Considering that frequency diverse array multiple-input multiple-output (FDA-MIMO) possesses extra range information to enhance sensing performance, this paper explores the FDA-MIMO-based integrated sensing and communication (ISAC) system. To reinforce the system communication capability, we propose the frequency offsets permutation index modulation (FOPIM) scheme, which conveys extra information bits by selecting and permutating frequency offsets from a frequency offsets pool. For the system communication function, considering the fact that the traditional maximum likelihood detection method suffers from high complexity and bit error rate (BER), the maximum likelihood-based two-stage detection (MLTSD) approach is presented to overcome this issue. For the system sensing function, we employ the two-step maximum likelihood estimator (TSMLE) to stepwise estimate the angle and range of the interested target. Furthermore, we derive the closed-form expressions for the tight upper bound on the communication BER, along with the sensing Cramér-Rao bound (CRB). The simulation results validate the theoretical analysis, demonstrating that the proposed system exhibits lower BER and superior range resolution than independent MIMO communication and sensing modules.

For multiple-input multiple-output (MIMO) frequency diverse array (FDA) communications, this paper proposes a frequency offsets index modulation (FOIM) scheme, which conveys extra information by selecting transmitting frequency offsets from a frequency offsets pool. To improve system spectral efficiency, we firstly design an orthogonal baseband waveform for FDA with the exact expression, then the corresponding receiver structure is proposed. Further, considering that the traditional maximum likelihood (ML) detection algorithm suffers from high complexity, an output combined maximum likelihood (OCML) approach is presented. Moreover, the closed-form expressions for the upper bound on bit error rates (BERs) of both ML and OCML methods are derived, as well as the counterpart of the system capacity. The simulation results show that the capacity of the proposed FOIM scheme outperforms the MIMO scheme, and meanwhile, our method achieves a higher communication rate when compared with the quadrature spatial modulation (QSM) scheme. Additionally, the proposed OCML algorithm can lead the BER performance of FOIM to be superior to that of the aforementioned approaches with significantly lower computational complexity.