The Narrowband Signal Parameter Estimation Based On Compressed Sensing Theory

In real life, narrowband signal are widely used in radar, sonar, communication, positioning, biomedical engineering and other fields. In addition, broadband signal can be divided into the sum of several narrowband signals. Thus, the problem of narrowband signal parameter estimation has attracted lots of people's attention. However, the method based on Nyquist sampling and the traditional information processing technology have increased the cost spending in numerous military and civilian fields. With the demand of information increasing,it needs higher and higher demands on information processing technology, how to effectively access information and to ensure the authenticity and reliability of information transmission has become a key issue in modern information processing field.Compressed sensing theory is a new signal analysis idea, has broken the constraint of the traditional Nyquist sampling theorem. It has represented its advantages in many applications and has many excellent features. This thesis brings compressed sensing theory into the array signal processing field, models the array signal around the spatial narrowband sources, derives a new parameter estimation algorithm of spatial narrowband signal frequency and DOA, The following is the summarization of the main work:1. Describe the spatial narrowband signal model, and model the uniform linear array antenna, study the basic principle of the spatial spectrum estimation.2. Describe the compressed sensing theory detailedly, expound three key contents of compressed sensing theory-the sparse representation of signal, the sample of signal, the reconstruction of signal. And design an improved reconstruction algorithm, the simulation results show that the improved algorithm has better anti-noise ability.3. Design a spatial narrowband signal frequency estimation algorithm based on compressed sensing theory in the Gaussian white noise environment, the algorithm establish a sparse base according to the spatial narrowband signal character, projects narrowband signal onto the CS observation matrix to get CS observation vector, Then it make use of these very little information to achieve high-precision estimation of the narrowband signal parameter, Computer simulation shows that the improved frequency estimation algorithm based on compressed sensing theory has better noise immunity than sparse decomposition algorithm in the same sampling points and very few cases, and the improved frequency estimation algorithm has higher stability than other existing CS algorithms,more importantly, in low SNR and multi-source cases,the improved algorithm still has good performance.4. Design a narrowband signal DOA estimation algorithm based on compressed sensing theory in the Gaussian white noise environment, and compare with sparse decomposition algorithm, MUSIC algorithm, ESPRIT algorithm. The new algorithm establishes a sparse base adaptively based on the array structure and characteristics of spatial narrowband signals received by the array, projects spatial narrowband signal onto CS observation matrix to get CS observation vector, then make use of these very little observational information to achieve high-precision narrowband signal parameter estimation. Computer simulation shows that the DOA estimation algorithm based on CS theory can estimate accurately the narrowband signal DOA information in relatively small samples case. Its anti-noise is better than MUSIC algorithm, ESPRIT algorithm, and can be comparable with the sparse decomposition algorithm, more importantly, the stored information and utilized information of this algorithm is far less than other algorithms, it is the unique charm of the CS algorithm.