Compressed sensing seeks to recover a sparse or compressible signal from a small number of linear and non-adaptive measurements. Gaussian random matrix is a kind of fundamental measurement matrices, but its performance isn’t perfect because of more errors in recovery. This paper studies a new kind of matrix based on improving Gaussian random matrices. Measure sparse signals with improved matrices and recover original signals with orthogonal matching pursuit. Numerical experiments showed that the quality of recovered signal by improved measurement matrices is better than Gaussian random matrices.

Aiming at satellite-based Automatic Identification System (AIS) signals, a blind carrier frequency-offset estimation method was investigated on AWGN channels. Estimation algorithm that is based on the autocorrelation function and a suitable smoothing function was deduced to estimate the frequency-offset. Simulation results show that its accuracy is better than the earlier methods and reduced the computational complexity.

In wireless communication system, the cooperative diversity is a new space diversity mode. Power allocation plan aiming at maximizing the signal-noise-ratio (SNR) for multi-relay cooperative nodes system is discussed. Diversity signals are combined by the maximum ratio at the destination node. The research results show that 1) when the received noise level at destination node is very low, it can be neglected; 2) when the power allocation coefficients are proportional to the square of the channel gains from the source node to the relay nodes, the SNR of system is maximized in the maximum ratio combination model; and 3) When the received noise at destination node cannot be neglected, the power allocation coefficients are correlative to the received noise at destination node, the amplifying coefficients and the fading coefficients. The SNR of system can be enhanced by using the plan compared with traditional equal power allocation plan.

Aiming at the problem of poor accuracy and small range of frequency estimation in the area of satellite-based AIS signals, this paper presents a novel data-aided estimation method based on the autocorrelation and DFT. The algorithm determines the principal value and the expansion of the frequency and then acquires high-precision estimation by data fitting. Based on that, other parameters can be estimated. Computer simulations were used to illustrate better estimation accuracy and a large estimation range.

Channel estimation is an important research direction in wireless communications; channel estimation based on the training sequence is the most commonly used method. Different training sequence is very different from the performance of channel estimation, in order to improve channel estimation accuracy. This paper analyzes the common m sequence and from the optimal channel estimated performance point design of applicable in any given length of sequence. The sequence, respectively, under the traditional channel estimated algorithm and based on compressed sensing to channel estimation algorithm has the criterion of Minimum Mean Square Error. Meanwhile, the sequence obtained after the demodulated training sequence through different modulation systems are different, so as to have greater flexibility.