array with larger
aperture than the physical receive array. We propose to exploit the permutation
of private subcarriers among the available subcarriers and the pairing between
active antennas and private subcarriers to recover some of the communication
rate loss. Exploiting the $1$-sparse property of private subcarriers, we also
propose a low complexity algorithm to identify private subcarriers and detect
the antenna-subcarrier pairing.
