## 1 Introduction  
Atom-based measurements have been successfully used as time, length, and frequency standards due to the unique properties of atoms and molecules [1; 2]. The measurement of microwave electric field (E-field) based on a Rydberg atom demonstrates advantages of traceability and self-calibration [3; 4; 5; 6; 7] by using the concept of electromagnetically induced transparency (EIT) [8; 9] in a room temperature vapor cell. The EIT spectroscopy is obtained by applying the coupling laser excites the atoms to Rydberg state when the probe laser is used to detect the response of the atom, which results in the transparency of the atoms. The microwave E-field measurement has widespread applications in the fields of antenna calibration [10], terahertz sensing [11], and the characterization of electronics [12; 13]. The E-field measurement method with dipole antenna [10] inevitably has the calibration drawbacks. The calibration error is introduced when the probe is calibrated in a reference field. The Autler-Townes (AT) splitting spectrum of Rydberg atoms effectively solves this problem [14] with the advantage of the consistent frequency of atomic transition. At the same time, it is possible to achieve the broadband microwave E-field measurement by using different Rydberg states due to the numerous available resonant frequencies from 100 MHz to sub THz. The AT splitting interval \(\Delta f_{0}\) is proportional to the microwave field intensity (E), which can be expressed as \(\Delta f_{0}=\Omega_{M}/(2\pi)=\mu_{M}E/(2\pi\hbar)\), in which \(\Omega_{M}\) is the Rabi frequency of the field, \(\mu_{M}\) is the Rydberg atoms transition dipole matrix element, \(\hbar\) is Planck constant. The AT splitting spectroscopy provides a link to direct International System of Units (SI) traceable, where the [PERSON]'s constant \(\hbar\) is the heart of this traceable method, and the measurement of the microwave field intensity is bridged to the determination of Autler-Townes splitting interval. Therefore, the E-field measurement based on the Rydberg atoms can be developed as a broadband, direct SI-traceable, and self-calibrating sensor. At present, the microwave E-field measurement based on the Rydberg atoms has widely application prospects [15; 16; 17] in the fields of self-calibrated measurements, sub-wavelength imaging, and electronic communication, which has shown promise to measure moderate to strong field intensity with a magnitude of \(\sim\)Vm\({}^{-1}\). However, the measurement by Rydberg atoms poses some difficulties for weak field intensity measurement lower than \(\sim\upmu\)Vcm\({}^{-1}\). In those cases, there is a pressing need to develop an experiment scheme, which is not only self-calibrating but also with high sensitivity. To improve the sensitivity of the microwave field measurement, several methods were employed including the primary methods of geometry structure of vapor cell [18] and frequency detuning [19]. Just recently, the advanced detection methods [20] and improved modulation approaches [21; 22] are reported. On the basis of this preliminary work, more effective methods are still needed to improve the measurement sensitivity of a microwave E-field. A multiple modulation scheme was used for digital frequency division multiplexing communication with the advantages of small size and low power consumption [23]. Here, a robust multi-carrier modulation (MCM) method is employed to improve spectral SNR, which is used to evaluate the resolving ability of the microwave E-field measurement. In this work, we demonstrate the improvement performance of the microwave E-field measurement sensitivity by using the MCM scheme in a four-level atomic system. The experiment scheme is conducted by using two laser fields and a microwave E-field, which couples nearby Rydberg transition (57\(D_{5/2}-58P_{3/2}\)) and causes the AT splitting of the Rydberg EIT spectrum. In addition, the variation of spectra with the evolution of this scheme is discussed in detail when the microwave frequency is detuned.