Optimizing sample structural parameters, magnetic field annealing, series-parallel bridge design, current thermal effect, and additional bias magnetic field are common methods used for controlling the tunneling magnetoresistance (TMR) magnetic sensing performance. By employing these methods, key performance parameters of TMR sensors such as sensitivity, noise resistance index, linearity, and linear magnetic field range can be optimized and improved. Changing the sample structural parameters, such as the pinning layer, free layer, and barrier layer materials and thickness of the TMR magnetic sensing unit, can change the exchange bias field and thus enhance the TMR magnetic sensing performance parameters. In this study, through micromagnetic simulation and experimental measurements, it is discovered that by modifying the exchange coupling in the free layer CoFeB/Ru/NiFe/IrMn, the exchange bias field magnitude of the TMR free layer can be modulated, leading to improved performance of the TMR magnetic sensing unit. As the IrMn pinning effect is gradually enhanced, the linear magnetic field range of the TMR magnetic sensing unit increases, but the magnetic field sensitivity decreases. It is further found that the linearity of the TMR magnetic sensor is optimal within a range of ±0.5 times the magnetic moment variation of the free layer (primarily the CoFeB layer). Through our work, the effect of exchange bias field (caused by the pinning IrMn of the free layer) on the magnetic sensing performance is verified in the TMR magnetic sensing unit. Our work demonstrates more possibilities for designing and optimizing TMR magnetic sensors, enriching the dimensions of magnetic sensing performance modulation.