Look-Up Table Based Linear Interpolation Algorithm for BPSK Signal Compensation

With the increasing use of 5G communication signals as viable transmission sources for radar systems, passive radar systems based on communication signals have become a focal point of research. In practical deployments, oscillator mismatches between the transmitter and receiver lead to frequency misalignment between the reference and received signals, thereby impairing tracking performance. To address this issue, this paper presents a joint compensation algorithm based on a look-up table (LUT) and a phase accumulator. The proposed algorithm achieves high-precision signal reconstruction without the need for hardware buffering by mapping the time delay to the initial value of the phase accumulator. It further incorporates dynamic superposition of the target frequency offset tuning word and employs linear interpolation to mitigate phase quantization noise. Operating at a sampling rate of 122.88 MHz, the algorithm performs signal generation, cyclic prefix (CP) insertion, and joint compensation for both frequency offset and time delay. This reconstruction method is well-suited for the pre-acquisition stage of synchronization system front-ends. Simulation results confirm that the discrepancy between the reconstructed and ideal signals is significantly reduced after compensation, with the error vector magnitude (EVM) decreasing to $0.000021251 \%$.