###### Abstract  
Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) technology is widely used in integrated radar and communication systems (IRCSs). Moreover, index modulation (IM) is a reliable OFDM transmission scheme in the field of communication, which transmits information by arranging several distinguishable constellations. In this paper, we propose a sparse reconstruction-based joint signal processing scheme for integrated MIMO-OFDM-IM systems. Combining the advantages of MIMO and OFDM-IM technologies, the integrated MIMO-OFDM-IM signal design is realized through the reasonable allocation of bits and subcarriers, resulting in better intercarrier interference (ICI) resistance and a higher transmission efficiency. Taking advantage of the sparseness of OFDM-IM, an improved target parameter estimation method based on sparse signal reconstruction is explored to eliminate the influence of empty subcarriers on the matched filtering at the receiver side. In addition, an improved sequential Monte Carlo signal detection method is introduced to realize the efficient detection of communication signals. The simulation results show that the proposed integrated system is 5 dB lower in the peak sidelobe ratio (PSLR) and \(1.5\times 10^{5}\) lower in the number of complex multiplications than the latest MIMO-OFDM system and can achieve almost the same parameter estimation performance. With the same spectral efficiency, it has a lower bit error rate (BER) than existing methods. integrated radar and communications; MIMO-OFDM; index modulation (IM); signal sparsity model; low-complexity detection 2024 16 1773.10.  
optimize transmitted waveforms and further improve received signal processing for better interoperability and efficiency [8; 9; 10; 11]. Orthogonal frequency division multiplexing (OFDM) is a special multicarrier modulation technique that has gained wide attention in the field of digital communications and radar sensing [12; 13; 14]. This technology can realize high-speed data transmission by virtue of effectively overcoming intersymbol interference, strong resistance to multipath fading, and high spectrum utilization. Several in-depth studies on integrated waveform design and received signal processing schemes based on OFDM signals can be found in the literature [15; 16; 17; 18; 19; 20]. Index modulation, on the other hand, is a reliable modulation technology with high spectrum and energy efficiencies. It transmits information using embedded indexes of building blocks of antennas, subcarriers, spreading codes, and time slots [21; 22]. OFDM with index modulation (OFDM-IM) is introduced to take advantage of both technologies. It can flexibly adjust the number and location of activated subcarriers to achieve a favorable compromise between system performance, spectrum utilization, and energy efficiency [23; 24]. Because of its flexible design, OFDM-IM has attracted great attention [25; 26]. In addition, the multiple-input multiple-output (MIMO) technology is one of the key technologies for future mobile and wireless communication systems, which is characterized by obtaining both reliability and effectiveness gains through the use of spatial resources on the basis of the full utilization of existing spectrum resources. Therefore, MIMO-OFDM technology is also considered as one of the key technologies in 5G or even 6G digital communication [27; 28; 29]. By combining the advantages of MIMO technology and OFDM-IM technology, the system proposed in [30] adopts a hybrid analog-digital (HAD) beamforming structure based on MIMO-OFDM-IM, which can be effectively applied to the millimeter wave field. In [31], a feasible solution is proposed by using a Pareto waveform optimization design to approximate the global Pareto optimal compromise between spectrum efficiency and energy efficiency, and it can effectively solve the variational constraint problem in combinatorial optimization models.