Parameter Estimation And Filtering Method Based On Spectral-correlation Density Analysis

Sinusoidal Frequency Modulation (SFM) scheme is a kind of classic cyclostationary signal, which is widely used as the echoed signals to detect moving targets in radar systems and to resist Doppler Frequency Shift (DFS) caused by high-speed moving plants in sonar systems. The Fractional Fourier Transformation (FrFT) can be exploited to analyze conventional Linear Frequency Modulation (LFM) rather than Sinusoidal Frequency Modulation (SFM). However, since the periodical keying and scanning processes makes some variables periodic, the Spectral-Correlation Density (SCD) technique, which is used to analyze the periodicity of frequency spectrum, can be used to dealing with SFM signals.First, a new SFM scheme-Sinusoidal Nonlinear Chirp Keying (SNCK) was stated in this paper. The fundamental characteristics of the SNCK scheme were introduced, including the mathematical model, the time-frequency modulation pattern, the waveform sample in the time domain, the Power Spectrum Density (PSD) and advantages of SNCK scheme.Furthermore, the cyclostationary features of SNCK were mentioned as well, such as the cyclic mean function, the cyclic auto-correlation function and the Spectral-Correlation Density(SCD) function.Then, based on the characteristics of the SNCK in the FrFT domain and in the SCD domain respectively, we stated the reason why the estimation algorithm in this paper was chosen. Also the localization method for the center frequency of the carrier frequency, the localization method for the keying rate, and the evaluation algorithm for the time-frequency bandwidth product were mentioned. The performance of the estimation algorithm based on the Root Mean Square Error (RMSE) was compared with its corresponding theoretical Cramer-Rao Lower Bound (CRLB). Given the differences between theoretical values and simulation results, we improved the proposed estimation algorithm of the time-frequency bandwidth product by adding one set of local ratio data in the receiving terminal. Simulation results showed that the Spectral-Correlation Density (SCD) of the SNCK scheme was obvious and the key parameters can be positioned and evaluated accurately.Finally, based on the specific cyclic frequency of the SCD, we used the FREquency-SHift (FRESH) filters and Cyclic Correlated Matched Filter (CCMF) to deal with the transmitted SNCK signals in the receiving terminals. Moreover, the Bit Error Rate (BER)of the wireless communication system with the classic Matched Filter (MF) was compared with that of the system with the Cyclic Correlation Matched Filters (CCMF). Simulation results showed that cyclic frequency chosen in the CCMF can affect the BER performance of the system drastically, which means the BER performance deteriorates when the parameters of the filters were set as non-cyclic frequencies.