Abstract: Two virtual frequency band extension algorithms based on the range-dimensional beamforming method are proposed to enhance the range resolution of pulse compression within the constraints of finite system instantaneous bandwidth. The received signal in the frequency domain undergoes subdivision into multiple sub-band components, and the inherent phase is eliminated. The phase shift induced by the target distance at the corresponding frequency points among the sub-bands forms a complex exponential geometric series. Exploiting this characteristic, linear prediction and least squares estimation are employed for virtual sub-band prediction. Linear prediction operates on frequency domain snapshots within each sub-band, while least squares estimation is performed on the sub-band units. The covariance matrix, constructed from the extended frequency band data, is utilized to derive the power spectrum. These two proposed algorithms can virtually expand the echo signal bandwidth without altering the transmission bandwidth. Additionally, they can effectively reduce the main lobe width in the range dimension and improve the range resolution performance. The efficacy of these algorithms is demonstrated through numerical simulations and lake test data.