In Vehicle-to-Everything scenarios, the mobility of devices and the complexity of the environment render them more vulnerable to malicious attacks, necessitating a secure and efficient authentication mechanism. Radio Frequency Fingerprinting (RFF) offers a novel approach to identity authentication in V2X networks. However, as device fingerprints are extracted directly from wireless signals, their stability is highly susceptible to channel variations. The combined effects of the wireless channel and receiver noise cause distortion in the received signal, making it challenging to directly isolate the authentic features of the transmitted signal. To address these issues, this paper proposes an RFF extraction method based on an improved Linear Minimum Mean Square Error channel estimation for the Physical Sidelink Broadcast Channel. First, a channel estimator based on the LMMSE criterion is constructed. By exploiting the time-frequency two-dimensional statistical properties of the channel, a corresponding 2D correlation matrix is established, which effectively captures the intrinsic coupling relationship between time-selective and frequency-selective fading. Based on this matrix, the random channel response can be optimally separated from the received signal. Subsequently, a channel equalization operation is performed to recover the hardware fingerprints contaminated by the channel, restoring their original feature information. Finally, a structurally optimized dual-branch heterogeneous neural network is employed for deep representation learning and high-precision classification of these hardware fingerprints. Experimental results demonstrate that, under low signal-to-noise ratio conditions, the proposed method achieves classification accuracy of 95.46% and 92.05% in static and mobile scenarios, respectively.