An analysis of CS algorithms efficiency for sparse communication signals reconstruction

Abstract

As need for increasing the speed and accuracy of the real applications is constantly growing, the new algorithms and methods for signal processing are intensively developing. Traditional sampling approach based on Sampling theorem is, in many applications, inefficient because of production a large number of signal samples. Generally, small number of significant information is presented within the signal compared to its length. Therefore, the Compressive Sensing method is developed as an alternative sampling strategy. This method provides efficient signal processing and reconstruction, without need for collecting all of the signal samples. Signal is sampled in a random way, with number of acquired samples significantly smaller than the signal length. In this paper, the comparison of the several algorithms for Compressive Sensing reconstruction is presented. The one dimensional band-limited signals that appear in wireless communications are observed and the performance of the algorithms in non-noisy and noisy environments is tested. Reconstruction errors and execution times are compared between different algorithms, as well.

Cooperative compressed sensing for joint terminal localization and spectrum sensing

“…If ℝ is sparse signal vector with nonzero element, can be measured with measurements ( > ) completely that is ≪ . Signal of length can be demonstrated by using the basis vectors as follows [13]:…”

“…In order to achieve the optimal solution, different minimization algorithms has been proposed [12], [13].…”

“…In each iteration, a set of columns will be expanded with an additional column that best correlates with the residual signal. OMP algorithm is described as follows [5], [13]:…”

“…IHT is an algorithm with low computational complexity that recently has been suggested [13], [16] for signal reconstruction using compressed sensing theory. At first, = 0, IHT finds solution of = by following iterative equation [13].…”

“…k largest coefficients will be selected and the rest of coefficients to be set zero. Iteration continues until achieving one of the conditions, > , | − | < [13]. The second condition can be changed to ‖ ‖ < 1 [16]:…”