  Orthogonal frequency division multiplexing (OFDM) has been widely adopted in
dual-function radar-communication (DFRC) systems, where radar and
communications are performed simultaneously with a common signal. However, with
random communication symbols (CS) in DFRC, the transmit signal has a random
ambiguity function that affects the radar's range-velocity estimation
performance, whose influence is remained uncovered. Hence, this paper focuses
on minimizing the outlier probability (OP) -- the probability of incorrectly
estimating a target's range-velocity bin -- in OFDM DFRC w.r.t the CS
probability distribution (i.e., the \emph{input distribution}). Conditioned on
the CSs, the OP only depends on the CS magnitudes. Hence, we consider the
following two schemes for the above optimization: CSs with (1) constant
magnitude (phase shift keying input), and (2) random magnitude (Gaussian
input). For (1), the problem reduces to the familiar power allocation design
across OFDM's subcarriers and symbols, with uniform power allocation across
subcarriers and a \emph{windowed} power allocation across symbols being
near-optimal. For (2), the mean and variance of the Gaussian distribution at
each subcarrier is optimized, with an additional communication constraint to
avoid the zero-variance solution where no CSs are carried. We observe that
subcarriers with strong communication channels feature strong variance (i.e.,
favour communications) while the others are characterized by a strong mean
(favouring radar). However, the overall power allocation (i.e., the sum of mean
and variance) across the OFDM subcarriers and symbols is similar to (1).
Simulations show that CSs with random magnitudes degrade the sensing
performance, but can be compensated significantly with the proposed input
distribution optimization.
