# Joint Transmit Waveform and Receive Mismatched Filter Design to Suppress Range Sidelobe
## 1 Introduction  
In recent years, the study of dual-function radar and communication (DFRC) systems has garnered significant attention, as they offer the potential to alleviate cross-interference between radar and communication infrastructures while enhancing spectral efficiency [1, 2, 3, 4]. To achieve the functionality of DFRC systems, integrated waveforms capable of performing both radar and communication tasks are typically designed, and matched filters (MF) are used to enhance signal quality and reduce noise interference. Nevertheless, the MF frequently exhibits elevated sidelobe levels (SLL), which can diminish the likelihood of detecting feeble targets obscured within the high sidelobes. To address the issue of high sidelobes near the target unit, especially in scenarios with strong interference from adjacent range cells, it is necessary to suppress the near-range sidelobe interference (NRSI) they cause. The main sources of interference include environmental clutter, cross-interference from other radar systems, and adversarial electronic countermeasures. Therefore, designing a mismatched filter (MMF) to replace MF has become an effective solution [5, 6, 7, 8]. For the design of mismatched filters aimed at sidelobe reduction and interference suppression, in [9], a complementary discrepant filter array is introduced to diminishthe sidelobe amplitude of the unequivocal output and the power of range-indeterminate reflections. In [10], it puts forward a synergistic waveform and filter methodology for coherent frequency diverse array radar, which can attenuate the sidelobes linked with range pulse compression. In [11], it introduces an innovative weighted mismatched filter (WMMF) capable of efficiently suppressing sidelobes, while preserving the requisite signal-to-noise ratio (SNR) and without altering the radar's transmission or reception components. In [12], it introduces a weighted convex optimization framework integrated with a cyclic algorithm to formulate mismatched filters that attain a versatile balance between mainlobe broadening and sidelobe attenuation. In [13; 14; 15], they all designed a specific filter that effectively suppresses the range sidelobes of the echo pulse compression for a particular transmitted waveform. The aforementioned mismatched filter design methods aim to reduce sidelobes and suppress interference while maintaining good signal performance, such as SNR and unchanged system configuration. Each method is optimized for specific waveforms or scenarios, such as coherent frequency diverse radar or ambiguous echo energy suppression, using techniques like complementary filter groups, weighted mismatched filters, and convex optimization. However, these methods may increase the mainlobe width while suppressing sidelobes, as they do not constrain the mainlobe width, which affects range resolution. Additionally, the computational complexity of some methods is high, making them less suitable for real-time applications. For the joint optimization design of integrated waveforms and filters, in [2], an alternating projection-maximum likelihood method is developed to achieve a more accurate calculation of the target characteristics in radar communication systems. In [16], a mismatched filter is proposed that can achieve information diffusion and sidelobe suppression using space-frequency modulation technology while reducing the SNR loss during the filtering process. In [17], a method is proposed to mitigate partial sampling repeater jamming through a joint optimization iterative algorithm. In [18], a synergistic design technique for radar waveforms and mismatched filters is proposed, aiming to suppress range sidelobes, though with an accompanying SNR degradation. In [19], a novel mismatched filtering approach is introduced, which simultaneously optimizes pulse compression and spatial beamforming. Optimizing communication performance is also essential for improving the overall system performance.