Existing spectrum sensing systems are commonly designed based on the famous Nyquist theorem. With the rapid development of radio frequency technology, the corresponding sampling frequency is so high that many problems may be brought about, such as the increasing hardware complexity, large volume of measurements and difficulties to meet the real time requirement etc. To tackle these problems caused by high sampling frequency, a novel scheme, adaptive modulated wideband converter, is proposed. By exploiting the band width of the narrow bands, the total sampling frequency is proved to be as low as four times of the sum of the narrow bands. There is a trade-off between the sampling complexity and the total sampling frequency for different choices of the repeating frequency of the random function. Sufficient conditions are derived to guarantee exact signal recovery from sub-Nyquist measurements. Conditions of full row rank of the equivalent unknown matrix are also explored to guarantee that the multiple signal classification can be adopted to implement the signal reconstruction. The simulations verify the analysis. This novel scheme can be used to implement front-end spectrum analysis for absorbing materials and detect the active channels in cognitive radio.
As the signal spectrum in modern information technology becomes wider and wider, multi-band signals are distributed in a frequency range of tens of GHz. It covers a very wide spectrum but each RF signal has a very narrow band, and the distribution location of the band (or carrier frequency) is completely unknown. For the receiver, the single-band signals transmitted together constitute a multi-band signal. The sampling rate required to jointly estimate the space domain and frequency domain parameters of these signals is getting higher and higher. Modulated wideband converter system is an analog information conversion system for multiband analog signals, which is based on compressed sensing theory and greatly reduces the sampling rate. First, we propose an L-shaped delay array structure based on modulated wideband converter, which can estimate carrier frequency and two-dimensional arrival angles with a small number of samples. Secondly, two parameter-estimating algorithms are proposed based on the proposed structure. One is based on the estimating of signal parameter via rotational invariance technique (ESPRIT), which requires a small number of computations and is suitable for real-time processing application scenarios; the other algorithm is based on CANDECOMP/PARAFAC (CP) technique, which has better robustness and is suitable for applications with low signal-to-noise ratio. The samples of the delay channels can be directly used to estimate the carrier frequencies, and then the two-dimensional arrival angles are calculated. No additional pairing issue is required between the parameters. Then we give the time complexity analysis and space complexity analysis of the two methods. It can be found that the computational complexity and space storage occupation of the method based on ESPRIT are lower than those of the CP decomposition method. Then the conditions for unique parameter estimation are given. Finally, simulation experiments show that the proposed methods can estimate the carrier frequencies and two-dimensional arrival angles from sub-Nyquist samples. It can be found that the estimation method based on CP decomposition is more robust than the method based on ESPRIT, but at the cost of increased complexity of the algorithm.
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