Input Distribution Optimization in OFDM Dual-Function Radar-Communication Systems

Orthogonal frequency division multiplexing (OFDM) has been widely adopted in dual-function radar-communication (DFRC) systems. However, with random communication symbols (CS) embedded in the DFRC waveform, the transmit signal has a random ambiguity function that affects the radar's delay-Doppler estimation performance, which has not been well explored. This paper addresses this gap by first characterizing the outlier probability (OP) - the probability of incorrectly estimating a target's (on-grid) delay-Doppler bin - in OFDM DFRC for any given CS realization. This subsequently motivates the OFDM DFRC waveform design problem of minimizing the OP w.r.t the CS probability distribution (i.e., the 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 input distribution (phase shift keying), and (2) variable magnitude input distribution (Gaussian). For (1), minimizing the OP reduces to the familiar power allocation design across OFDM's subcarriers and symbols, with uniform power allocation across OFDM subcarriers and a windowed power allocation across OFDM 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 a large variance (favour communications) while the others are characterized by a large mean (favour radar). However, the overall power allocation (i.e., the sum of the squared mean and variance) across the OFDM subcarriers and symbols is similar to (1). Simulations for (2) show that while random CS magnitudes benefit communications, they degrade radar performance, but this can be mitigated using our optimized input distribution.