Recently developed compressed sensing theory enables signal acquisition and reconstruction from incomplete information with high probability provided that the signal is sparsely represented in some basis. This paper applies compressed sensing for spectrum sensing in a networked system. To tackle the calculation and communication cost problems, this paper also applies structured compressed sensing and 1-bit compressed sensing. Measurement using the partial random circulant matrices can reduce the calculation cost at the sacrifice of a slightly increased number of measurements by utilizing the fact that a circulant matrix is decomposed by multiplications of structured matrices. This paper investigates the tradeoff between calculation cost and compression performance. 1-bit compressed sensing extracts only sign data (1-bit quantization) from measured data, and reconstructs the original signal from the extracted sign data. Therefore, 1-bit compressed sensing can save communication costs associated with spectrum sensing in a networked system. This paper evaluates the efficiency of 1-bit compressed sensing. In addition, this paper also proposes a block reconstruction algorithm for 1-bit compressed sensing that uses the block sparsity of the signals. Empirical study shows that partial random circulant matrices work as efficient as completely random measurement matrices for spectrum sensing and that 1-bit compressed sensing can be used for spectrum sensing with greatly reduced communication costs.